References

OpenAI283

OpenAI, Polynomial-Time Unitary Synthesis from a Boolean Oracle, 5 October 2026. Catalogue manuscript 283-01. Documentary claim; not independently verified or used as a premise. https://github.com/openai/math/blob/main/preprints/Polynomial-Time-Unitary-Synthesis-from-a-Boolean-Oracle-October-5-2026/paper.pdf

OpenAIOverview

OpenAI, Mathematics release overview, repository file overview.tex, entries 283 and 365. Documentary descriptions of oracle synthesis and boundary inverse problems; consulted 14 October 2026. https://github.com/openai/math/blob/main/overview.tex

OpenAI212

OpenAI, Strict convexity and differentiability of the planar exponential first-passage limit shape, 24 September 2026. Catalogue manuscript 212-02. Documentary only. https://github.com/openai/math/blob/main/preprints/Strict-convexity-and-differentiability-of-the-planar-exponential-first-passage-limit-shape-September-24-2026/main.pdf

OpenAI212Scope

OpenAI, Planar first-passage geometry and the absence of bigeodesics, formalization scope note lean/docs/212.md. Selected differentiability statements are distinguished from the paper's additional strict-convexity claim. No formal execution is asserted here. https://github.com/openai/math/blob/main/lean/docs/212.md

AaronsonKuperberg

S. Aaronson and G. Kuperberg, “Quantum versus classical proofs and advice,” Theory of Computing 3 (2007), 129–157. https://arxiv.org/abs/quant-ph/0604056

LombardiMaWright

A. Lombardi, F. Ma, and J. Wright, A one-query lower bound for unitary synthesis and breaking quantum cryptography, 2023. One-query complexity result, not an audit of the 2026 catalogue claim. https://arxiv.org/abs/2310.08870

WatrousBook

J. Watrous, The Theory of Quantum Information, Cambridge University Press, 2018. Chapter 3: state and channel distances, reference systems, and completely bounded trace norms. https://cs.uwaterloo.ca/ watrous/TQI/

WatrousSDP

J. Watrous, “Semidefinite programs for completely bounded norms,” Theory of Computing 5 (2009), 217–238. doi:10.4086/toc.2009.v005a011. https://arxiv.org/abs/0901.4709

NielsenChuang

M. A. Nielsen and I. L. Chuang, “Programmable quantum gate arrays,” Physical Review Letters 79 (1997), 321–324. https://arxiv.org/abs/quant-ph/9703032

BarencoEtAl

A. Barenco et al., “Elementary gates for quantum computation,” Physical Review A 52 (1995), 3457–3467. https://arxiv.org/abs/quant-ph/9503016

BennettEtAl

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Physical Review Letters 70 (1993), 1895–1899. doi:10.1103/PhysRevLett.70.1895.

OCB

O. Oreshkov, F. Costa, and Č. Brukner, “Quantum correlations with no causal order,” Nature Communications 3 (2012), 1092. https://arxiv.org/abs/1105.4464

Hoeffding

W. Hoeffding, “Probability inequalities for sums of bounded random variables,” Journal of the American Statistical Association 58 (1963), 13–30.

CheungEn08B

N. Cheung, En08-B: Resource-controlled operational approximation of null boundary transport, version 1, manuscript En08-B.tex. Relevant labels: thm:main, lem:identity, cor:gate-noise, prop:accumulation. Enter Calculus Companion; supplied passages and registry record.

CheungXXIID

N. Cheung, XXII-D, version 1, manuscript XXII-D.tex. Finite transport contracts, anchored-null and finite-future obstructions, endpoint/arrival and complete-channel certificates. Enter Calculus Companion; supplied passages.

CheungXXIIF

N. Cheung, XXII-F, version 1, manuscript XXII-F.tex. Relevant labels: thm:assembly, cor:approximation, prop:symmetry, target:existence. Conditional implication is distinct from operational instantiation. Enter Calculus Companion; supplied passages.

CheungXXIIA

N. Cheung, XXII-A, version 1, manuscript XXII-A.tex. Faithful generated affine representation and acceptance conditions. Enter Calculus Companion; supplied passages.

CheungXXIIB

N. Cheung, XXII-B, version 1, manuscript XXII-B.tex. Hypothesis ledger, finite-generation and tolerance audits, and the Stage 2 handoff. Enter Calculus Companion; supplied passages.

CheungXXIIC

N. Cheung, XXII-C, version 1, manuscript XXII-C.tex. Relevant labels: thm:order, spec:obligations, target:selection. Tripartite qubit access and component-order extraction. Enter Calculus Companion; supplied passages.

CheungEn10A

N. Cheung, En10-A: A Finite Enter Instrument on a Qubit–Antiqubit Interface, version 1, manuscript En10-A.tex. Complete destructive readout, source-weight estimation, and non-identification. Enter Calculus Companion; supplied passages and registry record. Not a theorem premise of XXII-F.

CheungEn10B

N. Cheung, En10-B: Physical Acquisition and Identification for a Declared Positron-Source Observable, version 1, manuscript En10-B.tex. Relevant labels: thm:derived, thm:calibrated, thm:competition, thm:main. The physical acceptance package is a separate obligation. Enter Calculus Companion; supplied passages and registry record.

CheungEn09A

N. Cheung, En09-A: Realization of Relational Time by Destructive Enter on a Clock Register, version 1, manuscript En09-A.tex. Complete clock-conditioned instrument and separate covariance hypotheses. Enter Calculus Companion; supplied passages and registry record.

CheungVIIJ

N. Cheung, VII-J, version 1, manuscript VII-J.tex. Scheduled dependencies, operational signalling, complete simulation, and separately certified physical containment. Enter Calculus Companion; supplied passages.

CheungEn08A

N. Cheung, En08-A, version 1, manuscript En08-A.tex. Relevant labels: thm:main, thm:mainpositive. Scheduler countermodels and conditional cone classification. Enter Calculus Companion; supplied passages.

CheungEm03E

N. Cheung, Em03-E: Microscopic Input Dependence and Certified Recovery in a Dynamical Radiation Model, version 1, manuscript Em03-E-v1.tex. Relevant labels: thm:evolution, thm:recovery, prop:distinguish. Declared Hamiltonian evolution, complete channels, and reference-preserving recovery comparisons. Enter Calculus Companion; supplied passages and registry record.

CheungEn02B

N. Cheung, En02-B, version 1, manuscript En02-B-v1.tex. Relevant label: thm:B1. Finite programme soundness, complete path maps, and live-name ledgers. Enter Calculus Companion; supplied passages.

CheungEn02C

N. Cheung, En02-C, version 1, manuscript En02-C-v1.tex. Relevant label: thm:C1. Reference-preserving sequential certificates and separate laboratory/external storage. Enter Calculus Companion; supplied passages.

CheungEn07B

N. Cheung, En07-B, version 1, manuscript En07-B.tex. Relevant labels: thm:global, thm:exact. Complete-output restoration and the distinct accessible-output recovery problem. Enter Calculus Companion; supplied passages.

CheungVIIIA

N. Cheung, VIII-A, version 3, manuscript VIII-A-v3.tex. Relevant labels: A:thm:residual, A:prop:instrument. Classical record agreement is weaker than residual-instrument agreement. Enter Calculus Companion; supplied passages.

CheungXXIIE

N. Cheung, XXII-E, version 1, manuscript XXII-E.tex. Metric-jet and source-rule separation in a declared dynamics comparison. Enter Calculus Companion; supplied source record.

CheungXIVI

N. Cheung, XIV-I, version 1, manuscript XIV-I.tex. Relevant labels: thm:I2, thm:I3, thm:release. Constructed internal amplitude and unresolved full joint map. Enter Calculus Companion; supplied passages.

CheungXIVJ

N. Cheung, XIV-J, version 1, manuscript XIV-J.tex. Relevant labels: prop:descent, thm:reference, thm:J2, cor:noadmission. Enter Calculus Companion; supplied passages.

CheungXVB

N. Cheung, XV-B, version 2, manuscript XV-B.tex. Relative-lifting interfaces and the continuing graph-specific admission boundary. Enter Calculus Companion; supplied passages.

CheungXVIN

N. Cheung, XVI-N, revision r12, manuscript XVI-N.tex. Relevant label: thm:massless-obstruction. Conditional Route A obstruction and undischarged Route B discussion. Enter Calculus Companion; supplied passages.

CheungRegistry

N. Cheung, Enter Calculus Companion: registered manuscript catalogue. Registry and scope descriptions consulted 14 October 2026. A searchable source record, not a proof checker. https://enter.grok.me/