fep_lean

fep_lean is a standalone catalogue of 159 Free Energy Principle, Active Inference, Bayesian Mechanics, Information Geometry, and Thermodynamics topics. Each row contains a reviewed invariant, explicit assumptions, a Lean 4 theorem body, and typeset signatures. The pinned Lean workspace is the compilation authority; the semantic review separately records how far each theorem reaches toward its topic label. The schema-2 roster spans 20 reviewed families in five areas and is a versioned interface, not an exhaustive census of the FEP literature. The twenty families include five second-expansion families for finite-sample risk, closed-loop policy trees, native blanket transfer, finite exponential-family dual geometry, and exact two-state continuous time.

Release

Version 1.3.0 is the 159-topic publication cut. The canonical software release is GitHub v1.3.0, and the evolving scholarly record is identified by the Zenodo concept DOI. The GitHub release notes cross-reference the immutable Zenodo version DOI and publish the release-bundle checksum; the bundle manifest remains the owner of per-file hashes. Neither publication surface changes the evidence boundaries below.

Contract

full execution is strict. It requires the pinned Lean/Lake/Mathlib workspace, the gauss executable, configured Hermes credentials, and writable SQLite state. Every selected row must compile without sorry or Lean warnings, and a requested review workflow must complete its post-compile review turn. Missing capability or incomplete stage → complete: false, no report directory.

catalogue execution is deterministic and offline. It validates the complete YAML source and writes figures, manuscript variables, the unified appendix, and a report explicitly marked catalogue; it does not count topics as verified.

verify execution is Lean-only. It runs the sealed-roster native compile sweep without Hermes or OpenGauss. Add --receipt output/native-verification.json --fail-on-warnings to persist independently revalidatable native evidence.

atlas execution is deterministic and offline. It projects the canonical coverage join into a standalone SVG and an interactive, keyboard-accessible HTML graph; --check fails on missing or stale bytes. The graph distinguishes derivational formal edges from checked formal pairings that place two endpoint laws side by side without asserting implication. Both name qualified Lean witnesses; conceptual and blocker edges remain visibly non-proof evidence.

dashboard execution is also deterministic and offline. It renders static and interactive numerical witnesses for all fifteen expansion families. The first ten cover Bayesian inversion, variational duality, control, temporal inference, causal intervention, predictive coding, path thermodynamics, categorical Fisher geometry, consensus, and finite concentration; the latest five cover Laplace/Brier risk transfer, policy-tree feedback, native blanket conditional independence, exponential-family duality, and a two-state master equation. These witnesses expose computational behavior and boundary cases but never replace native Lean or axiom-audit evidence.

Formal depth

The live formalism is organized into theorem-connected strands rather than a headline theorem count: normalized finite probability and information algebras, including support-free separation for the explicitly totalized finite KL; posterior-form variational free energy and a uniquely attained evidence lower bound; both expected-free-energy decompositions; a transition-consistent infer--select--act joint and prior-sensitive Boolean policy witness; stage-dependent cumulative finite-horizon EFE; finite Bayesian inversion, variational duality, controlled and temporal inference, causal interventions, and generalized predictive coding; path-space fluctuation identities and reversible KL dissipation; categorical Fisher geometry, Cramér--Rao, natural-gradient, mirror-descent, and replicator laws; collective inference; finite concentration and model-evidence results; finite Laplace/Brier risk transfer; observation-contingent policy-tree recursion and dominance; native CondIndepFun blanket transfer; scalar exponential-family KL/Bregman duality; and an exact two-state continuous-time semigroup, master equation, detailed balance, relaxation, and Lyapunov law. The generated coverage report owns all current counts, and the atlas shows exactly which relations have Lean witnesses. The semantic firewall requires every non-formalized row to expose an explicit scope or assumption boundary. The reusable kernel is an explicit manifest of foundations and leaf composition modules; composed.lean is only their import aggregate. The maturity audit, rather than compilation alone, records which rows are direct formalizations and which remain conditional or structural proxies.

Current evidence boundary. The maintained catalogue spans 155 topics. H1.0--H1.8 have exited through their accepted gates, with optional H1.5 accepted separately; the archived Horizon 1 record owns the detailed evidence. Its terminal theorem is one finite, synthetic, one-step posterior--decision--action certificate on a shared 16-state Boolean carrier. The learned posterior, emitted action, sampled kernel, genuine sensory--active blanket factorization, and strict real/native KL decrease remain connected on that same carrier and kernel. The record also preserves the first H1.8 carrier-merge no-go. It does not establish transition-aware planning, EFE-optimal control, physical or causal adequacy, empirical validation, or a universal FEP claim.

The active Horizon 2 spec has accepted H2.0--H2.3b, H2.4a/b, H2.5a/b/c/d, H2.5b-R0, H2.5d-R0, H2.6a/b/c, and H2.6a-R0. The current smooth surface includes fixed-variance scalar Gaussian KL/information geometry, local coordinate duality, a same-joint native posterior martingale with its limiting-observation conditional-expectation endpoint, selected-model identification, joint-law and fixed-truth posterior consistency, weak convergence to the sampled-parameter Dirac law, bounded-continuous transfer, bounded zero-one risk convergence, native kernel/action semigroups, exact scalar and finite-axis linear-Gaussian transition families, the exact four-axis symmetric-precision specialization, an evidence-a.e. native Gaussian filter with chronological finite recursion, one-step transition-consuming quadratic decision risk, and monotone finite-grid path laws with explicit support and log-ratio boundaries. The accepted R0 repairs preserve the historical H2.0 no-go rows while their maintained owners derive the replacement mathematics. H2.5d-R0 reconstructs the centered Fin4 stationary joint. Maintained H2.5d extends that native conditional product to every stationary center, proves blanket-a.e. pair and scalar conditional laws plus endpoint CondIndepFun, and derives a fixed bivariate precision perturbation with actual covariance -1 / 15 and native non-independence. H2.7-R0 has accepted the continuous density-relative exact-posterior VFE and derived local natural-gradient seam. The H2.7 terminal record now validates 328 mandatory cases, the enabled Fin4 supplement, 180 bound source hashes, independent diagnostics, and three source-bound reviews. This opens only read-only H3.G0 eligibility; no study metadata has been selected and H3.0--H3.7 remain closed.

That formal exit is not current publication evidence. The retained exact-roster native, declaration/axiom, Python, and Chrome receipts validate the frozen v1.1.0 release snapshot only; their former counts and hashes remain historical. The coordinated refresh that re-binds every live-source validator to the live roster completed deterministically on 2026-09-12 (recorded in CHANGELOG.md). The local full-report path output/reports/run_20260820_183143_709998/ was historical evidence for the earlier 50-topic source snapshot and does not bind the 155-topic source; that retained copy is no longer present under output/reports/, and ignored provider reports are deliberately not shipped in a release. The earlier Kimi and Gemini one-topic runs are historical smoke evidence as well. No provider secret is stored in the repository, and no execution receipt authorizes publication or proves the FEP as a physical theory.

Quick start

Run operator commands from a source checkout. Installed wheels support the packaged FEPTopicCatalogue.default() API and fep-lean --help; substantive commands deliberately require the checkout-owned configuration, Lean workspace, and manuscript assets. From another directory, pass --project-root /path/to/fep_lean before the subcommand.

uv sync --locked --extra dev
uv run python docs/pin_audit.py --check-latest
uv run fep-lean catalogue
uv run fep-lean atlas
uv run fep-lean dashboard
uv run fep-lean setup
uv run fep-lean verify --fail-on-warnings \
  --receipt output/native-verification.json
uv run fep-lean preflight
uv run fep-lean run

Use uv run fep-lean --help for filters, workflow selection, and the explicit checkout root. The equivalent maintained scripts are thin command wrappers in scripts/.

The operator command quick reference lives at docs/quickref.md.

Source of truth

• config/catalogue_metadata.yaml maintains the stable roster's descriptive and Mathlib metadata.
• config/theorem_maturity.yaml maintains the semantic review independently of syntactic compilation maturity.
• config/formalism_novelty.yaml records every post-baseline topic's nearest predecessors, invariant, carrier delta, and required composition theorem.
• config/formalism_relations.yaml maintains reviewed formal, conceptual, and blocker relations plus retained open, partial, and satisfied capability history. Shared imports never create scientific-dependency edges.
• src/fep_lean/catalogue/bodies/ contains the family-owned Lean bodies; registry.py validates their canonical order and latex.py derives theorem signatures.
• config/topics.yaml and src/fep_lean/data/topics.yaml are generated, byte-identical catalogue projections; regenerate them with scripts/_maint_build_topics_catalogue.py.
• lean/FepSketches/fep_all.lean is the tracked aggregate generated by scripts/_maint_build_fep_all_lean.py.
• src/fep_lean/formal/manifest.py owns the formal-resource roster. Canonical cross-topic proofs live in formal/compositions/, while composed.lean is the import-only aggregate; all tracked Lake projections are generated by scripts/_maint_build_formal_modules.py.
• docs/formalism-coverage.md, docs/formalism-atlas.svg, and docs/formalism-atlas.html are generated views of the same canonical semantic graph.

Review contracts

• ISA.md defines the ideal state, anti-criteria, and evidence gates.
• TODO.md is the canonical open-only backlog with behavior-based acceptance probes.
• CHANGELOG.md records release changes and their evidence boundary.
• manuscript/04i_formalism_catalogue_155.md states the five new families, theorem assumptions, non-vacuity witnesses, and evidence boundaries in one authored chapter.
• HANDOFF.md gives the next reviewer the operating protocol, evidence pointers, and extension backlog.

Development checks

The complete release-gate list is maintained as "Required release gates" in docs/testing.md; the quick local dev checks are:

uv run pytest tests/ -q --cov=src --cov-fail-under=89 -m "not serial_lean"
uv run mypy src
uv run ruff check src tests scripts docs

The reproducible build and publication gates (release-bundle determinism, browser acceptance capture, receipt validation) are documented in HANDOFF.md; setup and pipeline gates live in docs/getting-started.md and docs/pipeline.md.

Layout

Path	Purpose
src/fep_lean/catalogue	typed semantic model, family-owned canonical bodies, generation, and coverage projections
src/fep_lean/formal	packaged foundations, leaf compositions, import aggregate, and workspace projection
src/fep_lean/verification	read-only capability checks, Lean compiler bridge, declaration/axiom audit, and GNN artifact-proof extraction and manifest verification
src/fep_lean/llm	configured Hermes HTTP client
src/fep_lean/gauss	SQLite sessions and per-topic orchestration
src/fep_lean/output	evidence receipts, fail-closed rendering, figures, reports, the offline formalism atlas, and the typed numerical dashboard
src/fep_lean/pipeline	strict full and explicit offline catalogue modes
lean	pinned Lake workspace and tracked aggregate
manuscript	source chapters and generated publication inputs

Notation

Lean identifiers are deliberately topic-prefixed (fepNNN_*) and should be read together with the corresponding invariant and assumption_review in config/theorem_maturity.yaml. The generated appendix renders exact theorem signatures; prose notation is never an alternative source for the Lean API.