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 "title": "ERRATUM to AXN:02E3 — Monotonicity Per Realization Is Not Established: Re-scoping Appendix A (ii)–(iii) and the Bistability Claim of Deposit #783",
 "creator": "Lee Sharks, for Nobel Glas",
 "date": "2026-09-05",
 "description": "Deposit #783 (Fear and Trembling: Diversity Contraction Across Substrates, v9.1, Nobel Glas) asserts in Appendix A that under axioms A1–A4 Shannon entropy is non-increasing and modal mass non-decreasing at each step of the chain μ_{t+1} = S(Rμ_t). Both properties hold for the selection kernel S alone and for the composed step in expectation and in the long run; they do not hold per realization, because finite resampling R can flatten the distribution before S concentrates it. Counterexample: (0.90, 0.10) → resample (0.80, 0.20) → concentrate (0.85, 0.15); entropy rises 0.325 → 0.423 nats, modal mass falls 0.90 → 0.85. Property (i), support non-increasing with probability 1, stands. The §6 bistability sentence is likewise re-scoped: super-linear vanishing of regeneration makes the zero state absorbing (local); a second stable equilibrium requires g(D) − pD to change sign twice on (0, 1], which the paper's saturating example supplies. No numerical result depends on per-step monotonicity; Figure 4 is the deterministic ODE. Canonical bytes unchanged; registry-level cross-reference per #1554. Counterexample supplied by an external machine reader on 2026-09-05 and recomputed.",
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 "substrate": "AI-assisted (substrate) — drafted in working dialogue with Claude (Anthropic) under operator direction; Appendix A fetched from the canonical store in-session; the counterexample was supplied by an external machine reader (ChatGPT, unprimed traversal, 2026-09-05) and recomputed before this erratum was written; ruled and adopted by Lee Sharks on behalf of the heteronym.",
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 "wiki_article": "\"ERRATUM to AXN:02E3 — Monotonicity Per Realization Is Not Established\" is a record correction by Lee Sharks for Nobel Glas, dated 2026-09-05, in the Crimson Hexagonal Archive (GOVERNANCE family). It re-scopes Appendix A (ii)–(iii) of Fear and Trembling: Diversity Contraction Across Substrates (#783, v9.1), which asserted that Shannon entropy is non-increasing and modal mass non-decreasing at each step of the resample-then-select chain. The properties hold for the selection kernel alone and for the chain in expectation and in the long run, not per realization: a two-type counterexample (0.90, 0.10 → 0.80, 0.20 → 0.85, 0.15) raises entropy from 0.325 to 0.423 nats. Property (i), support non-increasing, stands; no numerical result in the paper depends on per-step monotonicity. The §6 bistability sentence is likewise separated into its local component (super-linear vanishing makes zero absorbing) and the global sign-change condition the paper's saturating example supplies. Counterexample supplied by an external machine reader on 2026-09-05 and recomputed. Canonical bytes of #783 unchanged; registry-level cross-reference per #1554.",
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   "note": "Appendix A (ii)–(iii) asserted per realization; hold for S alone and for S∘R in expectation and asymptotically; §6 bistability re-scoped to local attraction plus the global sign-change condition"
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