Manuscript Hawk02-D@1 · Hawk02-D.tex · section · e6e4b72f

Audit of the external mathematics catalogue

Debugging the proposed imports and physical interpretation › Audit of the external mathematics catalogue · lines 1776–1847

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The supplied mathematics catalogue is a documentary record, not an independently verified theorem source SuppliedCatalogue. Its numbered families are not used as premises here.

Proposed ingredient	Required correction or application boundary
Proposed ingredient	Required correction or application boundary
Classical SK mixing	A classical heat-bath gap or cutoff theorem is not a quantum SYK complementary-channel estimate. A reduction between the processes and a reference-stable norm estimate would have to be proved.
Ground-state area law	Its state class, dimension, gap assumptions, and degeneracy conditions must be checked. Even a valid area bound does not imply complete residual independence; see Proposition prop:area-law.
Lieb–Thirring estimate	A spectral-energy inequality does not automatically bound a real-time encoded channel. The connecting spectral, propagator, preparation, and access estimates are separate obligations.
Bosonic occupation cutoff	The Gaussian-state cutoff reported in En02-E is a statement about its specified state and interface CheungEn02E. It is not an automatic regulator for a Majorana-chain message channel. A uniform encoded-input comparison is required.
Tree reconstruction threshold	A classical broadcast threshold does not calibrate a general coherent quantum detector algebra without a proved reduction to that broadcast model.
Penrose-type inequality	The classical constraint, energy-condition, dimension, asymptotic, and boundary hypotheses must hold for a specified geometry. Such an inequality does not construct the SYK–gravity dictionary, and an asymptotically flat initial-data result is not automatically a JT result.
Near-Kerr inextendibility	A category statement for two-ended vacuum Kerr perturbations is not a quantitative semiclassical breakdown time for an evaporating SYK/JT state.
Photon-number entropy inequality	Its precise proved domain would first have to be supplied and checked. An output-entropy bound is not a code-wide recovery or endpoint decoupling theorem.
Entanglement or secret-key diagnostic	Residual entanglement, distillability, and constant complementary channels are different properties. None replaces (eq:leakage-definition).