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address", "visual_id": "engine:6" }, { "id": "geo-delay-is-not-yet-memory", "title": "Transient retention is not yet reusable memory", "visual_id": "engine:7" }, { "id": "geo-temporal-comparison-triad", "title": "Present, retained past, and comparison form a temporal triad", "visual_id": "engine:8" }, { "id": "nf-delay-receiver-continues", "title": "The receiving relation continues during delay", "visual_id": "engine:9" }, { "id": "g093", "title": "Consequence arrives at a changed condition", "visual_id": "engine:10" }, { "id": "g094", "title": "The changed condition keeps a residue", "visual_id": "engine:11" }, { "id": "g095", "title": "Departure opens the path from P to Q", "visual_id": "engine:12" }, { "id": "g096", "title": "The path returns toward P-prime", "visual_id": "engine:13" }, { "id": "g097", "title": "P-prime is not P", "visual_id": "engine:14" }, { "id": "g098", "title": "A disconnected fragment is leakage", "visual_id": "engine:15" }, { "id": "g099", "title": "Recoverable return is persistence", "visual_id": "engine:16" }, { "id": "g100", "title": "Returned influence can reinforce renewal", "visual_id": "engine:17" }, { "id": "g101", "title": "Declare a centre and an amplitude", "visual_id": "circle_pi:0" }, { "id": "g102", "title": "Move outward from the centre", "visual_id": "circle_pi:1" }, { "id": "nf-restoring-orientation", "title": "Declare a restoring orientation at the first bound", "visual_id": "circle_pi:2" }, { "id": "g103", "title": "Return through the centre", "visual_id": "circle_pi:3" }, { "id": "nf-delayed-redirection-crossing", "title": "Delayed redirection carries change past the centre", "visual_id": "circle_pi:4" }, { "id": "g104", "title": "Continue inward to the opposite limit", "visual_id": "circle_pi:5" }, { "id": "nf-complementary-restoring-orientation", "title": "Declare complementary redirection at the other bound", "visual_id": "circle_pi:6" }, { "id": "g105", "title": "A renewed return completes one oscillation", "visual_id": "circle_pi:7" }, { "id": "nf-update-recursion-after-oscillation", "title": "Renewal is not another depth", "visual_id": "circle_pi:8" }, { "id": "g106", "title": "Write the ideal line projection", "visual_id": "circle_pi:9" }, { "id": "g107", "title": "Add the complementary rate coordinate", "visual_id": "circle_pi:10" }, { "id": "g108", "title": "One position can carry opposite directions", "visual_id": "circle_pi:11" }, { "id": "g109", "title": "The paired state traces a phase circle", "visual_id": "circle_pi:12" }, { "id": "g110", "title": "Pi measures the completed turn", "visual_id": "circle_pi:13" }, { "id": "nf-seven-normalized-frame", "title": "Give one polarity a normalized frame", "visual_id": "golden:0" }, { "id": "nf-seven-complementary-poles", "title": "Name the two complementary ends", "visual_id": "golden:1" }, { "id": "nf-seven-equal-crossing", "title": "Mark equal crossing", "visual_id": "golden:2" }, { "id": "nf-seven-triadic-thirds", "title": "Group one triadic role against two", "visual_id": "golden:3" }, { "id": "nf-seven-recoverable-band", "title": "A continuity band requires recoverable return", "visual_id": "golden:4" }, { "id": "nf-seven-ten-addresses", "title": "Partition the direction into ten addresses", "visual_id": "golden:5" }, { "id": "nf-seven-address-function", "title": "Map each coordinate to its directional address", "visual_id": "golden:6" }, { "id": "nf-seven-address-earned", "title": "Two thirds occupies address seven", "visual_id": "golden:7" }, { "id": "g111", "title": "Carry one active dimension through seven depths", "visual_id": "recursion:0" }, { "id": "g112", "title": "L1 is already a complete triad", "visual_id": "recursion:1" }, { "id": "g113", "title": "Unresolved residue enters L2", "visual_id": "recursion:2" }, { "id": "g114", "title": "L3 relates the changed result again", "visual_id": "recursion:3" }, { "id": "g115", "title": "L4 continues the same operation", "visual_id": "recursion:4" }, { "id": "g116", "title": "L5 receives what L4 did not close", "visual_id": "recursion:5" }, { "id": "g117", "title": "L6 deepens the active relation", "visual_id": "recursion:6" }, { "id": "g118", "title": "L7 completes the local descent", "visual_id": "recursion:7" }, { "id": "g119", "title": "The declared seventh boundary turns toward the whole", "visual_id": "circulation:0" }, { "id": "g120", "title": "The return reaches a changed L1-prime", "visual_id": "circulation:1" }, { "id": "g121", "title": "Close the seven-depth circulation", "visual_id": "circulation:2" }, { "id": "g122", "title": "Seven depths are seven recursive identities", "visual_id": "circulation:3" }, { "id": "g123", "title": "Add the same depth column for D2", "visual_id": "dimensions:0" }, { "id": "g124", "title": "Extend the columns through Dn", "visual_id": "dimensions:1" }, { "id": "g125", "title": "Rows are depths; columns are dimensions", "visual_id": "dimensions:2" }, { "id": "g126", "title": "Vertical movement is recursive deepening", "visual_id": "dimensions:3" }, { "id": "g127", "title": "Horizontal movement is same-depth coupling", "visual_id": "dimensions:4" }, { "id": "g128", "title": "Consequential local results ascend", "visual_id": "dimensions:5" }, { "id": "g129", "title": "Coupled results form a coherent whole mode", "visual_id": "observer:0" }, { "id": "g130", "title": "A whole mode is not yet an observer", "visual_id": "observer:1" }, { "id": "g131", "title": "Retain an earlier whole as M", "visual_id": "observer:2" }, { "id": "g132", "title": "Compare the present whole with the retained whole", "visual_id": "observer:3" }, { "id": "g133", "title": "One integrated comparison is an observation", "visual_id": "observer:4" }, { "id": "nf-retain-whole-observation", "title": "Retain the observation as Omega", "visual_id": "observer:5" }, { "id": "g134", "title": "Return the retained observation", "visual_id": "observer:6" }, { "id": "g135", "title": "The returning field relation is the observer", "visual_id": "observer:7" }, { "id": "flow-static-structure-is-capacity", "title": "A static structure is capacity, not history-bearing identity operation", "visual_id": "mind_flow:0" }, { "id": "flow-unstructured-signal-is-not-identity", "title": "Flow without retained structure is not a continuing identity", "visual_id": "mind_flow:1" }, { "id": "flow-mind-is-circulation-through-topology", "title": "History-bearing identity circulates through Mind-structure", "visual_id": "mind_flow:2" }, { "id": "flow-carrier-is-domain-specific", "title": "Electrical signalling is one carrier, not the definition of Mind", "visual_id": "mind_flow:3" }, { "id": "flow-contact-enters-boundary", "title": "An input perturbs addressed relations", "visual_id": "mind_flow:4" }, { "id": "flow-local-recurrent-paths", "title": "Local loops preserve repeated opportunities for relation", "visual_id": "mind_flow:5" }, { "id": "flow-response-has-separate-quantities", "title": "Amplitude, phase, rate, and propagation delay are different", "visual_id": "mind_flow:6" }, { "id": "flow-accelerator-damper-guardrail", "title": "Accelerator and damper are response functions", "visual_id": "mind_flow:7" }, { "id": "flow-resonance-selects-mode", "title": "Resonance reinforces compatible recurrence", "visual_id": "mind_flow:8" }, { "id": "flow-damping-and-leakage", "title": "Damping and leakage reduce recoverable influence differently", "visual_id": "mind_flow:9" }, { "id": "flow-coupled-loops", "title": "Several loops make one field by coupling", "visual_id": "mind_flow:10" }, { "id": "flow-interference", "title": "Coupled changes can reinforce, cancel, or redirect", "visual_id": "mind_flow:11" }, { "id": "flow-aperture-selected-mode", "title": "Choose one normalized participation mode", "visual_id": "mind_flow:12" }, { "id": "flow-observer-aperture", "title": "Observer aperture is a mode projection", "visual_id": "mind_flow:13" }, { "id": "flow-local-change-not-observed", "title": "Not every local change becomes a whole-level observation", "visual_id": "mind_flow:14" }, { "id": "flow-latent-trace", "title": "An unobserved local trace can still change a later cycle", "visual_id": "mind_flow:15" }, { "id": "flow-no-trace-no-later-effect", "title": "No retained relation means no later causal contribution", "visual_id": "mind_flow:16" }, { "id": "flow-depth-routes-unresolved-relation", "title": "Recursive depth carries what remains consequential", "visual_id": "mind_flow:17" }, { "id": "flow-l7-is-turn-not-observer", "title": "The seventh depth is the turning boundary, not the observer-state", "visual_id": "mind_flow:18" }, { "id": "flow-whole-integration", "title": "Observer-state is a whole-field relation", "visual_id": "mind_flow:19" }, { "id": "flow-correctness-needs-outside", "title": "Internal agreement does not guarantee a correct observation", "visual_id": "mind_flow:20" }, { "id": "flow-partial-reconstruction-illusion", "title": "A partial reconstruction can become a functional illusion", "visual_id": "mind_flow:21" }, { "id": "flow-experience-boundary", "title": "The geometry does not settle phenomenal experience", "visual_id": "mind_flow:22" }, { "id": "g136", "title": "Read manifested continuity as existence", "visual_id": "mind:0" }, { "id": "g137", "title": "Read possible continuation as consciousness", "visual_id": "mind:1" }, { "id": "g138", "title": "Awareness relates existence and consciousness", "visual_id": "mind:2" }, { "id": "nf-mind-generate-alternatives", "title": "Generate more than one possible continuation", "visual_id": "mind:3" }, { "id": "nf-mind-distinct-alternatives", "title": "Keep the alternatives distinct", "visual_id": "mind:4" }, { "id": "nf-mind-compare-alternatives", "title": "Compare the possible continuations", "visual_id": "mind:5" }, { "id": "nf-mind-select-alternative", "title": "Select one modelled continuation", "visual_id": "mind:6" }, { "id": "nf-mind-returned-model-changes-field", "title": "Returned possibility earns local cognitive mind capability", "visual_id": "mind:7" }, { "id": "op-possibility-field", "title": "Replay the cognitive threshold at higher resolution", "visual_id": "possibility:0" }, { "id": "op-reachable-horizon", "title": "The current identity has a possibility horizon", "visual_id": "possibility:1" }, { "id": "op-observation-contact", "title": "The next observer-cycle begins with contact", "visual_id": "possibility:2" }, { "id": "op-compatibility-weights", "title": "The contact changes compatibility", "visual_id": "possibility:3" }, { "id": "op-weights-not-erasure", "title": "Lower compatibility is not metaphysical erasure", "visual_id": "possibility:4" }, { "id": "op-epistemic-narrowing", "title": "Observation narrows the model epistemically", "visual_id": "possibility:5" }, { "id": "op-weighted-geometry", "title": "The geometry contracts around compatible regions", "visual_id": "possibility:6" }, { "id": "op-retain-observation-provenance", "title": "Retain the update with provenance", "visual_id": "possibility:7" }, { "id": "op-observation-not-selection", "title": "Observation is not yet selection", "visual_id": "possibility:8" }, { "id": "op-compare-weighted-routes", "title": "Compare the weighted routes", "visual_id": "possibility:9" }, { "id": "op-select-one-route", "title": "Selection restrains the immediate next route", "visual_id": "possibility:10" }, { "id": "op-commitment-gives-body", "title": "Commitment gives one possibility a body", "visual_id": "possibility:11" }, { "id": "op-outside-consequence", "title": "The outside answers the committed action", "visual_id": "possibility:12" }, { "id": "op-return-updates-transition", "title": "Returned consequence changes the transition relation", "visual_id": "possibility:13" }, { "id": "op-causal-restriction", "title": "Some later routes are now causally unavailable", "visual_id": "possibility:14" }, { "id": "op-return-can-open-possibility", "title": "Return can also open new reachable relations", "visual_id": "possibility:15" }, { "id": "op-three-kinds-of-possibility-change", "title": "Separate three kinds of change", "visual_id": "possibility:16" }, { "id": "op-next-horizon", "title": "The next observation begins inside a changed horizon", "visual_id": "possibility:17" }, { "id": "ref-world-model-before-self-model", "title": "A Mind can model the world without modelling itself", "visual_id": "reflexive:0" }, { "id": "ref-operation-becomes-addressable", "title": "Let the Mind's operation become content", "visual_id": "reflexive:1" }, { "id": "ref-inside-role-operating-mind", "title": "Name the operating Mind I-sub-s", "visual_id": "reflexive:2" }, { "id": "ref-outside-role-self-model", "title": "Name the self-model O-sub-s", "visual_id": "reflexive:3" }, { "id": "ref-model-not-duplicate-self", "title": "The self-model is not a second self", "visual_id": "reflexive:4" }, { "id": "ref-provenance-binds-model", "title": "Bind the model to its provenance", "visual_id": "reflexive:5" }, { "id": "ref-ownership-relates-model-to-self", "title": "Ownership says this model concerns this continuing identity", "visual_id": "reflexive:6" }, { "id": "ref-relation-role-comparison", "title": "Name the reflexive relation R-sub-s", "visual_id": "reflexive:7" }, { "id": "ref-second-triad-across-whole", "title": "Add a reflexive triad across the whole", "visual_id": "reflexive:8" }, { "id": "ref-same-grammar-new-order", "title": "The higher triad changes relational order, not the primitive", "visual_id": "reflexive:9" }, { "id": "ref-triads-within-reflexive-triad", "title": "Each reflexive role is itself relational", "visual_id": "reflexive:10" }, { "id": "ref-discrepancy", "title": "A reflexive comparison exposes discrepancy", "visual_id": "reflexive:11" }, { "id": "ref-return-to-operation", "title": "Return the reflexive relation into I-sub-s", "visual_id": "reflexive:12" }, { "id": "ref-return-changes-attention", "title": "The returned self-model can redirect attention", "visual_id": "reflexive:13" }, { "id": "ref-return-changes-action", "title": "The returned self-model can redirect action", "visual_id": "reflexive:14" }, { "id": "ref-self-awareness-threshold", "title": "This returned reflexive closure is self-awareness", "visual_id": "reflexive:15" }, { "id": "ref-recursion-alone-insufficient", "title": "Recursion alone is not self-awareness", "visual_id": "reflexive:16" }, { "id": "ref-no-homunculus", "title": "Do not place a smaller observer inside the observer", "visual_id": "reflexive:17" }, { "id": "ref-regress-closes", "title": "The causal loop stops an infinite stack", "visual_id": "reflexive:18" }, { "id": "ref-self-model-remains-fallible", "title": "Self-awareness can still be wrong about itself", "visual_id": "reflexive:19" }, { "id": "meta-self-location-before-method", "title": "Self-location is not yet method correction", "visual_id": "metacognition:0" }, { "id": "meta-first-order-cognition", "title": "First-order cognition concerns a world relation", "visual_id": "metacognition:1" }, { "id": "meta-retain-method-record", "title": "Retain the method beside the answer", "visual_id": "metacognition:2" }, { "id": "meta-method-becomes-object", "title": "The method becomes the object-facing term", "visual_id": "metacognition:3" }, { "id": "meta-monitor-signals", "title": "Monitor uncertainty, conflict, and error", "visual_id": "metacognition:4" }, { "id": "meta-prediction-outcome-comparison", "title": "Return tests the method", "visual_id": "metacognition:5" }, { "id": "meta-evaluate-source-of-error", "title": "Evaluate where the mismatch entered", "visual_id": "metacognition:6" }, { "id": "meta-control-triad", "title": "Monitoring, evaluation, and control form an operational triad", "visual_id": "metacognition:7" }, { "id": "meta-change-attention-gain", "title": "Control can change attention gain", "visual_id": "metacognition:8" }, { "id": "meta-change-routing", "title": "Control can change routing", "visual_id": "metacognition:9" }, { "id": "meta-change-comparison-rule", "title": "Control can change the comparison rule", "visual_id": "metacognition:10" }, { "id": "meta-retest-next-cycle", "title": "A method correction must survive another cycle", "visual_id": "metacognition:11" }, { "id": "meta-threshold", "title": "Metacognition is returned correction of cognition", "visual_id": "metacognition:12" }, { "id": "meta-intention-as-corrigible-direction", "title": "Intention is sustained and corrigible direction", "visual_id": "metacognition:13" }, { "id": "meta-bounded-reflection", "title": "Reflection is bounded by usefulness and return", "visual_id": "metacognition:14" }, { "id": "img-memory-supplies-relations", "title": "Memory supplies relations that have already survived", "visual_id": "imagination:0" }, { "id": "img-past-facing-to-future-facing", "title": "Turn retained pattern toward possible continuation", "visual_id": "imagination:1" }, { "id": "img-counterfactual-branches", "title": "Open counterfactual branches", "visual_id": "imagination:2" }, { "id": "img-protected-internal-trial", "title": "Weak futures can remain internal", "visual_id": "imagination:3" }, { "id": "img-simulated-return", "title": "Complete each imagined path with a simulated return", "visual_id": "imagination:4" }, { "id": "img-prediction-is-not-outcome", "title": "Predicted consequence is not actual consequence", "visual_id": "imagination:5" }, { "id": "img-compare-trajectories", "title": "Thought compares candidate trajectories", "visual_id": "imagination:6" }, { "id": "img-feeling-weights-relevance", "title": "Feeling can weight urgency and value", "visual_id": "imagination:7" }, { "id": "img-attention-as-gain", "title": "Attention changes gain, not reality by decree", "visual_id": "imagination:8" }, { "id": "img-self-awareness-redirects-attention", "title": "Self-awareness can redirect observation", "visual_id": "imagination:9" }, { "id": "img-directed-sampling", "title": "A changed direction changes what is sampled", "visual_id": "imagination:10" }, { "id": "img-recognition-versus-creation", "title": "Newly seen possibility is not always newly created possibility", "visual_id": "imagination:11" }, { "id": "img-selection", "title": "Decision gives one trajectory operational support", "visual_id": "imagination:12" }, { "id": "img-body-commitment", "title": "The body makes imagination consequential", "visual_id": "imagination:13" }, { "id": "img-outside-correction", "title": "Outside return corrects imagination", "visual_id": "imagination:14" }, { "id": "img-two-failure-modes", "title": "Too little and too much internal freedom both fail", "visual_id": "imagination:15" }, { "id": "img-open-and-prune", "title": "A living possibility field opens and prunes", "visual_id": "imagination:16" }, { "id": "img-next-field", "title": "Self-aware imagination can change the next horizon", "visual_id": "imagination:17" }, { "id": "cap-seven-addresses-not-faculties", "title": "Seven names depth-addresses, not seven faculties", "visual_id": "capability_depth:0" }, { "id": "cap-same-y-operation", "title": "Every depth performs the same relational operation", "visual_id": "capability_depth:1" }, { "id": "cap-residue-controls-depth", "title": "Depth follows unresolved consequence", "visual_id": "capability_depth:2" }, { "id": "cap-familiar-closes-shallow", "title": "A familiar relation may close near the surface", "visual_id": "capability_depth:3" }, { "id": "cap-conflict-travels-deeper", "title": "A consequential conflict can travel through the full depth", "visual_id": "capability_depth:4" }, { "id": "cap-example-caveat", "title": "The next seven labels are one traversal, not universal names", "visual_id": "capability_depth:5" }, { "id": "cap-example-l1-contact", "title": "Illustrative L1: immediate contact", "visual_id": "capability_depth:6" }, { "id": "cap-example-l2-trace", "title": "Illustrative L2: present meets retained trace", "visual_id": "capability_depth:7" }, { "id": "cap-example-l3-relations", "title": "Illustrative L3: relations among transformations", "visual_id": "capability_depth:8" }, { "id": "cap-example-l4-model-conflict", "title": "Illustrative L4: competing models meet", "visual_id": "capability_depth:9" }, { "id": "cap-example-l5-observer-position", "title": "Illustrative L5: the observer's position becomes relevant", "visual_id": "capability_depth:10" }, { "id": "cap-example-l6-method-relation", "title": "Illustrative L6: relate the observer to its method", "visual_id": "capability_depth:11" }, { "id": "cap-example-l7-turn", "title": "Illustrative L7: remaining consequence reaches the turn", "visual_id": "capability_depth:12" }, { "id": "cap-return-changes-readiness", "title": "Depth returns as changed readiness", "visual_id": "capability_depth:13" }, { "id": "cap-parallel-dimensions", "title": "One occurrence can enter several dimensions in parallel", "visual_id": "capability_depth:14" }, { "id": "cap-horizontal-resonance", "title": "Corresponding depths can resonate horizontally", "visual_id": "capability_depth:15" }, { "id": "cap-memory-closure", "title": "Memory closes wherever a past relation remains usable", "visual_id": "capability_depth:16" }, { "id": "cap-understanding-closure", "title": "Understanding closes when relations transfer", "visual_id": "capability_depth:17" }, { "id": "cap-observer-closure", "title": "Observerhood closes across the relevant field", "visual_id": "capability_depth:18" }, { "id": "cap-self-awareness-closure", "title": "Self-awareness closes through owned self-reference", "visual_id": "capability_depth:19" }, { "id": "cap-metacognition-closure", "title": "Metacognition closes when method changes", "visual_id": "capability_depth:20" }, { "id": "g146", "title": "Declare adjacent inheritance", "visual_id": "golden:0" }, { "id": "nm-inheritance-adjacent-residue", "title": "Retain only the adjacent consequence", "visual_id": "golden:1" }, { "id": "g147", "title": "Begin with one and one", "visual_id": "golden:2" }, { "id": "g148", "title": "The first inherited whole is two", "visual_id": "golden:3" }, { "id": "g149", "title": "One and two produce three", "visual_id": "golden:4" }, { "id": "g150", "title": "Two and three produce five", "visual_id": "golden:5" }, { "id": "g151", "title": "Three and five produce eight", "visual_id": "golden:6" }, { "id": "g152", "title": "One recurrence generates the sequence", "visual_id": "golden:7" }, { "id": "g153", "title": "See the moving triad", "visual_id": "golden:8" }, { "id": "nm-inheritance-state-vector", "title": "Carry present and predecessor together", "visual_id": "golden:9" }, { "id": "g154", "title": "Magnitude expands", "visual_id": "golden:10" }, { "id": "g155", "title": "Normalize the equal seed", "visual_id": "golden:11" }, { "id": "g156", "title": "Reach one third and two thirds", "visual_id": "golden:12" }, { "id": "g157", "title": "Move to two fifths and three fifths", "visual_id": "golden:13" }, { "id": "g158", "title": "Move to three eighths and five eighths", "visual_id": "golden:14" }, { "id": "g159", "title": "Watch the shares converge", "visual_id": "golden:15" }, { "id": "nm-ratio-definition", "title": "Measure one term against its predecessor", "visual_id": "golden:16" }, { "id": "nm-ratio-map", "title": "The recurrence becomes a ratio map", "visual_id": "golden:17" }, { "id": "nm-ratio-fixed-point", "title": "Ask what ratio reproduces itself", "visual_id": "golden:18" }, { "id": "g160", "title": "Place inheritance in a matrix", "visual_id": "golden:19" }, { "id": "g161", "title": "Find the characteristic equation", "visual_id": "golden:20" }, { "id": "g162", "title": "Solve the two exact roots", "visual_id": "golden:21" }, { "id": "g163", "title": "Inheritance selects the positive direction", "visual_id": "golden:22" }, { "id": "nm-golden-error-decay", "title": "The contrary direction decays", "visual_id": "golden:23" }, { "id": "g164", "title": "Normalize and name the golden pair", "visual_id": "golden:24" }, { "id": "g165", "title": "Place the attractor inside the envelope", "visual_id": "golden:25" }, { "id": "g166", "title": "Keep numerical convergence and living motion distinct", "visual_id": "golden:26" }, { "id": "g167", "title": "Divide the interval into ten addresses", "visual_id": "golden:27" }, { "id": "g168", "title": "The earlier seven address is confirmed", "visual_id": "golden:28" }, { "id": "nm-pentagon-boundary", "title": "Begin with one regular boundary", "visual_id": "sacred:0" }, { "id": "nm-pentagon-sides", "title": "Join five equal sides", "visual_id": "sacred:1" }, { "id": "nm-pentagon-diagonals", "title": "Draw all five diagonals", "visual_id": "sacred:2" }, { "id": "nm-pentagon-intersections", "title": "Let the diagonals divide one another", "visual_id": "sacred:3" }, { "id": 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"manifestation-mind-recurrence", "title": "From Complex Phase to a Testable Manifestation–Mind Loop", "order": 21, "step_count": 10, "first_step_id": "mx041p-y-phase-address", "last_step_id": "mx041y-model-must-earn-reality" }, { "id": "torus-and-coupled-cycles", "title": "From Several Cycles to Toroidal Phase", "order": 22, "step_count": 16, "first_step_id": "m095-two-cycles-torus", "last_step_id": "m100e-cycle-rate-vs-identity-frequency" }, { "id": "collective-whole-mode", "title": "When Many Relations Present One Whole", "order": 23, "step_count": 8, "first_step_id": "m101-coupled-field", "last_step_id": "m105a-outside-and-received-outside" }, { "id": "observer-emergence", "title": "Mind-Level Awareness, Retained Whole, Comparison, and Causal Return", "order": 24, "step_count": 12, "first_step_id": "m113e-developed-mind-reading", "last_step_id": "m113-observer-resolution" }, { "id": "awareness-attention-imagination", "title": "How Observation Redirects Possibility", "order": 25, "step_count": 29, "first_step_id": "m113a-observation-horizon", "last_step_id": "m122c2-shared-reality-collective-mind" }, { "id": "seven-depth-address", "title": "The Ratio-Addressed Seven-Depth Return", "order": 26, "step_count": 12, "first_step_id": "m122d-equal-polarity-start", "last_step_id": "m129b-depth-whole-torus-construction" }, { "id": "fibonacci-and-golden", "title": "Additive Inheritance and the Golden Relation", "order": 27, "step_count": 15, "first_step_id": "m130-two-state-inheritance", "last_step_id": "m137a-practice-changes-capacity-not-phi" }, { "id": "operational-ten-by-ten", "title": "After Observerhood: the Operational Field", "order": 28, "step_count": 8, "first_step_id": "m138-tenth-coordinate-after-observer", "last_step_id": "m142c-five-ninety-nine-views" }, { "id": "complete-dynamic-mind", "title": "Mind Is Structured Flow", "order": 29, "step_count": 20, "first_step_id": "m143-static-array-insufficient", "last_step_id": "m148a-creation-can-become-creative" }, { "id": "projection-architecture", "title": "From Source to Identity Field to Page", "order": 30, "step_count": 19, "first_step_id": "m149-source-units", "last_step_id": "m153e-five-source-projections" }, { "id": "typed-domain-mapping", "title": "One Relational Pattern, Different Carriers", "order": 31, "step_count": 19, "first_step_id": "m154-map-roles-not-names", "last_step_id": "m159-refresh-is-instrument" }, { "id": "matrix-geometry-bridge", "title": "Geometry Shows; Matrix Computes", "order": 32, "step_count": 4, "first_step_id": "m160-geometry-shows-relations", "last_step_id": "m163-vortex-versus-torus" }, { "id": "complex-mathematics-to-mind", "title": "The Exact Complex Bridge into Mind", "order": 33, "step_count": 12, "first_step_id": "mx046-three-proof-layers", "last_step_id": "mx057-hidden-relation-final" }, { "id": "matrix-complete-route", "title": "The Matrix Route, Complete", "order": 34, "step_count": 4, "first_step_id": "m165-full-route", "last_step_id": "m168-implementation-and-empirical" } ], "steps": [ { "id": "m001-relation-before-array", "title": "Begin with relation, not digits", "visual_id": "source_relational_triad" }, { "id": "m002-matrix-is-projection", "title": "Preview: the matrix will be a projection, not a second theory", "visual_id": "intro_pair_projection" }, { "id": "m003-one-earned-step", "title": "Preview rule: add only one earned distinction at a time", "visual_id": "matrix_sequence_spine" }, { "id": "m004-five-status-axes", "title": "Keep five status axes visible", "visual_id": "evidence_layer_guardrail" }, { "id": "m005-possible-not-possible", "title": "Possible is readable only with not-possible", "visual_id": "source_relational_triad" }, { "id": "m005a-primitive-polarity-exact", "title": "The primitive two poles are exact complements at their declared reference", "visual_id": "primitive_polarity_exact" }, { "id": "m006-relation-third-role", "title": "The relation is the third role", "visual_id": "triadic_roles" }, { "id": "m006a-relation-becomes-participant", "title": "A relation can become one participant in a wider relation", "visual_id": "relation_becomes_participant" }, { "id": "m006b-triad-renews-together", "title": "Every renewed occurrence changes the three-role state together", "visual_id": "triad_occurrence_renewal" }, { "id": "m006c-each-role-can-open", "title": "Each role can open as another inside–outside–relation field", "visual_id": "recursive_role_opening" }, { "id": "m007-possibility-to-existence", "title": "Change the subject, preserve the grammar", "visual_id": "source_to_existence_types" }, { "id": "m007a-possibility-field-before-probability", "title": "Possibility gives alternatives; probability requires a measure", "visual_id": "possibility_field_to_probability_measure" }, { "id": "m007b-relation-weights-exact-poles", "title": "The relation carries graded support; the poles remain exact", "visual_id": "relational_probability_support" }, { "id": "m008-existence-to-binary", "title": "The two relations can themselves form a triad", "visual_id": "source_to_existence_types" }, { "id": "m008b-binary-registration", "title": "Choose a binary registration", "visual_id": "binary_polarity_frame" }, { "id": "m008c-source-engine-manifestation-boundary", "title": "Source, Y Engine, and manifestation are three different descriptions", "visual_id": "source_engine_manifestation_boundary" }, { "id": "m008d-representation-not-world", "title": "A geometric manifestation is not yet a manifested world", "visual_id": "representation_carrier_boundary" }, { "id": "m009-source-not-clock", "title": "Source availability is not a clock sequence", "visual_id": "source_vs_manifestation" }, { "id": "m009a-source-polarity-not-spatial-points", "title": "At Source, polar unity is availability—not two spatial points", "visual_id": "source_dimensional_polarity" }, { "id": "m010-bit-is-reading", "title": "A bit records one present reading", "visual_id": "state_not_transition" }, { "id": "m011-arrow-adds-direction", "title": "The arrow adds direction", "visual_id": "directed_transition_pair" }, { "id": "m012-preservation-is-transition", "title": "Remaining is also an ordered relation", "visual_id": "transition_field_2x2" }, { "id": "m013-one-point-loses-path", "title": "One point cannot carry its own path", "visual_id": "matrix_state_history" }, { "id": "m014-change-is-relational", "title": "Change belongs to the relation", "visual_id": "ordered_difference_pair" }, { "id": "m015-origin-destination-axes", "title": "Give origin and destination separate axes", "visual_id": "transition_field_2x2" }, { "id": "m016-diagonal-retains", "title": "The diagonal retains the selected polarity", "visual_id": "transition_diagonal" }, { "id": "m017-off-diagonal-exchanges", "title": "The off-diagonal exchanges polarity", "visual_id": "transition_off_diagonal" }, { "id": "m018-transition-field-not-gate", "title": "The transition matrix is not XOR, OR, AND, or NOT", "visual_id": "logic_input_space" }, { "id": "m019-not-and-identity", "title": "NOT and identity select different transitions", "visual_id": "logic_readouts" }, { "id": "m020-boolean-readouts", "title": "XOR, OR, and AND read four joint inputs", "visual_id": "logic_readouts" }, { "id": "m021-two-coordinates-four-addresses", "title": "Two binary coordinates give four joint addresses", "visual_id": "state_square" }, { "id": "m022-square-is-address-geometry", "title": "The square is the address geometry", "visual_id": "state_square_repeat" }, { "id": "m023-path-is-not-space", "title": "A path is not the state-space", "visual_id": "manifested_square_path" }, { "id": "m024-gray-cycle", "title": "A Gray cycle changes one coordinate per edge", "visual_id": "manifested_square_path" }, { "id": "m025-complete-cyclic-state", "title": "A cyclic state needs more than its visible bit", "visual_id": "phase_addressed_square" }, { "id": "m026-four-transitions-not-flat-1010", "title": "A full cycle is four directed transitions, not a flat ‘1010’", "visual_id": "four_directed_quarter_cycle" }, { "id": "m026a-three-of-twelve-is-quarter", "title": "Three of twelve phase units make one quarter-turn", "visual_id": "twelve_quarter_bridge" }, { "id": "m027-circle-carries-phase", "title": "One closed phase freedom is a circle", "visual_id": "one_rotation_block" }, { "id": "m027a-triangle-and-phase-circle", "title": "Triangle and circle answer two consecutive questions", "visual_id": "triangle_phase_circle" }, { "id": "m027b-normalized-triad-phase-chart", "title": "One phase can be decoded as a normalized triadic correlation", "visual_id": "normalized_triad_phase_chart" }, { "id": "m028-quarter-chart", "title": "Four quarters form a coarse phase chart", "visual_id": "four_directed_quarter_cycle" }, { "id": "m029-recursive-phase-digits", "title": "A second digit refines the first sector", "visual_id": "recursive_phase_lattice" }, { "id": "m030-phase-address-value", "title": "The digit string locates a finite phase cell", "visual_id": "recursive_phase_lattice" }, { "id": "m031-phase-resolution-count", "title": "Resolution grows as four to the address depth", "visual_id": "binary_address_count_rule" }, { "id": "m032-resolution-not-depth", "title": "Phase resolution is not Mind depth", "visual_id": "resolution_vs_dimension" }, { "id": "m033-n-binary-coordinates", "title": "N separately addressable binary questions give 2^N joint addresses", "visual_id": "four_dimension_address_cube" }, { "id": "m034-hypercube-adjacency", "title": "The N-cube records one-coordinate adjacency", "visual_id": "four_dimension_address_cube" }, { "id": "m035-rank-three-array", "title": "A third independent index produces a tensor", "visual_id": "three_dimension_address_cube" }, { "id": "m036-state-space-versus-tensor", "title": "The address-space and the values on it are different", "visual_id": "matrix_state_history" }, { "id": "m037-path-visits-subset", "title": "One history visits only part of what was possible", "visual_id": "structure_vs_trajectory" }, { "id": "m038-freedom-before-number", "title": "A dimension begins as an independent relational freedom", "visual_id": "relational_freedom_chart" }, { "id": "m038a-operational-dimension-test", "title": "An earned dimension passes four operational tests", "visual_id": "dimension_operational_tests" }, { "id": "m038b-dimensional-polarity-product", "title": "Each earned relational freedom can be read through a declared polar chart", "visual_id": "dimensional_polarity_product" }, { "id": "m039-coordinate-map", "title": "A coordinate map assigns addresses", "visual_id": "coordinate_chart" }, { "id": "m040-state-vector", "title": "A state vector is one ordered joint address", "visual_id": "state_vector_address" }, { "id": "m041-reference-and-basis", "title": "Coordinates require a reference and basis", "visual_id": "basis_reference" }, { "id": "m042-same-point-new-coordinates", "title": "The same point can have different coordinate values", "visual_id": "basis_change" }, { "id": "mx001-representation-question", "title": "Begin with representation, not metaphysics", "visual_id": "math_number_field" }, { "id": "mx002-natural-addition", "title": "Natural numbers close counting under addition", "visual_id": "math_number_field" }, { "id": "mx003-subtraction-boundary", "title": "Subtraction exposes the first boundary", "visual_id": "math_operation_boundary" }, { "id": "mx004-integers-direction", "title": "Integers add signed direction", "visual_id": "math_number_field" }, { "id": "mx005-division-boundary", "title": "Division exposes another boundary", "visual_id": "math_operation_boundary" }, { "id": "mx006-rational-ratios", "title": "Rational numbers retain quotients", "visual_id": "math_number_field" }, { "id": "mx007-irrational-diagonal", "title": "The unit-square diagonal escapes every rational ratio", "visual_id": "math_irrational_diagonal" }, { "id": "mx008-real-continuum", "title": "Real numbers complete the one-dimensional continuum", "visual_id": "math_number_field" }, { "id": "mx009-square-fold", "title": "Squaring folds both real directions onto one side", "visual_id": "math_square_fold" }, { "id": "mx010-negative-root-boundary", "title": "No real address squares to negative one", "visual_id": "math_operation_boundary" }, { "id": "mx011-cardano-bombelli", "title": "A real cubic answer forced passage through complex terms", "visual_id": "math_cubic_tunnel" }, { "id": "mx012-extension-not-abandonment", "title": "Each extension preserves the earlier field", "visual_id": "math_number_tower" }, { "id": "mx013-define-imaginary-unit", "title": "Define i through its relation", "visual_id": "complex_plane_extension" }, { "id": "mx014-complex-pair", "title": "One complex number retains two real coordinates", "visual_id": "complex_plane_extension" }, { "id": "mx015-real-line-embedded", "title": "The former line survives inside the plane", "visual_id": "complex_plane_extension" }, { "id": "mx016-i-quarter-turn", "title": "Multiplication by i is an exact quarter-turn", "visual_id": "complex_quarter_turn" }, { "id": "mx017-powers-of-i", "title": "Four quarter-turns close one phase cycle", "visual_id": "complex_quarter_turn" }, { "id": "mx018-quarter-turn-matrix", "title": "The quarter-turn has an exact real Matrix", "visual_id": "complex_matrix_equivalence" }, { "id": "mx019-j-squared-half-turn", "title": "Two quarter-turn operators make one half-turn", "visual_id": "complex_matrix_equivalence" }, { "id": "mx020-continuous-rotation", "title": "A rotation Matrix advances any declared angle", "visual_id": "complex_matrix_equivalence" }, { "id": "mx021-polar-magnitude-phase", "title": "A complex address separates magnitude from phase", "visual_id": "complex_polar_form" }, { "id": "mx022-euler-formula", "title": "Euler's formula is the translation bridge", "visual_id": "euler_unit_circle" }, { "id": "mx023-euler-series-separation", "title": "Powers of i sort one series into cosine and sine", "visual_id": "euler_series_partition" }, { "id": "mx024-euler-tangent-flow", "title": "The change is perpendicular to the current state", "visual_id": "euler_tangent_flow" }, { "id": "mx025-euler-identity", "title": "At pi, the phase reaches the real antipode", "visual_id": "euler_unit_circle" }, { "id": "mx025a-opposite-quarter-turns", "title": "i and −i turn the same state in opposite directions", "visual_id": "complex_opposite_quarter_turns" }, { "id": "mx025b-inverse-quarter-turns", "title": "The opposite quarter-turns undo one another", "visual_id": "complex_opposite_quarter_turns" }, { "id": "mx025c-same-antipode-opposite-paths", "title": "One visible antipode can retain two opposite histories", "visual_id": "complex_opposite_quarter_turns" }, { "id": "mx025d-i-minus-i-separation", "title": "i and −i are half a cycle apart from each other", "visual_id": "complex_opposite_quarter_turns" }, { "id": "mx025e-relative-phasor", "title": "Phase difference is a directed relation between two addresses", "visual_id": "complex_relative_phasor" }, { "id": "mx025f-reverse-reference-conjugates", "title": "Reversing the reference conjugates the relation", "visual_id": "complex_relative_phasor" }, { "id": "mx025g-quarter-phase-from-two-references", "title": "+i and −i are the same quarter separation read in reverse", "visual_id": "complex_relative_phasor" }, { "id": "mx025h-common-frame-cancels", "title": "A shared rotation changes both addresses but not their relation", "visual_id": "complex_common_rotation" }, { "id": "mx025i-relation-real-imaginary", "title": "One relative phasor carries alignment and direction together", "visual_id": "complex_relation_components" }, { "id": "mx025j-engine-phase-kernel", "title": "The existing engine already computes both coordinates of this relation", "visual_id": "complex_relation_components" }, { "id": "mx025k-four-relational-addresses", "title": "The four quarter addresses separate agreement, opposition, and direction", "visual_id": "complex_relation_components" }, { "id": "mx025l-conjugate-manifestation", "title": "Counter-rotating conjugate branches combine into a real projection", "visual_id": "complex_conjugate_manifestation" }, { "id": "mx025m-reference-projection", "title": "Manifestation is a declared projection relative to an observation axis", "visual_id": "complex_reference_projection" }, { "id": "mx025n-relation-matrix", "title": "Many phase-addressed identities form a Matrix of directed relations", "visual_id": "complex_relation_matrix" }, { "id": "mx025o-relation-cycle-closure", "title": "A consistent one-phase relation field closes around every triangle", "visual_id": "complex_relation_matrix" }, { "id": "mx025p-source-manifestation-bridge", "title": "The source problem and manifestation problem are now different and connected", "visual_id": "complex_source_manifestation_bridge" }, { "id": "m043-general-update", "title": "Begin with a general update relation", "visual_id": "general_update_operator" }, { "id": "m044-space-operator-path", "title": "State-space, operator, and path are different objects", "visual_id": "state_operator_path" }, { "id": "m045-iteration-produces-history", "title": "Iteration turns a rule into one history", "visual_id": "matrix_state_history" }, { "id": "m046-linearity-test", "title": "A fixed matrix is the linear special case", "visual_id": "linear_special_case" }, { "id": "m047-entry-is-directed", "title": "A matrix entry points from input j to output i", "visual_id": "matrix_entry_direction" }, { "id": "m048-column-basis-image", "title": "A column is one basis direction’s complete output pattern", "visual_id": "matrix_column_image" }, { "id": "m048a-output-as-column-sum", "title": "The full matrix output is the simultaneous sum of scaled columns", "visual_id": "matrix_output_column_sum" }, { "id": "m048b-one-change-redistributes-through-structure", "title": "One coordinate change can adjust many coordinates through its relation column", "visual_id": "relation_column_redistribution" }, { "id": "m048c-dimension-count-does-not-set-gain", "title": "More dimensions do not automatically create unity, damping, or acceleration", "visual_id": "dimension_count_not_gain" }, { "id": "m049-composition-order", "title": "Matrix multiplication composes transformations", "visual_id": "matrix_composition" }, { "id": "m049a-noncommuting-relations", "title": "Two compatible directions can generate a third change", "visual_id": "commutator_third_direction" }, { "id": "m050-identity-operator", "title": "The identity matrix preserves the coordinate state", "visual_id": "identity_operator" }, { "id": "m051-operator-change-of-basis", "title": "A basis change conjugates one linear endomorphism", "visual_id": "operator_basis_conjugation" }, { "id": "m052-similarity-invariants", "title": "Some properties survive the coordinate change", "visual_id": "matrix_invariants" }, { "id": "m052a-viable-state-boundary", "title": "An identity usually occupies a viable subset of the represented state-space", "visual_id": "viable_state_boundary" }, { "id": "m053-local-jacobian", "title": "A nonlinear relation can have a local matrix", "visual_id": "local_jacobian" }, { "id": "m053a-coordinate-block-partition", "title": "Partition the state vector before partitioning its operator", "visual_id": "coordinate_block_partition" }, { "id": "m054-block-operator", "title": "An outer matrix may contain complete inner operators", "visual_id": "matrix_inside_matrix" }, { "id": "m055-kronecker-product", "title": "The Kronecker product builds an independent product system", "visual_id": "kronecker_product" }, { "id": "m056-product-not-interaction", "title": "Independent product is not yet mutual influence", "visual_id": "coupled_block_operator" }, { "id": "m057-many-inside-one-outside", "title": "A closed inner field presents one face outside", "visual_id": "many_inside_one_outside" }, { "id": "m057a-reference-relative-outside-field", "title": "One identity’s outside is the rest of the declared identity field", "visual_id": "reference_relative_outside_field" }, { "id": "m057a1-structural-outside-not-event-complement", "title": "An identity's outside field is not its probability complement", "visual_id": "outside_field_vs_event_complement" }, { "id": "m057b-each-identity-reframes-field", "title": "Every identity can become the reference of its own inside–outside field", "visual_id": "reciprocal_identity_views" }, { "id": "m057c-group-boundary-recursion", "title": "A selected group can be repartitioned through the same boundary grammar", "visual_id": "group_boundary_recursion" }, { "id": "m057d1-coexisting-joint-address", "title": "Coexisting identity criteria need a joint configuration address", "visual_id": "joint_coexisting_configuration" }, { "id": "m057d2-typed-factors-assign-joint-support", "title": "A typed factor assigns support to its declared relational scope", "visual_id": "joint_identity_factor_field" }, { "id": "m057d3-normalize-joint-support", "title": "A finite positive total turns support into joint probability", "visual_id": "normalize_joint_factor_field" }, { "id": "m057d4-declared-group-event", "title": "A wider identity probability requires a declared group event", "visual_id": "group_event_projection" }, { "id": "m057e-normalized-redistribution-boundary", "title": "If one probability falls, others rise only in a closed alternative frame", "visual_id": "normalized_redistribution_boundary" }, { "id": "m058-compression-needs-interface", "title": "Identity compression requires an interface", "visual_id": "identity_interface" }, { "id": "m059-recursion-not-elapsed-time", "title": "Nested scale is not elapsed time", "visual_id": "update_vs_depth_recursion" }, { "id": "m060-inside-outside-relation", "title": "Use I, O, and R as typed roles", "visual_id": "triadic_roles" }, { "id": "m061-relation-not-observer", "title": "The third role is relation, not yet observer", "visual_id": "triadic_roles" }, { "id": "m062-nine-directed-channels", "title": "Three typed origins by three destinations give nine channels", "visual_id": "triad_relation_matrix" }, { "id": "m063-living-relation-packet", "title": "Each cell can carry a living relation", "visual_id": "living_triad_matrix" }, { "id": "m064-topology-versus-state", "title": "Topology says what can couple; state says what is happening", "visual_id": "living_triad_matrix" }, { "id": "m065-triad-inside-triad", "title": "Opening the three roles yields nine inner role positions", "visual_id": "corrected_nested_triad" }, { "id": "m066-role-axis", "title": "Role recursion answers ‘which relational position?’", "visual_id": "role_depth_phase_axes" }, { "id": "m067-phase-axis", "title": "Phase answers ‘where in the return cycle?’", "visual_id": "role_depth_phase_axes" }, { "id": "m068-depth-axis", "title": "Depth answers ‘how far through recursive transformation?’", "visual_id": "role_depth_phase_axes" }, { "id": "m069-dimension-axis", "title": "Dimension answers ‘which independent freedom varies?’", "visual_id": "resolution_vs_dimension" }, { "id": "m069a-derived-relational-dimension", "title": "A stable relation among dimensions can become another dimension", "visual_id": "derived_relational_dimension" }, { "id": "m070-scale-and-occurrence", "title": "Scale and occurrence are not interchangeable", "visual_id": "reciprocal_scale_arrows" }, { "id": "m071-two-twelvefolds", "title": "Three plus nine and four times three are different twelvefold views", "visual_id": "two_twelvefold_views" }, { "id": "m072-nine-inside-nine-outside", "title": "A complete nine-mode inside faces a complete nine-mode outside", "visual_id": "structural_ninety_nine" }, { "id": "m072a-general-closure-count", "title": "The structural count is one case of a general closure rule", "visual_id": "general_closure_count" }, { "id": "m073-eighty-one-directed-crossings", "title": "Nine by nine gives eighty-one bipolar relation positions", "visual_id": "directed_ninety_nine" }, { "id": "m074-structural-count", "title": "The structural field contains ninety-nine positions", "visual_id": "structural_ninety_nine" }, { "id": "m075-closure-one", "title": "The ninety-nine belong to one closure", "visual_id": "structural_ninety_nine_closure_one" }, { "id": "m076-closure-not-observer", "title": "Closure-one is not observer-one", "visual_id": "structural_and_operational_ninety_nine" }, { "id": "m077-source-field-available", "title": "At Source, the relation field is available without a travelled row order", "visual_id": "source_vs_manifestation" }, { "id": "m078-manifestation-orders", "title": "Manifestation adds ordered transit", "visual_id": "dynamic_history_update" }, { "id": "m079-delay-retains-relation", "title": "Delay is the retained noncoincidence between successive identity-states", "visual_id": "delay_retention_circuit" }, { "id": "m080-delay-not-memory", "title": "Transit retention leaves residue", "visual_id": "residue_formation" }, { "id": "m081-residue-becomes-trace", "title": "Identifiable residue becomes trace", "visual_id": "trace_identification" }, { "id": "m082-trace-becomes-memory", "title": "A returned trace functions as memory", "visual_id": "trace_becomes_memory" }, { "id": "m082a-external-trace-versus-structural-trace", "title": "A record about the system is not the same as a changed relation inside it", "visual_id": "trace_location_distinction" }, { "id": "m082b-history-bearing-cycle-state", "title": "The cyclic state can now include retained history", "visual_id": "history_bearing_cycle_state" }, { "id": "m082c-geometry-as-retained-trace", "title": "Geometry first records the path left by correlated change", "visual_id": "geometry_trace_memory" }, { "id": "m083-relation-as-transducer", "title": "A change in relation can become a directed signal", "visual_id": "relation_derivative_flow" }, { "id": "m084-flow-needs-path", "title": "A changing relation can transduce change", "visual_id": "relation_transducer" }, { "id": "m084a-reciprocal-transduction", "title": "Generator and motor are reciprocal transduction readings", "visual_id": "reciprocal_transduction" }, { "id": "m084b-thought-is-not-electron-flow", "title": "Do not rename physical current as thought", "visual_id": "thought_not_electron_flow" }, { "id": "m085-concurrent-contributions", "title": "Interacting channels contribute concurrently", "visual_id": "concurrent_relation_update" }, { "id": "m086-continuity-path", "title": "Produced change persists only through a continuity path", "visual_id": "compatible_return_path" }, { "id": "m087-reinforcement", "title": "Reinforcement makes a compatible return easier", "visual_id": "continuity_allocation_band" }, { "id": "m088-leakage", "title": "Leakage is influence unavailable to the same return", "visual_id": "leakage_allocation" }, { "id": "m088a-damping-regulation", "title": "Damping regulates without erasing the relation", "visual_id": "damping_regulation" }, { "id": "m088a1-identity-support-balance", "title": "Persistence is renewed support relative to leakage and disruptive change", "visual_id": "identity_support_balance" }, { "id": "m088a2-identity-formation-dissolution", "title": "A manifested identity population changes when closures form or continuity dissolves", "visual_id": "identity_population_flow" }, { "id": "m088a3-nested-return-extends-persistence", "title": "A wider relation can return what would otherwise be local leakage", "visual_id": "nested_return_persistence" }, { "id": "m088b-earned-relation-record", "title": "The living relation record can now be opened", "visual_id": "earned_relation_record" }, { "id": "m088c-symmetric-availability", "title": "Perfect symmetry supplies possibility, not a travelled direction", "visual_id": "symmetric_transition_field" }, { "id": "m088d-retained-difference", "title": "A retained difference gives the next passage a direction", "visual_id": "retained_asymmetry_direction" }, { "id": "m088e-restoring-overshoot", "title": "Restoring relation plus delayed overshoot produces oscillation", "visual_id": "restoring_overshoot_cycle" }, { "id": "m089-rotation-operator", "title": "A two-coordinate rotation matrix advances phase", "visual_id": "one_rotation_block" }, { "id": "m090-rotation-circle-exact", "title": "Repeated undamped rotation lies on a circle", "visual_id": "one_rotation_block" }, { "id": "m091-complex-mode", "title": "A complex mode separates amplitude from phase advance", "visual_id": "complex_eigenmode" }, { "id": "m092-amplitude-regimes", "title": "Leak, conservation, and reinforcement appear as amplitude regimes", "visual_id": "complex_eigenmode" }, { "id": "m093-nonidentical-return", "title": "The relational form can return while history changes", "visual_id": "nonidentical_return_spiral" }, { "id": "m094-what-oscillates", "title": "The evolving state oscillates through the relation field", "visual_id": "structure_vs_trajectory" }, { "id": "m094a-omnidirectional-boundary-input", "title": "Outside change can meet one boundary from many directions", "visual_id": "omnidirectional_boundary_input" }, { "id": "m094b-axis-and-vortex", "title": "Retained asymmetry selects an axis; restoring return can circulate around it", "visual_id": "axis_vortex_formation" }, { "id": "mx026-growth-and-rotation", "title": "A complex exponent separates radial change from phase change", "visual_id": "complex_growth_rotation" }, { "id": "mx027-coupled-oscillator", "title": "Two changing coordinates form one circulating flow", "visual_id": "complex_coupled_oscillator" }, { "id": "mx028-radius-invariant", "title": "The components change while their whole magnitude remains", "visual_id": "complex_invariant_circle" }, { "id": "mx029-complete-phase-state", "title": "The complex state carries the complete circular phase", "visual_id": "complex_invariant_circle" }, { "id": "mx030-real-shadow", "title": "One real projection appears as oscillation", "visual_id": "complex_projection_wave" }, { "id": "mx031-correct-partial-projection", "title": "The projection is correct and incomplete", "visual_id": "complex_projection_wave" }, { "id": "mx032-same-projection-different-phase", "title": "One observed value can belong to two different projected futures", "visual_id": "complex_hidden_phase" }, { "id": "mx033-hidden-coordinate-shapes-next", "title": "The coordinate absent from view still shapes the next view", "visual_id": "complex_hidden_phase" }, { "id": "mx034-delay-retains-phase", "title": "Delay carries a definite relation between phase addresses", "visual_id": "complex_delay_phase" }, { "id": "mx035-delay-coordinate-pair", "title": "Present and delayed observations can recover the missing distinction", "visual_id": "complex_delay_reconstruction" }, { "id": "mx036-retention-restrains-future", "title": "Retained relation removes otherwise compatible futures", "visual_id": "complex_possibility_restriction" }, { "id": "mx037-many-circular-modes", "title": "A general periodic signal may require many circular modes", "visual_id": "complex_fourier_modes" }, { "id": "mx037a-fourier-mode-addresses", "title": "Fourier analysis gives every resolved mode a complex address", "visual_id": "complex_fourier_spectrum" }, { "id": "mx037b-time-frequency-charts", "title": "Time and frequency are two charts of the same represented signal", "visual_id": "complex_time_frequency" }, { "id": "mx037c-dft-is-a-matrix", "title": "The discrete Fourier transform is a Matrix of phase-progressing references", "visual_id": "complex_dft_matrix" }, { "id": "mx037d-fft-recursive-factorization", "title": "The FFT accelerates the DFT by reusing recursive symmetry", "visual_id": "complex_fft_recursion" }, { "id": "mx037e-phase-superposition", "title": "Alignment reinforces; opposition cancels; every other phase leaves a resultant", "visual_id": "complex_phase_superposition" }, { "id": "mx037f-sound-and-fft", "title": "Sound is measured as a real pressure history; complex modes expose its composition", "visual_id": "complex_sound_modes" }, { "id": "mx037g-light-harmonic-field", "title": "A harmonic electromagnetic field also needs amplitude and phase", "visual_id": "complex_em_wave" }, { "id": "mx037h-complex-refractive-index", "title": "One complex material parameter separates phase advance from attenuation", "visual_id": "complex_optical_index" }, { "id": "mx037i-iq-relational-carrier", "title": "Two quadratures can carry one changing message", "visual_id": "complex_iq_carrier" }, { "id": "mx037j-phase-is-relational-information", "title": "Magnitude alone cannot reconstruct what phase has discarded", "visual_id": "complex_phase_information" }, { "id": "mx038-ac-phasor", "title": "A phasor retains amplitude and relative phase", "visual_id": "phasor_signal" }, { "id": "mx039-impedance-operator", "title": "Impedance is the typed relation between voltage and current", "visual_id": "phasor_impedance" }, { "id": "mx040-rlc-phase-relations", "title": "Resistance, inductance, and capacitance occupy distinct phase relations", "visual_id": "phasor_impedance" }, { "id": "mx041-energy-storage-and-return", "title": "Reactive relation stores and returns; resistance dissipates", "visual_id": "phasor_energy_relation" }, { "id": "mx041a-classical-realification", "title": "In classical models, complex notation can be unpacked into paired real equations", "visual_id": "quantum_classical_real_pair" }, { "id": "mx041b-quantum-state-space", "title": "Pure states are rays; general states are density operators", "visual_id": "quantum_state_space" }, { "id": "mx041c-basis-superposition", "title": "A basis turns one state into a coordinated superposition", "visual_id": "quantum_basis_coordinates" }, { "id": "mx041d-position-wavefunction", "title": "A position wavefunction is a field of complex amplitudes, not a smeared classical ball", "visual_id": "quantum_position_amplitude" }, { "id": "mx041e-amplitude-before-probability", "title": "Probability is obtained from amplitude only after the measurement is declared", "visual_id": "quantum_born_map" }, { "id": "mx041f-global-relative-phase", "title": "A global phase is redundant; relative phase remains observable through later relations", "visual_id": "quantum_relative_phase" }, { "id": "mx041g-interference-before-probability", "title": "Quantum alternatives interfere as amplitudes before they become probabilities", "visual_id": "quantum_interference" }, { "id": "mx041g1-two-path-amplitudes", "title": "Indistinguishable paths contribute amplitudes to one outcome", "visual_id": "quantum_two_path_amplitudes" }, { "id": "mx041g2-constructive-destructive-amplitudes", "title": "Relative phase makes one outcome reinforce and another cancel", "visual_id": "quantum_constructive_destructive" }, { "id": "mx041g3-interference-screen", "title": "The bright and dark bands are a map of changing path relation", "visual_id": "quantum_interference_screen" }, { "id": "mx041g4-which-path-relation", "title": "A which-path record changes the joint state that can interfere", "visual_id": "quantum_which_path_boundary" }, { "id": "mx041h-schrodinger-equation", "title": "The Schrödinger equation makes phase-bearing change fundamental to the standard dynamics", "visual_id": "quantum_schrodinger_flow" }, { "id": "mx041h1-atomic-stationary-state", "title": "Atomic orbitals are stationary quantum modes, not miniature planetary orbits", "visual_id": "quantum_stationary_state" }, { "id": "mx041i-unitary-preservation", "title": "Closed-system evolution changes phase relations while preserving total norm", "visual_id": "quantum_unitary_norm" }, { "id": "mx041j-real-pair-schrodinger", "title": "Removing the glyph i reveals an equivalent coupled real flow", "visual_id": "quantum_realification" }, { "id": "mx041k-complex-structure-survives", "title": "Realification moves the complex structure; it does not erase phase", "visual_id": "quantum_complex_structure" }, { "id": "mx041k1-real-formulations-and-composition", "title": "Real-number quantum formulations must restore the missing composition structure", "visual_id": "quantum_real_formulations" }, { "id": "mx041k2-experiments-test-models", "title": "Experiments test complete models, not the reality of a mathematical glyph", "visual_id": "quantum_evidence_boundary" }, { "id": "mx041l-measurement-is-interaction", "title": "Quantum measurement is a declared physical interaction, not conscious looking", "visual_id": "quantum_measurement_coupling" }, { "id": "mx041m-observation-restrains-quantum-continuation", "title": "A registered outcome conditions the next assigned state", "visual_id": "quantum_instrument_update" }, { "id": "mx041n-quantum-record-boundary", "title": "A stable quantum record is still not a complete Mind", "visual_id": "quantum_record_boundary" }, { "id": "mx041o-quantum-to-mind-bridge", "title": "Quantum mathematics strengthens the relational lesson without proving observerhood", "visual_id": "quantum_mind_boundary" }, { "id": "mx042-ratio-driven-complex-update", "title": "A ratio-driven operator generates circle or spiral", "visual_id": "complex_ratio_engine" }, { "id": "mx043-leak-retain-reinforce", "title": "One magnitude ratio separates leakage, retention, and reinforcement", "visual_id": "complex_ratio_regimes" }, { "id": "mx044-bounded-feedback-cycle", "title": "Opposing radial effects can generate a bounded stable loop", "visual_id": "complex_bounded_feedback" }, { "id": "mx045-one-phase-two-phases", "title": "One phase gives a circle; two independent phases give a torus", "visual_id": "complex_circle_to_torus" }, { "id": "mx041p-y-phase-address", "title": "Begin the model from the exact normalized Y phase address", "visual_id": "manifest_y_address" }, { "id": "mx041q-phase-bearing-identity-field", "title": "A field retains phase without erasing identity, depth, or scale", "visual_id": "manifest_identity_field" }, { "id": "mx041r-history-retains-relation", "title": "History turns an instantaneous address into a retained relation", "visual_id": "manifest_history_delay" }, { "id": "mx041s-typed-recursive-operator", "title": "The operator separates local change, inward feed, outward return, and memory", "visual_id": "manifest_recursive_operator" }, { "id": "mx041t-evolution-before-outcome", "title": "Evolution comes before an outcome is registered", "visual_id": "manifest_evolution_stage" }, { "id": "mx041u-outcome-instrument", "title": "A declared instrument maps compatible amplitudes to a recorded alternative", "visual_id": "manifest_quantum_instrument" }, { "id": "mx041v-retained-record", "title": "Retention makes the outcome available to a later cycle", "visual_id": "manifest_retention_memory" }, { "id": "mx041w-changed-return", "title": "Mind becomes a testable claim only when retained comparison changes return", "visual_id": "manifest_changed_return" }, { "id": "mx041x-complete-manifestation-loop", "title": "The full recurrence separates change, manifestation, retention, observation, and return", "visual_id": "manifest_complete_loop" }, { "id": "mx041y-model-must-earn-reality", "title": "Exact equations make Y Theory testable; tests decide its physical scope", "visual_id": "manifest_test_ladder" }, { "id": "m095-two-cycles-torus", "title": "Two independent phase cycles form a two-torus", "visual_id": "two_rotation_blocks" }, { "id": "m096-n-cycles-n-torus", "title": "N independent phases form an N-torus", "visual_id": "ratio_driven_n_torus" }, { "id": "m097-off-diagonal-coupling", "title": "Off-diagonal blocks make the cycles interact", "visual_id": "coupled_rotation_blocks" }, { "id": "m098-delayed-coupling", "title": "Delayed coupling returns to a changed field", "visual_id": "delayed_cross_coupling" }, { "id": "m099-torus-is-domain", "title": "The torus is the phase-domain of coexisting returns", "visual_id": "matrix_and_torus_roles" }, { "id": "m100-spiral-is-trace", "title": "A spiral is a projected history, not a different topology", "visual_id": "torus_spiral_trace" }, { "id": "m100a-parametric-torus", "title": "The familiar torus drawing is generated from two phase coordinates", "visual_id": "parametric_torus_equation" }, { "id": "m100a1-reversible-torus-chart", "title": "An embedded torus point can be decoded back to its two phase addresses", "visual_id": "torus_reversible_chart" }, { "id": "m100a1a-decode-torus-to-two-triads", "title": "A torus point decodes to two recurrent triadic correlations", "visual_id": "triadic_torus_decode" }, { "id": "m100a1b-same-torus-different-reference", "title": "One intrinsic torus can produce different three-dimensional views", "visual_id": "intrinsic_torus_viewpoint_projection" }, { "id": "m100a2-commensurate-phase-return", "title": "Commensurate phases close; incommensurate phases keep sampling the torus", "visual_id": "commensurate_incommensurate_traces" }, { "id": "m100a3-weighted-trace-field", "title": "Renewed passages strengthen a trace field; unrenewed passages fade", "visual_id": "weighted_trace_deposition" }, { "id": "m100b-helix-depth-trace", "title": "A helix adds accumulated depth to recurrent phase", "visual_id": "helix_from_phase_and_depth" }, { "id": "m100c-ascent-descent", "title": "Ascent and descent are reciprocal readings of one recursive path", "visual_id": "ascent_descent_helix" }, { "id": "m100d-mind-dna-bridge", "title": "Mind-DNA names structural inheritance, not molecule identity", "visual_id": "double_helix_inheritance" }, { "id": "m100e-cycle-rate-vs-identity-frequency", "title": "Ordinary cycle rate and identity-frequency are different readings", "visual_id": "cycle_rate_identity_pattern" }, { "id": "m101-coupled-field", "title": "Coupling allows local modes to constrain one another", "visual_id": "collective_whole_mode" }, { "id": "m101b-fast-local-slow-whole", "title": "Fast local cycles can form a slower identifiable whole", "visual_id": "local_fast_whole_breathing" }, { "id": "m101a-whole-mode-policy", "title": "Declare the executable whole-mode selection policy before projecting", "visual_id": "whole_mode_selection" }, { "id": "m102-whole-coordinate", "title": "A whole mode is a distributed coordinate", "visual_id": "formal_observer_projection" }, { "id": "m103-remainder", "title": "The remainder preserves what the whole mode does not integrate", "visual_id": "observer_aperture_corrected" }, { "id": "m104-agreement-not-observer", "title": "Collective agreement is not yet an observer", "visual_id": "collective_agreement_diagnostic" }, { "id": "m105-identity-boundary", "title": "A whole mode must remain coupled to an identity boundary", "visual_id": "many_inside_one_outside" }, { "id": "m105a-outside-and-received-outside", "title": "The outside and the Mind’s received outside are not identical", "visual_id": "outside_received_model" }, { "id": "m113e-developed-mind-reading", "title": "At local cognitive capability depth, the triad receives a cognitive reading", "visual_id": "existence_consciousness_awareness" }, { "id": "m106-retained-whole", "title": "Retain the present whole amplitude as whole-memory", "visual_id": "retained_whole_memory" }, { "id": "m107-present-history-comparison", "title": "Compare present whole with delayed whole-memory without discarding phase", "visual_id": "present_memory_comparison" }, { "id": "m107a-observation-is-comparison", "title": "One integrated present-versus-retained comparison is an observation", "visual_id": "observation_as_integrated_comparison" }, { "id": "m108-retained-comparison", "title": "Integrate observation into the retained observer-state Ω", "visual_id": "reflexive_observer_loop" }, { "id": "m109-causal-return", "title": "The return-gain discriminator separates collective identity from observer", "visual_id": "observer_return_discriminator" }, { "id": "m110-distributed-observer", "title": "Returned Ω participates in the next local field update", "visual_id": "whole_to_local_return" }, { "id": "m110a-observer-loop-complete", "title": "The observer is the complete distributed reflexive loop", "visual_id": "distributed_observer_readout" }, { "id": "m110b-local-whole-reciprocity", "title": "Local identities form the whole; the changed whole constrains local identities", "visual_id": "local_whole_reciprocity" }, { "id": "m111-aperture-mode-selection", "title": "Inspect the declared aperture policy and its tie boundary", "visual_id": "observer_aperture_corrected" }, { "id": "m112-aperture-breadth", "title": "Effective dimension measures participation breadth", "visual_id": "observer_aperture_corrected" }, { "id": "m113-observer-resolution", "title": "The internal observer question is resolved at the mechanism level", "visual_id": "reflexive_observer_loop" }, { "id": "m113a-observation-horizon", "title": "The observer can compare only what becomes accessible", "visual_id": "observation_horizon_intersection" }, { "id": "m113b-finite-observation-budget", "title": "A finite observer budget weights accessible relations unequally", "visual_id": "finite_observation_budget" }, { "id": "m113b1-observation-entry-threshold", "title": "Weight and entry are two different decisions", "visual_id": "observation_entry_threshold" }, { "id": "m113c-partial-whole-illusion", "title": "Illusion occurs when a partial whole is mistaken for the complete field", "visual_id": "partial_whole_and_remainder" }, { "id": "m114-observation-restricts-next", "title": "Observation changes the next viable field", "visual_id": "observation_restricts_possibility" }, { "id": "m115-restriction-not-determinism", "title": "Constraint narrows possibility without forcing one outcome", "visual_id": "observation_restricts_possibility" }, { "id": "m115a-three-kinds-of-change", "title": "Separate epistemic, causal, and generative change", "visual_id": "epistemic_causal_generative_change" }, { "id": "m116-awareness-breadth", "title": "Awareness is how broadly the whole relation is integrated", "visual_id": "breadth_depth_whole_return" }, { "id": "m117-attention-reweights", "title": "Attention gain reweights present participation", "visual_id": "formal_attention_projection" }, { "id": "m117a-three-observation-rates", "title": "Carrier rate, attentional sampling, and cross-dimensional switching are distinct", "visual_id": "three_observation_rates" }, { "id": "m117b-fixed-resource-budget", "title": "A fixed-resource schematic exposes the breadth–sampling tradeoff", "visual_id": "observer_resource_budget" }, { "id": "m117c-attention-control-tuple", "title": "Attention controls gain, sampling, dwell, and direction", "visual_id": "attention_control_tuple" }, { "id": "m117d-repetition-versus-understanding", "title": "Repeated sampling can reinforce a path without deepening understanding", "visual_id": "repetition_information_gain" }, { "id": "m117e-global-versus-focal-gain", "title": "Global gain broadens participation; focal gain deepens a narrower path", "visual_id": "global_focal_attention" }, { "id": "m117f-attention-profiles", "title": "Focused attention, open monitoring, and absorption are different profiles", "visual_id": "functional_attention_profiles" }, { "id": "m113d-observer-limit-across-domains", "title": "The same observer-limit grammar can now be typed across domains", "visual_id": "observer_limit_domain_bridge" }, { "id": "m118-self-location", "title": "Self-awareness requires a self-locating model", "visual_id": "mind_retained_model" }, { "id": "m119-self-awareness", "title": "Self-awareness is consequential self-comparison", "visual_id": "self_model_includes_modeler" }, { "id": "m119a-inward-outward-orientations", "title": "Inward and outward observation are two orientations of one cycle", "visual_id": "inward_outward_observation" }, { "id": "m119b-self-awareness-of-aperture", "title": "Self-awareness includes awareness of the aperture’s limit", "visual_id": "self_aware_aperture" }, { "id": "m120-metacognition", "title": "Metacognition changes how the Mind observes", "visual_id": "metacognitive_return" }, { "id": "m120a-thought-as-organized-relational-flow", "title": "Thought is an organized relational flow in a history-bearing Mind-field", "visual_id": "thought_relational_flow" }, { "id": "m121-imagination", "title": "Imagination runs retained relations as counterfactual paths", "visual_id": "counterfactual_paths" }, { "id": "m122a-intention", "title": "Intention gives the returned model a direction", "visual_id": "intention_choice_return" }, { "id": "m122b-choice", "title": "Choice commits one continuation to action", "visual_id": "intention_choice_return" }, { "id": "m122-directed-creation", "title": "Returned understanding can redirect manifested action", "visual_id": "reflexive_observer_loop" }, { "id": "m122c-awakening-cycle", "title": "Awakening is renewed awareness of the directing loop", "visual_id": "awakening_cycle" }, { "id": "m122c1-mutual-partial-observers", "title": "Two observers meet through delayed partial models", "visual_id": "mutual_partial_observers" }, { "id": "m122c2-shared-reality-collective-mind", "title": "Corrected overlap can become the inside of a collective Mind", "visual_id": "shared_reality_collective_mind" }, { "id": "m122d-equal-polarity-start", "title": "Begin ratio development from an equal two-pole reading", "visual_id": "thirds_envelope_sequence" }, { "id": "m122e-additive-ratio-sequence", "title": "Successive additive inheritance produces a converging ratio sequence", "visual_id": "thirds_envelope_sequence" }, { "id": "m122f-two-thirds-envelope", "title": "Two-thirds is the first expansion-facing envelope, not the limiting ratio", "visual_id": "two_thirds_outer_envelope" }, { "id": "m123-fixed-ten-metric", "title": "Begin with the declared ten-part directional metric", "visual_id": "ten_band_metric" }, { "id": "m124-seven-derived-not-literal", "title": "The seventh address is derived, not typed into the engine", "visual_id": "seven_address_derivation" }, { "id": "m125-depths-are-active-relations", "title": "Each depth is a complete active triad", "visual_id": "seven_depth_return_cycle" }, { "id": "m126-depth-carries-remainder", "title": "Depth advances by carrying what remains consequential", "visual_id": "depth_remainder_flow" }, { "id": "m127-l7-turning-boundary", "title": "L7 is the turning boundary, not the observer", "visual_id": "seven_depth_return_cycle" }, { "id": "m128-return-to-l1-prime", "title": "Depth returns as a changed L1-prime", "visual_id": "seven_depth_return_cycle" }, { "id": "m129-depth-dimension-role-tensor", "title": "Dimensions run in parallel; depth runs through each", "visual_id": "dimension_depth_role_field" }, { "id": "m129a-toroidal-identity-depth-bridge", "title": "A toroidal phase point can carry a typed identity at an earned depth", "visual_id": 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"id": "m135a-source-possibility-manifested-history", "title": "At Source the golden family is available; manifestation makes one path historical", "visual_id": "source_possibility_manifested_oscillation" }, { "id": "m136-pi-and-phi", "title": "π and φ answer different questions", "visual_id": "circle_return_vs_inheritance" }, { "id": "m137-golden-status", "title": "The golden result is settled at its declared level", "visual_id": "golden_observer_allocation" }, { "id": "m137a-practice-changes-capacity-not-phi", "title": "Practice can change effective capacity; it does not change φ", "visual_id": "practice_capacity_not_phi" }, { "id": "m138-tenth-coordinate-after-observer", "title": "The observer coordinate is added only after the loop exists", "visual_id": "operational_ten_by_ten" }, { "id": "m139-operational-hundred", "title": "Ten origins by ten destinations give one hundred operational channels", "visual_id": "operational_ten_by_ten" }, { "id": "m140-operational-decomposition", "title": "The hundred separates relation, read, write, and self-return channels", "visual_id": "operational_ninety_nine_plus_one" }, { "id": "m141-two-counts-one-correspondence", "title": "Structural 99 and operational 100 are related but different", "visual_id": "structural_and_operational_ninety_nine" }, { "id": "m142-three-ones", "title": "Closure-one, observer-one, and self-return-one are not interchangeable", "visual_id": "structural_and_operational_ninety_nine" }, { "id": "m142a-cyclic-compass-projection", "title": "The cyclic compass is a third, separately typed projection", "visual_id": "cyclic_compass_projection" }, { "id": "m142b-trace-decomposition", "title": "Every ten-by-ten operator has a one-plus-ninety-nine algebraic split", "visual_id": "trace_identity_decomposition" }, { "id": "m142c-five-ninety-nine-views", "title": "Five ninety-nine readings must remain distinguishable", "visual_id": "five_ninety_nine_views" }, { "id": "m143-static-array-insufficient", "title": "A 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"visual_id": "successive_identity_leaves" }, { "id": "m148a-creation-can-become-creative", "title": "Creation can become creative without becoming Ultimate Source", "visual_id": "creative_not_ultimate_source" }, { "id": "m149-source-units", "title": "The current source registry contains authored, provenance-bearing units", "visual_id": "source_packet_pipeline" }, { "id": "m149a-source-unit-types", "title": "Different source acts must remain different before relation", "visual_id": "source_unit_types" }, { "id": "m150-identity-packets", "title": "A Y-Identity Packet carries structure and provenance", "visual_id": "source_packet_pipeline" }, { "id": "m150a-identity-packet-complete-target", "title": "The target packet preserves everything needed to regenerate an identity", "visual_id": "identity_packet_contract" }, { "id": "m151-typed-relation-field", "title": "Packets form a typed recursive relation field", "visual_id": "source_packet_pipeline" }, { "id": "m151a0-relation-edge-types", "title": "Relation edges retain how one source unit bears on another", "visual_id": "source_relation_edge_types" }, { "id": "m151a-scale-indexed-living-field", "title": "A living source field is indexed by scale, reference, and time", "visual_id": "scale_indexed_identity_field" }, { "id": "m151b-attraction-compatible-difference", "title": "Relational attraction is compatible difference, not mere similarity", "visual_id": "compatible_difference_attraction" }, { "id": "m151b1-attraction-candidate-profile", "title": "A candidate attraction profile must expose every contributing relation", "visual_id": "attraction_candidate_profile" }, { "id": "m151c-contact-update-outcomes", "title": "New contact can strengthen, split, correct, or create structure", "visual_id": "contact_update_outcomes" }, { "id": "m151d-motion-means-reorganization", "title": "Motion in the identity field must mean a changed relation", "visual_id": "field_reorganization_motion" }, { "id": "m151e-versioned-saturation", "title": "Saturation is temporary coherence, not the end of learning", "visual_id": "versioned_saturation" }, { "id": "m152-runtime-snapshot", "title": "One coordinated adapter exposes source packet and candidate runtime views", "visual_id": "runtime_snapshot_projection" }, { "id": "m153-site-not-authority", "title": "The website is a projection, never the authority", "visual_id": "source_to_manifested_mind" }, { "id": "m153a-generative-compiler-target", "title": "The target compiler lets reconciled source generate every projection", "visual_id": "generative_compiler_target" }, { "id": "m153b-author-agent-continuity", "title": "Living-source continuity preserves author, correction, agent, and next action", "visual_id": "author_agent_continuity_loop" }, { "id": "m153c-projection-interface-target", "title": "Contextual lenses now; identity-preserving traversal remains the target", "visual_id": "projection_interface_target" }, { "id": "m153d-nested-field-traversal", "title": "Entering a 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"Projection mismatch is a source-audit signal", "visual_id": "source_packet_pipeline" }, { "id": "m158a-scope-provenance-ledger", "title": "Every deferred branch receives an explicit disposition", "visual_id": "scope_provenance_ledger" }, { "id": "m159-refresh-is-instrument", "title": "Refresh rate is an observation instrument, not the ontology", "visual_id": "sampling_window" }, { "id": "m160-geometry-shows-relations", "title": "Geometry makes adjacency, boundary, symmetry, and path visible", "visual_id": "geometry_relation_projection" }, { "id": "m161-matrix-computes-addressed-change", "title": "A matrix computes contributions in a chosen frame", "visual_id": "matrix_computation_projection" }, { "id": "m162-equation-drives-visual", "title": "The visual must be generated by the equation it explains", "visual_id": "equation_to_visual" }, { "id": "m163-vortex-versus-torus", "title": "Omnidirectional circulation is not automatically toroidal closure", "visual_id": "vortex_torus_distinction" }, { "id": "mx046-three-proof-layers", "title": "Keep exact result, interpretation, and wider architecture separate", "visual_id": "complex_claim_layers" }, { "id": "mx047-y-normalized-phase-chart", "title": "The existing Y chart already contains a circle", "visual_id": "complex_y_phase_chart" }, { "id": "mx048-polar-difference-coordinate", "title": "Outside minus inside is the signed polar coordinate", "visual_id": "complex_y_phase_chart" }, { "id": "mx049-y-circle-identity", "title": "Polar difference and relation orientation close exactly on a circle", "visual_id": "complex_y_phase_chart" }, { "id": "mx050-y-complex-address", "title": "One complex address retains polarity and relational orientation", "visual_id": "complex_y_phase_chart" }, { "id": "mx051-equal-poles-two-crossings", "title": "Equal pole weights do not determine the direction of passage", "visual_id": "complex_y_crossings" }, { "id": "mx052-y-quarter-turn-operator", "title": "The same quarter-turn acts on polar difference and relation", "visual_id": "complex_y_quarter_turn" }, { "id": "mx053-y-complex-matrix", "title": "The geometry-to-Matrix bridge is now reversible", "visual_id": "complex_matrix_equivalence" }, { "id": "mx054-address-not-whole-identity", "title": "The complex state is an address, not the whole identity", "visual_id": "complex_identity_address" }, { "id": "mx055-phase-dimension-depth-separation", "title": "Phase, dimension, depth, and scale remain different axes", "visual_id": "complex_axis_separation" }, { "id": "mx056-pi-not-golden-ratio", "title": "Circular phase earns pi; it does not earn phi", "visual_id": "complex_pi_phi_boundary" }, { "id": "mx057-hidden-relation-final", "title": "Hidden from one projection does not mean absent from the relation", "visual_id": "complex_final_bridge" }, { "id": "m165-full-route", "title": "Read the entire Matrix-to-Mind dependency once", "visual_id": "complete_matrix_branch" }, { "id": "m166-exact-bridges", "title": "The exact bridges are explicit", "visual_id": "evidence_layer_guardrail" }, { "id": "m167-internal-architecture", "title": "The Y-Theory architecture fixes how those bridges are related", "visual_id": "complete_dynamic_mind" }, { "id": "m168-implementation-and-empirical", "title": "Implementation fidelity and external universality remain testable", "visual_id": "evidence_layer_guardrail" } ], "default_view": "guided", "route_version": "MTR-2026.09.06.1", "route_lanes": { "guided": { "id": "guided", "label": "Guided human Matrix spine", "chapter_ids": [ "matrix-reading-contract", "source-to-binary-frame", "bit-and-directed-change", "local-transition-field", "joint-binary-square", "recursive-phase-address", "binary-dimensions", "coordinates-and-basis", "operator-and-path", "composition-and-invariance", "block-recursion", "triadic-relation-matrix", "independent-recursive-axes", "structural-ninety-nine", "manifested-dynamic-field", "continuity-circuit", 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"m057a-reference-relative-outside-field", "m057a1-structural-outside-not-event-complement", "m057b-each-identity-reframes-field", "m057c-group-boundary-recursion", "m057d1-coexisting-joint-address", "m057d2-typed-factors-assign-joint-support", "m057d3-normalize-joint-support", "m057d4-declared-group-event", "m057e-normalized-redistribution-boundary", "m058-compression-needs-interface", "m059-recursion-not-elapsed-time", "m060-inside-outside-relation", "m061-relation-not-observer", "m062-nine-directed-channels", "m063-living-relation-packet", "m064-topology-versus-state", "m065-triad-inside-triad", "m066-role-axis", "m067-phase-axis", "m068-depth-axis", "m069-dimension-axis", "m069a-derived-relational-dimension", "m070-scale-and-occurrence", "m071-two-twelvefolds", "m072-nine-inside-nine-outside", "m072a-general-closure-count", "m073-eighty-one-directed-crossings", "m074-structural-count", "m075-closure-one", "m076-closure-not-observer", "m077-source-field-available", "m078-manifestation-orders", "m079-delay-retains-relation", "m080-delay-not-memory", "m081-residue-becomes-trace", "m082-trace-becomes-memory", "m082a-external-trace-versus-structural-trace", "m082b-history-bearing-cycle-state", "m082c-geometry-as-retained-trace", "m083-relation-as-transducer", "m084-flow-needs-path", "m084a-reciprocal-transduction", "m084b-thought-is-not-electron-flow", "m085-concurrent-contributions", "m086-continuity-path", "m087-reinforcement", "m088-leakage", "m088a-damping-regulation", "m088a1-identity-support-balance", "m088a2-identity-formation-dissolution", "m088a3-nested-return-extends-persistence", "m088b-earned-relation-record", "m088c-symmetric-availability", "m088d-retained-difference", "m088e-restoring-overshoot", "m089-rotation-operator", "m090-rotation-circle-exact", "m091-complex-mode", "m092-amplitude-regimes", "m093-nonidentical-return", "m094-what-oscillates", "m094a-omnidirectional-boundary-input", "m094b-axis-and-vortex", "mx001-representation-question", "mx002-natural-addition", "mx003-subtraction-boundary", "mx004-integers-direction", "mx005-division-boundary", "mx006-rational-ratios", "mx007-irrational-diagonal", "mx008-real-continuum", "mx009-square-fold", "mx010-negative-root-boundary", "mx011-cardano-bombelli", "mx012-extension-not-abandonment", "mx013-define-imaginary-unit", "mx014-complex-pair", "mx015-real-line-embedded", "mx016-i-quarter-turn", "mx017-powers-of-i", "mx018-quarter-turn-matrix", "mx019-j-squared-half-turn", "mx020-continuous-rotation", "mx021-polar-magnitude-phase", "mx022-euler-formula", "mx023-euler-series-separation", "mx024-euler-tangent-flow", "mx025-euler-identity", "mx025a-opposite-quarter-turns", "mx025b-inverse-quarter-turns", "mx025c-same-antipode-opposite-paths", "mx025d-i-minus-i-separation", "mx025e-relative-phasor", "mx025f-reverse-reference-conjugates", "mx025g-quarter-phase-from-two-references", "mx025h-common-frame-cancels", "mx025i-relation-real-imaginary", "mx025j-engine-phase-kernel", "mx025k-four-relational-addresses", "mx025l-conjugate-manifestation", "mx025m-reference-projection", "mx025n-relation-matrix", "mx025o-relation-cycle-closure", "mx025p-source-manifestation-bridge", "mx026-growth-and-rotation", "mx027-coupled-oscillator", "mx028-radius-invariant", "mx029-complete-phase-state", "mx030-real-shadow", "mx031-correct-partial-projection", "mx032-same-projection-different-phase", "mx033-hidden-coordinate-shapes-next", "mx034-delay-retains-phase", "mx035-delay-coordinate-pair", "mx036-retention-restrains-future", "mx042-ratio-driven-complex-update", "mx043-leak-retain-reinforce", "mx044-bounded-feedback-cycle", "mx045-one-phase-two-phases", "m095-two-cycles-torus", "m096-n-cycles-n-torus", "m097-off-diagonal-coupling", "m098-delayed-coupling", "m099-torus-is-domain", "m100-spiral-is-trace", "m100a-parametric-torus", "m100a1-reversible-torus-chart", "m100a1a-decode-torus-to-two-triads", "m100a1b-same-torus-different-reference", "m100a2-commensurate-phase-return", "m100a3-weighted-trace-field", "m100b-helix-depth-trace", "m100c-ascent-descent", "m100d-mind-dna-bridge", "m100e-cycle-rate-vs-identity-frequency", "m101-coupled-field", "m101b-fast-local-slow-whole", "m101a-whole-mode-policy", "m102-whole-coordinate", "m103-remainder", "m104-agreement-not-observer", "m105-identity-boundary", "m105a-outside-and-received-outside", "m113e-developed-mind-reading", "m106-retained-whole", "m107-present-history-comparison", "m107a-observation-is-comparison", "m108-retained-comparison", "m109-causal-return", "m110-distributed-observer", "m110a-observer-loop-complete", "m110b-local-whole-reciprocity", "m111-aperture-mode-selection", "m112-aperture-breadth", "m113-observer-resolution", "m113a-observation-horizon", "m113b-finite-observation-budget", "m113b1-observation-entry-threshold", "m113c-partial-whole-illusion", "m114-observation-restricts-next", "m115-restriction-not-determinism", "m115a-three-kinds-of-change", "m116-awareness-breadth", "m117-attention-reweights", "m117a-three-observation-rates", "m117b-fixed-resource-budget", "m117c-attention-control-tuple", "m117d-repetition-versus-understanding", "m117e-global-versus-focal-gain", "m117f-attention-profiles", "m113d-observer-limit-across-domains", "m118-self-location", "m119-self-awareness", "m119a-inward-outward-orientations", "m119b-self-awareness-of-aperture", "m120-metacognition", "m120a-thought-as-organized-relational-flow", "m121-imagination", "m122a-intention", "m122b-choice", "m122-directed-creation", "m122c-awakening-cycle", "m122c1-mutual-partial-observers", "m122c2-shared-reality-collective-mind", "m122d-equal-polarity-start", "m122e-additive-ratio-sequence", "m122f-two-thirds-envelope", "m123-fixed-ten-metric", "m124-seven-derived-not-literal", "m125-depths-are-active-relations", "m126-depth-carries-remainder", "m127-l7-turning-boundary", "m128-return-to-l1-prime", "m129-depth-dimension-role-tensor", "m129a-toroidal-identity-depth-bridge", "m129b-depth-whole-torus-construction", "m130-two-state-inheritance", "m131-fibonacci-matrix", "m132-golden-eigenvalue", "m132a-reciprocal-cross-dimensional-scaling", "m132b-reciprocal-fibonacci-relations", "m132c-delayed-dimensional-phase", "m133-golden-complementary-shares", "m133a-golden-observer-allocation", "m133b-aperture-versus-allocation", "m134-outer-thirds-inner-golden", "m135-oscillate-around-attractor", "m135a-source-possibility-manifested-history", "m136-pi-and-phi", "m137-golden-status", "m137a-practice-changes-capacity-not-phi", "m138-tenth-coordinate-after-observer", "m139-operational-hundred", "m140-operational-decomposition", "m141-two-counts-one-correspondence", "m142-three-ones", "m142a-cyclic-compass-projection", "m142b-trace-decomposition", "m142c-five-ninety-nine-views", "m143-static-array-insufficient", "m143a-three-mind-thresholds", "m143b-stability-is-not-mind", "m143c-mind-capability-ladder", "m144-complete-mind-tuple", "m145-flow-through-structure", "m145b-bounded-recoverable-change", "m145c-evolution-as-coherent-differentiation", "m145d-direction-development", "m145e-mind-direction-of-integration", "m145f-grammar-capable-of-mind", "m145g-participating-in-continuation", "m145h-open-creation-mind-postulate", "m145a-changing-boundary", "m146-three-mind-views", "m147-mind-within-mind", "m147b-component-turnover-whole-continuity", "m147a-universe-widest-mind", "m148-successive-identity-leaves", "m148a-creation-can-become-creative", "m149-source-units", "m149a-source-unit-types", "m150-identity-packets", "m150a-identity-packet-complete-target", "m151-typed-relation-field", "m151a0-relation-edge-types", "m151a-scale-indexed-living-field", "m151b-attraction-compatible-difference", "m151b1-attraction-candidate-profile", "m151c-contact-update-outcomes", "m151d-motion-means-reorganization", "m151e-versioned-saturation", "m152-runtime-snapshot", "m153-site-not-authority", "m153a-generative-compiler-target", "m153b-author-agent-continuity", "m153c-projection-interface-target", "m153d-nested-field-traversal", "m153e-five-source-projections", "m154-map-roles-not-names", "m155-pattern-versus-carrier", "m155a-recursive-carrier-ladder", "m155b-equivalent-position-not-identity", "m155c-propagating-distinction", "m155d-signal-quantities", "m155e-creator-creation-relation", "m156-external-theories-as-lenses", "m156a-projection-is-true-but-partial", "m156b-developed-role-permutation", "m156c-seven-incidence-versus-depth", "m156d-higher-mind-by-relational-closure", "m156e-high-dimensional-projection-lens", "m156f-nested-golden-projection", "m156g-four-comparative-lenses", "m157-reversible-mapping-test", "m158-mismatch-corrects-source", "m158a-scope-provenance-ledger", "m159-refresh-is-instrument", "m160-geometry-shows-relations", "m161-matrix-computes-addressed-change", "m162-equation-drives-visual", "m163-vortex-versus-torus", "mx046-three-proof-layers", "mx047-y-normalized-phase-chart", "mx048-polar-difference-coordinate", "mx049-y-circle-identity", "mx050-y-complex-address", "mx051-equal-poles-two-crossings", "mx052-y-quarter-turn-operator", "mx053-y-complex-matrix", "mx054-address-not-whole-identity", "mx055-phase-dimension-depth-separation", "mx056-pi-not-golden-ratio", "mx057-hidden-relation-final", "mx041p-y-phase-address", "mx041q-phase-bearing-identity-field", "mx041r-history-retains-relation", "mx041s-typed-recursive-operator", "mx041t-evolution-before-outcome", "mx041u-outcome-instrument", "mx041v-retained-record", "mx041w-changed-return", "mx041x-complete-manifestation-loop", "mx041y-model-must-earn-reality", "m165-full-route", "m166-exact-bridges", "m167-internal-architecture", "m168-implementation-and-empirical" ], "step_count": 385, "first_step_id": "m001-relation-before-array", "last_step_id": "m168-implementation-and-empirical" }, "signal": { "id": "signal", "label": "Signal and engineering lens", "chapter_ids": [ "signal-engineering-lens" ], "chapter_count": 1, "step_ids": [ "mx037-many-circular-modes", "mx037a-fourier-mode-addresses", "mx037b-time-frequency-charts", "mx037c-dft-is-a-matrix", "mx037d-fft-recursive-factorization", "mx037e-phase-superposition", "mx037f-sound-and-fft", "mx037g-light-harmonic-field", "mx037h-complex-refractive-index", "mx037i-iq-relational-carrier", "mx037j-phase-is-relational-information", "mx038-ac-phasor", "mx039-impedance-operator", "mx040-rlc-phase-relations", "mx041-energy-storage-and-return" ], "step_count": 15, "first_step_id": "mx037-many-circular-modes", "last_step_id": "mx041-energy-storage-and-return" }, "quantum": { "id": "quantum", "label": "Quantum and physics lens", "chapter_ids": [ "quantum-physics-lens" ], "chapter_count": 1, "step_ids": [ "mx041a-classical-realification", "mx041b-quantum-state-space", "mx041c-basis-superposition", "mx041d-position-wavefunction", "mx041e-amplitude-before-probability", "mx041f-global-relative-phase", "mx041g-interference-before-probability", "mx041g1-two-path-amplitudes", "mx041g2-constructive-destructive-amplitudes", "mx041g3-interference-screen", "mx041g4-which-path-relation", "mx041h-schrodinger-equation", "mx041h1-atomic-stationary-state", "mx041i-unitary-preservation", "mx041j-real-pair-schrodinger", "mx041k-complex-structure-survives", "mx041k1-real-formulations-and-composition", "mx041k2-experiments-test-models", "mx041l-measurement-is-interaction", "mx041m-observation-restrains-quantum-continuation", "mx041n-quantum-record-boundary", "mx041o-quantum-to-mind-bridge" ], "step_count": 22, "first_step_id": "mx041a-classical-realification", "last_step_id": "mx041o-quantum-to-mind-bridge" }, "all": { "id": "all", "label": "Preserved all-angles edition", "chapter_ids": [ "matrix-reading-contract", "source-to-binary-frame", "bit-and-directed-change", "local-transition-field", "joint-binary-square", "recursive-phase-address", "binary-dimensions", "coordinates-and-basis", "mathematical-closure-to-complex", "directed-phase-relation", "operator-and-path", "composition-and-invariance", "block-recursion", "triadic-relation-matrix", "independent-recursive-axes", "structural-ninety-nine", "manifested-dynamic-field", "continuity-circuit", "rotation-and-oscillation", "euler-phase-projection-and-memory", "manifestation-mind-recurrence", "torus-and-coupled-cycles", "collective-whole-mode", "observer-emergence", "awareness-attention-imagination", "seven-depth-address", "fibonacci-and-golden", "operational-ten-by-ten", "complete-dynamic-mind", "projection-architecture", "typed-domain-mapping", "matrix-geometry-bridge", "complex-mathematics-to-mind", "matrix-complete-route" ], "chapter_count": 34, "step_ids": [ "m001-relation-before-array", "m002-matrix-is-projection", "m003-one-earned-step", "m004-five-status-axes", "m005-possible-not-possible", "m005a-primitive-polarity-exact", "m006-relation-third-role", "m006a-relation-becomes-participant", "m006b-triad-renews-together", "m006c-each-role-can-open", "m007-possibility-to-existence", "m007a-possibility-field-before-probability", "m007b-relation-weights-exact-poles", "m008-existence-to-binary", "m008b-binary-registration", "m008c-source-engine-manifestation-boundary", "m008d-representation-not-world", "m009-source-not-clock", "m009a-source-polarity-not-spatial-points", "m010-bit-is-reading", "m011-arrow-adds-direction", "m012-preservation-is-transition", "m013-one-point-loses-path", "m014-change-is-relational", "m015-origin-destination-axes", "m016-diagonal-retains", "m017-off-diagonal-exchanges", "m018-transition-field-not-gate", "m019-not-and-identity", "m020-boolean-readouts", "m021-two-coordinates-four-addresses", "m022-square-is-address-geometry", "m023-path-is-not-space", "m024-gray-cycle", "m025-complete-cyclic-state", "m026-four-transitions-not-flat-1010", "m026a-three-of-twelve-is-quarter", "m027-circle-carries-phase", "m027a-triangle-and-phase-circle", "m027b-normalized-triad-phase-chart", "m028-quarter-chart", "m029-recursive-phase-digits", "m030-phase-address-value", "m031-phase-resolution-count", "m032-resolution-not-depth", "m033-n-binary-coordinates", "m034-hypercube-adjacency", "m035-rank-three-array", "m036-state-space-versus-tensor", "m037-path-visits-subset", "m038-freedom-before-number", "m038a-operational-dimension-test", "m038b-dimensional-polarity-product", "m039-coordinate-map", "m040-state-vector", "m041-reference-and-basis", "m042-same-point-new-coordinates", "mx001-representation-question", "mx002-natural-addition", "mx003-subtraction-boundary", "mx004-integers-direction", "mx005-division-boundary", "mx006-rational-ratios", "mx007-irrational-diagonal", "mx008-real-continuum", "mx009-square-fold", "mx010-negative-root-boundary", "mx011-cardano-bombelli", "mx012-extension-not-abandonment", "mx013-define-imaginary-unit", "mx014-complex-pair", "mx015-real-line-embedded", "mx016-i-quarter-turn", "mx017-powers-of-i", "mx018-quarter-turn-matrix", "mx019-j-squared-half-turn", "mx020-continuous-rotation", "mx021-polar-magnitude-phase", "mx022-euler-formula", "mx023-euler-series-separation", "mx024-euler-tangent-flow", "mx025-euler-identity", "mx025a-opposite-quarter-turns", "mx025b-inverse-quarter-turns", "mx025c-same-antipode-opposite-paths", "mx025d-i-minus-i-separation", "mx025e-relative-phasor", "mx025f-reverse-reference-conjugates", "mx025g-quarter-phase-from-two-references", "mx025h-common-frame-cancels", "mx025i-relation-real-imaginary", "mx025j-engine-phase-kernel", "mx025k-four-relational-addresses", "mx025l-conjugate-manifestation", "mx025m-reference-projection", "mx025n-relation-matrix", "mx025o-relation-cycle-closure", "mx025p-source-manifestation-bridge", "m043-general-update", "m044-space-operator-path", "m045-iteration-produces-history", "m046-linearity-test", "m047-entry-is-directed", "m048-column-basis-image", "m048a-output-as-column-sum", "m048b-one-change-redistributes-through-structure", "m048c-dimension-count-does-not-set-gain", "m049-composition-order", "m049a-noncommuting-relations", "m050-identity-operator", "m051-operator-change-of-basis", "m052-similarity-invariants", "m052a-viable-state-boundary", "m053-local-jacobian", "m053a-coordinate-block-partition", "m054-block-operator", "m055-kronecker-product", "m056-product-not-interaction", "m057-many-inside-one-outside", "m057a-reference-relative-outside-field", "m057a1-structural-outside-not-event-complement", "m057b-each-identity-reframes-field", "m057c-group-boundary-recursion", "m057d1-coexisting-joint-address", "m057d2-typed-factors-assign-joint-support", "m057d3-normalize-joint-support", "m057d4-declared-group-event", "m057e-normalized-redistribution-boundary", "m058-compression-needs-interface", "m059-recursion-not-elapsed-time", "m060-inside-outside-relation", "m061-relation-not-observer", "m062-nine-directed-channels", "m063-living-relation-packet", "m064-topology-versus-state", "m065-triad-inside-triad", "m066-role-axis", "m067-phase-axis", "m068-depth-axis", "m069-dimension-axis", "m069a-derived-relational-dimension", "m070-scale-and-occurrence", "m071-two-twelvefolds", "m072-nine-inside-nine-outside", "m072a-general-closure-count", "m073-eighty-one-directed-crossings", "m074-structural-count", "m075-closure-one", "m076-closure-not-observer", "m077-source-field-available", "m078-manifestation-orders", "m079-delay-retains-relation", "m080-delay-not-memory", "m081-residue-becomes-trace", "m082-trace-becomes-memory", "m082a-external-trace-versus-structural-trace", "m082b-history-bearing-cycle-state", "m082c-geometry-as-retained-trace", "m083-relation-as-transducer", "m084-flow-needs-path", "m084a-reciprocal-transduction", "m084b-thought-is-not-electron-flow", "m085-concurrent-contributions", "m086-continuity-path", "m087-reinforcement", "m088-leakage", "m088a-damping-regulation", "m088a1-identity-support-balance", "m088a2-identity-formation-dissolution", "m088a3-nested-return-extends-persistence", "m088b-earned-relation-record", "m088c-symmetric-availability", "m088d-retained-difference", "m088e-restoring-overshoot", "m089-rotation-operator", "m090-rotation-circle-exact", "m091-complex-mode", "m092-amplitude-regimes", "m093-nonidentical-return", "m094-what-oscillates", "m094a-omnidirectional-boundary-input", "m094b-axis-and-vortex", "mx026-growth-and-rotation", "mx027-coupled-oscillator", "mx028-radius-invariant", "mx029-complete-phase-state", "mx030-real-shadow", "mx031-correct-partial-projection", "mx032-same-projection-different-phase", "mx033-hidden-coordinate-shapes-next", "mx034-delay-retains-phase", "mx035-delay-coordinate-pair", "mx036-retention-restrains-future", "mx037-many-circular-modes", "mx037a-fourier-mode-addresses", "mx037b-time-frequency-charts", "mx037c-dft-is-a-matrix", "mx037d-fft-recursive-factorization", "mx037e-phase-superposition", "mx037f-sound-and-fft", "mx037g-light-harmonic-field", "mx037h-complex-refractive-index", "mx037i-iq-relational-carrier", "mx037j-phase-is-relational-information", "mx038-ac-phasor", "mx039-impedance-operator", "mx040-rlc-phase-relations", "mx041-energy-storage-and-return", "mx041a-classical-realification", "mx041b-quantum-state-space", "mx041c-basis-superposition", "mx041d-position-wavefunction", "mx041e-amplitude-before-probability", "mx041f-global-relative-phase", "mx041g-interference-before-probability", "mx041g1-two-path-amplitudes", "mx041g2-constructive-destructive-amplitudes", "mx041g3-interference-screen", "mx041g4-which-path-relation", "mx041h-schrodinger-equation", "mx041h1-atomic-stationary-state", "mx041i-unitary-preservation", "mx041j-real-pair-schrodinger", "mx041k-complex-structure-survives", "mx041k1-real-formulations-and-composition", "mx041k2-experiments-test-models", "mx041l-measurement-is-interaction", "mx041m-observation-restrains-quantum-continuation", "mx041n-quantum-record-boundary", "mx041o-quantum-to-mind-bridge", "mx042-ratio-driven-complex-update", "mx043-leak-retain-reinforce", "mx044-bounded-feedback-cycle", "mx045-one-phase-two-phases", "mx041p-y-phase-address", "mx041q-phase-bearing-identity-field", "mx041r-history-retains-relation", "mx041s-typed-recursive-operator", "mx041t-evolution-before-outcome", "mx041u-outcome-instrument", "mx041v-retained-record", "mx041w-changed-return", "mx041x-complete-manifestation-loop", "mx041y-model-must-earn-reality", "m095-two-cycles-torus", "m096-n-cycles-n-torus", "m097-off-diagonal-coupling", "m098-delayed-coupling", "m099-torus-is-domain", "m100-spiral-is-trace", "m100a-parametric-torus", "m100a1-reversible-torus-chart", "m100a1a-decode-torus-to-two-triads", "m100a1b-same-torus-different-reference", "m100a2-commensurate-phase-return", "m100a3-weighted-trace-field", "m100b-helix-depth-trace", "m100c-ascent-descent", "m100d-mind-dna-bridge", "m100e-cycle-rate-vs-identity-frequency", "m101-coupled-field", 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