# Learning DiscoSCM Claim Register

> Status legend: `definition`, `assumption`, `proved`, `planned evidence`,
> `boundary`, `deferred`.

| ID | Claim | Status | Evidence / location | Nearest non-claim |
|---|---|---|---|---|
| C01 | A stable selector role is necessary to express persistent token heterogeneity and same-token cross-query linkage. | definition/ontology argument | `sections/unit_selection.tex` | variable name and numerical code are not data-identified |
| C02 | Discrete token identity and computational code are separate layers; `iota` is injective by assumption. | assumption | `sections/unit_selection.tex` | response map may be non-injective; coordinates are not identified |
| C03 | Retaining latent token codes while observing one factual `(O,X^F,Y^F)` record requires a Perception--Abduction--Reduction interface: admissible `O` forms one `Q_i`, while `X^Q` enters only query perception and response reduction. | definition-level derivation | `sections/abduction_geometry.tex` | does not force a Bayesian posterior, identify `Q_i`, or make every factual coordinate admissible token evidence |
| C04 | Point, Gaussian, and Cauchy are alternative learner-side abduction parameterizations about the same actual token. | definition | Eqs. point/Gaussian/Cauchy | none is automatically calibrated |
| C05 | Cauchy is a natural tractable choice under the declared stable-family desiderata. | bounded design claim | `sections/abduction_geometry.tex` | not globally unique or universally superior |
| C06 | Cauchy--affine assumptions yield the stated exact predictive location and scale. | proved | propagation proposition | tractability is not identification |
| C07 | Fixed-scale Cauchy location score is bounded and redescends for gross residuals. | proved | Eq. Cauchy location score | not robustness to all shifts |
| C08 | Proper log score is Fisher-consistent for the composed factual law on observed `(O,X^F)` support. | proved | factual-support theorem | no alternative-query, focal-belief, latent, or causal recovery |
| C09 | Invertible latent reparameterizations preserve composed predictions. | proved | latent reparameterization theorem | latent axes lack unique semantics without extra restrictions |
| C10 | Token/event Cauchy scale allocation is non-identifiable in the scalar example. | proved | scale-split proposition | does not say every architecture is non-identifiable in the same way |
| C11 | Equality on factual support leaves same-evidence alternative-query laws underdetermined. | proved | alternative-query proposition | shared structure may extrapolate but needs separate validation |
| C12 | Same-token computation requires both admissible-evidence construction of one `Q_i` and its fixed reuse while only the query branch changes. | interface contract | `sections/causal_queries.tex` | caching alone is insufficient; not counterfactual identification |
| C13 | Causal interpretation needs intervention, support, identification, stability, distribution-consistency, and noise-coupling assumptions. | boundary | causal assumptions list | interface alone is insufficient |
| C14 | E01 evaluates a truth-isolated evidence-indexed composed response grid, not recovery of the simulator-selected token realization. | confirmatory test completed; factorization advantage not confirmed | `implementation/evidence/yshuffle/confirmatory/analysis/verdict.json` | mean delta was slightly negative and its interval crossed zero; no robustness superiority or actual-token claim is promoted |
| C15 | Existing tabular robustness is secondary evidence about predictive objectives only. | boundary | evaluation section / experiment ledger | cannot establish token factorization or DiscoSCM validity |
| C16 | Learning DiscoSCM, Unit Mechanism Learning, and Token Causation remain independent active paper identities. | repository/paper contract | introduction and discussion | claims do not transfer automatically |
| C17 | In the selected-token V2 diagnostic, evidence-only abduction approaches its finite-test evidence-conditioned Bayes reference when the shared mechanism is frozen, but the both-learned one-shot factorization fails the clean semantic-recovery gate. | executed diagnostic; no robustness promotion | `selected-token-experiment-v2-zh.md`; selected-token V2 semantic verdict | does not make `U` observable, identify unique latent coordinates, or establish Unit-over-Direct robustness |
| C18 | In sealed selected-token V3, masking the DGP-irrelevant randomized factual action at the abduction encoder strongly lowers fixed-realization curve error and enforces exact query invariance, but the gain is not token-semantics-specific and the frozen-mechanism Cauchy belief is underdispersed. | executed development diagnostic; interface evidence only | `selected-token-semantic-repair-v3-results-zh.md`; sealed clean/stress verdicts | does not establish recovery or calibration of \(Q_i\approx P(U\mid O=o_i)\), latent-coordinate identification, corruption robustness, or confirmatory superiority |
| C19 | E07 descriptively motivates explicit query perception and a response nonlinear in perceived query coordinates but affine in the token candidate. | preconfirmatory descriptive diagnostic; `semantic_not_ready`; architectural motivation only | `perception-conditional-p0-results-zh.md`; P0 semantic verdict | does not validate P--A--R, establish invertibility as necessary, eliminate bad basins or spurious unit effects, or confirm factorized superiority |

## Prohibited abstract/conclusion language

Do not write:

- “we identify the individual token mechanism from one observation”;
- “Cauchy is the unique uncertainty law for token causation”;
- “the factual likelihood learns counterfactual response curves”;
- “fixed abduction solves Layer 3 inference”;
- “robust tabular prediction validates DiscoSCM factorization.”
- “P--A--R, invertible perception, or conditional factorization is validated by P0.”