{ "workTitle": "Causal prediction of rare recovery responses and the optimal scale of observation time", "sourceVersion": "2026-11-11.2", "sourceEntryPoint": "main.tex", "humanContributor": { "name": "HUANG Man", "orcid": "0009-0003-3809-5105" }, "aiTools": [ { "provider": "OpenAI", "name": "GPT models", "models": [ "GPT-6.1 Sol" ] }, { "provider": "xAI", "name": "Grok", "models": [ "Grok 4.7" ] }, { "provider": "OpenAI", "name": "Codex", "usage": "Proof review, manuscript restructuring, diagnostic code, consistency checks and local submission-package preparation." } ], "assistance": "Literature synthesis, theoretical and argumentative structure, proof drafting, mathematical checking, language revision and local packaging, as disclosed in the manuscript.", "verificationEvidence": "Mathematical proofs are in the main text and Technical Supplement A–E in the same document. Finite diagnostic code is available separately in the linked Zenodo archive.", "licenses": { "hexagonSubmission": "CC BY 4.0", "originalCodeInZenodo": "MIT" }, "canonicalText": "English canonical Markdown and regeneration scripts are retained in the local submission record. The public bilingual source archive is linked above.", "referenceStatus": "Harris (1960) is cited for historical attribution; its original full text was not acquired. The independent-coordinate inequality is attributed through van den Berg and Kesten (1985, Section 3), and a heterogeneous Bernoulli product proof is supplied in the supplement. This source package includes no third-party literature full texts.", "declarations": { "textOrigin": "Primarily AI-generated", "humanUnderstanding": "Some parts of this contribution, but not all, have been checked and understood by a human.", "formalization": null, "humanUnderstandingSource": "Author response on 2026-11-12" }, "distributionStatus": "Prepared for the author-authorized Hexagon submission; platform receipt recorded separately.", "edition": "English Hexagon submission, 2026-11-12", "publicBilingualArchive": "https://doi.org/10.5281/zenodo.24138927", "codeArchive": "https://zenodo.org/records/24138927/files/Paper3_bilingual_source_and_code.zip" }