References

SK1975

D. Sherrington and S. Kirkpatrick. Solvable model of a spin-glass. Physical Review Letters 35 (1975), 1792–1796. doi:10.1103/PhysRevLett.35.1792.

LevinPeres

D. A. Levin and Y. Peres, with contributions by E. L. Wilmer. Markov Chains and Mixing Times. Second edition, American Mathematical Society, 2017. Finite heat-bath chains, reversibility, mixing conventions, and continuous time. https://pages.uoregon.edu/dlevin/MARKOV/mcmt2e.pdf

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.

Chatterjee

S. Chatterjee. A generalization of the Lindeberg principle. Annals of Probability 34 (2006), 2061–2076. doi:10.1214/009117906000000575. https://arxiv.org/abs/math/0508519

FarhiEtAl

E. Farhi, J. Goldstone, S. Gutmann, and L. Zhou. The quantum approximate optimization algorithm and the Sherrington–Kirkpatrick model at infinite size. Quantum 6 (2022), 759. doi:10.22331/q-2022-07-07-759. Cited for the quantum-circuit and energy-expectation interface, not for identification with heat-bath dynamics. https://quantum-journal.org/papers/q-2022-07-07-759/

OAI227Quench

OpenAI. Universality of critical quench autocorrelations in the Sherrington–Kirkpatrick model. External Family 227-01 manuscript, dated 5 October 2026. Relevant source: Section 1, especially thm:main. Documentary claim record, not a premise of the finite theorem. https://github.com/openai/math/blob/main/preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/build/sections/01-introduction.tex

OAI227Stationary

OpenAI. Functional universality of critical SK autocorrelations. External stationary companion, dated 5 October 2026. Non-point stationary limit is recorded, not independently verified here. https://github.com/openai/math/blob/main/preprints/Functional-universality-of-critical-SK-autocorrelations-October-5-2026/build/main.tex

OAI227Background

OpenAI. The stationary edge input. Section 2 of the external critical-quench manuscript. Finite forms, replica coordinates, conditioned edge inputs, and relaxed-energy interface. https://github.com/openai/math/blob/main/preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/build/sections/02-background.tex

OAI227Edge

OpenAI. Gaussian estimates at the bottom edge scales. Section 3 of the external critical-quench manuscript. Relevant source label: prop:edge-estimates. Audited without importing its estimates. https://github.com/openai/math/blob/main/preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/build/sections/03-edge-estimates.tex

OAI227Warming

OpenAI. Warming at the critical scale. Section 4 of the external critical-quench manuscript. Relevant source label: thm:warming. Audited without importing its positive-time estimates. https://github.com/openai/math/blob/main/preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/build/sections/04-warming.tex

OAI227Entrance

OpenAI. Selection of the entrance law. Section 6 of the external critical-quench manuscript. Relevant source label: thm:entrance-selection. Audited without importing its uniqueness or existence theorem. https://github.com/openai/math/blob/main/preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/build/sections/06-entrance-selection.tex

OAI227History

OpenAI. Clock-history cutoffs. Section 7 of the external critical-quench manuscript. Documentary replacement interface. https://github.com/openai/math/blob/main/preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/build/sections/07-history-cutoffs.tex

OAI227Scores

OpenAI. Clock scores. Section 8 of the external critical-quench manuscript. Documentary score-projection interface. https://github.com/openai/math/blob/main/preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/build/sections/08-clock-scores.tex

OAI227Replacement

OpenAI. Replacement. Section 9 of the external critical-quench manuscript. Documentary disorder-comparison and functional-tightness interface, not a locally verified universality theorem. https://github.com/openai/math/blob/main/preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/build/sections/09-replacement.tex

Lean227

OpenAI. Critical SK autocorrelation processes and dynamics across the temperature transition. Repository scope note lean/docs/227.md. Consulted 14 October 2026. A scope description is distinguished from an executed proof. https://github.com/openai/math/blob/main/lean/docs/227.md

LeanSKRatio

OpenAI. SKRatio.lean. Repository Comparator target. The inspected ratio_cutoff theorem body contains sorry. Consulted 14 October 2026. https://github.com/openai/math/blob/main/lean/ComparatorChallenges/SKRatio.lean

LeanCriticalMixing

OpenAI. CriticalSKMixing.lean. Repository Comparator target. The inspected critical_mixing_bounds theorem body contains sorry. Consulted 14 October 2026. https://github.com/openai/math/blob/main/lean/ComparatorChallenges/CriticalSKMixing.lean

Catalogue

OpenAI. External mathematics catalogue, repository overview.tex. Family identifiers and their nominated comparisons are documentary records, not theorem premises. https://github.com/openai/math/blob/main/overview.tex

CheungEm04A

N. Cheung. Em04-A, version 2. Supplied manuscript Em04-A-v2.tex, section “Physicality and exact reduction.” Relevant label: thm:reduction. A specified zero-temperature XY-chain reduction; not a classical SK heat-bath generator. Enter Calculus Companion.

CheungHawk02D

N. Cheung. Hawk02-D, version 1. Supplied manuscript Hawk02-D.tex, section “Actual complete-residual recovery.” Relevant labels: thm:main and cor:window. A specified quadratic fermionic model and its complete residual, not the present classical spin chain. Enter Calculus Companion.

CheungHawk02E

N. Cheung. Hawk02-E, version 1. Supplied manuscript Hawk02-E.tex, section “Gravitational correspondence and a common validity interval,” subsection “Audit of the proposed auxiliary mathematics.” Explicitly separates classical SK gap estimates from quantum SYK dilation estimates. 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 external thermal inputs, not an identification of SK inverse temperature. Enter Calculus Companion.

CheungI

N. Cheung. Landmark I, version 2. Supplied manuscript I.tex. Relevant label: thm:main. Finite Born probabilities and destructive projective residuals within a stated strategy class. Enter Calculus Companion.

CheungVIIIB

N. Cheung. Landmark VIII-B, version 3. Supplied manuscript VIII-B-v3.tex, section “Classical table decoding is not quantum recovery.” Relevant label: prop:classical-recovery. Record-only quantum recovery obstruction, not a classical autocorrelation theorem. Enter Calculus Companion.

CheungHawk04B

N. Cheung. Hawk04-B, version 2. Supplied manuscript Hawk04-B.tex. Complete-complement recovery, typed destructive readout, and record-only recovery distinctions. Enter Calculus Companion.

CheungEn01B

N. Cheung. En01-B, version 2. Supplied manuscript En01-B-v2.tex. The supplied dossier's bounded-statistic and calibration coverage comparison is used only as a methodological template. No collapse-model generator is imported. Enter Calculus Companion.

CheungEn01C

N. Cheung. En01-C, version 1. Supplied manuscript En01-C.tex. Relevant comparison: thm:certificate, bounded complete-record finite-sample coverage. Its named physical statistic is not an SK autocorrelation. 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-resource lower bounds and growing-resource transmission are kept separate. Enter Calculus Companion.

CheungOai265A

N. Cheung. Oai265-A, supplied version 1. Relevant labels: def:determination and thm:separation. Static-record, complete-channel, and temporal-history separations. Enter Calculus Companion.

CheungXXIIA

N. Cheung. XXII-A, version 1. Supplied manuscript XXII-A.tex. Relevant label: thm:separation. Scheduled ancestry, operational influence, and a separately supplied causal relation. Enter Calculus Companion.

CheungXIVI

N. Cheung. Landmark XIV-I, version 1. Supplied manuscript XIV-I.tex. Relevant labels: thm:I2, thm:I3, and thm:release. Internal amplitude construction and the distinct unresolved joint characteristic map. Documentary boundary only.

CheungXIVJ

N. Cheung. Landmark XIV-J, version 1. Supplied manuscript XIV-J.tex. Relevant labels: prop:descent, thm:reference, thm:J2, and cor:noadmission. Supported-sector references do not constitute the full joint characteristic construction. Documentary boundary only.

CheungXVB

N. Cheung. Landmark XV-B, supplied version 2. Relevant labels: thm:lifting and thm:release. Abstract reconstruction-lifting and extension interfaces; the supplied graph-specific construction remains unresolved. Documentary boundary only.

Dossier

User-supplied Oai227-A plan and comparative source dossier. Includes version-specific Cheung excerpts, family catalogue descriptions, and nominations of Oai272-A and Oai283-A. Supplied retrieval label: 178f233f (retrieval-3). Not an exhaustive corpus scan or independent proof verification.