# Learning DiscoSCM > Paper identity: active flagship end-to-end ML paper > Working title: **Learning DiscoSCM under One Factual Event per Token: Stable > Identity, Learnability Boundaries, and Semantic Tests** > Version markers: `LDSCM-WP-2026-07-17-V4` and > `LDSCM-GUIDE-ZH-2026-07-17-V4` ## Mandatory Agent notation preflight Before editing the manuscript, experiment designs, implementation interfaces, or reader-facing projections, read [`../../entrances/DISCOSCM_UNIT_SELECTION_NOTATION.md`](../../entrances/DISCOSCM_UNIT_SELECTION_NOTATION.md) ([public reader](../../entry-site/learning-discoscm/unit-selection-variable/index.html)). The non-negotiable object contract is: \[ U\text{ is the single model-level selector},\qquad U=u_i\text{ is sample }i\text{'s truth},\qquad Q_i(B)\approx P(U\in B\mid X=x_i)\text{ is its belief}. \] Sample indices may belong to observations, realizations, and belief objects. They must not replicate the Unit Selection Variable. Alternative queries reuse the same factual-evidence belief `Q_i`. Here `selection` means token identity/code selection only. It does not mean a treatment/action `A/T`, sample inclusion `S^obs`, or a propensity score. `P_U` describes token composition in a declared target population; `Q_i` is the evidence-indexed belief about one focal token. Latent-code `q` or Cauchy full support is not causal positivity. Unit abduction does not by itself repair sample-selection bias or treatment confounding. ## Question and scientific role The paper opens with **How to learn DiscoSCM?** and studies the first bounded slice: - fixed context; - one factual observation per token; - one predictors-to-outcome mechanism; - point, Gaussian, and Cauchy learner-side abduction; - factual prediction plus a fixed-abduction/changed-query interface. Its refined logic is: ```text declared target-population law P_U^tar -> one actual realization U=u_i -> admissible factual evidence O_i -> Perception P_F -> focal-token belief Q_i -> query perception P_Q and Reduction -> observable law, identification boundary, and falsifiable tests ``` The positive learning target is the composed factual predictive law on observed factual support. The paper does **not** claim that one-shot data identify an actual token code, a unique representation--mechanism decomposition, an alternative-query response law for the same focal token, or a complete Layer 3 joint law. ## Three active paper identities - `../learning-discoscm/`: flagship DiscoSCM learning question and its first token-modulated outcome-mechanism slice. - `../unit-mechanism-learning/`: general ML method family, including shared unit-modulated generators and predictive-law learning beyond DiscoSCM. - `../token-causation/`: token ontology, same-token linkage, and the boundary between response prediction and singular causal attribution. The three papers may cross-reference one another but keep independent theorem, experiment, failure, and submission truth. ## Technical research extensions - `../../entrances/CAUSAL_FOREST_UNIT_ABDUCTION_BRIDGE.md` explains the shared `evidence -> adaptive measure -> causal reduction` skeleton without equating forest weights with posterior abduction. - `../../entrances/UNIT_ABDUCTED_HETEROGENEITY.md` is a `proposal_only` sequel. It specifies a belief-neighborhood DR baseline and a unit-effect operator-inversion learner, but it is not part of the current manuscript's proved claims or confirmatory evidence. Any future assimilation requires an explicit estimand, integrability contract, abductor-calibration evidence, and a separate theorem/experiment gate. ## Sources and artifacts ```text main.tex English manuscript wrapper sections/ English manuscript sections main-guide.tex synchronized Chinese question-led guide guide-sections/ Chinese guide sections references.bib bibliography assumption-ledger.md assumption tiers and promotion rules claim-register.md status and boundary of each paper claim theorem-targets.md proved results and deferred theorem targets learnability-seed.md derivation from ontology to tractable learner calibration-proof-seed.md appendix continuity lemma, not flagship theorem validation-criteria.md evidence and promotion criteria experiment-ledger.md planned and secondary evidence provenance experiment-guide-zh.md reader guide to the completed Y-shuffle experiment selected-token-experiment-v2-zh.md target-corrected selected-token semantic diagnostic selected-token-semantic-repair-v3-results-zh.md sealed action-invariant abduction repair and limits experiment-design-k1-zh.md proposal-only K=1 high-dimensional nonlinear benchmark implementation/ paper-specific runner/tests using hash-pinned UML figures/ vector architecture source and standalone wrapper output/pdf/ stable built PDFs output/build-logs/ build logs ``` The paper-specific implementation consumes the canonical Unit Mechanism Learning implementation through `implementation/dependency-lock.json`; model code is not duplicated here. ## Build From this directory: ```bash bash build.sh bash build-guide.sh bash build-figure.sh ``` Stable outputs: ```text main.pdf main-guide.pdf output/pdf/learning-discoscm.pdf output/pdf/learning-discoscm-guide-zh.pdf output/pdf/learning-discoscm-architecture.pdf ``` The build scripts compile isolated temporary snapshots and reject undefined references or citations. They do not copy artifacts to a public site. ## Reader-facing notation contract - World truth: `Y(x)=f_0(x,E;U)` and, after token selection, `y=f_0(x,e;u*)`. - Learner family: `f_theta`, not silently equated with world truth. - Admissible factual evidence: `O_i`; perceived evidence: `z_i^F=P_F(O_i)`; factual mechanism query: `X_i^F`; alternative query: `x^Q`; perceived query: `z^Q=P_Q(x^Q)`. - Learner candidate uncertainty: `Q_i(du)=q_phi(U in du|X=x_i^F)`, semantically intended to approximate the corresponding conditional law. This does not require an explicit prior-times-likelihood Bayesian parameterization, is not a physical identity redraw, and is not automatically identified by predictive fit. - Identity/code and response-equivalence class are distinct: injective token addressing does not make the code-to-response map injective, and recovery of a response class is not recovery of physical token identity. - Prediction: `p_{phi,theta}(y|O_i,x^Q)`; reader-facing response-kernel notation is not used. - Same-token alternative query: reuse factual abduction and change only `x^Q`. ## Current truth status Proved in the manuscript: - Cauchy conditional-affine predictive propagation under explicit independence and scale assumptions; - proper-log-score Fisher consistency for the composed law on factual support; - latent reparameterization observational equivalence; - token/event Cauchy-scale split non-identifiability; - same-evidence alternative-query underdetermination from factual-only support; - bounded/redescending Cauchy location score for fixed scale. Implemented and executed under the frozen protocol: - marginal-preserving Y-shuffle at five corruption ratios in four 6,000-token worlds with a hidden 21-point fixed-abduction grid; - seven-model comparison with a sub-1% primary parameter-count gap; - 8-row mechanics smoke, 700-row development, and one-shot 1,400-row confirmatory projections with disjoint confirmatory seeds; - frozen primary t-interval/sign-test gate, no-heterogeneity attribution guardrail, full secondary summaries, and within-family Holm correction; - source/dependency/config/analysis checkpointing and post-run artifact seals. The existing E00 smoke remains untouched. The Y-shuffle smoke completed 8/8 cells and remained `mechanics_only`; development completed 700/700 cells and remained `development_only`; confirmatory completed 1,400/1,400 cells with no failures under checkpoint SHA `54944cd2...bee0120`. The formal result is `not_confirmed`. At `matched, rho=.4`, mean `log(E_direct/E_unit)` was `-0.00715`, with 95% t interval `[-0.0496, 0.0353]`, 4/10 Unit wins, and one-sided exact sign-test `p=0.8281`. The no-heterogeneity guardrail passed (95% geometric-advantage upper bound about 6.01%, below 10%), but the primary robustness gate failed all three conditions. Thus this experiment does not support a Unit-factorization robustness advantage; it also does not support any stronger latent, counterfactual, distribution-consistency, or Layer 3 claim. Canonical evidence is under `implementation/evidence/yshuffle/confirmatory/analysis/`. An independent selected-token V2 diagnostic now fixes the simulator-selected latent code across the hidden response grid and keeps `O=X=x`. Its semantic matrix completed `72/72` formal cells plus `18/18` oracle-isolated diagnostics, but returned `development_ready=false`: frozen-mechanism abduction approached its finite-test evidence-conditioned Bayes reference, while the both-learned encoder/mechanism factorization failed matched and no-heterogeneity clean-recovery gates. It therefore stopped before development or confirmatory execution. This result is documented in `selected-token-experiment-v2-zh.md`; it is not pooled with the frozen V1 `not_confirmed` result. A further sealed V3 development diagnostic repairs a concrete network boundary: the abduction encoder reads token cue `z` but not the manipulable action coordinate, while the mechanism still receives the full query. In matched clean data this lowered fixed-realization curve MAE from `0.223607` to `0.030654` (`86.291%`) and made cached abduction exactly action-invariant. However the no-token-heterogeneity control improved even more, so semantic-specific attribution failed; the frozen-mechanism Cauchy belief was also strongly underdispersed (80% coverage `0.3822` versus `0.7917` for the exact posterior). At 40% corruption `z_only` remained absolutely better but degraded much more from clean, so no robustness claim is promoted. V3 is interface evidence only, not \(Q_i\) recovery or confirmatory evidence. See `selected-token-semantic-repair-v3-results-zh.md`; all V1/V2 artifacts remain immutable and unpooled. A preconfirmatory Perception + Conditional Mechanism P0 diagnostic has also completed `108/108` formal fits and `48/48` nonranking diagnostics. Explicit query perception and response functions nonlinear in perceived query but affine in the token candidate improved bounded hidden-surface diagnostics, yet the run returned `semantic_not_ready`: the flow did not beat residual-MLP perception, isolated response paths and initialization stability missed their gates, and the no-unit control retained spurious evidence dependence. This is E07 architectural motivation only, not validation of P--A--R, invertibility, factorized superiority, or causal identification. See `perception-conditional-p0-results-zh.md`. No public deployment or Git submission is performed by the paper build. ## Next experiment design boundary `experiment-design-k1-zh.md` is a `proposal_only / unrun` protocol for the next K=1 benchmark. It does not revise the completed Y-shuffle verdict and is not evidence for a new paper claim. It keeps one factual outcome per unit, adds high-dimensional pre-action proxy evidence and nonlinear multi-action response geometry, and evaluates sealed same-unit counterfactual outcomes against strong conditional GP and generative-function baselines with legal single-point marginal likelihoods. The cross-world coupling family is public and frozen for all competitors; it is not claimed to be learned freely from K=1 records.