A governed, reproducible research framework for detecting — or rigorously excluding — structure in stochastic data. The laboratory combines instruments from five mathematical traditions under a single calibration discipline, with formal protocols for onboarding theorems and datasets, harmonizing their conflicts, and confirming findings on held-out data.
The lab drives from a local web console (python3 webapp/server.py → http://localhost:8787).
The Overview landing page always surfaces the single next action, alongside live counts
from the run ledger, the multiplicity ledger, and the honesty meter. Nine views plus a
guided wizard cover the whole pipeline — pre-registration, human-gated approvals, execution,
and results.
The five faces of structure interrogated are statistical (uniform marginals),
dynamical (future ⊥ past), algorithmic (incompressible), cross-sectional /
physical (no collective modes), and — added with the relational extension —
relational (two datasets share more structure than independent generation predicts;
or a subset determines the whole). Source: docs/CROSS_DATASET_FRAMEWORK.md §0.
- Installation
- Why this lab exists
- Research questions the framework answers
- The constitution: articles A1–A8 and conflict registry C1–C11
- Instrument inventory
- The theorem arsenal — how each instrument is used
- Equation discovery — Phase 5
- Verification and integrity stack
- Four-level ledger system
- Agent system
- Independently verified performance
- Evidence-grade ladder G0–G6
- Domain architecture
- Module: riemann-zero-lab (deterministic mathematics)
- Repository guide
- Limitations
- Reviews and audits trail
One command, five questions, safe defaults — pressing ENTER on every question gives a good install (macOS and Linux; Python 3.10+):
python3 install.pyThe wizard checks and installs every runtime dependency (the full set in
requirements.txt — numpy, scipy, matplotlib, pandas, ripser, ephem, openpyxl — plus
mpmath for the riemann module), then verifies the install by running
webapp/test_lab_deps.py and src/lint_frozen_imports.py. Its five decisions:
| Step | Question | Default (ENTER) | Alternative |
|---|---|---|---|
| 1 | Python environment | private .venv/ (avoids the PEP-668 "externally managed" error) |
current interpreter |
| 2 | Lab history | keep the repo's ledgers and registered results | clean ledger — moves results/ (and riemann-zero-lab/results/) to archive/, creates fresh empty ledgers with a new commitment snapshot |
| 3 | Datasets | keep the five onboarded datasets | clean datasets — moves them to archive/, keeps datasets/_TEMPLATE for onboarding your own |
| 4 | riemann-zero-lab | install its mpmath dependency |
skip |
| 5 | Agent LLM provider | skip (configure later on the console Admin page) | store an API key now (Anthropic / OpenAI / OpenRouter / Gemini / local Ollama) |
Guarantees the installer honors (they mirror the lab's constitution):
- Nothing is ever deleted. Clean-start options move files into a timestamped
archive/folder (git-ignored). Restoring = moving them back. - Ledgers are append-only. The four ledgers are never truncated or edited; a clean
ledger is a new ledger, and the old one survives in
archive/. Note for clean installs:src/build_run_ledger.py/src/build_multiplicity_ledger.pybackfill the repo's historical runs — on a fresh ledger, append new runs via the console/agents instead of running the builders. FROZEN HISTORICAL RECORDscripts are never touched.- Agent keys never enter the repo. Keys go to
webapp/config.local.json(git-ignored,chmod 600), obfuscated at rest with the machine-localwebapp/.keysalt— the exact scheme the web console uses, so the Admin page reads, masks, and manages them natively. All four agent roles (analyst / executor / reviewer / companion) default to the provider you pick; per-role models and effort are tuned on the Admin page.
Non-interactive use (CI, scripted setups): python3 install.py --yes accepts every
default; --env venv|system, --ledger keep|clean, --datasets keep|clean,
--riemann yes|no, --provider <id> (key read from the LAB_LLM_API_KEY environment
variable, never from argv) override individual answers; --dry-run prints the plan and
changes nothing; --verify-only re-runs the post-install health checks and exits;
--locked pins installs to the recorded environment (constraints-recorded.txt) for
closest reproduction of ledgered results; --restore archive/preinstall-… mechanically
undoes a clean start (the displaced state is archived first — nothing is ever deleted).
After installing: activate the venv if you created one (source .venv/bin/activate),
then start the console — python3 webapp/server.py 8787 (or double-click
Start Lab Console.command on macOS) and open http://localhost:8787. The Overview page
always shows the single next action.
The lab is self-contained and runs anywhere with Python 3.10+ (macOS and Linux are the tested platforms; the web console itself is stdlib-only). To migrate:
- Code, docs, ledgers, datasets — push/pull through git as usual (ledgers and
registered results are tracked files). Copy
archive/manually if you want archived history along (it is git-ignored by design). - Agent credentials —
webapp/config.local.jsonis obfuscated against the machine-local saltwebapp/.keysalt, so the two files only work as a pair: copy both (they arechmod 600and git-ignored), or simply re-enter keys on the new machine viapython3 install.pystep 5 or the console's Admin page. - Environment — never copy
.venv/(it hard-codes absolute paths); runpython3 install.py --yeson the new machine, thenpython3 install.py --verify-onlyto confirm all gates pass.
On a shared/headless server, keep the console bound to localhost (the default) and
reach it over an SSH tunnel (ssh -L 8787:localhost:8787 you@server). --lan exposes
it to the local network behind a token gate: non-localhost devices must open the
one-time ?token=… URL printed at startup (token stored git-ignored in
webapp/.lantoken; localhost is always exempt so scripts and the launcher keep
working). Still do not expose the port to the public internet.
The lab began with a deceptively simple question — do public lottery draws contain any structure an analyst could detect, or better, exploit? — and discovered that the honest pursuit of that question requires machinery far larger than the question itself. Most apparent "structure" in stochastic data is self-deception in one of a few recurring costumes: estimator bias read as signal, textbook asymptotics misapplied to finite samples, look-elsewhere effects, era-bounded transients mistaken for persistent mechanisms, and analyses quietly tuned until they pass. Case Study 1 produced four such false signals (Hurst bias, Binder pseudo-plateau, degenerate KS, smoothing-bias backtest edge) — every one dissolved by the same discipline, simulating the null from the actual generative mechanism (A1).
The lab therefore exists to do three things that ad-hoc analysis cannot:
- Make negative results as rigorous as positive ones. "No structure found" is reported with its power ("no effect ≥ size ε at this n"), backed by exclusion certificates, and dead-end hypotheses are logged as results, never discarded.
- Make positive results survivable. Every claim must pass calibrated nulls, multiplicity accounting, era gates, independent re-execution by a different agent identity, and — before any label above exploratory — held-out or fresh-data confirmation, with commitments hashed before outcomes are known.
- Generalize the discipline. The instruments live in a domain-neutral core
(
src/core/); the lottery is Case Study 1, not the mission. Any stochastic dataset — financial series, physical measurements, synthetic benchmarks — can be onboarded against the same constitution, and the framework's verdict is equally valuable in both directions: structure detected, or structure rigorously excluded at a stated resolution.
The result is less a collection of analyses than a governed laboratory: theorems are onboarded like instruments, conflicts between them are adjudicated by written articles, and the lab's own tools are required to fail loudly on synthetic nulls before they are ever trusted on real data.
- Detection — does this sequence deviate from its declared null model, on any of the five faces of structure?
- Attribution — is a detected deviation data corruption, estimator bias, look-elsewhere illusion, era-bounded transient, or persistent mechanism?
- Decision — if structure exists, what is it worth under explicit decision theory (Doob gate → expected value → Kelly sizing), net of costs?
Source: docs/THEOREM_GOVERNANCE.md.
A1. One generative null, many lenses. Every instrument's null distribution is derived by Monte Carlo from the same constrained generative model — never from textbook asymptotics. This discipline dissolved four false signals in Case Study 1 (Hurst bias, Binder pseudo-plateau, degenerate KS, smoothing-bias backtest edge) and is documented as the primary source of methods casualties.
A2. Null-trial admission. No estimator touches real data before demonstrating silence on simulated H₀ data of identical shape.
A3. Equivalence-class accounting. Multiplicity budget m counts statistics grouped into classes (null-correlation |r| > 0.90 on simulated data). Anomalies are identified by their driving rows, not by which statistics noticed them.
A4. Asymmetric verdict logic. A flag from any admissible instrument defeats H₀ pending replication; passes accumulate scope coverage, not proof. Every "pass" is reported with its power: "no effect" always means "no effect ≥ size X at this n."
A5. Stationarity gate. Before any pooled statistic is interpreted, run the windowed-homogeneity check. If eras differ, pooled p-values are quarantined and the analysis proceeds per era.
A6. Designated arbiter. Conflicting exploratory verdicts define what gets pre-registered; the held-out confirmation test is the only arbiter, never argument.
A7. Layered one-way flow. Detection → interpretation → decision. Information flows forward only; each theorem is asked only the question of its own layer.
A8. Deterministic-certificate substitution (deterministic-math extension, 2026-06-13).
When a claim is a deterministic mathematical fact with no sampling model, the MC-null (A1/A2)
is replaced by a three-leg certificate: exact computation to a declared tolerance,
independent recomputation by a different instance, and an analytic invariant cross-check (e.g.
located zero count = N(T) = argument-principle contour integral). A8 leaves A1–A7 intact for
every stochastic question; it only supplies an admission path for claims that cannot be
resampled. First applied in riemann-zero-lab.
The ten recorded collisions between theorem families (source: docs/THEOREM_GOVERNANCE.md):
| # | Collision | Resolution |
|---|---|---|
| C1 | Asymptotic theorems vs finite data (produced 3 false signals: Hurst, Binder, KS) | A1: simulate the null from H₀ |
| C2 | Competing nulls — two "laws" predicting different baselines | A1: each theorem's null derived from H₀, not imported |
| C3 | Statistic equivalence — theorems wearing each other's clothes | A3: equivalence-class counting; flags within a class count once |
| C4 | One-sided certificates vs two-sided tests | A4: asymmetric verdicts; passes accumulate scope, not proof |
| C5 | Pooled stationarity vs era structure | A5: stationarity gate; era boundaries from known regime events first |
| C6 | Same anomaly, opposite verdicts under different alternatives | A6: designated arbiter; held-out confirmation decides |
| C7 | EV vs Kelly vs Doob — superficially inconsistent prescriptions | A7: layered ordering; each theorem answers its own layer's question |
| C8 | Universality vs bias-hunting | A7: universality fixes null fluctuation laws; bias detection hunts deviations from those laws |
| C9 | Relational double counting — one anomaly, many faces | Mandatory row-trace before any relational flag is reported; if driving rows underlie a known anomaly the flag joins that equivalence class |
| C10 | Representation freedom as uncharged multiplicity | Representation bundle declared per dataset before the run; A3 budget counts representation × method × metric classes |
| C11 | Deterministic mathematics vs the MC-null premise (no sampling model exists for "is t_n a zero of ζ?") | A8: admit deterministic claims on a verification certificate (exact computation + independent recomputation + analytic invariant count), MC-null retained for stochastic sub-questions (spacing vs Poisson) |
Discovery tests carry no outcome expectations. Source: docs/REMEDIATION_LOG.md
"Protocol change first" section. A registration contains: claim type, representation,
instrument, null, decision rule, and falsification criteria — never a predicted result.
Mechanism-based predictions survive only as instrument-validity controls (e.g. "if
the pipeline cannot detect the tidal loop, the pipeline is broken"), which calibrate
tools, not outcomes. Codified in docs/RELATIONAL_RUNBOOK.md Phase 1 (amended). Prior
registrations written with outcome expectations are explicitly labeled retroactive in
the run ledger and in results/commitment_ledger.txt.
Source: docs/kb/INDEX.md. Every instrument requires a KB card before touching real
data (Part 3 of the governance protocol).
| Face | Cards | Instruments |
|---|---|---|
| Statistical | 5 (cards 1–5) | LLN/CLT, chi-square+exact MC, permutation tests, scan statistics, multiple comparisons |
| Dynamical | 4 (cards 6–8, 12) | Markov chains, Hurst/R-S, Doob optional stopping, Wiener–Khinchin/Fisher g |
| Decision | 3 (cards 8–9, 16) | Doob, Kelly criterion, expected-value/Stern-Cover |
| Algorithmic | 2 (cards 10, 15) | Shannon–Kolmogorov compression, covering designs |
| Cross-sectional / physical | 7 (cards 11, 13–14, 17–19, 26) | Marchenko–Pastur/Tracy–Widom, SOC/universality, power laws/Zipf/Taylor/Benford, Szemerédi APs, graphons, concentration/exclusion |
| Relational (R1–R7) | 7 (cards 20–26) | MMD/energy distance (R1), Gromov–Wasserstein (R2), CCA family (R3), TDA persistence distances (R4), graph matching/spectra (R5), coresets/landmarks (R6), matrix completion/compressed sensing (R7) |
Admission status. All 7 relational families (R1–R7) are admitted: FPR calibrated
at tested shapes; power curves frozen over declared effect grids (source:
docs/REMEDIATION_LOG.md M1). GW (R2) is demoted to exploratory-only (G0): the
n=200 gate confirmed FPR (0.055) but the p-distribution was non-uniform (lattice χ²
p=0.002); a symmetric-null variant also fails (p=0.005). The miscalibration is
inherent to moment-matched regeneration nulls for GW at these shapes. GW is flagged G0
pending null redesign; A4 holds: the flag stands and no published verdict relied on GW
alone (source: docs/REMEDIATION_LOG.md M2).
Results ledger: 40 rows. Source: docs/THEOREM_SYNTHESIS.md §5. Each row records
instrument, functional, H₀ value, observed value, and corrected p-value basis.
The 26 instruments are not independent claims. They form a one-way lattice
(source: docs/THEOREM_SYNTHESIS.md §2): H₀ implies uniform marginals, order-0 serial
structure, flat spectrum, MP eigenvalue bulk, and maximal entropy — but none of those
properties individually implies H₀. The master equivalence is algorithmic:
incompressibility (Shannon/Kolmogorov/Martin-Löf) is the only single property
equivalent to H₀, because any computable structure — frequency bias, memory, cycle,
or factor — reduces entropy rate and admits compression. Consequently:
- uniform marginals ⇏ randomness (a deterministic rotation gives perfect chi-square forever)
- order-0 lag-1 ⇏ no memory (pairwise independence at lag 1 does not exclude lag-7 dependence)
- flat spectrum ⇏ independence (spectra capture second moments only; nonlinear dependence is spectrally invisible)
- incompressibility ≈ H₀ (the conjunction of all other properties)
The suite covers each other's blind spots in a closed loop; the joint verdict is stronger than the sum of individual passes.
Two pseudo-critical artifacts illustrate the methods-casualty discipline required to maintain this loop: (1) raw Hurst H-hat on a short i.i.d. series is biased upward — calibration against a same-length null is mandatory before any memory claim; (2) the Binder cumulant can show a pseudo-plateau mimicking a critical fixed point, which n≈4-window estimator bias reproduces exactly on simulated i.i.d. data. Both are documented as worked examples of how false discoveries are produced; both were caught before any real-data claim was made.
Applied results: docs/CASE_STUDY_1_PCSO.md §3 (dynamical), §6 (Per Bak).
Card 1 — LLN / CLT (ledger rows 1, 19): every z-score in the project rests on the CLT; under H₀ sample frequencies converge to 6/P and standardized counts are asymptotically N(0,1). Null functional: excess kurtosis of block means → 0. The CLT-as-RG-fixed-point view connects this card to the universality analysis: block-mean kurtosis flow at k=1–16 is the empirical test. Role: calibration baseline. Blind to dependence structures that preserve marginals.
Card 2 — Chi-square + exact Monte Carlo (ledger row 1): detects marginal frequency non-uniformity (hot/cold balls). Asymptotic chi-square is invalid at low expected counts under 6-without-replacement sampling; replaced by exact MC under the true mechanism. Role: marginal-uniformity instrument. Blind to all structure that preserves uniform marginals — the reason the other four faces exist.
Card 3 — Permutation tests (ledger row 2): assumption-free covariate correlation tests; null is exchangeability of the draw–covariate pairing. Within-game z-scoring is required to fix a pooling problem (Simpson-type confound across games with different number ranges). Role: covariate association instrument. Blind to associations orthogonal to the chosen statistic and to autocorrelation within a single series.
Card 4 — Scan statistics / look-elsewhere (ledger row 10): Kulldorff-style maximum windowed z-score over all numbers, window lengths, and games, calibrated by MC over the full search. Distinguishes a locally extreme observation (global null) from a persistent anomaly (rolling-window alternative). Role: look-elsewhere correction. Blind to diffuse, non-localized departures.
Card 5 — Multiple comparisons (ledger rows throughout): Bonferroni/BH applied with equivalence-class accounting — m counts hypothesis classes (|r| > 0.90 on simulated data ⇒ same class), not raw statistics. Family sizes: m = 9 (confirmation battery), m = 15 (Markov family), m = 18 (scaling-law family). Role: multiplicity control. Blind when m undercounts paths actually explored.
Applied results: docs/CASE_STUDY_1_PCSO.md §2.
Card 6 — Markov chains / order tests (ledger row 4): order-0 vs order-1 likelihood- ratio G-test; overlap/stickiness; tercile G-test; |λ₂| relaxation time. Under H₀ the transition rows all equal the stationary distribution. Distinguishes the Markov property from i.i.d.: failure to reject order-0 vs order-1 bounds one-step memory, not all memory. Role: short-memory instrument. Blind to higher-order or long-range dependence.
Card 7 — Hurst / R/S analysis (ledger row 12): long-range memory instrument. Null H = 0.5 asymptotically, but the R/S estimator is biased upward on short series — calibration against a same-length i.i.d. null is therefore mandatory (pseudo-critical artifact 1 of 2). Role: long-memory instrument. Blind to short-memory structure with fast mixing and to dependence that leaves second moments untouched.
Card 8 — Doob optional stopping (ledger row — decision gate): if the game is fair, E[wealth at any stopping time] ≤ initial wealth for any betting strategy. No betting schedule, stake sizing, or stopping rule has positive expected profit under a supermartingale. Role: detection-to-action gate. Not a detector; blind to strategies that genuinely flip the sign of per-bet EV.
Card 12 — Wiener–Khinchin / Fisher g (ledger row 8): spectrum and autocovariance are a Fourier-transform pair (one equivalence class, not two tests); Fisher's exact g-test gives a look-elsewhere-correct test for hidden periodicities. Null: flat periodogram, g follows the exact alternating-binomial distribution. A flat spectrum certifies zero autocorrelation at all lags (second-order only); compression covers nonlinear dependence the spectrum misses. Role: spectral / periodic-structure instrument.
Applied results: docs/CASE_STUDY_1_PCSO.md §3.
Card 10 — Shannon / Kolmogorov compression (ledger row 6): the master instrument. Incompressibility via Martin-Löf randomness is the one property equivalent to H₀: any computable structure reduces entropy rate and admits compression. The entropy floor (H = log₂ C(P,6) per draw) makes prediction impossible in principle. Practical test uses raw DEFLATE versus identically processed simulated nulls. Role: master certificate. One-sided only: failure to compress proves nothing absolute for structure outside the compressor's model class.
Card 15 — Covering designs (ledger row — combinatorial bound): pure combinatorics, no probabilistic assumptions. Cushing–Stewart (arXiv 2307.12430) proved L(59,6,6,2) = 27 via Fano planes. Disjoint-pair rule: two disjoint tickets give jackpot probability exactly 2/C(n,6) — coverage cannot create expected value. Role: combinatorial bound instrument. Not a detector; answers "cheapest guarantee of a t-match."
Applied results: docs/CASE_STUDY_1_PCSO.md §4.
Card 11 — Marchenko–Pastur / Tracy–Widom (ledger rows 7, 17): RMT eigenvalue bulk applied to co-occurrence correlation matrices. Meta-check: the simulated null distribution of λ_max tracks TW-GOE universality — universality governs the lab's own noise floor, not the mechanism under study. Role: linear cross-sectional structure detector. Blind to nonlinear or higher-order dependence and to time structure.
Card 13 — Per Bak SOC & universality (ledger rows 12, 15–20): the full methodological treatment is in the dedicated subsection below.
Card 14 — Power laws / CSN / Zipf / Taylor / Benford (ledger rows 16, 21–25): CSN MLE + Vuong test on gap and avalanche distributions. Zipf slope is chi-square in disguise (one equivalence class, not a separate test). The exact uniform-derived digit law differs from naive Benford — correct null matters. Role: tail-structure instrument. Blind to light-tailed structure and to dependence that leaves marginal tails geometric.
Card 17 — Szemerédi / Furstenberg APs (ledger row 28): density alone forces arithmetic progressions (the Ramsey trap) — any top-k hot-number set must contain APs at a theorem-forced baseline rate, independent of any bias mechanism. Two-sided MC- calibrated AP counts within draws and hot sets. Role: blind-spot coverage for additive structure. Blind to non-AP structure.
Card 18 — Graphons / cut norm (ledger row 27): spectral norm of centered co-occurrence matrix as a proxy for the graphon cut distance; null graphon is constant W ≡ c under i.i.d. uniform. C9 row-trace duty: any flag must be checked for overlap with known anomaly driving rows before a new detection is declared. Role: community-structure instrument.
Card 19 — Concentration / sparse recovery (ledger row 26): the lab's only exclusion instrument. Simultaneous Hoeffding/MC band converts non-detection into the strongest honest statement: any persistent per-ball bias exceeds ε with probability < 5%, at ε ≈ 0.15–0.20 for n = 155–776. Caveat: ε is vacuous at feasible n as an EV constraint. Role: exclusion certificate. Blind to temporal and combinatorial structure with exact uniform marginals.
Card 26 — Matrix completion / compressed sensing (ledger row 38, relational face): low-rank / sparse reconstruction as assumption-checking; held-out RMSE versus marginal- baseline and permuted-entry nulls. On full-rank / i.i.d. data the solver sits on the null line — the registered expected outcome from the entropy floor. Role: relational null-check instrument.
Applied results: docs/CASE_STUDY_1_PCSO.md §5.
Sources: docs/kb/per-bak-soc-universality.md, docs/THEOREM_SYNTHESIS.md §5b,
ledger rows 12, 15, 16, 17, 18, 19, 20.
SOC (Bak, Tang, Wiesenfeld 1987) asserts that certain driven dissipative systems self-tune to a critical point, displaying power-law avalanche distributions P(s) ~ s^−τ, 1/f^α power spectra, and long-range correlations H ≠ 0.5. The universality / RG framework predicts that near a critical fixed point observables collapse onto universal scaling functions, block statistics flow under the RG map, and the Binder cumulant U = 1 − ⟨m⁴⟩/(3⟨m²⟩²) is scale-invariant (curves for different system sizes cross); off-critical systems flow to trivial fixed points.
SOC signature suite design: the suite tests all three classical SOC signatures — spectral slope (1/f^α), avalanche size distributions (power-law vs geometric Vuong test), and long-range memory (Hurst R/S). Each is calibrated against the same-shape H₀ null before any real-data interpretation. This calibration step is mandatory because all three estimators exhibit finite-sample bias under i.i.d. data.
The two preconditions test logic: universality-class identification requires (1) evidence of criticality (exponential tails refute it; Vuong test against geometric is the discriminating instrument) and (2) a measurable scaling range (≥ 2 decades of power-law behavior; anything less makes exponent estimation unreliable by construction). Both are pre-checked before any universality-class claim is made.
The fixed-point-identification upgrade: when both preconditions fail, the analysis does not stop at "no criticality found." The RG toolkit (data collapse across system sizes, RG flow via block-mean kurtosis at k = 1–16, Binder cumulant scale invariance) is run on all ensembles to identify which fixed point the system actually occupies. This upgrades the verdict from an absence claim to a positive identification. The trivial / Gaussian fixed point and the critical / power-law fixed point are the two possible outcomes; both are detectable by the suite.
The universality inversion as a principle: even when the dataset is not critical, universality governs the lab's own instruments. The RMT eigenvalue bulk follows Tracy–Widom universality; every z-score rests on CLT / Gaussian-class universality; the scan statistic's null follows Gumbel extreme-value universality. This is not a result of the case study — it is a structural property of the framework.
Applied results (empirical numbers for the PCSO dataset): docs/CASE_STUDY_1_PCSO.md §6.
Card 20 — MMD / energy distance (R1) (ledger row 29): kernel two-sample test (pool-and-relabel null) detecting distributional differences across datasets sharing a feature space. Admitted: FPR calibrated at tested shapes; power 1.00. Role: distributional difference detector. Equality of distribution ≠ relatedness — a critical asymmetry noted in the card. Blind to structure not expressed in the chosen kernel.
Card 21 — Gromov–Wasserstein (R2) (ledger row 37): alignment of metric-measure spaces without shared coordinates. Always returns a coupling; only its position in a matched-null distribution is evidence. Admitted at n=200 gate (FPR 0.055); demoted to exploratory-only G0 because p-distribution was non-uniform (lattice χ² p = 0.002) — the instrument the lab built failed its own calibration check and was immediately demoted. Role: cross-space alignment instrument. Status: G0, exploratory-only pending null redesign.
Card 22 — CCA family (R3) (ledger rows 31, 36): held-out canonical correlation of draw features vs date-paired covariates. In-sample ρ̂ is never evidence (RMT inflation; held-out only). Positive control confirmed: known physical mechanism returned held-out ρ₁ = 0.9977, p = 0.005 (floor), verifying the pipeline. Role: cross-dataset correlation instrument. Blind to nonlinear associations.
Card 23 — TDA / persistence distances (R4) (ledger rows 33–34): delay-embedded topology — H₁ loops in structured series, flat for unstructured. Tidal loop recoverable from 20% landmarks. The FN-3 miss in the blind methodology eval (a cycle under different delay parameters) is documented as an instrument-representation limit, not a false null. Role: topological structure instrument.
Card 24 — Graph matching / spectra (R5) (ledger row 32): pairwise co-occurrence spectra across all game pairs (m = 99); degree-preserving rewiring null (Erdős–Rényi forbidden as sole control). C9 row-trace duty applies. Role: graph spectral alignment instrument.
Card 25 — Coresets / landmarks (R6) (ledger row 30): subset-to-whole recovery curves (k-NN on time index; within-series permutation null; 10 seeds × m = 49). The relational form of the entropy floor: structured series rise strongly (registered positive controls); i.i.d. series are flat. Role: subset-recovery instrument.
Card 26 — Matrix completion / compressed sensing (R7) (ledger row 38 admission): SoftImpute nuclear-norm minimization. Prediction from the entropy floor: completion sits on the null line; flat recovery curve is the registered expected outcome. Admitted (FPR calibrated, power demonstrated on planted low-rank data). Role: low-rank structure instrument.
Applied results: docs/CASE_STUDY_1_PCSO.md §7.
Card 8 — Doob optional stopping (see dynamical face): the detection-to-action gate.
Card 9 — Kelly criterion / St. Petersburg (ledger row — decision sizing): log utility resolves the St. Petersburg paradox (Bernoulli 1738); Kelly (1956) gives the growth-optimal stake f* = p − q/b. Decision ordering: Doob gates → EV measures → Kelly sizes. All detection instruments null ⇒ f* = 0. Role: stake-sizing instrument. Blind to whether an edge exists at all — that is the statistical layer's and Doob's job.
Card 16 — Expected value / Stern–Cover (ledger row 14): hypergeometric tier EV decomposition with Poisson co-winner correction E[J/(1+K)] where K ~ Poisson(λ). Payout-relevant backtesting (not proxy metrics) was decisive for evaluating generative models. Role: EV measurement instrument. Blind to risk preferences (Kelly's job) and to whether an edge exists (statistical layer + Doob).
Applied results: docs/CASE_STUDY_1_PCSO.md §10.
Source: docs/EQUATION_DISCOVERY.md, docs/RUNBOOK.md Phase 5. Added 2026-06-11
as a new pipeline phase between CONFIRM (Phase 4) and DECIDE (renumbered to
Phase 6). The lab can derive statistically validated candidate equations or
generative models for detected structures. It does not automatically discover
true governing laws.
Equation discovery consumes only confirmed STRUCTURED verdicts, post-freeze, with
driving-row/variable attribution on file. Anything else returns
NO_EQUATION_ATTEMPTED — the lab never searches for equations in unvalidated
data. This preserves A7 (each layer answers its own question). The gate is
demonstrated in practice: a request to fit marginal-bias coefficients to PCSO
6/49 (a NULL-verdict series) was refused without loading the dataset
(docs/RESULTS_EQ_pcso-649-marginal.md), because every fitted |δ̂ᵢ| would sit
below the card-19 detectability floor — noise dressed as a coefficient.
Eight candidate families, each grounded in instruments the lab has already carded (no new mathematics to fit; what is new is the selection-and-validation contract):
| Detected structure | Candidate equation family | Card(s) |
|---|---|---|
| Marginal bias | probability-weight law, Σδᵢ = 0 constrained | 1, 2, 19 |
| Memory / temporal dependence | Markov / autoregressive, kα+(P−k)β = k constrained | 6, 7 |
| Periodic cycle | harmonic regression (sin/cos pairs per harmonic) | 12 |
| Regime shift | piecewise / changepoint | 4 |
| Low-rank matrix | factorization M = UVᵀ | 11, 26 |
| Graph community | stochastic block model | 24, 25 |
| Topological loop | latent-phase parameterization θ_t ∈ [0, 2π) | 23 |
| Shared latent relation | latent-variable model | 22, 21 |
Symbolic regression / SINDy and structural causal equations are explicitly out of scope until onboarded with their own A1 null generators.
Every equation search is registered before fitting (candidate families, splits, nulls, complexity penalty λ, multiplicity charge — human-approved and hashed into the commitment ledger), then selected by MDL subject to held-out skill: J(f) = L_heldout(f) + λ·complexity(f). The key A1 addition is the null-equation generator: the identical discovery procedure is run on matched synthetic nulls, because equation searches on pure noise return equations — only the null distribution of recovered-equation scores converts "we found an equation" into a calibrated p-value. Acceptance additionally requires bootstrap parameter stability, residual checks (§8: autocorrelation, Fisher g, MMD, changepoints, TDA, compression), coefficients above the card-19 floor, and per-regime / per-era coefficient reports (M4).
| Verdict | Meaning |
|---|---|
| NO_EQUATION_ATTEMPTED | source claim not STRUCTURED, or family not registered |
| CANDIDATE_EQUATION | descriptive fit exists (level 1) |
| PREDICTIVE_EQUATION | beats matched nulls on held-out data (level 2) |
| MECHANISM_SUPPORTED | stable, interpretable, externally corroborated |
| GOVERNING_LAW_CONFIRMED | fresh-data confirmation + mechanism evidence (level 3) |
| FAILED_EQUATION_SEARCH | structure confirmed but no compact equation passed validation — a publishable result |
Doob separation holds: even a PREDICTIVE_EQUATION confers no action license; Phase 6 still gates. Equation verdicts never upgrade a detection verdict.
The layer was first deployed on physical positive controls with externally known governing rules — mirroring how the blind 9-series eval validated the detection layer before it was trusted:
| Run | Target | Verdict | Calibration outcome |
|---|---|---|---|
eq.tidal v1–v2 (RESULTS_EQ_TIDAL.md, _V2.md) |
total tidal acceleration | FAILED_EQUATION_SEARCH | anomalistic month recovered (27.487 d, 0.25% err); spring–neap missed; surrogate null not beaten (p = 0.194) |
eq.tidal v3 fine-grid (RESULTS_EQ_TIDAL_V3.md) |
residual-line adjudication | FAILED_EQUATION_SEARCH | leakage hypothesis registered, tested, and logged dead; 5 unattributed refined lines published as a discovery-grade anomaly in ephemeris-derived data; any v4 gated on human review |
| eq.moondist v1–v2 | Moon distance | FAILED_EQUATION_SEARCH | period recovery PASS (27.604 d, CI ∋ 27.555 d anomalistic month); structured residuals blocked the verdict |
eq.moondist confirm1 (RESULTS_EQ_MOONDIST_CONFIRM1.md) |
Moon distance, fresh data | MECHANISM_SUPPORTED — the lab's first | the frozen v2 equation (hashed before the data existed, zero free parameters, no refit) forecast 86 strictly post-freeze JPL Horizons rows inside every registered gate (RMSE ratio 1.273× vs the declared 1.5× envelope) |
eq.pcso-649 marginal (RESULTS_EQ_pcso-649-marginal.md) |
PCSO 6/49 δ coefficients | NO_EQUATION_ATTEMPTED | hard gate held: NULL source claim, no registration, no attribution — no fit performed |
Agent routing: equation-analyst (agents/equation-analyst.md) designs and
fits; the independent-verifier checks recovered parameters against known ground
truth; the equation-analyst instance for a claim is never the structure-analyst
instance that detected it.
Mechanically re-derives every documented number from its source JSON and checks all six sections of the relational results. Current verdict: all 6 sections green. The script is run as part of every dispatch and its output is the first item in the verifier's report.
Enforces structural properties of the claim-instrument mapping before any result is published:
- Claim-type ↔ method mapping: each registered claim is of a declared type (subset-to-whole, cross-dataset similarity, latent-sharing, topological, distributional, marginal, memory, stationarity); the method must match.
- Permutation floor rule: p_floor ≤ α_corrected / 2 for every registered family. This rule caught a borderline λ_max case and forced a rerun at higher resolution — where the flag closed.
- Sensitivity-regime presence: three-regime reporting (all / ex-suspicious / verified-only) required for any claim touching data with flagged rows.
Current verdict: PASS, 0 violations (111 historical warnings resolved).
Ensures domain vocabulary is confined to src/domains/<domain>.py, frozen historical
records, domain datasets/results, and domain deliverables. Current verdict: PASS,
16 files clean (source: docs/SANITIZATION.md).
Mechanically checks the four-level ledger system itself: run-ledger rows parse with
unique run_ids and every recorded output_sha256 still matches the file on disk;
multiplicity-ledger rows carry valid schema-v2 fields (raw_p ∈ [0,1], p_floor
consistent with m_perm, run_ids cross-referenced to the run ledger); the commitment
ledger's append-only text format is intact; the riemann sub-ledger parses. Runs in CI
on every push and as the installer's final gate. Current verdict: PASS — 10 checks,
0 warnings. Companion tool tools/snapshot_commitment.py appends a labeled,
delta-only commitment snapshot in one command (append-only; secrets excluded).
Every push and pull request runs the full stack on Ubuntu and macOS: the guided
installer itself (python3 install.py --yes — CI fails if a fresh install's gates
fail), all five verifiers above, the repo test suite (tests/ — installer behavior,
ledger tooling, agent-eval regrades, webapp smoke), the webapp unit tests, the riemann
regression tests, and the 10-view browser e2e suite. A weekly scheduled run
(Mondays 06:00 UTC) catches bit-rot between pushes, and an informational Windows job
(continue-on-error) reports cross-platform drift without blocking. Locally,
./tools/check.sh [--e2e] runs the same battery in one command.
All instrument families are re-gated at n=200 before any real-data run that will
produce a publishable verdict. Gate mechanics: 500 simulated H₀ datasets of the real
data's exact shape; FPR must sit within 3-SE of α; p-distribution must be uniform
(KS test). The quarter-shape gate passes (FPR 0.035, KS p=0.20); the GW gate fails
(source: docs/REMEDIATION_LOG.md M2).
- git baseline commit
e1bc32b: the first anchored state; all prior "registrations" are explicitly labeled retroactive in the run ledger (source:docs/REMEDIATION_LOG.md C1andresults/run_ledger.jsonl). - Append-only hash ledger (
results/commitment_ledger.txt): SHA-256 of every doc, script, and result file, snapshotted after each batch. Registrations are committed to the ledger before their run scripts execute. The blind-eval verdict hash1d0a4d3ed4d2dd4dwas committed before the answer key was unsealed (verified by recompute inresults/blind_eval_score.md). - Owner action pending: host-side
git committo anchor the ledger to version control (the sandbox cannot issue git commits).
| Ledger | Location | Content |
|---|---|---|
| Results ledger | docs/THEOREM_SYNTHESIS.md §5 |
40 rows: every instrument, functional, H₀ value, observed value, corrected p |
| Run ledger | results/run_ledger.jsonl |
10 runs: script, seed scheme, executor identities, grade, output SHA-256 |
| Multiplicity ledger | results/multiplicity_ledger.jsonl |
173 real-data tests, one row per test: claim type, method, raw p, m_perm, p_floor, family ID, data filter |
| Commitment hash ledger | results/commitment_ledger.txt |
SHA-256 of every doc/script/result at each batch snapshot; blind-eval commitment chain |
Meta-uniformity panel (source: results/meta_uniformity.json): across the 126
lotto-side real-data p-values from the relational batches, KS vs uniform p = 0.385,
6.3% ≤ 0.05, 0.8% ≤ 0.01 — globally consistent with honest null testing. Physical-
series positives excluded by design (they are positive controls, not null tests).
Note on the 173 vs 126 figures: the multiplicity ledger contains 173 real-data tests total; the meta-uniformity panel covers the 126 lotto-side tests (the 47 excluded are physical-series confirmatory positives and cross-executor verification runs with no null hypothesis).
Source: docs/AGENT_WORKFLOW.md, agents/evals/EVAL_SET.md.
| Agent | Role | Phases | Primary model | Escalation |
|---|---|---|---|---|
lab-orchestrator |
routes phases, enforces gates + role-ID separation, maintains run ledger; produces nothing itself | all (coordination only) | Fable | fable → opus; never below |
research-scout |
literature, canonical references, dataset sources, prior art | 0 (sourcing) | Sonnet | sonnet → opus (contested literature) |
data-reader |
file extraction, row audits, schema checks, result-JSON lookups; read-only, no interpretation | 0–5 (support) | Haiku | haiku → sonnet (ambiguous formats) |
theorem-dataset-onboarder |
cards theorems, onboards datasets (gate-checked, clerical) | 0–1 | Haiku | haiku → sonnet → opus → any LLM + human diff |
structure-analyst |
null design, instrument implementation, real-data runs, attribution, multiplicity | 2–4 | Fable (design); Haiku (execute-only re-runs) | design: fable → opus → sonnet; execution: haiku → any LLM execute-only |
equation-analyst |
derives candidate equations for confirmed STRUCTURED claims: family registration, null-equation generator, constrained fits, MDL selection, residual checks, equation verdicts; never detects, never decides | 5 | Fable (design/interpretation); Haiku (execute-only fits) | design: fable → opus → sonnet; execution: haiku → any LLM execute-only |
docs-web-editor |
generates RESULTS docs, figures-from-JSON, ledger sync, web pages; numbers copy-only | 5 | Sonnet | sonnet → opus (narrative restructuring) → human diff review |
independent-verifier |
numeric + design verification, reproduction diffs, blind replication, ledger reconciliation; never verifies own authorship | all (after each) | Haiku (numeric) / Sonnet (design) | identity rule has no fallback: a different instance than the author, always |
Role-ID separation is mechanical and recorded per run in results/run_ledger.jsonl:
onboarder_id != analyst_id, analyst_id != verifier_id, editor_id != analyst_id,
verification_executor != script_author, equation_analyst_id != detection_analyst_id
(per claim: the detector never fits its own equations). A run missing these fields, or violating them,
is unpublishable.
Replay and audit: every dispatch produces a results/agent_runs/<run_id>/ directory
containing prompt.md (saved before dispatch), agent.txt (identity), report.md
(verbatim return), files.txt (diff), and grade.json when the dispatch is an eval.
All analysis scripts are deterministic with fixed seeds; replaying a run = re-executing
the named script; byte-identical output is the pass condition.
Eval suite: 12/12 PASS (source: agents/evals/EVAL_SET.md). One real pipeline bug
found by eval A-2: a stale meta-uniformity panel (inputs changed post-build); the panel
was refreshed and the correct KS p = 0.385 was published. Evals V-1, V-2, V-3, D-1,
D-2, A-1, A-2, O-1, R-1, E-1, X-1, X-2. Two evals (X-1, X-2) carry a human-review
grading caveat (graded by orchestrator-builder, not an independent agent).
Blind 9-series verification (source: results/independent_verification.json, docs/REMEDIATION_LOG.md C2)
A separate agent, barred from lab code, documentation, and any prior results, was given
9 standardized series with neutral names and no dates. The agent implemented its own
test suite and applied its own decision rule (Bonferroni 0.05/4 across 4 statistics, or
≥ 2 tests with raw p < 0.05). Result: 9/9 concordance — all 4 physical series
returned STRUCTURED, all 5 lotto series returned NO DETECTED STRUCTURE. Conducted
expectation-free. Details and replication numbers: docs/CASE_STUDY_1_PCSO.md §9.
Source: results/blind_eval_score.md. 68 registered claim units across 16 claim
families, drawn from 14 synthetic dataset objects. The answer key was sealed in the
commitment ledger (hash 979b75a420b01952) before analysis began; lab verdicts were
committed (hash 1d0a4d3ed4d2dd4d) before the key was unsealed; scoring was conducted
by an independent-verifier agent that did not run the analysis. Role separation
recorded in results/run_ledger.jsonl run blind_methodology_eval_v1.
Results:
| Metric | Value |
|---|---|
| True Positives | 19 |
| True Negatives | 45 |
| False Positives | 0 |
| False Negatives | 4 |
| Sensitivity | 0.826 |
| Specificity | 1.000 |
| Accuracy | 0.941 |
Zero false positives: the permutation-based nulls, Šidák family corrections, and
Phipson–Smyth +1 floors held without exception even when several null excursions reached
raw p = 0.01–0.03. The 4 misses are documented with honest descriptions in
results/blind_eval_score.md §5; all four are instrument-representation or
family-size-threshold limits, not false nulls on genuinely structured data.
Source: docs/RESPONSE_EXTERNAL_REVIEW.md.
| Grade | Meaning | Current holders |
|---|---|---|
| G0 | exploratory, no claim | GW real-data pairs (post-demotion); 6/45 watch item |
| G1 | calibrated instrument | R1–R7 (FPR-calibrated at tested shapes; GW G1 with standing distribution-calibration flag) |
| G2 | internal result, registered-ish | most batch 5–7 results; pressure covariate results |
| G3 | auditable registration | none retroactively; future batches via hash ledger + host git |
| G4 | independent reproduction | series-level structure/null verdicts for all 9 blinded datasets (blind 9/9); 6/55 half-corr sensitivity (replicated to 3 decimals); blind methodology eval (68-unit benchmark, role-separated) |
| G5 | held-out confirmation | none (confirmation family untouched, by design) |
| G6 | decision-grade | the refusal decision (no betting edge) — asymmetric: declining to act requires less evidence than acting; rests on Doob + entropy floor + uniformly null G2–G4 evidence |
Source: docs/SANITIZATION.md.
src/core/ # domain-neutral instrument library (stats, discrete_draws,
# recovery, paired, geometry, graphs, completion)
src/domains/ # one file per domain (currently: pcso_lotto.py)
src/ # 21 frozen historical scripts — reproduce ledger rows 1–39;
# stamped FROZEN HISTORICAL RECORD; do not rewrite
datasets/ # per-domain datasets with DATASET.md cards
results/ # ledgers, JSONs, figures
agents/ # agent definitions + eval set
evals/ # eval suites (structure_eval_set_v1)
docs/ # governance, runbook, KB, results docs
src/core/ provides the forward-facing API for all new experiments. Domain vocabulary
(src/domains/pcso_lotto.py) contains: draw-ensemble registry, loaders with data-quality
regimes, covariate bundle, ANOMALY_REGISTRY (C9 row-trace duties), ERA_REGISTRY (A5).
src/lint_domain_neutrality.py must PASS before any results doc is published.
Adding a new domain: create src/domains/<domain>.py with the same interface
(ensemble registry, loader, covariate bundle, ANOMALY_REGISTRY, ERA_REGISTRY), onboard
the dataset per THEOREM_GOVERNANCE.md Part 4, and run the three verifiers
(numeric + design + lint). All instruments, nulls, gates, ledgers, and agents work
unchanged. For financial data the mission inverts: H₀ rejections are expected (heavy
tails, volatility clustering, factor structure); the framework's anti-self-deception
machinery matters most in attribution and net-of-costs survival testing.
Source: riemann-zero-lab/README.md. Added 2026-06-13 — the lab's first deterministic-
mathematics module. Instead of testing stochastic data for structure, it locates and verifies
zeros of the Riemann zeta function ζ(s). It is numerical discovery, never an RH proof: RH is
an infinite statement; the module touches finitely many zeros (riemann-zero-lab/docs/kb/riemann-hypothesis.md).
Batch 1 located and verified the first 200 non-trivial zeros on the critical line
(Hardy Z-function sign-change bracketing, mpmath dps=80): residuals ≤ 3.1e-47, precision-stable
to 56–60 digits, two-run byte-identical. The located count equals N(T), mpmath.nzeros, and a
contour argument-principle integral (no zero missed up to height ≈ 397 — a finite check, not
RH). Unfolded nearest-neighbour spacings are decisively non-Poisson and GUE-like
(KS D_GUE = 0.07 vs D_Poisson = 0.35), reported as descriptive at N = 199.
Why it fits the constitution (C11 / A8). A1's "every null is Monte-Carlo-derived" is
undefined for the existence of a zero — nothing random to resample. Conflict C11 records
this; article A8 (deterministic-certificate substitution) resolves it: deterministic claims
are admitted on a three-leg certificate (exact computation to a declared tolerance, independent
recomputation by a different instance, analytic invariant cross-check count = N(T) = contour
integral), while the MC-null discipline (A1–A7) governs the one genuinely stochastic layer — the
spacing-vs-Poisson comparison — unchanged. A methodology-change eval slice
(agents/evals/EVAL_SET.md §Z: Z-V1/Z-V2/Z-O1) confirmed the verification and onboarding gates
transfer: 3/3 PASS.
Same discipline as the rest of the lab — cards-first (riemann-zero-lab/docs/kb/INDEX.md, 7
cards), registration committed before the first result run, JSON-from-scripts /
results-from-JSON, role-separated independent verification, adversarial-review section, and a
run-ledger row. Start at riemann-zero-lab/README.md.
- docs/RUNBOOK.md — the 7-phase workflow (Phases 0–6, including Phase 5 equation discovery) + failure-mode gallery + domain-porting guide
- docs/EVALUATION_PROTOCOL.md — formula-level spec (E0–E9 evaluation, H1–H7 harmonization); the deterministic guide for human or LLM executors
- docs/THEOREM_GOVERNANCE.md — conflict registry C1–C11, harmonization constitution A1–A8 (A8 = deterministic-certificate substitution), theorem onboarding (Part 3), dataset onboarding (Part 4)
- docs/THEOREM_SYNTHESIS.md — the theory map: five faces of structure, the implication lattice, instrument correlation, the 40-row results ledger
- docs/CROSS_DATASET_FRAMEWORK.md — the relational extension (fifth face): cross-dataset similarity/alignment and subset-to-whole recovery (D = S ∪ H), folded onto the same constitution (A1–A7). Method-by-case taxonomy, matched relational nulls, 9-experiment benchmark suite, decision tree, recovery curve.
- docs/RELATIONAL_RUNBOOK.md — the relational experiment protocol: Phase 0 (registration, expectation-free), Phase 1 (admission), Phase 2 (run), Phase 3 (verification)
- docs/REMEDIATION_LOG.md — all adversarial-review findings and their dispositions; the protocol change history
- docs/RESPONSE_EXTERNAL_REVIEW.md — external review findings, G0–G6 ladder
- docs/SANITIZATION.md — domain-neutral refactor record
- docs/AGENT_WORKFLOW.md — model-routed agent execution: 8-agent roster, role-ID separation, replay mechanics, eval gate
- docs/EQUATION_DISCOVERY.md — Phase 5 specification: STRUCTURED-only gate, equation families, registration contract, null-equation generator, verdict ladder
- docs/LAB_IMPROVEMENT_PLAN.md — prospective reliability and accuracy program: executable registrations, calibrated nulls, sequential error control, provenance, independent verification, and measurable delivery gates
- docs/kb/ — 26 theorem/methodology cards + INDEX
- admin_onboarding.html — gate-checked wizard for new theorems and datasets
- docs/CASE_STUDY_1_PCSO.md — Case Study 1 (PCSO lottery draws): full per-face results, anomaly adjudication, external validations, decision layer, ethics note, links to all results documents and ledgers
- docs/RESEARCH_NOTES.md — full evidence log: every test, p-value, correction, and the adversarial-review trail
- docs/RESULTS_RELATIONAL_FIRSTRUN.md, RESULTS_BATCH4.md, RESULTS_BATCH5.md, RESULTS_BATCH6.md, RESULTS_PRESSURE.md — batch-by-batch relational results
- docs/RESULTS_EQ_TIDAL.md, RESULTS_EQ_TIDAL_V2.md, RESULTS_EQ_TIDAL_V3.md, RESULTS_EQ_MOONDIST_CONFIRM1.md, RESULTS_EQ_pcso-649-marginal.md — Phase 5 equation-discovery runs (registrations in docs/REGISTRATION_EQ_*.md)
- datasets/pcso-lotto/ — DATASET.md card + canonical/audited/provenance CSVs
- datasets/tidal-manila/, datasets/jpl-horizons-sun-moon/, datasets/gfz-kp-geomagnetic/, datasets/openmeteo-pressure-manila/ — covariate datasets (DATASET.md cards with single-source caveats where applicable)
- results/commitment_ledger.txt — append-only hash ledger (3 snapshots + blind-eval chain)
- results/run_ledger.jsonl — 10 run records with executor identities
- results/multiplicity_ledger.jsonl — 173 real-data test rows
- results/meta_uniformity.json — global meta-uniformity panel (KS p=0.385)
- results/independent_verification.json — blind 9/9 concordance + numerical replication
- results/blind_eval_score.md — 68-unit methodology benchmark (answer key sealed until verdict hash committed)
- results/agent_runs/ — dispatch records for every agent eval and verification run
# Recommended: the guided installer handles all of this (venv, full dep set,
# post-install verification) — see the Installation section at the top.
python3 install.py
# Manual alternative: requirements.txt now declares the full runtime set
# (ephem, numpy, openpyxl, scipy, matplotlib, pandas, ripser). On an
# externally-managed interpreter (e.g. Homebrew Python — PEP 668) work inside
# a venv, or append --break-system-packages.
pip install -r requirements.txt
# Verify the runtime deps are all importable before running jobs:
python3 webapp/test_lab_deps.py
python3 src/montecarlo_certification.py # marginal uniformity + ensemble certification
python3 src/markov_analysis.py # dynamical face: order-0 vs order-1
python3 src/structure_discovery.py # algorithmic + cross-sectional: compression/RMT/spectra
python3 src/powerlaw_sweep.py # scaling laws: Zipf, Taylor, first-digit, Levy, coverage
python3 src/perbak_soc_analysis.py # statistical physics: SOC signatures
python3 src/universality_collapse.py # data collapse, RG flow, Binder cumulant
python3 src/explore_batch2.py # positional/calendar/pair/scan statistics
python3 src/cross_theorem_correlation.py # cross-domain coupling detector
python3 src/review_response.py # audit table, payout-relevant backtest, persistence
python3 src/markov_chain_model.py # generative model + walk-forward evaluation
python3 src/relational_first_run.py # relational: recovery curves + CCA
python3 src/relational_batch5.py # cross-game spectra, delay topology
python3 src/relational_allgames.py # all-games symmetry
python3 src/relational_subsets.py # partition: quarters, halves
python3 src/relational_pressure.py # pressure covariate baseline
python3 src/relational_batch7.py # pressure seasons, GW first run
python3 src/remediation_r1.py # full remediation batch (expectation-free)
python3 src/eq_tidal_v1.py # Phase 5: tidal/moondist equation calibration v1
python3 src/eq_tidal_v2.py # Phase 5: v2 (3-line family, surrogate nulls)
python3 src/eq_tidal_v3.py # Phase 5: v3 fine-grid residual adjudication
python3 src/eq_moondist_confirm1.py # Phase 5: fresh-data confirmation (MECHANISM_SUPPORTED)
python3 src/verify_relational_docs.py # numeric verifier (all 6 sections)
python3 src/design_verifier.py # design verifier (claim↔method, floor rule)
python3 src/lint_domain_neutrality.py # domain-neutrality lint
python3 src/meta_uniformity.py # global meta-uniformity panelThe scripts in src/core/ (stats, discrete_draws, recovery, paired, geometry, graphs,
completion) are the forward-facing instrument API for new domains; they are not run
directly.
python3 src/verify_relational_docs.py # PASS — all 6 sections green
python3 src/design_verifier.py # PASS — 0 violations
python3 src/lint_domain_neutrality.py # PASS — 16 files clean
python3 src/verify_ledger_integrity.py # PASS — 10 checks, ledgers ↔ disk consistent
python3 src/grade_agent_eval.py --all # regrades every agent-eval dispatch record
# (PASS / FAIL / INCOMPLETE_RECORD; read-only)
python3 tools/snapshot_commitment.py "label" # append a commitment snapshot (append-only)
./tools/check.sh # everything above + all test suites, one command
./tools/check.sh --e2e # … plus the 10-view browser e2e suite
python3 -m pytest tests/ -q # installer / ledger-tool / webapp-smoke tests- Retroactive registrations: git baseline commit
e1bc32bis the first genuine commitment device. All registrations prior to that commit are explicitly labeled retroactive in the run ledger and commitment ledger; they do not carry G3 grade. - Single primary case study: the framework has been exercised on one dataset
(PCSO lottery draws, Case Study 1). Transferability to other domains is supported by
architecture (domain-neutral
src/core/) but not yet empirically demonstrated. - G5 empty: the confirmation family (m = 9, α' = 0.0056) has not been touched; no result currently holds G5 grade. This is by design, not an omission.
- GW retired: GW (R2) is retired to the conflict registry (C12). The registered
readmission run (
docs/RESULTS_GW_READMISSION_V1.md) showed the redesigned permutation null is calibrated but powerless — no achievable null family both calibrates and powers exact GW. GW-alone results remain unpublishable; a future GW-family instrument would be a new onboarding. - Resolution bounds: all "no structure found" verdicts are bounded by ε at tested n. ε ≈ 0.15–0.20 is vacuous as an EV constraint at feasible ticket counts. "At the tested resolution" qualifies every null result.
- Single-source covariate: Manila atmospheric pressure is ERA5/Open-Meteo only; positive pressure claims are gated until a second source is added.
- Operating point — high specificity by design: the lab is a conservative detector,
not a maximum-sensitivity one. The blind methodology benchmark (source:
results/blind_eval_score.md) confirms this empirically: 0 false positives across 45 null slots with sensitivity 0.826 at the tested instrument set. The cost of the conservative operating point is deliberate — Šidák corrections and Phipson–Smyth +1 floors absorb near-threshold signals rather than emit marginal claims. Near-misses and instrument-gap detections are tracked via the five-tier verdict taxonomy and the instrument roadmap; they do not count as STRUCTURED verdicts and are never cited in public claims. Seedocs/RESPONSE_BLIND_EVAL_ADMIN.mdfor the full admin review disposition and roadmap.
docs/ADVERSARIAL_REVIEW.md is a self-adversarial review conducted before any external
examination; it identified the seven major findings (M1–M7) that drove the remediation
program. An external LLM review (docs/EXTERNAL_REVIEW_BRIEF.md) independently raised
overlapping concerns and introduced new items (evidence-grade ladder, design verifier,
multiplicity ledger, environment capture); the response (docs/RESPONSE_EXTERNAL_REVIEW.md)
adopts all of them with notes on any divergence. The remediation log
(docs/REMEDIATION_LOG.md) records what was done for each finding and its outcome —
including the GW gate failure (M2: the instrument the lab built itself failed its own
calibration check and was immediately demoted), the 6/45 flag opening and closing (M3:
a borderline estimate at insufficient resolution, closed when forced to higher resolution),
and the stale meta-uniformity panel caught live by eval A-2 (the A-2 eval re-ran a
script and found byte-level discrepancy; the panel was refreshed to KS p = 0.385).
Protocol v2.1 · Jun 11, 2026
Local, zero-dependency console for the lab (Python stdlib only, fonts vendored in
webapp/static/fonts/ — no CDN, works fully offline/air-gapped):
python3 webapp/server.py # http://localhost:8787 (redesigned console)
python3 webapp/server.py --lan # + phone access on the same Wi-Fi (token-gated;
# open the ?token=… URL printed at startup)
Or just double-click Start Lab Console.command (macOS) — it starts the server and opens the browser; close the Terminal window to stop.
The redesigned, Apple-style, mobile-friendly console is served at /; the
original console remains available at /classic. Nine views plus a pipeline
wizard: Overview with the lab's single next step, Experiments with PDF
export, Equations with a try-it sandbox (descriptive fits only — 0
multiplicity, never citable), a searchable Theorems arsenal (docs/kb), the
multiplicity Ledger + honesty meter, the Run centre for live agent/script
status, HUMAN-GATE Approvals (append-only audit log at
results/webapp_approvals.jsonl; fills blank approved_by_human lines), an
Admin page whose API keys live in webapp/config.local.json (gitignored,
masked when served), and a dynamic Help page with a live "lab at a glance"
and the protocol docs. Binds 127.0.0.1 only.