Topics — What a work is about. Nucleation holds whatever reading the owner files here, whether or not an Anthology of the SOTA topic could also hold it; instruction for ML practice belongs to the anthology (ADR-048). The words are seeded from the clusters the reading-time triage of 2026-09-25 found, and grow by decision.
Mathematical statistics — the theory of statistical inference read for itself — comparison and sufficiency of experiments (Blackwell, Le Cam deficiency), statistical decision theory, the sufficiency theorems (Fisher–Neyman, Basu, Bahadur) and bounds on estimation. Bayesian modelling is probabilistic-modeling (ADR-031).
27 of 547 CLAIM documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| CLAIM-014 | Krifka’s performative updates fix which changes in conversational standing count, and Blackwell comparison tests whether a rendering preserves the information needed to recover them | A93 §5, recovered: “could become one of the manuscript’s distinctive theoretical integrations.” Krifka was in C6’s references and A93’s priority list (ninth) and is absent from the manuscript and the record. | Proposed |
| CLAIM-050 v6 | For report fidelity, fidelity is relative to the communicative decisions receivers make, and Blackwell’s order on rendering procedures, over a designed distribution of situations, makes precise the ceiling a rendering sets on those decisions | The manuscript’s §5: rate–distortion makes coding cost explicit, Blackwell comparison (restricted to a family Q of communicative decision problems) makes fidelity operational, and decoder side information is a Wyner–Ziv problem. | Active |
| CLAIM-126 v3 | Model stitching tests whether a transport preserves decision-relevant information only in its reconstruction form: a map fitted to reproduce the target representation certifies one direction of Blackwell sufficiency, while task-loss stitching compares one decision problem through a fixed head, and a failure to stitch is no evidence against sufficiency | Proposed by the record on 2026-10-09 as an operational handle on the decision-relevant half of CLAIM-125, and qualified by the reading of Bansal, Nakkiran & Barak before it was filed: only reconstruction-fitted stitching certifies sufficiency, and only within the map class. | Active |
| CLAIM-135 v3 | Recovering latent structure from relational data is three achievements, reconstruction, identification up to stated ambiguities, and constitution of a communicative kind, and identifiability theory reaches the second at most | The assistant’s, at A207 §5 (three profiles) and A214 §1 (three problems, two warrants), kept as A218 §5’s five objects of inquiry. A214 asked for it as a THEORY; it is the record’s own distinction, so it is a claim. It answers QUESTION-001 in part, by naming a failure that question did not. It does not say identified factors are never kinds, or that the second step is open. | Active |
| CLAIM-152 v6 | Any individuation built on sufficiency is relative to the target it is sufficient for: fix the outcomes differently and a different partition wins, so no boundary drawn this way is universal | Dual-filed from MOM-POS-001 (ADR-037). A sufficient statistic is sufficient for a target Y, so every partition chosen as minimal sufficient inherits Y. MOM’s example: fix the outcomes differently and “organism” wins instead of “animal”. In this record it is the standing caution on every boundary criterion filed beside it (CLAIM-154, CLAIM-161). It does not say boundaries are arbitrary, only that each is relative to a stated target. | Active |
| CLAIM-209 | Probes and statistical models recover only the distinctions identifiable from the relational evidence they are given, and a signature sufficient for a stated family of communicative decisions outside the observed probes can be identified when the full latent factorization is not | The assistant’s second thesis at U62 (A240 T2), the positive answer to QUESTION-027. It has now been asserted four times: A214 §7, A218 (RQ3 and the priority theorem target), A232 (§3.2 and F2) and A240. Filed with QUESTION-027’s scope: the unrestricted claim is answered by standard results, so its content is in decisions outside the observed probes. No signature is yet named. A proposal; the owner argued none of it. | Proposed |
| CLAIM-218 | The task-paired risk difference the record uses in place of Blackwell’s order, D_Q = sup_q |R_q(U) − R_τ(q)(V)|, is a different quantity: it reduces each risk set to one number, needs the losses of paired tasks on one scale, and its absolute value counts improvement as distortion | Found in the record’s audit of the line on 2026-10-10 (formal lens); no turn of the exchange raises it. CLAIM-050 is stated in Blackwell’s order, and the record’s decision term is A86’s D_Q. A risk per task needs a prior or a minimax summary, where Blackwell’s order compares whole risk sets. Subtracting the risks of two tasks needs their losses on one scale, which nothing supplies. The absolute value makes D_Q symmetric, against CLAIM-106. Granted, because each point is elementary. It objects to CLAIM-106 by undermining the measure meant to realize it, not CLAIM-106’s truth, and it does not say a decision term is unworkable. | Active |
| CLAIM-228 v4 | D_obs restated over a rendering procedure, with one kernel family fitted on some source items and scored on held-out ones and the target term the readers’ response averaged over the procedure’s output, separates rendering procedures that receivers’ task-indexed recovery separates, so restated it measures observational fidelity informatively | The record’s repair, on 2026-10-10, of the manuscript’s L_obs and the profile’s D_obs after CLAIM-207, CLAIM-230 and CLAIM-235. For one pair a constant kernel makes D_obs zero (CLAIM-207); fixed across items, it fits only if the target readers’ responses do not vary with the item. The repair ties the outcome-level kernels to the text channel, makes the transport a property of a procedure (CLAIM-230), and makes deficiency a finite computation over judgement outcomes (CLAIM-235). A proposal: the derivation is elementary, but whether the restated measure is informative is the defeat condition’s empirical question. It does not say a fitted kernel is the translator’s process. | Proposed |
| CLAIM-230 v3 | Blackwell comparison needs the state each rendering is about, which natural texts do not supply, so a decision measure is fixed by whoever labels the state, and it orders translation procedures, not single renderings | Found in the record’s audit of the line on 2026-10-10 (empirical lens); no turn of the exchange raises it. Testing Blackwell’s order needs the joint law of the situation and the signal. For natural texts the situation is what interpretation recovers, so it comes from the stimulus design, the analyst’s labels or the judges, and decision-relevant information is measured against whoever fixed it. An experiment is a family of distributions, one per state, so a single rendering of a single poem is not one. CLAIM-050’s defeat condition, “one rendering is a garbling of another”, is then not well typed. It does not say a design-based state is illegitimate. | Active |
| CLAIM-235 v3 | The line’s proposed quantities have no finite-data estimators: plug-in signalling from one or a few occurrences per context is positive in expectation when the true marginals agree, so the contextual fraction is undefined on raw tables, and deficiency over text-valued renderings has no estimator | Found in the record’s audit of the line on 2026-10-10 (formal and empirical lenses); no turn of the exchange raises it. The plug-in signalling of two empirical marginals is positive in expectation when the true marginals agree, so raw tables signal, and the contextual fraction is undefined on them. With one occurrence per context, a non-signalling rank-2 system gives Δ of 0, 2 or 4, with expectation 2: the values NOTE-654 finds in 51 of the 90 systems behind CLAIM-125’s “69 of the 90 systems signal”. The data are author-assigned corpus senses, not judgements. Deficiency over text-valued renderings has no estimator. It does not say signalling is rare in pragmatic judgements, where order effects are themselves signalling. | Active |
| CLAIM-237 v2 | The first open problem of directed transport is not yet posed: a contextual model is a menu of incompatible experiments, and under the natural order on menus any state-independent classical simulation is dominated automatically, so what is open is only the converse or a deficiency bound | Found in the record’s audit of the line on 2026-10-10 (formal lens); no turn of the exchange raises it. Blackwell’s order compares experiments, each a family of distributions over one parameter. An empirical model has no parameter, and if it is contextual it has no joint distribution, only one per context. Posing CLAIM-125’s first part needs models indexed by situations and an order on menus of experiments. Under the natural order, the preservation direction is automatic for a classical simulation that does not depend on the situation. Granted, because the argument is elementary. It narrows what is open; it does not close it. | Active |
| CLAIM-238 v2 | Many of the line’s defeat conditions cannot in practice be met: the comparative ones are null results with no margin over an observable set the thesis may re-choose, and the possibility theses’ are universal negatives that no finite study establishes | Found in the record’s audit of the line on 2026-10-10 (empirical and structure lenses); no turn of the exchange raises it, though CASE-029 records the decision rules that were dropped. Three shapes of defeat condition cannot be met. “As well as” is a null result, which needs an equivalence margin and power, and no entry states either. The observables are “not fixed in advance” (CLAIM-115). And the “can” theses are defeated only by “never” or “always”, so one construction confirms them and no study refutes them, while what the main thesis needs from them is prevalence and magnitude, which none states. Granted: each point is read off the texts. It does not say the theses are false or untestable in principle. | Active |
| CLAIM-258 v2 | Blackwell’s order compares experiments about one parameter, so it does not reach the normal translation case: source and target readers decide about situations with changed coordinates, and where the state is common a translator with context knowledge yields a rendering that is not a garbling of the source, which the order typically leaves incomparable with it and about which the direction the manuscript uses is silent | Found in the record’s audit of the line on 2026-10-10 (formal and structure lenses); no turn of the exchange states it. CLAIM-050’s comparison is over one state Z. Compensation (CLAIM-091) changes the social coordinates, so the target reader decides about a different situation. Where the situation is common, a translator who knows the context makes a rendering that depends on Z other than through the source, so it is not a garbling. Blackwell’s order is still defined then, but typically leaves source and target incomparable, and the direction the manuscript uses says nothing. It does not say decision-relative fidelity is wrong. | Proposed |
| CLAIM-259 v2 | For report fidelity, the decision term should be the positive part of the risk increase on the same decision problem, with losses in [0, 1] and a stated prior; so restated it is directed, counts no improvement as loss, and vanishes for every problem and prior exactly when the rendering is at least as informative as the source in Blackwell’s order | The record’s repair, on 2026-10-10, of A86’s D_Q after CLAIM-218. Define D⁺_Q(U → V; π) = sup over q in Q of [r_q,π(V) − r_q,π(U)]⁺, with r the Bayes risk under the prior π. It is directed and blind to improvement. With Q all finite problems and π all priors, it is zero exactly when V is at least as informative as U in Blackwell’s order, by the Bayes form of Blackwell’s theorem for finitely many states. A86’s D_Q, with the identity on tasks, is its symmetrization. Under report fidelity (CLAIM-212) the paired task is the same task, so no scale between tasks is needed. The mathematics is checkable; the claim that this is the right decision term is a proposal. It does not say Q is fixed. | Active |
| CLAIM-268 v2 | Model stitching certifies an order of information only in its reconstruction form: a map fitted to reproduce the target layers shows the source representation is at least as informative for every decision on the label, task-loss stitching compares one decision problem through a fixed head, and a failure to stitch is no evidence against sufficiency | The general content of CLAIM-126, filed alone under ADR-040 so that the result about stitching does not rest on CLAIM-050’s account of fidelity. Reconstruction-fitted stitching makes the target a garbling of the source given the label, which certifies one direction of Blackwell sufficiency (THEORY-176). Task-loss stitching (LIT-850) compares one decision problem through a fixed head, orders neither representation, and is not invariant under reparametrisation. In both forms a failure says only that no map in the class works. | Active |
| CLAIM-300 | A state sufficient for a family of decisions under a model makes the rest of an inquiry’s history worthless for those decisions, and it can stop being sufficient when a source is discredited, the model is revised or the decisions change | A10’s answer to the owner’s U10, with A8’s fourth case and A10’s normal constructions (CASE-082, CASE-087). Under a fixed, correctly specified model a sufficient posterior makes the history redundant for those decisions. The same sample mean that sufficed cannot say which reading remains when one instrument is discredited, or test a mixture. Sufficiency was always relative to the model and the family. CLAIM-152 says the same of individuation by target; this says it of a retained state over time. | Active |
| CLAIM-305 | Resolving a singularity by blow-up reparametrizes the states and adds no observation, so it cannot make indistinguishable states distinguishable: every point over a singular point gives the same distribution, and the Fisher information can stay degenerate there; what the resolution buys is a normal form for the divergence, and so the learning coefficient | The owner’s LEGO monograph says, in Part I (chapters 4, 6, 7, 9, the Overview and “Definitions and Theorems”), that blow-up “restores identifiability”, “introduces new observables” and makes the Fisher information non-degenerate, and maps it onto splitting a LEGO bin. The pulled-back model is p(x | π(u)), a function of u only through π(u), so every point of the exceptional divisor gives the distribution of the singular point. In p(x | a, b) = N(ab, 1), the chart a = u, b = uv gives mean u²v and a Fisher matrix of zero all along u = 0. Splitting a bin is refining the observable, which can separate states. MOM-CLM-099 records that the monograph uses “blow-up” in three senses; this records why the analogy cannot hold in any of them. | Active |
| CLAIM-323 v2 | Where source and rendering are experiments about one common situation, a rendering that depends on the situation other than through the source is not a garbling of it and can be incomparable with it in Blackwell’s order: with Z uniform on {1, 2, 3}, a source that tells whether Z = 1 and a rendering that tells whether Z = 3 each have the lower 0–1 risk on one of the problems of saying whether Z = 1 and whether Z = 3, so neither dominates | Split from CLAIM-258 under ADR-043: the worked case that objection uses, stated on its own so that its warrant can be. Over a common situation Z uniform on three values, U reports whether Z = 1 and V whether Z = 3. V is not a garbling of U, since given U = 0 it still varies with Z, and the risks on “say whether Z = 3” (0 from V, 1/3 from U) and “say whether Z = 1” (the reverse) show neither experiment dominates. It is an existence result by construction. It does not say this is the normal translation case, which is CLAIM-258’s reading and is interpretive. | Active |
| CLAIM-326 v5 | With losses in [0, 1] and a stated prior, the positive part of the Bayes-risk increase on the same decision problem, D⁺_Q(U → V; π), is directed, is zero from a garbling back to its source, vanishes for every finite problem and prior exactly when the rendering is at least as informative as the source in Blackwell’s order, over finitely many states and a source whose outcome space is standard Borel, and has A86’s D_Q, with the identity on tasks, as its symmetrization | Split from CLAIM-259 under ADR-043: the properties of the restated decision term, which CLAIM-259 called “elementary and checkable”, stated on their own so that their warrant can be. Define D⁺_Q(U → V; π) = sup over q in Q of [r_q,π(V) − r_q,π(U)]⁺. A garbling never gains; with Q all finite problems and π all priors, the term vanishes exactly when V is at least as informative as U, by the Bayes form of Blackwell’s theorem for finitely many states (THEORY-156); it is directed; and A86’s D_Q is its symmetrization. It does not say this is the right decision term, which is CLAIM-259’s proposal, and it does not state the prior-free relation to Le Cam’s deficiency. | Active |
| CLAIM-333 | Measuring every relevant variable is necessary but not sufficient for a Granger-causal analysis to say anything about interventions: the intervention must also be an isolated exogenous change and no influence may act within one sampling step, and then Granger noncausality implies no intervention effect and the effect is identified from the observational predictor, but a Granger-causal relation is still only potentially causal | The record’s answer to NOTE-010’s C5, “if all relevant variables are measured, Granger- and Pearl-type analyses coincide”, which the ΦID review asserts without conditions. Eichler and Didelez (THEORY-704) give sufficient conditions, and complete measurement is one of them. A two-variable process with nothing hidden shows it is not enough: a acts on b within one step, a is Granger-noncausal for b, and setting a(t) changes the mean of b(t + 1) by ργ. Checked by hand and by simulation. | Active |
| CLAIM-350 v2 | A coarse-graining preserves a deterministic judgment exactly when the judgment is constant on its fibres: the judgment then factors through the coarse description, uniquely on its image, and otherwise two states the judgment tells apart have been merged | A21 §3 and §18 (Candidate 1) of the exchange of 2026-10-17, and A22’s Construction A: for a judgment J and a coarse-graining C on the same states, J = j∘C for some j exactly when C(x₁) = C(x₂) implies J(x₁) = J(x₂). Granted, because it is elementary (the universal property of a quotient) and Ak’s; the proof is in the body. It is CLAIM-152’s judgment-valued special case with the converse added: CLAIM-152 says a partition sufficient for one target need not be for another, and this says which partitions serve a deterministic judgment, those whose fibres lie inside its level sets, so the coarsest is the judgment’s own partition. The sharp edge: it says when a description keeps a judgment, never whether the judgment is right. A21’s probabilistic and causal versions are recorded in the body, not claimed. | Active |
| CLAIM-380 v2 | With finitely many states and finitely many outcomes, the positive part of the Bayes-risk increase on the same decision problem is directed, is zero from a garbling back to its source, vanishes for every finite problem and prior exactly when the rendering is at least as informative as the source, and has A86’s D_Q as its symmetrization | The finite-outcome part of CLAIM-326. Define D⁺_Q(U → V; π) = sup over q in Q of [r_q,π(V) − r_q,π(U)]⁺, with losses in [0, 1] and a stated prior. A garbling never gains. The term is directed. A86’s D_Q is its symmetrization. And with every finite problem and prior, it vanishes exactly when V is at least as informative as U, by Blackwell’s Theorem 6 (THEORY-717). It does not cover outcome spaces that are not finite, or say this is the right decision term. | Active |
| CLAIM-381 | Over a finite class of items with finite judgement outcomes, a constant outcome kernel fits every item only when the target readers’ averaged responses do not vary with the item, an exact fit is a garbling with the item as common parameter, and Le Cam’s deficiency and its restriction to finitely many decision problems are finite computations | The derivational core of CLAIM-228. Over a finite class of items, the target term is the readers’ response averaged over a procedure’s output, and one outcome kernel family is fixed across the items. Then a constant kernel fits only target responses that carry no information about the item. An exact fit is a garbling, with the item as the common parameter. And Le Cam’s deficiency between the two finite tables is one linear programme. Its restriction to finitely many decision problems is a finite computation. It does not say the measure is informative, which is CLAIM-228’s empirical question. | Active |
| CLAIM-450 v5 | Three standards for a communicative distinction come apart: statistical distinguishability of an interpreter’s response profiles, measured locally by the Fisher metric and never raised by a parameter-independent garbling; usability by a bounded receiver, which a transformation can raise; and pragmatic efficacy in the act; and where response models are singular, as Watanabe’s theory treats, a missing response can come from an absent attempt or an unresponsive receiver alike, and only intervention or later dynamics separate them | The owner’s, 2026-10-24, after setting aside the belief–knowledge distinction: “forget about that distinction then and let’s connect back to the communicative act stuff and amari/watanabe theory”. Worked through the same day (workbench entry of 2026-10-24, U27). Amari’s geometry and Watanabe’s singular learning are given different jobs in one modelling architecture, alongside bounded legibility and the communicative-act account, rather than read as rival characterizations. | Active |
| CLAIM-452 | For an organization whose response in each probe context is the authority-weighted mixture of its processes’ known response profiles, the authority shares are identifiable from a set of contexts exactly when the processes’ stacked profiles over those contexts are affinely independent; because the response is linear in the shares, local and global identifiability coincide, the condition is that the Fisher information of any design supported on those contexts is positive definite on the simplex’s tangent space, and with binary outcomes at least one context fewer than there are processes is needed | When an organization’s response in context c is p_π(·|c) = Σᵢ πᵢ pᵢ(·|c), the mixture CLAIM-444 reduces the replicator model to, which probe contexts reveal its authority shares π? Exactly those over which the profiles are affinely independent. The response is linear in π, so there is no gap between local and global identifiability, and the condition is the Fisher information of CASE-159’s pullback being positive definite on the tangent space of the simplex. Each binary context adds at most one rank, so k processes need at least k − 1 contexts. It is a condition checkable before any data, which is what QUESTION-031 asks for; none of the three works read on 2026-10-25 states it. | Active |
| CLAIM-488 v3 | Le Cam deficiency, after Torgersen, would quantify the approximate case of the Blackwell order for translation, and decoder-only audience knowledge would make the coding problem a Wyner-Ziv problem | The two steps of the manuscript’s §5 that CLAIM-050 carried until the status review of 2026-10-28 and that rest on works the record has not read: deficiency for the approximate case (Torgersen) and the Wyner-Ziv form of decoder side information. Split off when CLAIM-050 was narrowed to what its read sources support (ADR-047’s third ruling). | Active |
| CLAIM-503 | Over finitely many states and finite outcome sets, one experiment is ε-deficient relative to another in every decision problem with losses in [0, 1] exactly when a single Markov kernel brings it within ε in total variation at every state, so the deficiency computed as a linear programme is the least such ε | Le Cam’s randomization criterion for finite experiments, uniform in the state, with losses in [0, 1]. The least ε for which some kernel brings M within ε of N in total variation at every state, which CLAIM-381 computes as a linear programme, equals the least ε for which M is ε-deficient relative to N in every finite decision problem. One direction composes N’s rule with the kernel; the other is one minimax step over a bilinear objective. At ε = 0 it is the finite Blackwell order (THEORY-717). | Active |