YT-CORE-001Canonical definition
Reality as continuing relational change
Reality is approached as continuing relational change rather than as a collection of finished, self-sufficient objects.
Boundary and source
This is Y-Theory's organizing definition; it is not by itself an empirical proof that every scientific domain has one identical mechanism.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-CORE-001
Open claim address →YT-CORE-002Latest canonical correction
One origin, two non-identical polar expressions, one relation
One originating differentiation manifests as two genuinely non-identical polar changes and the relation that keeps them distinguishable while belonging to one expression.
Boundary and source
One refers to origin; two refers to polar expression; three refers to the complete living structure. Do not collapse the poles into sameness or treat them as unrelated origins.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-CORE-002
Open claim address →YT-CORE-003Canonical structural law
The living triad
Every situated identity is expressed through inside, outside, and relation. The relation both separates and connects the poles and helps constitute what each pole is.
Boundary and source
The whole is not a fourth primitive sibling. Inside and outside are reference-relative roles, not absolute locations.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-CORE-003
Open claim address →YT-CORE-007Canonical structural synthesis
Closure, leakage, and recoverability
Closure is sufficient return to renew a distinguishable pattern; leakage is influence no longer recoverably available to the declared continuity; recoverability is the capacity to return after leaving an ordinary stable region before identity is lost.
Boundary and source
Always name the identity, scale, variable, and recovery boundary. Zero leakage is not automatically healthy; local closure can export destructive leakage.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-CORE-007
Open claim address →YT-CORE-008Canonical definition set
Existence, persistence, stability, and recoverability are distinct
Existence is continuing distinguishability; persistence is continuation now; stability is bounded persistence under ordinary variation; recoverability is return after destabilization before distinguishability is irreversibly lost.
Boundary and source
Do not use stability, persistence, and recoverability as interchangeable praise words.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-CORE-008
Open claim address →YT-ID-002Canonical structural distinction
Update recursion and depth recursion
Update recursion produces another state of the same continuing identity at one depth. Depth recursion allows a completed whole to become one participant in a wider relation.
Boundary and source
Repeated updates do not automatically create a wider identity. The wider relation must acquire its own consequence, return, and continuity.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-ID-002
Open claim address →YT-DIM-001Canonical definition
Dimension as consequential non-redundant variation
A dimension is a repeatedly available, consequential, identifiable, and non-redundant way in which one continuing relation can vary under a declared reference and resolution.
Boundary and source
One value is not a dimension. A temporary combination is not automatically a new dimension.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-DIM-001
Open claim address →YT-DIM-002Canonical distinction
Dimension, depth, resolution, bandwidth, and scale
Dimensionality counts irreducible freedoms; depth tracks relations becoming terms in wider relations; resolution tracks fineness of distinction; bandwidth tracks how many modes can be coherently active; scale names the declared identity and reference.
Boundary and source
Dividing one range into ten or one hundred intervals increases resolution, not dimensionality.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-DIM-002
Open claim address →YT-GEO-001Structural and geometric model sequence
Wave, spiral, and helix
A wave represents recurring identity through changing states. Residue makes a return occur at a changed phase or scale, giving a spiral. Two complementary directional recurrences around a common continuity axis admit a helix representation.
Boundary and source
These are representations whose physical realization must be established separately; they are not interchangeable proof.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-GEO-001
Open claim address →YT-GEO-003Canonical method rule
Geometry does not replace ontology
Line, triangle, circle, square, cube, hypercube, helix, and torus answer different structural questions. A shared image or count is not a derivation.
Boundary and source
Do not infer physical shape, sacred necessity, or dimensional count from a convenient diagram.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-GEO-003
Open claim address →YT-ETH-001Canonical moral synthesis
Morality as continuity across nested identities
Goodness cannot be defined as local persistence alone. Moral alignment preserves recoverability across self, other persons, relationships, agency, repair, vulnerable participants, and future possibility without exporting intolerable leakage.
Boundary and source
Cancer, oppression, domination, and addiction may be locally stable. Stability is not goodness.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-ETH-001
Open claim address →YT-CORR-001Direct author correction / canonical mapping rule
Cross-dimensional structural position
Identities in different dimensions may correspond when their inside, outside, relation, polarity role, and ordered Y-Engine behaviors occupy matching structural positions at declared scales. The correspondence concerns relational organization and behavior; it does not make the identities, substances, or domain mechanisms literally identical.
Boundary and source
Shared words, images, numbers, adjacency, or post-hoc resemblance do not establish correspondence. Both identities, both scales, the mediating structural position, the domain mechanisms, the invariant, the expected difference, and the falsifier must remain explicit.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-CORR-001
Open claim address →YT-CORR-003Y-Theory predictive research hypothesis
Behavior from structural position
When identities in different dimensions occupy a sufficiently specified corresponding Y-Engine position, Y-Theory predicts analogous behavior expressed through each domain's own variables and mechanisms. A valid prediction must be declared before evaluation and state the proposed invariant, expected dimensional difference, rival explanation, evidence, and falsifier.
Boundary and source
A correspondence found only after seeing the result is exploratory, not predictive confirmation. Failure in one domain must remain visible and may narrow or reject the proposed structural invariant.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-CORR-003
Open claim address →YT-METHOD-001Canonical epistemic rule
Claim-status discipline
Every substantial proposition must be typed as definition, structural derivation, model bridge, Y-Theory postulate, empirical claim, interpretive lens, application architecture, rejection, or open question.
Boundary and source
One layer cannot borrow proof status from another. Internal coherence, implementation, simulation, beauty, repetition, and author approval are not the same as external empirical proof.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-METHOD-001
Open claim address →YT-METHOD-004Canonical research protocol
Zero-to-one challenge and return
Every bounded challenge preserves its question, method, baseline, evidence, falsifier, result, limitations, and next action. A zero remains valuable; a one requires replication, correction, productive action, or a genuinely new domain.
Boundary and source
A one is evidence of one bounded change, not proof of the whole theory.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-METHOD-004
Open claim address →YT-METHOD-006Canonical research and teaching method
Relational reuse across external theories
External theories, geometries, symbols, and engineered systems are mined first as libraries of already-developed relational structures, transformations, address systems, and projections. A valid reuse preserves the source relation while translating role names and scale, states the boundary of the source, and continues the structure through Y-Theory.
Boundary and source
Do not turn a requested structural harvest into a proof contest. Do not rename elements while silently changing incidence, orientation, transformation, or closure. Limits are stated only to protect the transfer, not to dominate it.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-METHOD-006
Open claim address →