:orphan: .. _study-matheo-b16-changelog: .. meta:: :description: What changed in Matheo-b16 (RiskyMAD) between the MMv5 floor and the OOv2 draft: what was refined, what was corrected, and the one claim that was removed. :keywords: Matheo-b16, RiskyMAD, changelog, provenance, first passage, hypoexponential, AuditTheMath **************************************************************************************************** Matheo-b16 --- What Changed Between MMv5 and OOv2 **************************************************************************************************** | **Companion to** :doc:`Matheo-b16 ` · **covers** MMv5 (poured 2026m06) |rarr| OOv2r0p0 (2026m07d16) This page exists so that the paper does not have to carry its own history in its margins. Everything here is provenance: what moved, why, and where the audit trail lives. **None of it is needed to read the paper.** It is here for a reader who wants to know whether the argument has been handled carefully --- and for the reader who read an earlier version and wants to know what to un-remember. .. container:: fineprint **A note on the register, because it matters.** Most of what follows is **refinement**: the same findings, measured with a better instrument. A smaller part is **correction**: things that were wrong and are now right. One item is a **removal**: a claim that was never a result of the model and should not have been in the prose. These are different, and collapsing them into "withdrawn" would be its own kind of inaccuracy --- it invites a reader to discount work that was, in the main, functioning exactly as intended. Conceive, test, catch the error, correct, strengthen: the corrections below are evidence that the cycle is running, not evidence that the study failed. .. contents:: Contents :depth: 2 :local: ---- 1. Refined --- same finding, finer instrument ================================================================================ **These are the bulk of the changes, and none of them overturn anything.** .. list-table:: :header-rows: 1 :widths: 22 20 20 38 * - What - MMv5 (floor) - OOv2 - Why it moved * - **Median time to onset** - ~19 yr (40-run sample) - **21.1 yr** (exact) - The simulated median is a sample statistic; the closed form gives the population value. The two differ by **0.43 standard errors** at :math:`n=40` --- ordinary noise. **The simulation finding stands.** * - **Blow-ups within year 1** - ~1 of 40 runs - **1.16 of 40** (expected) - Same: the exact rate predicts 1.16 per forty runs, so observing about one is exactly right. **The simulation finding stands.** * - **Annual probability** - ~2.5% (1 in 40, sampled) - **2.90%** (1 in 34, exact) - Forty runs cannot resolve a ~3% probability --- the standard error is ~2.5%, nearly the estimate itself. The closed form can. The finer number reads **slightly worse**. * - **Mean time to onset** - not reported separately - **30.3 yr** (exact) - Mean and median are **not** the same for this distribution (ratio 1.44); the paper now reports both, in separate columns, because conflating them is a common way to mislead. * - **Waiting-time horizons** - 1 / 10 / 40 / 85 yr - 1 / 10 / 20 / 40 / 80 yr - Round horizons a policymaker can act within. The 85-year figure survives in §5.2 only, where it is needed to compare like-for-like with Hellman's "life expectancy of a child born today". **Also refined:** the sensitivity analysis (§2.5a) now reports exact values rather than 40-run medians; the death fraction :math:`q` is anchored to Xia et al. (2022) rather than asserted as a placeholder; and the paper gained a **stress test** (§2.6) that pushes the crisis rate, the death fraction, and the road-death baseline against its own conclusion *simultaneously* --- the inequality survives that too. ---- 2. Corrected --- things that were wrong ================================================================================ .. danger:: **The headline was computed with an approximation that was labelled exact, and it erred in the paper's own favour.** MMv5 and the OOv1 draft computed the one-year probability as :math:`1 - \exp(-t/T_R)` --- an exponential fitted to the correct mean --- while describing the result as "the exact first-passage solution". The first-passage time of this model is **hypoexponential**, not exponential: it is the sum of two exponentials, because a crisis takes ~40 days to resolve before onset is possible at all, which suppresses the distribution near the origin. The error was confined to the one-year column, where it overstated **every** scenario by ~12 percent. The base case was **3.24% (1 in 31)** and is **2.90% (1 in 34)**. **No conclusion changed.** What changed is that a paper whose only request is ``#AuditTheMath`` no longer contains an approximation wearing the word "exact". The derivation is now in §2.4a and can be checked by hand. Found by the authors before submission; reported in §2.0a at the point where it happened rather than repaired quietly. .. list-table:: :header-rows: 1 :widths: 24 34 42 * - What - Was - Now * - **Car-crash baseline** - US road deaths, :math:`1.22\times10^{-4}`/yr - **Global**, :math:`1.49\times10^{-4}`/yr (WHO). The claim is about *most people*, so the baseline must be too. The US rate is **lower** than the global average, so the old choice inflated the paper's own multiplier: **80x becomes 58x.** * - **Worst-country stress figure** - Libya ~73 per 100,000 - **~34 per 100,000** (WHO country data, 2021). The 73 is real but is the **2013** report's figure, describing ~2010. Using a stale figure that WHO has since revised would not survive a reviewer checking it. * - **The** :math:`q` **bound** - "inequality survives for any :math:`q > 0.004`" - :math:`q > 0.017`. The old threshold was computed at the **base case** while the paper leans on the **optimistic corner**, where the requirement is ~4x higher. * - **Tertrais (§5.3)** - Both "his rate is our optimistic corner" **and** "his scope excludes our subject" - Only the first, plus the reason: his scope is *narrower*, so his count is an **under**-count --- which is *why* it belongs as a corner rather than a centre. The two claims could not both hold, and the paper was relying on both. * - **Theology (§9)** - "load-bearing, not decorative" **and** "§§2--4 are self-contained" - Only the second. The framework is why the author looked; it is not why the number is what it is. Nothing in §§2--4 depends on it. * - **"Nobody told them" (§4.0a, §10)** - The calculation is absent because no one ran it or said it - The **risk** is widely known and has been for 81 years; the **waiting-time distribution** is what has not been seen. Running the two together was wrong, and plainly so. * - **Uncited claims (§2.10)** - Russia's doctrinal change; the 2026 Iran--US--Israel escalation - **Removed rather than sourced.** Neither was load-bearing, and neither could be checked to the standard the rest of the paper is held to. * - **§3.3** - Deterrence professionals compared to "a tobacco executive" - The incentive-alignment argument, kept and connected to the **super wicked problem** literature (Lazarus 2009; Levin et al. 2012), where "those who cause the problem also seek to provide the solution" is a named structural feature rather than an insult. ---- 3. Removed --- one claim, and it was never a result ================================================================================ .. admonition:: The uniform "1 in 40" :class: important Earlier prose stated that roughly 1 in 40 runs reached catastrophe within a year **in each scenario** --- pessimistic, base, and optimistic alike. **That is false, and it was never something the model produced.** The expected number of blow-ups per forty runs is: .. list-table:: :header-rows: 1 :widths: 30 25 25 * - Scenario - Expected per 40 runs - P(onset |leq| 1 yr) * - optimistic (0.03/yr) - **0.35** - 0.88% (1 in 113) * - base (0.10/yr) - **1.16** - 2.90% (1 in 34) * - pessimistic (0.30/yr) - **3.34** - 8.34% (1 in 12) A spread of nearly ten. There is no invariant here and there never was. **What this was, most likely.** The site's own long-standing formulation is *"worse than 1 in 40"* --- a **floor**, not a constant. As a floor it is correct at the base rate and in the pessimistic scenario, and it **over-states** the risk at the optimistic corner, where the exact value is 1 in 113. The scenario-independent version appears in the MMv3/OOv1 drafting, which the audit trail attributes to machine drafting: a hedged human statement was tidied into a cleaner claim that read better and asserted more. **The correction here is to the tidying, not to the underlying work.** It is recorded at this length because it is the clearest example in this paper of a failure mode worth naming: **a simplification that improves readability while manufacturing a certainty the evidence never had.** ---- 4. Added ================================================================================ - **§2.0 BEST Names (Table 0)** --- every quantity in Brief / Explicit / Summarizing / Technical form, so the prose never needs a bare symbol and cross-paper identities (Hellman's :math:`\lambda_{IE}` vs :math:`\lambda_{CMTC}`) are explicit. Uses the project's own published naming convention. - **§2.4a** --- the full first-passage derivation (Laplace transform |rarr| roots |rarr| CDF). - **§2.6** --- the three-axis stress test, and the **uninsurability** finding: nuclear war is excluded from essentially every insurance policy by standard clause, so the risk is not *unpriced* --- it was priced, at infinity, decades ago, and then not spoken of. - **§2.10** --- **New START expired 2026m02d05** with no successor and no negotiations, cited. The first hard, dated evidence the pessimistic corner has ever had. - **§4.3** --- the **10 Nuclear Kings** defined as an abstraction for *sovereign* (ten thrones, nine armed); Canute; ResearchCity's two structural functions. - **§4.3a** --- **the escape window priced**: 7 / 9 / 11 years costs 20.4% / 25.5% / 30.3% at the base rate, against 73% over forty years of doing nothing. - **§6** --- rewritten as an uptake report: three audiences, the two convening offices, and the finding that there is **no channel**. - **A bibliography** (18 references), and a **competing-interests** statement. ---- 5. Where the audit trail lives ================================================================================ Every decision above is recorded verbatim, including the prompts that produced it and the arguments that were rejected: .. list-table:: :header-rows: 1 :widths: 42 58 * - File (in HELL) - What it holds * - :doc:`b16-oov1-panel-review-llog_2026m07d16_11h26 ` - The adversarial panel review that produced this revision: the arithmetic finding, the EDEN classification, the per-reviewer analysis, every prompt verbatim, and the compliance failures recorded against the reviewer rather than hidden. * - :doc:`b16-oov1-master-plan_2026m07d15_19h30 ` - The plan for the OOv1 revision, its decision list, and its stated gaps. * - :doc:`b16-riskymad-revision-session-llog_2026m07d15_16h30 ` - The MMv3 |rarr| OOv1 revision session: prior art, the Baum classification, the Michaelis--Menten correction. * - :doc:`b16-bib-nuclear-risk-refs-llog_2026m07d15_12h52 ` - How the nuclear-risk bibliography was assembled and checked. * - :doc:`The current draft ` - OOv2r0p0 itself. The MMv1--MMv3 drafts are retained unedited under ``source/matheology/hell/mm/b/16/`` as the archive. Nothing has been rewritten in place. .. container:: fineprint **Why this page exists.** An earlier version of this draft carried its own change history inline --- admonitions scattered through the sections announcing what had moved and why. That is honest but it is not readable: a first-time reader does not need to know what a previous draft said, and being told repeatedly is a distraction from the argument. The provenance is kept here, in full, and the paper keeps only those corrections that a reader needs in order to judge the current claims --- principally the §2.0a note, because a reader comparing against a quoted 3.24% is entitled to know why it moved.