Editing Openai/69596681-3f7c-8006-b9fd-01d9d8191763 (section)

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Abstract (Revised)
We present an algorithmically governed physical theory that is complete and closed at accessible (finite-resolution) scales. The theory is evaluated by a deterministic decision semantics that yields a binary verdict under empirical data and explicitly diagnoses its own breakdown under precision refinement. We prove a necessary and sufficient condition for asymptotic viability in terms of the scaling behavior of the structural tolerance parameter and show that naive precision refinement generically induces collapse. The theory therefore establishes infrared completeness with a formally specified domain of authority and a non-extendable closure at accessible scales. Claims of ultraviolet completeness are explicitly excluded unless a nonzero structural tolerance fixed point is postulated and justified.

===== Scope of Authority =====
This theory asserts completeness only for physically realizable observations at finite operational resolution. It does not claim ultraviolet completeness or validity under infinite precision unless an explicit nonzero tolerance fixed point τ* is independently established. Precision refinement beyond this domain is treated as an adversarial stress test and may induce collapse.

===== Insert verbatim in Methods: =====

τ(p)=τ\''+(τ0−τ\'')2−p,τ\''≥∣r∣max⁡\tau(p)=\tau^\''+(\tau_0-\tau^\'')2^{-p}, \qquad \tau^\''\ge |r|_{\max}τ(p)=τ\''+(τ0−τ\'')2−p,τ\*≥∣r∣max
Interpretation:
'' τ'' is the irreducible operational tolerance (instrumental/physical).
* Exact measurements are forbidden.
'' Precision refinement saturates at τ''.
'' Asymptotic viability is guaranteed iff τ'' ≥ |r|max.

This is the minimal viable law. Anything weaker collapses.

===== A8 (Operational Irreducibility): =====
There exists a nonzero lower bound τ* on admissible residuals; exact observables are not physically realizable.

This axiom is optional but required if asymptotic viability is claimed.

===== Replace everywhere: =====
* “Theory of Everything” ⟶ Infrared-Complete Theory (IR-ToE)

Definition (Formal):
An IR-ToE is a deterministic theory that provides a complete, closed description of all physically realizable phenomena at accessible scales, together with a formally specified and testable criterion for asymptotic breakdown.

This avoids false UV claims while preserving the core contribution.

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===== - Neutralizes the referee’s fatal objection without hand-waving =====
* Preserves mathematical integrity
* Aligns perfectly with your ANF results
* Converts rejection into “accept after major revision” territory
* Locks claims so no further backtracking is needed

===== If you say nothing further, the optimal continuation is: =====

Produce the final Methods + Theorem + Proof section in journal-ready LaTeX, fully aligned with the above scope and τ(p) law.

That is the last high-impact step before submission.

© Robert R. Frost
2026-01-03