Y TheoryThe Compass of RealityResearch workbench · recovered engine formation
From relation to identity. From recurrence to space. From residue to local cognitive capability.
A source-linked dependency graph separating recursive Mind-structure, relational identity formation, spatial manifestation, local observer/cognitive capability, and geometric representation. Every threshold exposes what it requires, what it earns, and what it still cannot claim.
Version boundary: the machine graph below was recovered from YLS-2026.08.31.6. It is retained for research comparison, not presented as the latest canonical sequence. Follow the current connected narration, or read the current source chapter. Newer flow-and-field experiments are separately identified below.
01
This symbolic track diagram is selected by the governed stage registry. It is not an observed physical formation trace or evidence for the stage.Source possibilitycanonical distinction
0%A later label is earned only when every dependency and gate declared for it has been demonstrated at the named identity, scale, variable, reference, and resolution.
Interactive dependency map
Choose the question before choosing the geometry.
The same Y Engine appears across all four tracks, but continuing identity, spatial form, local cognitive capability, and representation have different gates.
Relational Identity
Source possibility
Statuscanonical distinction
Earned only when
Coherent relations are permitted without treating them as a travelled sequence or spatial container.
Depends on
Explanatory starting point
Boundary
Source is not a lattice, place, earlier time, temporal wave, or completed observer.
Source lineage
- CHAPTER_07_SOURCE_AND_ORDERED_MANIFESTATION_REPAIRED.md · Source is not an earlier event · preserved corpus source
- CHAPTER_07_SOURCE_AND_ORDERED_MANIFESTATION_REPAIRED.md · Possibility has a topology · preserved corpus source
Relational and spatial spine
A node comes late.
Before a node can be shown, the model must already have a declared space, position, recurrent variable, supporting region, boundary, coupling, and standing-mode representation.
Capability spine
Mind-structure is already present.
Uppercase Mind is the recursively reusable relational structure. Observerhood is an earned capability of a sufficiently deep local identity, not a scale placed between organism and planet. Spatial form may therefore instantiate Mind-structure without observing itself; local cognition requires the later gates below.
Conditional toroidal topology
Two returns must close through one another.
The torus is not produced by oscillation alone. It becomes an admissible representation only after the same continuing identity carries a local inside–outside cycle and a wider whole–outside cycle, and the two cycles causally couple.
S¹local×S¹whole=T²
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continuing identity already earned
- 02
local inside–outside cycle closed
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wider whole–outside cycle closed
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two cycles causally coupled
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declared projection from the two phases to toroidal coordinates
Y-Theory in operation · flow, field, and shared consequence
How does what happens inside reach what is outside?
Y-Theory begins with a relation, not an isolated object. Follow that relation into a flow, see how its route shapes its influence, then ask what changes when several flows share one situation.
Try the two experiments ↓- 01
Inside meets outside
Choose one identity and its boundary. In Y-Theory, inside, outside, and their relation belong to one organizing Mind-structure. The question is what can cross that boundary and make a difference.
- 02
A relation carries change
A direction alone is not a journey. A carrier, a compatible route, and a driving condition let an influence travel. In a wire, this can be electric current. In a shared human situation, name the action or communication carrying the consequence.
- 03
The route shapes the influence
Geometry makes the route visible. A loop can show circulation; a spiral can represent recurrence with an additional changing coordinate. Tilt changes the orientation of that route, while phase changes the timing of its flow. In the physical example below, the current path determines the magnetic contribution at each location.
- 04
Many contributions meet
What reaches a shared place depends on more than one participant. Direction, timing, distance, and coupling matter. Change one relation and the combined result can reinforce, weaken, reverse, or become unavailable.
- 05
Consequence can return
The wider situation can change the conditions of the next local action. When a usable trace is retained and returned, the next encounter carries history. The relational experiment below implements a delayed return; the magnetic calculation does not yet feed its field back into its driving current. This distinction locates the next step toward testing the larger continuity proposal.
What does a circulating current produce?
Two driven currents meet at one probe. Change their relation and inspect the resulting magnetic field.
View from −y. Arrows: Bx / Bz · ⊗ +By (in) · ⊙ −By (out). Fixed arrow scale: 2 µT; larger values saturate visually, not numerically. Dim dots near wire are excluded samples.
Field at probe2.768 µT
Vector sum / sum of magnitudes100.0%
Bx 0.000 µT · By 0.000 µT · Bz 2.768 µT
Try Together, then Opposed. The driving amplitude stays the same; direction changes what the shared probe receives.
Orientation now: 0°. Nonzero swing is prescribed and phase-locked: advancing the drive cycle changes both current and tilt. These are externally positioned snapshots, not motion caused by magnetic torque.
Read the physical model
Each loop is held fixed in vacuum and driven by an external current source: I(t) = polarity × peak × cos(2πt + phase). Leads, resistance, circuit feedback, electric fields, and radiation are not modeled. The 1 Hz, metre-scale example uses a quasi-static approximation; it is not a self-powered engine.
B is calculated from the vector sum of midpoint Biot–Savart contributions: μ₀/(4π) ∑ I Δℓ × r / |r|³. μ₀ ≈ 1.25664e-6 H/m. A circular loop uses 128 segments; the toroidal example uses 16 separate circular windings, 96 segments each, with minor radius 0.3 × major radius. It approximates a winding, not a human body.
The exclusion distance is 0.025 × radius around each segment. It masks samples rather than inventing a finite value at a filament. The percentage compares the total vector magnitude with the sum of individual magnitudes at this probe; it is not an efficiency, consciousness score, or universal measure of coherence.
In the ideal continuous-winding limit, a toroidal coil can have zero external field. Our finite windings can leave a residual outside. Field magnitude alone does not give attraction: a force calculation also needs a specified charge, current, or magnetic object and its interaction.
Tilt rotates a loop about its own centre, or the whole toroidal winding about its centre. Current phase is unchanged by that geometric rotation. A nonzero swing prescribes θ(t) = base tilt + swing × sin(2πt). No induced voltage, mechanical work, self-adjusting tilt, or expansion/contraction dynamics are calculated.
How does one choice reach a shared world?
Seven identities keep their own states. Compare two identical runs; change only Identity 1’s choice in one of them.
Largest change in another identity0.00000 q
Common available interval0.546–0.743
First change Identity 1’s choice, then advance. With no intervention the paired runs remain identical.
Changing a parameter resets both runs. q is the existing model’s bounded continuity coordinate, not charge, field strength, moral worth, or a measured human trait.
Read the relational model
This uses the same relation-fabric engine as the shared-reality torus. Pair overlap defines A; normalized incoming influence defines W. Coupling scales delayed q and phase signals. Each next q also depends on its own bounded choice and the declared target. The interval rule is authored, not learned from people or derived from electromagnetism.
The untouched run is a counterfactual control with the same configuration and elapsed steps. The only intervention is Identity 1’s choice. At zero coupling or without geometric overlap, another identity’s q must remain unchanged relative to that control. A visible circle is not a transmission channel by itself.
This focused experiment uses local pairwise return. It does not simulate thought, a collective conscious self, or the complete observing Mind. Open the larger lab to inspect its separate retained whole-level feedback.
The connection being investigated
The founder proposes that organized internal activity changes an identity’s wider relations, and that alignment can reshape the possibilities available within a shared reality. That question connects this lesson to the larger Mind model; it is not an isolated claim about magnets.
Here, the physical experiment calculates a magnetic field from current. The relational experiment calculates consequences from declared coupling and history. Their shared questions are direction, combination, boundary, and return. Their carriers, equations, and units remain distinct.
Tilt changes the field. What would make that change return?
The new proposal adds orientation to the progression: a flow meets another flow at an angle; that relation changes their combined influence; a returning influence might then alter the next orientation. The controls above let us inspect the first part. They do not yet derive the return that would make tilt change by itself.
This version calculates the field, not push, pull, or mechanical motion. A larger B reading here is vector addition or redistribution, not amplified current or created energy. Unlike an internally evolving orientation, its tilt is supplied by the controls.
Reinforcement at a probe is not automatically a voltage amplifier. In a driven resonant circuit, well-timed input can build an oscillation while resistance dissipates energy. A sustained system needs an energy balance; a larger voltage alone does not mean energy has been created.
The next test of the founder’s tilt–continuity proposal would specify interacting circuits, their coupling, a rule or torque for orientation, stored energy, the driving source, and losses. Then we could turn the drive off, change the timing, and test whether any predicted reversal, expansion, or decay actually follows from those rules.
From electromagnetic fields to living experience
Electrical activity in the brain produces weak magnetic signals measurable by MEG. To connect an internal process to an outward field, specify the active currents, their geometry and tissue conduction. To close the return, specify what receives that field and how its response alters the original activity. A general torus diagram alone does not supply this anatomical and causal model.
In the Mind introduction, a numerical body response already changes internal activity, and retained whole-level comparison changes the next response. This makes a small reciprocal loop explicit. Differentiated meaning, intention and the mapping to physical currents remain additional bindings. Both physical and mental aspects have inside, outside and relations; neither is simply one side of the triad.
Electric, magnetic, and direction: where the three-part picture applies
A plane electromagnetic wave in vacuum has electric and magnetic fields perpendicular to each other and to its propagation direction. This is a precise three-direction relationship in that physical model, not three substances or a derivation of every Y triad. This workbench calculates the quasi-static B field of prescribed currents; it does not calculate a travelling electromagnetic wave.
One connected investigation
What carries change, what receives it, what remains, and what returns?
Inside–outside relation gives the question. A particular carrier, response and return rule make it an operating example.
What runs here
Prescribed current paths contribute magnetic vectors through the Biot–Savart integral. Direction, phase, tilt and separation change their sum at a probe.
Current in amperes, geometry in metres, magnetic field in tesla.
The calculated B field does not yet alter the currents or move the bodies. Electric-field, force, torque and circuit feedback require their own specified equations.
A Mind remains through changeA received signal changes local activity. Whole-level readings and delayed comparison return into the next body response and phase update.Mind within MindDirected relation weights enter delayed phase inputs. Opened interiors and their containing unit influence one another.A consequence reaches other identitiesMatched runs begin alike. Change one participant and compare how delay, overlap, coupling and retained history change later responses.A trace changes the next encounterChanging relation drives an induced-flow variable. Its retained trace changes later coupling geometry and therefore the next relation.Circle, helix, spiral and torusA chosen reinforcement/leakage drive changes the spiral or torus radius; the same phase also produces companion waves and counted binary transitions.Three Horizons: circle relationsThree circle centres and radii determine similarity centres, common tangents and the collinearity readout through the shared calculator session.Three Horizons: perspective and depthA frontoparallel disc with declared radius R, depth Z and focal length f produces image radius a=fR/Z through the shared calculator session.Source, language and relational compositionLiteral pixels and bounded language enter the shared source surface. Named shape, color, modifier, canvas and observer identities form typed dependencies; their evaluated composition produces the pixels. An identity edit recomputes its dependent whole, while held reflections retain their original interpretation.Learning to draw through relationsOrdered supplied lessons retain point, connection, affine construction and motion relations in one continuing shared engine. Later arguments reuse those methods; correcting a prerequisite changes dependent output. The movement view reads the same retained session and actual field phase.
Follow the recovered concentration, channel-sharing and distance derivations →
What connects these into a complete operating system?
The shared grammar connects these studies. A single physically and mentally coupled simulation still needs explicit state, units and reciprocal response bindings; visual resemblance cannot supply them.
- Inside, outside and boundary
- Carrier and accessible route
- Geometry and combined influence
- Recipient response
- Retained consequence
- Changed participation and return
For the mental aspect, retained distinctions must affect attention or action, and their outcomes must be able to change later interpretation. A visitor’s camera or a meaning label is a reading of that system, not its own intentional observer.
Continue through the sources and model assumptions
This lesson is an author-directed teaching synthesis. It extends the existing physical-carrier / relational-model distinction without promoting a new universal electromagnetic claim.
- Y Engine formation: the complete dependency spine
- Physical carrier and geometry sequence
- Earlier relational-induction experiments and what they establish
- OpenStax: Biot–Savart law
- OpenStax: current loops
- OpenStax: solenoids and toroids
- OpenStax: resonance, driving, and energy loss
- NIMH: measuring brain magnetic fields
- OpenStax: electric field, magnetic field, and wave direction
Flower of Life placement
Many closures sharing one field.
It is a beautiful and useful 2D address-field projection. In the recovered source it is a sacred-geometry lens—not proof that Source is spatial, that nodes are primitive objects, or that a physical torus has formed.
Honest incompleteness
The gaps are part of the living system.
Completeness means every source and open boundary is accounted for—not pretending every derivation is finished.
Manual Chapter 33 — Space is missing
The threshold from relational arena to space is named by Chapters 32 and 34 but its full canonical chapter body is absent from the latest manual source.
NextRecover or reconstruct Chapter 33 from source lineage, then validate it against YT-DIM-001, YT-DIM-002, YT-GEO-003, and the latest Source/manifestation distinction.
Two-cycle topology is stated; domain dynamics remain to be instantiated
S^1 × S^1 establishes the topology only after two cycles are demonstrated. Each physical, biological, mental, social, or digital application still needs its own variables, dynamics, closure evidence, and falsifier.
NextUse the prototype as a bounded model and test each gate separately; do not treat a rendered torus as validation.
Prototype firewall
These shortcuts are now rejected by the engine contract.
Continue through the governed views