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-ETH-002Moral and theological synthesis
Mercy, truth, justice, and repair
Mercy preserves a truthful path of return where repair remains possible; justice restores relations across levels; truth allows reality to correct the model; protection may require boundaries.
Boundary and source
Mercy is not denial of harm, justice is not revenge, and repair is not restoration of trust without evidence.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-ETH-002
YT-FAITH-001Interpretive and social synthesis
Faith and religion as guidance and preservation architectures
Religions preserve source-orientation, moral boundaries, narratives, ritual memory, correction practices, and collective return while remaining vulnerable to power distortion, rigid compression, and loss of meaning.
Boundary and source
Structural correspondence does not make all religions identical or settle their distinct theological truth claims.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-FAITH-001
YT-COL-001Conditional architectural criterion
Distributed cognitive-mind capability
A wider collective identity earns distributed cognitive-mind capability only when local centres remain distinguishable while their activity enters shared memory, communication, integration, correction, direction, and recoverable whole-level return.
Boundary and source
A crowd, network, institution, synchronized group, or consensus is not automatically a higher identity, observer, or distributed cognitive mind.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-COL-001
YT-COL-002Application architecture and moral synthesis
Governance as distributed judgment and correction
Healthy governance distributes observation, judgment, dissent, responsibility, appeal, memory, and correction so that no local centre becomes unanswerable and wider continuity remains recoverable.
Boundary and source
Agreement is not truth; emergency power requires expiry; minority reports and dissent may carry indispensable residual information.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-COL-002
YT-COL-003Specified application; pilot not yet demonstrated
Community Intelligence Network / NAPAM
The proposed community network connects needs, offers, guidance, missions, action, verification, residue, and correction through consent-based human governance.
Boundary and source
No human-worth scoring, coercive matching, hidden ranking, or claim of proven social transformation.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-COL-003
YT-COS-001Internally derived structural placement under functional/local observer definition; phenomenal cosmic subject unestablished
The universe as containing Mind
Given observer as retained present-trace integration returned into later manifestation, local minds inside the universe are situated observer-centers whose models and actions return consequence to the same containing field. Y-Theory names that field the Containing Mind and calls the resulting observer function distributed; this does not assert one unitary phenomenal cosmic subject.
Boundary and source
Do not infer a giant human-like personality, universe-wide phenomenal unity, integrated autobiographical memory, intention, agency, or consciousness from containment, local observation, structural consequence-return, or collective science alone.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-COS-001
YT-DIG-002Canonical application architecture
Local Root and expansion cortex
Local Root owns identity, source-of-truth boundaries, final integration, recovery, and governance. Cloud or expansion cortex may search, simulate, correlate, and scale, but returns proposals or deltas rather than silently owning closure.
Boundary and source
The most capable subsystem does not automatically gain authority over identity, source, consent, or final judgment.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-DIG-002
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-METHOD-008Application architecture
Relation-governed application loop
A bounded application should not evaluate only an isolated input-to-function-to-output path. It places a measured comparison-and-return loop around the primary operation so consequence may change only the relevant context coupling, while recurrence reliability, efficiency, and continuity or viability remain separate objectives constrained by cost, harm, exported leakage, and intervention authority.
Boundary and source
This is ordinary feedback and control enriched by explicit continuity and recoverability accounting, not the invention of contextual control. It supplies no generic electricity, magnetism, velocity, retention, faster-feedback, or timeless-machine intervention. Every carrier-specific claim must declare variables, units, sensors, actuators, baseline, rivals, intervention limits, stop rule, stability constraints, cost, harm, and comparison evidence.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-METHOD-008
YT-PROJ-001Journey Graph foundation implemented; later routes and controlled intake remain staged
Y-Theory Teacher and Challenge Lab
The Teacher is the public learning projection of the governed Living Source. A typed Journey Graph separately represents learner order, structural dependency, manifestation sequence, subject entry, and corrective return; the public tree, node reader, and source-guided question locator are generated from that graph. The Challenge Lab retains learner questions, evidence, and return.
Boundary and source
The public site is an output generated from a named canonical source version. Graph mapping is not proof; teaching order is not automatically manifestation chronology; a visible gap is not an established claim; and the site must not become the sole editable source or silently approve learner, agent, or uploaded-source proposals.
living-source:atlas/CANONICAL_CLAIM_REGISTRY.json #YT-PROJ-001
