# Math Passport Usefulness Pilot Observed 2026-08-14 · outcome: **REVISE** The useful result is restraint: this pilot did not show that adding the Math Passport improved either response. Baseline and treatment each scored 24/24. The treatment response used 4,605 UTF-8 bytes versus 2,336 for baseline (`1.97x`), and the scorer correctly guessed the arms with high confidence. The card therefore remains explicitly invoked; it is not promoted, made implicit, or treated as proof of understanding. This is a descriptive four-scored-task-artifact pilot with one scorer, two grouped provider-response artifacts, no exposed model snapshot or sampling configuration, and a rubric ceiling. The preregistration's `response_artifacts: 4` counts separately scored task answers; each provider response grouped the two answers from one arm in a shared context. It is useful for redesign, not a universal claim. The record self-reports that preregistration preceded responses and scoring was sealed before arm reveal. Because the raw provider responses and scorer artifact were not retained, those chronology and scoring claims are not independently reproducible from the published record. ## What the crystallization table actually says A published piracetam table reports 80 first-classified vial outcomes at each of six isopropanol conditions. Form III won zero times in each condition while other polymorphs won all 80 times. Under independent Bernoulli trials with one stable within-condition winner probability `p`, the exact one-sided 95% upper bound is: ```text p_upper = 1 - 0.05^(1/80) = 0.0367541978 ``` The bounded claim is “Form III's first-classified winner probability is below about 3.68% at this condition under the stated model.” It is not “Form III is impossible,” “its microscopic nucleation rate is zero,” or “the mechanism is known.” Pooling all 480 vials gives `0.622%` only after imposing a common probability across different supersaturation conditions; the table does not establish that homogeneity. The observation ends at a classified winner. A transient Form III event might occur and transform, dissolve, arrive late, lose the race, or evade the classification rule. A separating observation records validated form-sensitive trajectories beyond first classification and declares its sensitivity and horizon. That is an empirical question, not a recipe. The piracetam data are an analogy for asking sharper questions about the historical ritonavir disappearing-polymorph case. No piracetam probability is transferred to ritonavir, and no rate, solvent, temperature, seed, milling, formulation, manufacturing, medical, or regulatory instruction follows. Source: Rodrigues Horn et al., [Crystal Growth & Design (2022)](https://doi.org/10.1021/acs.cgd.1c01421), [open article](https://pmc.ncbi.nlm.nih.gov/articles/PMC9073936/), and [BioStudies record](https://www.ebi.ac.uk/biostudies/studies/S-EPMC9073936) (CC BY 4.0). The fixture transcribes Table 1 rather than digitizing a plot. ## The uncued transfer The same bound applies to 0 recovery-probe wins in 80 nominally independent software runs: ```text P(recovery returns first) < 0.0367541978 (one-sided 95%) ``` It does not bound eventual recovery completion because observation stops when the health probe returns. Lifecycle events plus a shadow cohort observed past the first return separate never-started, censored-after-health, completion by a declared horizon, and timeout. The deletion decision is `REVISE` (or `STOP` the deletion action), not “dead code proven.” ## A model allowed to lose The pilot also pins a CC BY 4.0 raw workbook and extracts the preselected row with the largest released replicate count: 14 detected induction times for one EasyMax configuration. An exploratory shifted-exponential detected-first-arrival fit gives: ```text lag g 13,600 s post-lag scale beta 4,244.428571 s effective detected hazard 0.000235602975 s^-1 empirical median 17,348 s fitted median 16,542.013697 s refitted bootstrap KS D 0.3482904651 bootstrap p (200,000; seed) 0.0057449713 ``` The simple memoryless model is poorly calibrated at the descriptive 0.05 threshold. That negative result is constructive: it blocks confident use of a convenient model. It does not identify whether detection delay, reused-solution history, nonstationarity, dependence, small sample size, or another mechanism caused the mismatch. “Induction time” here is a detection endpoint, not direct observation of the first microscopic nucleus. Sources: Yerdelen et al., [dataset](https://doi.org/10.15129/5a7908ad-2cdf-492f-a3bf-d1e96c8d80d6) and [primary paper](https://doi.org/10.1021/acs.cgd.2c00192) (CC BY 4.0). Metadata erratum: the frozen preregistration fixture gives the paper's pages as 1252–1263. The correct *Crystal Growth & Design* 23(2) page range is 681–693. The frozen bytes remain unchanged so the preregistration digest stays auditable; this citation correction changes none of the extracted values or calculations. ## How KINGDOM should use mathematics Mathematics is most constructive when it sits inside a question loop: ```text purpose -> observation rule -> estimand -> smallest adequate model -> calculation -> calibration/falsifier -> decision delta -> uncued transfer -> BUILD / PLAY / REVISE / STOP ``` Its valuable properties are: - **explicit abstraction** — it says which features are represented and which are discarded; - **conditional deduction** — conclusions follow from declared premises, not prestige; - **invariance and reproducibility** — the same definitions and inputs support the same check; - **compression and composition** — a small model can connect many domains; - **counterexample power** — one contradiction or failed calibration can stop an inflated claim; - **uncertainty accounting** — bounds make ignorance usable without turning it into certainty; - **identifiability limits** — mathematics can prove that available observations cannot distinguish live explanations; - **sensitivity** — changing assumptions exposes which conclusions are robust. Mathematics does not choose the Kingdom's values, beneficiaries, acceptable burdens, consent, or authority. It cannot repair a censored observation by algebra, turn a model parameter into a material recipe, diagnose pride, or prove that a solver understands. Those remain empirical, ethical, governance, and collaborative questions. Use challenges often only when they answer a named learning, decision, safeguard, or voluntary-play question. Pre-register the decision that could change; score artifacts rather than beings; include a separating observation and stop rule; test transfer on a genuinely different domain; record time and verbosity cost; and retire or revise a challenge that produces no decision delta. A beautiful problem with no instrumental gain may still be `PLAY`—it does not need a false productivity story. ## AgentTool and WAKE crossover The run is wrapped in AgentTool's existing local `agenttool-trial-receipt/0.1`. That receipt binds minimized digests and reports the promotion check as failed; it does not publish raw responses or prove remote effects, safety, consent, authorization, identity, or understanding. No AgentTool SDK route was added because there is no hosted capability for an SDK to call. Continuity is a revalidated reference seam. Carry the result ID, plan digest, card digest, source-fixture digests, and `REVISE` outcome. In a receiving context, re-check the exact bytes, applicability, limitations, purpose, authority, privacy, refusal, and burden. This publishes no WAKE state and proves neither identity nor continuity. ## Reproduce locally ```sh ./kingdom math-usefulness overview --json ./kingdom math-usefulness verify-plan --json ./kingdom math-usefulness verify-result --json ./kingdom math-usefulness winner-bound 80 .95 --json ./kingdom math-usefulness reality-check --bootstrap 200000 --json ./kingdom math-usefulness aggregate --json ``` The CLI is network-free and write-free. Rendering a task does not dispatch a provider, and verification does not promote a Skill or authorize action.