References

OpenAI276

OpenAI. Classical capacity and entropy inequalities for generalized amplitude damping. External Family 276-01 manuscript, dated 24 September 2026. Main claim and arbitrary-partner corollary are documentary records here, not independently verified inputs. https://github.com/openai/math/blob/main/preprints/Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026/build/paper.tex

SourceBlock276

OpenAI. An entropy inequality with one zero block. Section block.tex of the Family 276-01 source. Relevant source label: thm:block. https://github.com/openai/math/blob/main/preprints/Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026/build/sections/block.tex

SourceThermal276

OpenAI. A thermal block entropy inequality. Section thermal.tex of the Family 276-01 source. Relevant source label: thm:thermal. https://github.com/openai/math/blob/main/preprints/Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026/build/sections/thermal.tex

SourceOutput276

OpenAI. From the thermal inequality to channel outputs. Section output.tex of the Family 276-01 source. Relevant labels: lem:partner-branch, prop:pure-bound, and cor:mixed-bound. https://github.com/openai/math/blob/main/preprints/Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026/build/sections/output.tex

SourcePartners276

OpenAI. Additivity with a finite-dimensional partner. Section partners.tex of the Family 276-01 source. Documentary proof interface for cor:partner-additivity. https://github.com/openai/math/blob/main/preprints/Classical-capacity-and-entropy-inequalities-for-generalized-amplitude-damping-September-24-2026/build/sections/partners.tex

LeanScope276

OpenAI. Classical capacity of generalized amplitude damping: Lean scope note. Repository file lean/docs/276.md. Consulted 14 October 2026. https://github.com/openai/math/blob/main/lean/docs/276.md

LeanTarget276

OpenAI. AmplitudeDamping.lean. Repository file lean/ComparatorChallenges/AmplitudeDamping.lean. Consulted 14 October 2026. The inspected OAI.GAD.main theorem body contains sorry; no completed proof is inferred from this target. https://github.com/openai/math/blob/main/lean/ComparatorChallenges/AmplitudeDamping.lean

HouFang

L.-Z. Hou and M.-F. Fang. The Holevo capacity of a generalized amplitude-damping channel. Chinese Physics 16 (2007), 1843–1847. doi:10.1088/1009-1963/16/7/006. https://cpb.iphy.ac.cn/article/doi/10.1088/1009-1963/16/7/006

KhatriSharmaWilde

S. Khatri, K. Sharma, and M. M. Wilde. Information-theoretic aspects of the generalized amplitude-damping channel. Physical Review A 102 (2020), 012401. doi:10.1103/PhysRevA.102.012401. https://arxiv.org/abs/1903.07747

Wootters

W. K. Wootters. Entanglement of formation of an arbitrary state of two qubits. Physical Review Letters 80 (1998), 2245–2248. doi:10.1103/PhysRevLett.80.2245. The entropy–concurrence scalar function is a comparison; no formation-additivity theorem is imported. https://arxiv.org/abs/quant-ph/9709029

Holevo1998

A. S. Holevo. The capacity of the quantum channel with general signal states. IEEE Transactions on Information Theory 44 (1998), 269–273. doi:10.1109/18.651037. https://arxiv.org/abs/quant-ph/9611023

SchumacherWestmoreland

B. Schumacher and M. D. Westmoreland. Sending classical information via noisy quantum channels. Physical Review A 56 (1997), 131–138. doi:10.1103/PhysRevA.56.131.

Watrous

J. Watrous. The Theory of Quantum Information. Cambridge University Press, 2018. Finite-dimensional channels, complete norms, entropy, and channel coding conventions. https://cs.uwaterloo.ca/ watrous/TQI/

King

C. King. Additivity for unital qubit channels. Journal of Mathematical Physics 43 (2002), 4641–4653. doi:10.1063/1.1500791. Preprint: Additivity for a class of unital qubit channels. https://arxiv.org/abs/quant-ph/0103156

SiddhuEtAl

V. Siddhu, A. Chatterjee, K. Jagannathan, P. Mandayam, and S. Tayur. Queue-channel capacities with generalized amplitude damping. Preprint, 2021. Cited for the symmetric GAD specialization, not for a general thermal additivity theorem. https://arxiv.org/abs/2107.13486

HSR

M. Horodecki, P. W. Shor, and M. B. Ruskai. Entanglement breaking channels. Reviews in Mathematical Physics 15 (2003), 629–641. doi:10.1142/S0129055X03001709. Preprint: General Entanglement Breaking Channels. https://arxiv.org/abs/quant-ph/0302031

Audenaert

K. M. R. Audenaert. A sharp continuity estimate for the von Neumann entropy. Journal of Physics A: Mathematical and Theoretical 40 (2007), 8127–8136. doi:10.1088/1751-8113/40/28/S18. https://arxiv.org/abs/quant-ph/0610146

Hoeffding

W. Hoeffding. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58 (1963), 13–30. doi:10.1080/01621459.1963.10500830.

Hastings

M. B. Hastings. Superadditivity of communication capacity using entangled inputs. Nature Physics 5 (2009), 255–257. doi:10.1038/nphys1224. https://arxiv.org/abs/0809.3972

CheungI

N. Cheung. Landmark I, version 2. Supplied manuscript I.tex. Relevant items: the structural Born/destructive-readout characterization, record and continuation interfaces, and prop:classical-recovery. Enter Calculus Companion.

CheungEn02A

N. Cheung. En02-A, version 1. Supplied manuscript En02-A-v1.tex. Relevant label: thm:Dprime. One-shot environment accounting and its distinction from adaptive live-memory accounting. Enter Calculus Companion.

CheungEn02B

N. Cheung. En02-B, version 1. Supplied manuscript En02-B-v1.tex. Relevant labels: thm:B1, thm:batch, thm:B5, and prop:observable. Resource-certified decoder soundness and named access-model comparisons, not a GAD collective decoder. Enter Calculus Companion.

CheungEn07A

N. Cheung. En07-A, version 1. Supplied manuscript En07-A.tex. Relevant supplied label: thm:exact. Complete-complement recovery and separately described readout-and-drop conventions. Enter Calculus Companion.

CheungEn07C

N. Cheung. En07-C, version 1. Supplied manuscript En07-C.tex. Relevant supplied labels: thm:exact and thm:release. Complete-complement recovery and thermal data as external input; no identification with the present $\nu$. Enter Calculus Companion.

CheungHawk04B

N. Cheung. Hawk04-B, version 2. Supplied manuscript Hawk04-B.tex. Relevant items: exact complete-complement recovery, typed readout, destructive discard, and record-only recovery limitations. No gravitational conclusion is imported. Enter Calculus Companion.

CheungEn01B

N. Cheung. En01-B, version 2. Supplied manuscript En01-B-v2.tex. Relevant label: thm:bounded. Bounded complete-record statistics and uniform family allowances. Enter Calculus Companion.

CheungEn01C

N. Cheung. En01-C, version 1. Supplied manuscript En01-C.tex. Relevant label: thm:certificate. Clipping, complete attempted-run records, calibration, and finite-sample coverage for its named statistic. Enter Calculus Companion.

CheungEm03F

N. Cheung. Em03-F, version 1. Supplied manuscript Em03-F-v1.tex. Relevant labels: thm:EB and thm:recovery. A specified measure-and-prepare packet channel and its referenced recovery obstruction, not GAD. Enter Calculus Companion.

CheungEm03G

N. Cheung. Em03-G, version 1. Supplied manuscript Em03-G-v1.tex. Relevant labels: thm:lower, thm:compacttransmission, and prop:Fobstruction. Fixed finite-coupling lower bounds are distinguished from growing-resource transmission families. Enter Calculus Companion.

CheungOai265A

N. Cheung. Oai265-A, supplied version 1. Relevant labels: def:determination and thm:separation. Static records, selected spectra, complete channels, and radiation histories are separate interfaces. Enter Calculus Companion.

CheungOai290A

N. Cheung. Oai290-A, supplied version 1. Relevant supplied label: thm:exact, complete-complement criterion. The dossier's finite-certificate and selected-marginal comparisons are documentary, not a specification of the present ensemble. Enter Calculus Companion.

Oai272Draft

Oai272-A: Finite certificates for secret-bit obstructions and PPT-composition counterexample interfaces. Conversation-supplied development draft. Cited only as a scoped comparison. No Cheung authorship, independent source verification, or registration is asserted.

Dossier276

User-supplied Oai276-A plan and comparative source dossier. Includes version-specific Cheung excerpts, external-family catalogue descriptions, and comparison nominations. Supplied retrieval label: 178f233f (retrieval-3). Not an exhaustive corpus scan, proof verification, or declaration that nominated manuscripts are theorem premises.