References

OpenAI212

OpenAI, Strict convexity and differentiability of the planar exponential first-passage limit shape, manuscript 212-02, 24 September 2026. External preprint record; its regularity assertions are conditional inputs in the present paper. https://github.com/openai/math

Companion212

Enter Calculus Companion, Family 212, manuscript 212-02. Catalogue and scope record, not independent proof verification. Accessed 14 October 2026. https://enter.grok.me/openai/212-02

CoxDurrett

J. T. Cox and R. Durrett, “Some limit theorems for percolation processes with necessary and sufficient conditions,” Annals of Probability 9 (1981), 583–603. doi:10.1214/aop/1176994364.

ADH

A. Auffinger, M. Damron, and J. Hanson, 50 Years of First-Passage Percolation, University Lecture Series 68, American Mathematical Society, 2017. https://arxiv.org/abs/1511.03262

NahumVijayHaah

A. Nahum, S. Vijay, and J. Haah, “Operator spreading in random unitary circuits,” Physical Review X 8 (2018), 021014. https://arxiv.org/abs/1705.08975

ZhouNahum2018

T. Zhou and A. Nahum, “Emergent statistical mechanics of entanglement in random unitary circuits,” Physical Review B 99 (2019), 174205. https://arxiv.org/abs/1804.09737

ZhouNahum2020

T. Zhou and A. Nahum, “The entanglement membrane in chaotic many-body systems,” Physical Review X 10 (2020), 031066. https://arxiv.org/abs/1912.12311

SkinnerRuhmanNahum

B. Skinner, J. Ruhman, and A. Nahum, “Measurement-induced phase transitions in the dynamics of entanglement,” Physical Review X 9 (2019), 031009. https://arxiv.org/abs/1808.05953

BrandCoopmansElkouss

S. Brand, T. Coopmans, and D. Elkouss, Efficient computation of the waiting time and fidelity in quantum repeater chains, 2019 preprint. https://arxiv.org/abs/1912.07688

LiCoopmansElkouss

B. Li, T. Coopmans, and D. Elkouss, Efficient optimization of cut-offs in quantum repeater chains, 2020 preprint. https://arxiv.org/abs/2005.04946

ItoLourenco

M. Itô and B. F. Lourenço, “The $p$-cones in dimension $n\ge 3$ are not homogeneous when $p\ne 2$,” Linear Algebra and its Applications 533 (2017), 326–335. https://arxiv.org/abs/1701.05801

Hoeffding

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

CheungEn05A

N. Cheung, Manuscript En05-A, version 1. Supplied excerpts: thm:cone, thm:invariantspeed. Scheduled locality and metric-envelope versus invariant-speed distinctions. Documentary comparison, not an imported model. Enter Calculus Companion. https://enter.grok.me

CheungEn05B

N. Cheung, Manuscript En05-B, version 1. Supplied excerpt: thm:main, isotropic matched operational existence for prescribed $c$. Documentary comparison. Enter Calculus Companion. https://enter.grok.me

CheungEn06B

N. Cheung, Manuscript En06-B, version 1. Supplied excerpt: thm:T, finite transport contract on the specified increasing-stencil family. Documentary comparison. Enter Calculus Companion. https://enter.grok.me

CheungEn08A

N. Cheung, Manuscript En08-A, version 1. Supplied excerpts: thm:main and conditional cone-representation statements. Scheduler consistency is not Lorentz-cone selection. Documentary comparison. Enter Calculus Companion. https://enter.grok.me

CheungEn08B

N. Cheung, Manuscript En08-B, version 1. Supplied excerpts: thm:main, prop:accumulation. Prescribed-boundary SWAP transport and accumulation of local error. The relevant accumulation pattern is re-proved here. Enter Calculus Companion. https://enter.grok.me

CheungVIIJ

N. Cheung, Manuscript VII-J, version 1. Supplied excerpt: thm:certificate, together with its scheduled, operational, and physical-causality distinctions. Documentary comparison. Enter Calculus Companion. https://enter.grok.me

CheungVIIIA

N. Cheung, Manuscript VIII-A, version 3. Supplied excerpt: A:thm:residual. Record agreement does not imply residual-channel agreement. Enter Calculus Companion. https://enter.grok.me

CheungEn09A

N. Cheung, Manuscript En09-A, version 1. Supplied excerpt: thm:main, relational destructive-Enter instrument and its consumption and covariance hypotheses. Documentary comparison. Enter Calculus Companion. https://enter.grok.me

CheungXIXC

N. Cheung, Manuscript XIX-C, version 1. Supplied excerpt: thm:main, finite incidence does not determine continuum evolution. Documentary comparison. Enter Calculus Companion. https://enter.grok.me

CheungEn07B

N. Cheung, Manuscript En07-B, version 1. Supplied excerpt: prop:no-landauer-from-channel. Channel equality does not determine a thermal implementation cost. Enter Calculus Companion. https://enter.grok.me

CheungXIVH

N. Cheung, Landmark XIV-H: Internal kernel relations on the operator route, version 1, supplied manuscript excerpts. Labels: prop:K5exact, thm:H2, thm:release. Documentary predecessor scope; no full characteristic map is imported. Enter Calculus Companion. https://enter.grok.me

CheungXIVI

N. Cheung, Manuscript XIV-I, version 1, supplied excerpts. Labels: prop:pole, thm:I2, thm:I3, thm:release. Constructed internal amplitude module and unresolved joint characteristic map, on their stated domains. Enter Calculus Companion. https://enter.grok.me

CheungXIVJ

N. Cheung, Manuscript XIV-J, version 1, supplied excerpts. Labels: prop:descent, lem:null, thm:reference, thm:conditionalextension, thm:J2, cor:noadmission. Descent and supported-sector reference are not the full joint map. Enter Calculus Companion. https://enter.grok.me

CheungXVB

N. Cheung, Manuscript XV-B, version 2, supplied excerpts. Labels: thm:lifting, thm:jetnull, thm:pointcorrection, thm:release. Standalone relative-lifting and extension interfaces; the graph-specific characteristic construction remains unresolved. Enter Calculus Companion. https://enter.grok.me

CheungXVIN

N. Cheung, Manuscript XVI-N, revision r12, supplied excerpts. Label: thm:massless-obstruction, with its explicit Route A hypotheses and undischarged Route B discussion. A conditional instance is not universal completion. Enter Calculus Companion. https://enter.grok.me