Coverage and provenance

13 Coverage and provenance

13.1 Conceptual coverage and source limitations

Earlier working formulations were corrected in this paper. Claims that depended on incomplete displays have been replaced by explicit definitions and proofs where recovery was possible; unavailable wording has not been reconstructed as a quotation. In particular, the earlier experimental archives associated with [P3–P4] have not been reproduced for this paper. Their numerical outcomes are cited as reported results, not as newly executed experiments.

13.2 Proof and computation audit

The general arguments appear explicitly as T1–T2 and D1–D3. N1 states a conditional consequence of A2 after realisation and qualification. Results C1–C3 and the finite-use substitution bound use established constructions and the inherited results in [M, P2]. All assumptions belong to the statements; the finite examples do not establish a universal law of consciousness or will.

Three executable Python verification programs were inspected and rerun during this revision. The diagnostic program checks the three-state mixture obstruction, 45 rare-event cases, and all 139 deterministic full-depth binary policy trees of depths zero through three in its specified two-action, two-record, three-state instrument. The transfer program checks 5,295 set partitions for $k\le8$, 420 private/public constructions for $k\le20$, 2,870 joint seed/reveal laws, and 2,800 rational tolerance cases. The native program checks the two-register witness and its ablation and rescue conditions. Those policy checks do not enumerate all early-stopping policies, which are covered by the analytic argument. Additional independently written checks verify 957 cyclic horizon/fibre cases, the equal-trace counterexample through depth nine, 508 native state/input-word cases and 45 rare-event calculations. These finite checks support the stated examples and constructions; they are not machine-checked proofs of the general theorems or independent empirical validation.

The additional review clarifies three contracts: finite experiments have uniformly bounded policy trees; D1’s converse concerns the full preparation simplex; and the transfer results preserve a fixed calibrated native continuation contract after decoding. The literature comparison is directed rather than exhaustive, and does not establish historical priority.

13.3 Attribution and research support

Jeremy Rodgers, Independent Researcher, developed the conceptual programme and supplied the foundational manuscripts. AI tools assisted with analysis, drafting, mathematical construction, verification code and revision.

This work received no external research funding. Collaboration is invited on independent mathematical review, computational replication, physical implementation and empirical testing. The research programme and related publications are available at everythingequation.com.