Manuscript Hawk07-B@1 · Hawk07-B.tex · section · b9785538

Debugging the extrapolation

Enter philosophy, the analogy, and necessary corrections › Debugging the extrapolation · lines 183–292

Hawk07-B@1#tab:corrections

{}1.13

required for the extrapolated claims.
Proposed inference	Corrected statement
Proposed inference	Corrected statement
The accessible dimension is $O (d^{2} f / ε)$ .	The supplied diamond certificate gives a sufficient released dimension $r_{} = O (d^{2} f / (ε^{2} p))$ . The complete receiver has dimension $r_{} h$ , with early-memory dimension $h$ .
The $d^{2}$ threshold is a universal necessary cost.	It is a sufficient bound from the particular Choi-to-diamond argument. Its dimension factor cannot be omitted from that argument, but a different encoding can recover exactly with smaller released dimension.
Before the sufficient threshold, recovery must be poor.	At cut zero the accessible channel is exactly replacement. At other cuts, failure of a sufficient estimate is inconclusive; it is not a lower recovery bound.
Hawk07-A's measure $1/64$ applies unchanged as $d$ grows.	That constant was proved for its dimension- $16$ construction. The scaled turnover calculation below has its own dimensions, hypotheses, and measure.
A receiver certified at every later cut returns the same input repeatedly.	These are alternative stopping interfaces before decoding. One actual quantum return consumes or transforms its receiver input. The statement is not repeated copying of one payload.
Nested access licenses a convoy through one reused vault.	A convoy needs new injection and memory contracts. Independent stock-prepared sessions and a uniformly certified memory-reset device are different constructions.
Previous residual leakage is small, so the next resource is fresh.	Logical input independence does not imply the required resource state, independence from old systems, or workspace restoration.
A beacon works, so the whole ship works.	An effect can be reconstructed while full-code recovery fails. Conversely, full-code recovery implies accurate measurement of every specified effect.
Residual Enter yields an album containing the recovered quantum payload.	It yields an appended residual record. Its Shannon entropy is nondecreasing, but the record need not encode the payload. Quantum return remains a different interface.
The ideal error already uses all of $ε$ , so small implementation errors preserve the same allowance.	Channel and decoder errors require reserved headroom. Their half-diamond allowances add to the ideal error.
An energy condition must be assumed in every geometric successor.	A successor must state and justify its stress and energy-condition properties. They may be assumptions or derived consequences of a specified gravitational model.

All companion sheets are comparisons with their own models. The calculations below are stated and proved locally. In particular, the attached Hawk07-A is a predecessor CheungHawk07A, not permission to change its model without rechecking the hypotheses.