Manuscript Hawk05-C@1 · Hawk05-C.tex · section · ba0719f1

Debugging the proposed extrapolations

Enter background, provenance, and the corrected extrapolation › Debugging the proposed extrapolations · lines 178–266

Hawk05-C@1#tab:debug

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required before extrapolating the finite proxy.
Proposed inference	Corrected statement
Proposed inference	Corrected statement
Choose arbitrary continuous $r (t), b (t)$ by exponentiating two entropies.	Finite dimensions are integers. In a fixed tensor-release proxy, $r (t) b (t) = D$ ; logarithmic capacities must therefore have constant sum, up to declared rounding error.
Clock replacement has only a channel-continuity error.	The budget also includes finite Page deficit, capacity rounding, ensemble mismatch, and temporal compatibility. A collection of snapshot formulas is not automatically one emission history.
A greybody occupation fixes a cell dimension.	An occupation is a state statistic. Turning it into a dimension, probability, cutoff, or entropy-rate weight requires a specified additional map and truncation convention.
The record–quantum entropy gap measures all consumed information.	For a specified basis it equals relative-entropy coherence of one accessible marginal. It is state- and basis-dependent and is not whole-code recovery loss.
Restricting access produces a Page tent.	Restriction defines an observable task. A tent additionally requires a state ensemble and a compatible capacity history. A product state has zero entropy on every tensor prefix.
Two commuting copies of a matrix algebra cannot exist.	They can exist on independent tensor factors. What is obstructed is two commuting faithful representations that both act as the same unknown logical algebra on the encoded code.
A conserved sector remains an ordinary tensor product.	A fixed total additive charge generally decomposes into a direct sum of charge-compatible tensor blocks. Its entropy includes charge weight entropy; the unrestricted Page formula cannot be applied with only two aggregate dimensions.
A falling radiation entropy implies a constant complement.	A pure input's output entropy and the complete complement's dependence on all code inputs are different questions. Exact recovery may coexist with a mixed fixed syndrome.
A positive-cutoff plot necessarily includes a Page turnover.	It includes a turnover only if the declared capacity crossover is reached before the cutoff. The clock can stop on the increasing branch.
A named Petz map establishes physical recovery.	It must be a well-defined deterministic channel on the actual access interface, have a proved task error, and have a certified implementation. An algebraic target may be narrower than a whole code.

The proposal's unspecified “2026 algebraic reading” is not treated as an established universal statement or attributed to an unidentified recent paper. Section sec:algebras instead states a finite access theorem and separately identifies an external asymptotic proposal with its own hypotheses.