Manuscript Hawk04-D@1 · Hawk04-D-v1.tex · section · 39b16f67

Mathematical repairs incorporated into the paper

Debugging and provenance ledger › Mathematical repairs incorporated into the paper · lines 2364–2430

Draft shortcut	Replacement used here
Draft shortcut	Replacement used here
Decoder allowance $2 d e + b$	The general complementary-Choi allowance is $2 d e + b$ . A specified decoded Choi state instead gives $d r_{dec} + b$ .
Diamond convergence with changing $d_{n}$	Fixed-subcode comparisons or separate whole-code certificates are required. Whole-code upper certificates retain $d_{n} e_{n}$ .
One regulator for scalar reservoir and collapse Bogoliubov map	The finite-band theorem is proved for its printed Hamiltonian. A field bridge has separate representation, implementability, access, and approximation obligations.
Exact finite oscillator algebra	Finite matrices cannot obey the full CCR. Normalized finite preparations and finite-channel comparisons are used instead.
Bits emitted imply mass decrease	Energy and mass updates use declared flux observables and a clock. Record count alone is not an energy ledger.
$T \propto M^{- 1}$ implies $M^{3}$ lifetime	Fixed species, greybody scaling, flux normalization, and mass balance are also required; the theorem stops at $M_{c} > 0$ .
Half the quanta imply recovery of the whole code	The target and accessible dimension are fixed first. The SWAP calibration and dimension lower bound obstruct that universal claim.
Entropy turnover implies small complete leakage	Explicit equal-entropy/unequal-recovery channels disprove this inference. A separate complete-complement certificate is required.
Final Enter creates an energetic burst	Readout-and-drop leaves prior radiation unchanged. Any burst requires a new energetic dynamics and detector model.
Thermalization makes the environment disappear	Input independence, thermal state preparation, and physical absence are different claims. Purifiers remain in complete accounting.
Null remnant detection proves no remnants	Only a stated class can be statistically excluded under a production, efficiency, and background model.
Finite termination proves irreversible evaporation	Finite syntax terminates; finite autonomous proxies recur. An endpoint needs its own limit and access construction.