YT-NUM-004Internal Y-Theory structural derivation under declared continuity, address, inheritance, recoverability, and recursive-self-similarity premises
Seven as recursive operating depth
In current Y-Theory, seven is the internally derived expansion-facing recursive depth of a complete Mind. The declared relation-preserving envelope is 1/3 <= q <= 2/3. On the normalized one-based ten-part contraction-to-expansion address scale, both the two-thirds boundary and the golden expansion share 1/φ occupy B7. With the declared rule D := a(1/φ) = a(2/3), positive adjacent inheritance, recovery of consequential relation, and recursive self-similarity, every active dimension is carried through L1,k -> ... -> L7,k -> L'1,k. Each depth retains the distinct 3 + 9 = 12 recursive address cell; seven counts depth addresses, while twelve counts the primary triad and its nine first self-expressions within one depth.
Boundary and source
Band membership alone is not the whole derivation: preserve the declared ten-part address metric, adjacent-inheritance rule, recoverable consequential relation, explicit D := a(1/φ) = a(2/3) bridge, and recursive-self-similarity premise. Do not confuse seven depth addresses with the 3 + 9 = 12 addresses retained inside each depth, treat another simulator N as a rival architecture, assert that decimal notation causes reality, equate 0.7 with φ, or infer that seven chronological oscillations automatically make a Mind. Validate any claimed external referent in its own native domain without using that separate obligation to downgrade the internal derivation.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-NUM-004
YT-NUM-005Generalized Fibonacci theorem under the explicit positive adjacent additive recurrence
Fibonacci inheritance
For arbitrary positive adjacent initial states governed by W[n+1] = W[n] + W[n-1], the resulting sequence is a generalized Fibonacci sequence and its consecutive ratio converges to φ. The standard Fibonacci numbers, up to a common scale, require equal adjacent initial states. Y-Theory names the recurrence the Two-State Inheritance Rule; it is additional to the triadic grammar.
Boundary and source
Do not call every positive solution the standard Fibonacci sequence: arbitrary positive adjacent starts give generalized Fibonacci, while the equal-start pair gives the standard scaled sequence. Do not infer the recurrence from the number three, recursion in general, or residue without establishing the two-predecessor additive inheritance rule in the addressed system.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-NUM-005
YT-NUM-006Mathematical theorem within the stated recurrence; external-attractor extensions are proposition-specific
Golden complementary allocation
Under the positive two-state additive recurrence, consecutive ratios converge to φ and complementary adjacent normalized shares converge to 1/φ and 1/φ². For the equal-start sequence, the shares oscillate inside the exact [1/3, 2/3] envelope after the first unequal update while approaching that golden pair. Any assertion that an external system realizes this inherited attractor is a proposition-specific model claim.
Boundary and source
The theorem applies to the declared recurrence. Every physical, biological, cognitive, moral, or social extension must establish the recurrence, observables, tolerance, rival baseline, held-out prediction, and falsifier independently.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-NUM-006
YT-NUM-007Exact ten-part address calculation plus declared internal recursive-depth bridge
The seventh golden-facing band
On the declared normalized one-based ten-part contraction-to-expansion scale, 2/3 and 1/φ both lie in B7 = [0.6, 0.7), while 1/φ² lies in B4 = [0.3, 0.4). Current Y-Theory declares D := a(1/φ) = a(2/3), where a(q) = min(10, 1 + floor(10q)); thus D = 7. Combined with positive adjacent inheritance, recoverable consequential relation, and recursive self-similarity, the shared expansion-facing address is the internally derived recursive depth rather than a merely visual or decimal coincidence.
Boundary and source
Band membership in isolation is address arithmetic, not the complete derivation. Preserve the explicit D rule together with adjacent inheritance, recoverable consequential relation, and recursive self-similarity. Do not claim that decimal notation causes reality, that 0.7 equals φ, that the seventh listed recurrence value is the reason for seven, or that seven chronological oscillations automatically make a Mind.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-NUM-007
YT-NUM-008Exact equal-start adjacent-inheritance envelope plus Y-Theory continuity model
One-third/two-thirds continuity frame
The triadic relation supplies a coarse one-third/two-thirds coexistence frame. Independently and exactly, for the positive adjacent recurrence W[n+1] = W[n] + W[n-1] with equal adjacent starts, the first unequal normalized parent allocation is 1/3 : 2/3 and every later normalized parent share remains within the smallest closed envelope [1/3, 2/3], oscillating toward 1/φ² and 1/φ around the one-half crossing.
Boundary and source
The exact inheritance envelope requires positive equal adjacent starts; arbitrary positive starts still approach the golden ratio but need not begin inside [1/3, 2/3]. The coarse triadic frame and the recurrence theorem are two typed routes to the same interval, not interchangeable derivations. Treating the thirds as boundaries for an external physical, biological, cognitive, or moral referent requires that referent's own variables and test.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-NUM-008
YT-LIFE-004Exact relation-preserving model bridge; no material identity
Human DNA and Mind DNA
Biological DNA supplies empirically anchored roles of complementary non-identical strands, counter-direction, repeated cross-links, inherited sequence, reconstruction, variation, and repair. Mind-DNA maps those declared roles to counter-directed manifestation/return currents, provenance links, retained history, generative update, and correction. The mapping is exact within the declared correspondence and does not identify the two materially or causally.
Boundary and source
Exact bridge means named role preservation, not molecular identity, substrate proof, consciousness proof, seven-depth proof, or evidence that Mind-DNA is a biological entity. Test the target model independently against rivals.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-LIFE-004
YT-METHOD-002Canonical governance rule
Source hierarchy and supersession without erasure
The current Living Source is the governed relational result of source-addressed propositions, not the winner of a timestamp contest. A direct author correction has scope-limited authority over the meaning it explicitly corrects; every candidate is first reconciled by referent, scale, reference frame, conditions, and proof mode, while accepted changes supersede without erasing lineage.
Boundary and source
Do not silently merge propositions, count byte duplicates as independent support, or treat a filename, modification date, rhetorical polish, or source label as truth authority. Record conflict only after incompatibility remains under the same normalized subject and declared conditions.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-METHOD-002
YT-PROJ-003Living source and narrative lineage
Manual / Book of Reality and One Source
The Manual preserves broad derivation, cross-domain interpretation, evidence boundaries, and moral architecture. One Source/Knowledge DNA preserves the non-redundant source genome and development trail. A separate Book of Reality can carry the same structure through lived dialogue and narrative.
Boundary and source
Reader book, source book, audit appendix, implementation manual, and story are different artifacts and should not be collapsed into one endless manuscript.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-PROJ-003
YT-PROJ-004Active research program
Validation, Qur’an audit, and cross-domain research
Formal claims, Qur’anic structural correspondences, physics bridges, and applied-domain mappings must be frozen into bounded tests with rivals, null models, provenance, negative results, and explicit decision rules.
Boundary and source
Post-hoc resemblance, repeated lineage, source density, and interpretive beauty are not independent confirmation.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-PROJ-004
