Docs: explain LeanTransitionCorpus for ATP training

README.md

@@ -13,10 +13,55 @@ configs:
 
 # LeanTransitionCorpus
 
-Incrementally published archival Lean proof transitions. **Partial extraction;
-not the complete planned corpus.** Original source and environment provenance are
-retained per row. The existing repository license metadata is preserved; source
-corpus licenses and restrictions still apply and are not replaced by this card.
+> **Status: incremental upload in progress.** This repository is useful now, but
+> it is not the complete planned corpus. Counts, source coverage, and shard
+> inventory will grow as verified batches are added.
+
+LeanTransitionCorpus is a dataset for training and studying automated theorem
+proving systems in Lean. Its unit of data is one tactic transition: the proof state
+before a tactic, the tactic that was executed, and the resulting state. This makes
+it suitable for tactic prediction, proof-state representation learning, premise
+selection, retrieval, verification, and trajectory-level training.
+
+Many Lean datasets expose a theorem, tactic, and pretty-printed goal strings. This
+corpus retains those human-readable views, but also preserves richer information
+from Lean's elaborator: the tactic `Syntax` tree, resolved identifiers, recursive
+Lean `Expr` trees, local context, metavariables, universe metavariables, source
+ranges, and premise/context information. The extra representations make it
+possible to investigate models that use Lean's internal structure rather than
+recovering it from printed text.
+
+Original source and environment provenance are retained per row. The repository's
+MIT metadata applies to this packaging; source corpus licenses and restrictions
+remain applicable and are not replaced by this card.
+
+## Source datasets
+
+The extraction pipeline draws from pinned snapshots of the following Lean sources.
+Rows identify their origin in `source_dataset`, `source_url`, `repo_commit`, and
+toolchain columns. Coverage is incremental: a source listed here may have less
+published coverage than another at any point in time.
+
+| Source | Role in the corpus |
+|---|---|
+| NuminaMath-CoT | Lean formalizations from the Numina mathematical reasoning corpus. This is the source of the initial uploaded seed. |
+| DeepSeek-Prover | Lean proof data used to broaden theorem and tactic coverage. |
+| Goedel Lean Workbook | Lean workbook proofs, retained as a separately attributable source. |
+| Mathlib | The pinned Mathlib snapshot supplies the theorem-proving environment and contributes directly extracted Mathlib theorems. |
+
+## How the data is produced
+
+For each selected theorem, the extractor runs the matching pinned Lean and Mathlib
+environment, records the sequence of tactic-state transitions, and canonicalizes
+the result into one row per transition. It validates internal-state structure and
+continuity between adjacent transitions, assigns deterministic splits, and keeps
+provenance needed to trace a row back to its source theorem and environment.
+
+Rows are written as Parquet shards. Before publication, every shard is checked
+against its source rows; uploaded bytes are read back and verified at an immutable
+Hugging Face revision. Batch manifests record shard hashes, source-batch identity,
+and extraction evidence. A `replay_status` value records whether an additional
+replay check was performed; publication alone does not mean replay certification.
 
 ## Format
 
@@ -37,6 +82,28 @@ Null stays null; an empty object stays the JSON string `{}`.
 identity of the provenance-based proof key plus `step_index`, prefixed by
 `ltc-v2:`. The earlier colliding source IDs are not retained in another column.
 
+## Schema in plain language
+
+Each row is a single ordered step within a proof. The fields fall into these groups:
+
+| Fields | Meaning |
+|---|---|
+| `example_id`, `proof_id`, `step_index`, `split`, `schema_version` | Stable identity, position in the proof, dataset split, and format version. `example_id` is globally unique; `proof_id` alone may not be. |
+| `source_dataset`, `source_url`, `repo_commit`, `file_path`, `lean_version`, `mathlib_version`, `extractor_version`, `pantograph_version`, `provenance` | Where the theorem came from and the exact environment and extraction provenance needed to reproduce or audit it. |
+| `theorem_name`, `theorem_statement_raw`, `theorem_source_raw`, `namespace`, `imports` | The theorem and its surrounding Lean source context. |
+| `state_before_raw`, `tactic_raw`, `state_after_raw` | The familiar human-readable goal display and tactic text for the transition. |
+| `state_before_structured`, `state_after_structured` | Parsed versions of the displayed proof states. |
+| `state_before_internal`, `state_after_internal` | Lean's detailed elaborator state: active goals, local declarations, targets, metavariables, universe metavariables, and recursive expressions. |
+| `atomic_tactics`, `tactic_internal` | The tactic's atomic view and its full Lean `Syntax` representation, including identifier resolution, premise references, and nested tactic structure when available. |
+| `used_premises`, `available_context`, `source_start`, `source_end` | Referenced declarations, candidate context, and the tactic's source span. |
+| `terminal`, `terminal_marker`, `terminal_raw` | Whether this step closes the proof and the source/display marker associated with closure. |
+| `theorem_fingerprint`, `state_fingerprint`, `transition_fingerprint` | Deterministic hashes useful for deduplication, grouping, and integrity checks. |
+| `replay_status`, `replay_error` | Result of optional replay validation; `not_run` means no independent replay was attempted. |
+
+The recursive structures are stored as lossless JSON strings in Parquet. Parse them
+with `json.loads` when you need their tree structure; leave them as strings for
+text-only training baselines.
+
 Each shard is round-trip compared against every original JSON row before upload.
 Remote bytes are streamed back and checked for SHA-256 and size at a pinned commit.
 `manifests/batches/` records verified shard hashes/revisions, original batch