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The catalog, and what it refuses to order

33 kinds of evidence, 5 scored axes each (I, S, rho, sigma, T), ordered by componentwise dominance.

The partial order, drawn as a Hasse diagram

One kind dominates another when it scores at least as high on all 5 axes and strictly higher on at least one. The diagram draws the cover relation, the transitive reduction of that order, so an edge means nothing sits between those two kinds. Levels run bottom to top by longest chain below, and two kinds on the same level with no path between them are genuinely incomparable.

RCT on the target population (experimental, empirical domain) - I5 S5 rho5 sigma4 T5Adversarial collaboration, joint prereg (experimental, empirical domain) - I5 S5 rho4 sigma6 T4A/B test, valid sequential analysis (experimental, empirical domain) - I5 S5 rho5 sigma3 T4Regression discontinuity (quasi-experimental, empirical domain) - I4 S3 rho4 sigma3 T2Natural experiment / exogenous shock (quasi-experimental, empirical domain) - I4 S3 rho4 sigma3 T3Instrumental variables / 2SLS (quasi-experimental, empirical domain) - I4 S3 rho3 sigma3 T2Diff-in-diff / synthetic control (quasi-experimental, empirical domain) - I3 S2 rho3 sigma3 T3Matching / propensity / TMLE + sensitivity (observational, empirical domain) - I2 S2 rho3 sigma3 T3Cross-sectional regression (observational, empirical domain) - I1 S1 rho2 sigma1 T2Production telemetry (observational, empirical domain) - I0 S1 rho4 sigma1 T5Third-party panel / scraped data (observational, empirical domain) - I0 S1 rho1 sigma1 T2Backtest, unpurged (computational, empirical domain) - I0 S1 rho2 sigma0 T1Purged / walk-forward CV (computational, empirical domain) - I1 S2 rho4 sigma2 T3Held-out test set, first look (computational, empirical domain) - I1 S4 rho5 sigma3 T3Shadow deployment / canary (computational, empirical domain) - I1 S4 rho5 sigma3 T5Property / metamorphic testing, fuzzing (formal, formal domain) - I5 S3 rho6 sigma4 T4Machine-checked proof (formal, formal domain) - I6 S2 rho6 sigma4 T5Example-based test suite (formal, formal domain) - I3 S1 rho6 sigma2 T3Simulation / Monte Carlo (computational, synthetic domain) - I6 S1 rho6 sigma1 T0Audited financials / regulatory filing (testimonial, empirical domain) - I0 S3 rho5 sigma5 T4Calibrated forecaster track record (testimonial, empirical domain) - I0 S4 rho4 sigma4 T3Structured elicitation (SHELF / Cooke) (testimonial, empirical domain) - I0 S2 rho3 sigma3 T3Unstructured expert judgment (testimonial, empirical domain) - I0 S1 rho1 sigma1 T3Cross-provider LLM adversary, measured ρ (machine, empirical domain) - I0 S3 rho4 sigma4 T2Retrieval-grounded entailment check (machine, empirical domain) - I0 S2 rho4 sigma3 T2Single LLM judge, unmeasured ρ (machine, empirical domain) - I0 S1 rho0 sigma1 T1LLM-generated citation or specific (machine, empirical domain) - I0 S0 rho0 sigma0 T0Single anecdote / demo (testimonial, empirical domain) - I0 S1 rho3 sigma1 T2Reproduced counterexample (formal, any domain) - I0 S6 rho6 sigma2 T3Negative control / regime-change probe (experimental, empirical domain) - I2 S5 rho5 sigma3 T4Cryptographic hash comparison (formal, formal domain) - I0 S6 rho6 sigma0 T0Hostile short-seller report, no stated method (testimonial, empirical domain) - I0 S1 rho1 sigma5 T2Preregistered, blinded, powered observational slope study (observational, empirical domain) - I0 S4 rho5 sigma4 T3RCTAdv. collabA/B (seq)RDDNat. experimentIV / 2SLSDiD / synthMatching / TMLECross-sectionTelemetry3P panelBacktestPurged CVHoldoutShadow / canaryProperty testsProofUnit testsSimulationAudited filingTrack recordSHELF elicitExpert opinionX-provider LLMEntailment checkSingle LLM judgeLLM citationAnecdoteCounterexampleNegative controlHashShort-sellerPrereg slope262 COMPARABLE + 266 INCOMPARABLE = 528 PAIRS TOTAL - 49.6% OF THE ORDER DECIDABLE WITHOUT NAMING A DECISION

Hover a node for its full name, its family, its domain and its five coordinates. The census printed inside the figure is computed from the catalog rather than transcribed: 262 comparable pairs and 266 incomparable, out of 528, so 49.6% of the order is decidable before anyone names a decision.

What four records can do to that number

Drop four records and recompute. Over all C(33,4) = 40,920 four-record removals from this catalog, the comparable fraction ranges from 36.9% to 60.8%, a 23.9-point band. The shipped 49.6% sits inside that band, and which four you drop decides where.

Blackwell has no completion for credal evidence. Once information is a set of measures rather than a measure, "is E more informative than F" has no settled definition. Dominance on every axis, over hand-assigned levels, is a PROXY for Blackwell's order rather than that order, because no garbling kernel (an explicit noisy channel from one experiment to the other) is constructed. The intersection-of-decision-orders claim holds over the full weight simplex, not only the four decisions shipped here.

Dominance isn’t the only ordering that avoids naming a decision, so which order we treat as the reference is a choice. Mutual information, any single f-divergence, and Le Cam deficiency each rank experiments without a loss function, and each disagrees with dominance about some pair. We take Blackwell’s order as the reference because it decides a pair only when every decision problem agrees about that pair.

The construct-domain gate

Every kind above carries a construct domain - empirical, formal, synthetic, or any - and every scored decision below declares which domains it admits. A support outside the admitted set gets dropped before the axes are scored, and a warrant left with nothing admitted is refused outright. Nothing gets discounted on the way through. Simulation / Monte Carlo carries the synthetic domain:

Derives consequences from an assumed model and cannot check that model against the system being modeled. Monte Carlo error is driven to zero by buying compute, which is why reporting it as uncertainty is a category error.

Under all 4 scored decisions below, Simulation is refused, with the identical reason: “synthetic evidence, not admitted here”

What each decision admits, and refuses, and why

Pick one of the 4 scored decisions. It ranks only the kinds it admits. The kinds it refuses follow, in a separate list. A kind lands there for one of three reasons - a domain mismatch, a failed axis gate, or a meet below the floor - and the text beside it names which. A refused kind has no score to show, because scoring it would imply a ranking this decision never joined.

No weights here, so nothing is scorable and every kind sits in the refused list. Under componentwise dominance, 266 of the 528 pairs are incomparable.

0 of 33 admitted - no decision named, so nothing is scorable

    Refused - no score, because there is no ranking to join

    1. 3P panelno decision named, so there is no ranking to join
    2. A/B (seq)no decision named, so there is no ranking to join
    3. Adv. collabno decision named, so there is no ranking to join
    4. Anecdoteno decision named, so there is no ranking to join
    5. Audited filingno decision named, so there is no ranking to join
    6. Backtestno decision named, so there is no ranking to join
    7. Counterexampleno decision named, so there is no ranking to join
    8. Cross-sectionno decision named, so there is no ranking to join
    9. DiD / synthno decision named, so there is no ranking to join
    10. Entailment checkno decision named, so there is no ranking to join
    11. Expert opinionno decision named, so there is no ranking to join
    12. Hashno decision named, so there is no ranking to join
    13. Holdoutno decision named, so there is no ranking to join
    14. IV / 2SLSno decision named, so there is no ranking to join
    15. LLM citationno decision named, so there is no ranking to join
    16. Matching / TMLEno decision named, so there is no ranking to join
    17. Nat. experimentno decision named, so there is no ranking to join
    18. Negative controlno decision named, so there is no ranking to join
    19. Prereg slopeno decision named, so there is no ranking to join
    20. Proofno decision named, so there is no ranking to join
    21. Property testsno decision named, so there is no ranking to join
    22. Purged CVno decision named, so there is no ranking to join
    23. RCTno decision named, so there is no ranking to join
    24. RDDno decision named, so there is no ranking to join
    25. Shadow / canaryno decision named, so there is no ranking to join
    26. SHELF elicitno decision named, so there is no ranking to join
    27. Short-sellerno decision named, so there is no ranking to join
    28. Simulationno decision named, so there is no ranking to join
    29. Single LLM judgeno decision named, so there is no ranking to join
    30. Telemetryno decision named, so there is no ranking to join
    31. Track recordno decision named, so there is no ranking to join
    32. Unit testsno decision named, so there is no ranking to join
    33. X-provider LLMno decision named, so there is no ranking to join