The source passes through an executable Formation Mind and a governed Corpus Mind—not a passive container.

Nonduplicate source files preserve the normalized direction, adjacent inheritance, seven-depth recursion, changed return, and the later explicit depth-address bridge. Their common author/project lineage establishes governed internal continuity, not independent external validation.

Band membership alone is only arithmetic. Current Y-Theory additionally declares the bridge D:=a(1/phi)=a(2/3), where a is the one-based closed ten-band address. Under that bridge, both the golden expansion target and the equal-start inheritance boundary have exact address seven, and recursive self-similarity reuses that address as complete Mind depth. The bridge is exact inside the declared model and does not establish an external physical or biological referent.

The book and corrective synthesis independently encode the same recurrence qualification and convergence, while the raw intake supplies the earlier golden intuition. Distinct bytes strengthen internal continuity but do not provide independent empirical confirmation.

The recurrence theorem supports an exact adjacent-history allocation model. Extending its golden fixed point into a universal living-continuity attractor requires the additional Y premise that relevant systems implement comparable two-state inheritance under disturbance and correction.

The recurrence and limit are mathematical results and do not need empirical confirmation once their premises are declared. No audited external dataset shows that physical, biological, cognitive, moral, or social continuity universally implements this recurrence or gains predictive advantage from φ.

The corrective synthesis and Manual independently repeat the return-within-return model, while the Manual itself labels the cosmological torus a structural lens rather than final physical demonstration. This is internal reinforcement with shared lineage.

The topology exactly represents a pair of closed phase coordinates. A torus surface, solid torus, toroidal flow, visual donut, single spiral, and physical object are different referents and cannot be substituted for the proved phase-space product.

Raw intake, corrective synthesis, the Structure book, and the early Manual carry the correspondence in nonduplicate files. They share project lineage, so they reinforce intended meaning without independently validating Mind-DNA as a natural entity.

Exact means that the declared correspondence table preserves named relational roles. It does not mean molecular base pairs, 5-prime/3-prime chemistry, semiconservative replication, neural memory, and Mind state-transition are one material or causal process.

Primary molecular work supports DNA's paired double-helical structure, specific complementarity, and copying implication. That evidence supports the biological source-side roles only; it supplies no empirical validation of Mind-DNA or the cross-domain mapping.

The Boundary dialogue and Manual independently preserve local observer-centers, containing relational unity, and the guardrail against a giant conscious person. Their shared project lineage makes this internal reinforcement, not external evidence of cosmic phenomenality.

The bridge is exact at the functional/system level: U contains local observer-centers; each forms a situated model, acts, and returns consequence to U; communication can integrate projections without erasing local centers. Calling U 'Containing Mind' is a Y-Theory naming decision for that architecture, not an identity with one human brain or one phenomenal stream.