Paper 2 · Section 11Boundary
The domain and evidence of the result
The finite classical assumptions, verification record, related computational studies, funding and research-assistance disclosure are recorded together.
11 Limitations and verification status
The main composition mathematics is finite and classical. A general continuum quotient, unbounded hidden-history implementation, arbitrary nondeterministic internal scheduler or instantaneous algebraic feedback law is not supplied. Even in a finite system, a useful proper strong quotient need not exist. A new port can reveal a previously hidden distinction and force the retained state to expand.
The resource-relative construction assumes declared alternative processes and physically meaningful ownership. It does not identify those alternatives from target records alone. The exact decoder of a statistical experiment is not necessarily an available apparatus, a secure erasure mechanism or a lower-cost replacement. A realization that omits a returning environment, a shared seed or a consumed blank can invalidate an application without falsifying the conditional theorem.
No biological consciousness experiment, independent AI-awareness experiment or direct phenomenal measurement is reported. The separate opaque-interface-learning programme belongs to the companion computational study [21], not to this paper's evidence for a consciousness claim. Its results are not used here to validate A0 or supply a universal subject selector. The companion intervention-law study [20] examines conditional identification of binary realizations, recoding obstructions and a bounded SPC-2/IIT comparison; it likewise does not provide empirical validation of a consciousness claim.
The proofs in this preprint are analytic under their stated assumptions and are accompanied by finite arithmetic and implementation checks. Outside mathematical review and proof-assistant verification have not been completed. Priority and completeness of the literature comparison also remain review obligations, particularly for the programme-specific masking application and the exact combination of composition and resource contracts. The present version has undergone an internal hostile audit with the resulting scope corrections and exact checks recorded in its supplement. These checks are not independent external review and do not replace a proof with a claim of experimental verification.
Funding and collaboration.
This research was conducted independently by Jeremy Rodgers without external research funding. The author welcomes collaboration on independent mathematical review, computational replication, physical implementation and empirical testing, particularly where specialist expertise, equipment or institutional resources are required.
AI assistance disclosure.
This research programme used OpenAI GPT-family models, including Astra configurations used in the research workflow, for mathematical exploration, adversarial review, code generation and checking, literature assistance, and manuscript drafting and editing under the author's direction. Anthropic Claude was used for an additional independent AI review and reconstruction of central finite calculations. Claim selection, source selection, final interpretation, and authorship responsibility remain with the author. AI-based checking is not represented as independent human review or formal proof verification.
Section F specifies the proof and artifact status. Standard results are credited as such. The appended finite tests check formula transcription, normalization and illustrative mechanisms; no finite enumeration is substituted for the general arguments.