Merge pilot recovery into the semantic simplex schema delivery

Reviewed-on: #8

README.md

@@ -276,6 +276,12 @@ Experiments have IDs (`P0`, `E0`-`E11`); the registry, phases, gates and convent
 [`docs/experiments/README.md`](docs/experiments/README.md). CI runner and environment notes:
 [`docs/infrastructure/runner-lean435.md`](docs/infrastructure/runner-lean435.md).
 
+Browse the [65-item semantic simplex schema review](docs/reviews/simplex-schemas.html)
+by opening that HTML file in a browser after cloning, or downloading it from Git.
+It shows role schemas and Lean signature expressions; textbook passages and full assistant
+judgment explanations remain private. The [schema design and replay instructions](docs/simplex-schema.md)
+explain how the page is generated and which annotations still need review.
+
 ## What this does not claim
 
 Lean says whether the code is *legal*, and — when there is a proof — whether it is
@@ -285,4 +291,5 @@ well-formed statement of the wrong theorem passes every check here. `confidence`
 possible; spot-check before trusting a dataset.
 
 Source books are not committed. `.gitignore` keeps PDFs and extracted text out of
-the repository; only code and the short Lean datasets belong in git.
+the repository. The tracked schema review contains semantic annotations and Lean signatures,
+while source-inclusive inputs remain in the ignored data directory.

docs/experiments/P0-execution-2026-10-28.md

@@ -0,0 +1,84 @@
+# P0 execution report: 2026-10-28
+
+**Status: blocked by provider billing. No GO, PARTIAL or NO-GO decision.**
+The owner requested delivery of the fixes and this report now, with the remaining paid calls deferred.
+
+## What ran
+
+The owner explicitly authorized sending the 65 textbook passages and corresponding Lean code
+through the existing DashScope endpoint to `qwen-max`, at temperature 0 and a cumulative ceiling
+of 400 HTTP requests. The run issued **131 HTTP requests**. Provider responses accounted for
+**37,699 input tokens and 7,790 output tokens**, 45,489 total. These are recorded token counts,
+not an invoice or a monetary cost estimate. The client counted 89 received model responses;
+a received response is not necessarily a usable detector result.
+
+| Coverage | Count |
+|---|---:|
+| Original cohort | 65 |
+| Items with both detectors complete | 42 |
+| Items with one or both detectors missing | 23 |
+| Successful role-extraction/alignment components | 45 |
+| Successful judge components | 43 |
+| Missing role components | 20 |
+| Missing judge components | 22 |
+| Remaining request reservations | 269 |
+
+DashScope returned HTTP 400 with error code `Arrearage` and its overdue-payment reference.
+The first runner implementation recorded the failures and continued through the cohort, so
+65 saved rows did not mean 65 successful items. The scorer rejected these incomplete outputs.
+No partial-sample gate decision or performance comparison has been produced.
+
+## Inputs and labels
+
+The default `items.jsonl` export omitted `source_text`. All 65 original passages were recovered
+from the matching detection spans and checked byte-for-byte against the archived private
+`review.json`. Item IDs and Lean code were unchanged. The recovery tool also verifies every
+exported field against the archive, normalizing the archive's JSON-encoded imports field.
+Source-inclusive inputs and the regenerated labeling HTML remain in the ignored data directory.
+
+The owner replaced the planned Kimi/human labeling with Codex annotation. All 65 labels were
+frozen before the first detector request. They contain 30 faithful, 25 wrong, 7 minor drift and
+3 not-formalizable verdicts. This is one AI annotator, **not human gold**. The annotator saw the
+detector implementation and aggregate compilation counts, but not per-item compiler outcomes
+or detector outputs. Syntax/proof defects were ignored when the intended semantics were recoverable;
+no compiler or API-name audit was performed. Independent human auditing remains necessary before
+using these labels as evidence for paper-level claims.
+
+## Execution repairs
+
+- Empty passages and mismatched frozen inputs/labels are rejected before paid calls.
+- Each HTTP attempt reserves cumulative budget before sending, including transport and JSON retries.
+  Model, endpoint, temperature, input/label/prompt hashes and cumulative token usage are persisted.
+- Billing/authentication errors now stop immediately, preserving partial results.
+- Resume keeps every successful detector component and retries only missing components. Existing
+  rows are replaced atomically rather than duplicated. A budget stop also preserves completed work
+  within the current item. A lock prevents concurrent writers.
+- `--audit-only` reconciles saved metadata without API calls. It confirmed 42 complete items,
+  23 incomplete items, 42 missing components and 131 already-consumed request reservations.
+- Scoring requires complete results and unchanged frozen-label/result hashes. It restores the
+  preregistered complementary-signal PARTIAL rule and uses wrong versus faithful for primary metrics;
+  minor drift is included as positive only in the secondary comparison.
+- Detector prompts, matching thresholds, the concept table and frozen annotations were not tuned
+  against these outputs. Recovery changes concern transport, persistence and accounting only.
+
+The private first-attempt output and metadata were backed up before reconciliation. The results
+hash and the frozen-label hash did not change during the offline audit.
+
+## Validation and next action
+
+149 offline unit tests passed, including billing-stop and partial-resume regressions; repository-wide
+Ruff and diff checks passed. These checks did not compile Lean or build Docker locally.
+The initial PR revision passed Python tests and real Lean validation on
+`ubuntu24.04-x64-lean4.35`, runner 7, in [CI #427](https://gitea.entroia.com/Zayden-Jung/lean-bench/actions/runs/427).
+The image job was skipped by the PR workflow. The recovery revision passed [CI #433](https://gitea.entroia.com/Zayden-Jung/lean-bench/actions/runs/433).
+The recovery changes from PR #6 are consolidated with the semantic schema and review page
+in PR #9; the combined head is checked separately there.
+
+After the owner confirms billing recovery, resume the existing run with the same inputs, frozen
+labels and cumulative budget. There are 42 missing components; retries may consume more requests.
+Do not change model or prompts to work around the provider block. Only after all 65 items have
+successful outputs should the scorer produce the registered decision and disagreement report.
+Phase 1 has not started.
+
+Tracked audit data: `experiments/P0-pilot/results/execution.json` (counts and hashes only).
+Private raw files: `experiments/P0-pilot/data/` (gitignored).

docs/experiments/P0-pilot.md

@@ -2,7 +2,11 @@
 
 Experiment ID **P0**, Phase 0. Registry and conventions: [README.md](README.md).
 
-Status: **approved 2026-10-22; 65 AI labels frozen 2026-10-28; detector execution pending explicit data-transfer approval. No pilot API request has been sent.**
+Status: **approved 2026-10-22; 65 AI labels frozen 2026-10-28; detector run blocked by DashScope Arrearage after 131 requests. 42 items are complete, 23 need missing detector components. No gate decision has been issued.**
+
+The owner explicitly authorized sending the 65 passages and Lean code to DashScope/qwen-max,
+then requested fixes and an execution report now, with paid recovery calls deferred.
+Execution report: [P0 execution, 2026-10-28](P0-execution-2026-10-28.md).
 
 Owner amendment (2026-10-28, in the execution chat): Codex now handles preparation,
 annotation, detector execution and reporting; Kimi's participation is no longer required.

docs/research-plan.md

@@ -8,9 +8,15 @@ Evidence base: repo README and code (`leanbench/`, 4,345 lines incl. tests), pro
 
 ## 0. The idea in one page
 
+**Terminology clarification (2026-10-28).** The owner uses "simplex" for a semantic,
+multi-role relation schema: one statement joins objects, assumptions and a conclusion.
+It does not mean a geometric simplex or assert a mathematical simplicial complex.
+See [the implemented schema design](simplex-schema.md) for scoped slots, storage and
+candidate retrieval. Existing signature projections and AI source annotations remain partial.
+
 **Simplex, as it exists in the archived code.**
 - `Role(name, context, choices)`: a named semantic slot with a description and an optional closed set of allowed values (`is_constrained`, `validate_value`).
-- `Simplex(name, roles: {alias: Role})`: a reusable unit of **at least two** roles. A Simplex is itself a `Role`, so simplices nest; nesting gives a *simplicial complex*. `Equivalence` is the two-role special case.
+- `Simplex(name, roles: {alias: Role})`: a reusable unit of **at least two** roles. A Simplex is itself a `Role`, so explicitly supplied schemas can be nested as semantic composition. `Equivalence` is the two-role special case.
 - `State` / `Fact` / `Goal`: a role plus a value. A `Fact` has a value, a `Goal` does not; `SolvingTask.is_completed()` is "every goal resolved".
 - `SchemaRegistry` (SQLite): `set_role`, `set_simplex`, `search_roles`, `find_by_roles(known_roles)`, `find_solvable(known_role_names)`.
 - `SchemaParserAgent`: turns a query into a Simplex through a forced tool call whose JSON schema says `minItems: 2`, with a **search-first, reuse-before-create** rule for roles. `AnalogySchemaMiner`: proposes new simplices by the ratio *Simplex B : Role B :: Simplex A : Role A*.
@@ -19,11 +25,11 @@ Evidence base: repo README and code (`leanbench/`, 4,345 lines incl. tests), pro
 
 | Lean | Simplex view |
 |---|---|
-| `(G : Type*) [Group G]` | role `G`, `context` = "carrier", `choices` = admissible type/class constraints |
+| `(G : Type*) [Group G]` | role `G`, `context` = "carrier", type/class constraints as attributes; `choices` only for explicit finite value sets |
 | `(h : P x)` hypothesis | `Fact` role |
 | conclusion after the final `:` | `Goal` role |
 | `def` / `structure` being introduced | `own` role (what the thing *is*) |
-| a lemma used inside a proof | nested simplex (edge in the complex) |
+| a lemma used inside a proof | explicit nested schema reference (when recorded) |
 
 `leanbench/typeindex.py` already extracts exactly this split: `input` (binders and hypotheses), `goal` (the conclusion), `own` (definitions). So the type index is a simplex index in all but name. The new work is to make it a **first-class schema that steers inference** instead of a passive index.
 

docs/simplex-schema.md

@@ -0,0 +1,170 @@
+# Simplex schema: a semantic relation joining roles
+
+Here **simplex** means the owner's multi-role relation pattern: one statement relates
+objects, assumptions and a conclusion. The implementation does not construct geometric
+simplices, faces, boundaries or a mathematical simplicial complex.
+
+## The model
+
+| Concept | Representation | Meaning |
+|---|---|---|
+| Reusable role definition | `Role` | A semantic slot type with optional textual type/context and finite `choices` |
+| Statement/relation pattern | `Simplex` | A named mapping from at least two local aliases to roles |
+| Object or assumption supplied by a caller | `Fact` | A role plus a non-None value |
+| Requested result | `Goal` | A role whose value is not supplied yet |
+| Application to particular objects | `SimplexInstance` | Facts and goals bound by local slot alias |
+| Explicit composition | A `Simplex` used as a role | A supplied nested pattern; no proof dependency is discovered automatically |
+| Persistent catalog | `SchemaRegistry` | JSON/SQLite nodes and alias-to-definition references |
+
+`kind` separates `object`, `fact`, `goal`, `own` and nested `simplex` roles.
+A role's `attrs.references` may name other aliases in the same simplex; unknown aliases
+are rejected. These references can describe the objects mentioned in an assumption or
+conclusion. They are not geometric edges. Their provenance must distinguish manually
+supplied relationships from incomplete syntactic candidates.
+
+`type_text` is descriptive Lean/mathematical text, not an executable type checker.
+`choices` is a finite set of admissible values, not a replacement for arbitrary Lean typeclass
+constraints. Supplied fact and resolved goal values are checked against explicit choices.
+No registry method establishes that a string is a proof or that a mathematical premise is true.
+
+## Concrete example: two groups and a homomorphism
+
+One schema joins these slots:
+
+| Local alias | Role | Type/claim | References |
+|---|---|---|---|
+| `left` | object | group carrier | none |
+| `right` | object | group carrier | none |
+| `map` | object | `left →* right` | left, right |
+| `bijective` | fact | `Bijective map` | map |
+| `goal` | goal | `Nonempty (left ≃* right)` | left, right |
+
+The simplex is this complete relation pattern, not an individual role or an asserted
+geometric object. `left` and `right` may explicitly reuse the same `role:group` definition
+while binding to different group objects. Reusing a role definition does not equate their values.
+
+Run the synthetic, offline example:
+
+```sh
+PYTHONPATH=. python3 examples/simplex_registry.py
+```
+
+It binds symbolic caller values for the input slots, leaves the goal unresolved, and returns
+a structurally ready candidate. It does not run a Lean proof.
+
+## Scope, persistence and reuse
+
+`SchemaRegistry.set_simplex` assigns every child a scoped key by default:
+`<schema-key>/slot/<escaped-alias>`. Thus `G` in one theorem is not the same object as `G`
+in another. Corpus keys also include the frozen annotation hash and item identity.
+
+To reuse a definition, register it with `set_role` and explicitly pass a `role_keys` mapping
+to `set_simplex`. The referenced definition must match the supplied role exactly. A shared
+definition still has distinct occurrence keys for every alias. No role is semantically merged
+merely because its spelling, type text or keywords resemble another role.
+
+Keys are immutable within a registry. Identical registration is idempotent; changed content
+or changed definition references require a new version key. `get_role` and `get_simplex`
+resolve exact keys, not ambiguous bare names. `search_roles` returns literal-substring candidates
+for a caller to review; it does not approve semantic reuse.
+
+Serialization includes names, kinds, context, types, choices, attributes and nested aliases.
+`role_from_dict` restores JSON snapshots. SQLite uses one connection and one transaction per
+nested registration, foreign keys and JSON payloads; it does not load archived pickle blobs.
+Cyclic nesting and failed reuse checks roll back the complete write. Returned objects are
+restored snapshots; changing one does not silently update a registered definition.
+
+## Query and binding APIs
+
+```python
+from leanbench.schema_registry import SchemaRegistry, slot_key
+
+with SchemaRegistry("private-registry.sqlite") as registry:
+    schema = registry.get_simplex("schema:example")
+    matches = registry.search_roles("group")
+    containers = registry.find_by_roles(["role:group"], match_all=True)
+    candidates = registry.find_solvable([
+        slot_key("schema:example", "left"),
+        slot_key("schema:example", "right"),
+        slot_key("schema:example", "map"),
+        slot_key("schema:example", "bijective"),
+    ])
+```
+
+`find_by_roles` searches definition references, including descendants of nested schemas.
+`find_solvable` retains the archived API name but implements **structural readiness only**:
+all input occurrences must be supplied and at least one marked goal/own occurrence must
+remain unresolved. It returns `structural_candidate_only: true`, not a proof or a computed value.
+Having one `role:group` definition cannot satisfy two distinct group slots. A nested input
+must itself be explicitly supplied; the registry does not apply its internal theorem automatically.
+
+`SimplexInstance(schema, facts=..., goals=...)` binds local aliases. Facts and goals must be
+distinct declared slots. Omitting `goals` uses roles marked `goal` or `own`; `resolve` checks
+a supplied goal value against choices. Completion means that declared goals have values,
+not that Lean verified them. Value unification, dependent type checking and proof search
+remain outside this implementation.
+
+## Materialization of the 65 P0 items
+
+The builder consumes the frozen current-chat GPT diagnostic's source descriptions and
+unchanged Lean strings. It makes no model request, revises no assessment and performs no
+Lean compilation. Results:
+
+| Artifact | Count |
+|---|---:|
+| Source annotation seed schemas | 65 |
+| Lean signature schema seeds | 50 |
+| Items with fewer than two projected Lean roles | 15 |
+| Stored schemas | 115 |
+| Scoped role records / slot occurrences | 483 / 483 |
+
+These 115 seeds deliberately do not auto-reuse definitions across statements. Explicit reuse
+is supported and tested by the synthetic example; a reviewed shared ontology is future work.
+The 15 incomplete Lean sides remain in the index with status `insufficient_projected_roles`.
+A closed declaration may mention concrete objects inside its conclusion that the binder-based
+projector misses. No object roles were invented to hide this limitation.
+
+Source schemas are marked `unreviewed_annotation_seed`. Existing `given` tags are preserved
+with `quantifier_status: unreviewed`; they are not silently converted to universal/existential
+quantifiers. References on the source side use explicit symbol candidates; Lean references
+are syntactic identifier candidates. Neither is a complete dependency analysis.
+For example, P11's source seed lists a named size while Lean uses `Fintype.card G` inline.
+The materializer preserves both representations; it does not invent a validated cardinality
+binding or repair the old alignment result. Annotation quality and semantic normalization
+still require a separate review.
+
+Private outputs under `experiments/P0-pilot/data/simplex-schemas-v1/`:
+
+- `registry.sqlite`: queryable catalog with the 115 schemas and scoped slots.
+- `schemas.json`: all 65 source/Lean pairs, retaining incomplete Lean projections.
+- `schemas.html`: a local generated copy of the schema-only review tracked below.
+- `schema-inputs.json`: input hashes; an existing directory rejects changed inputs.
+
+Tracked outputs:
+
+- `experiments/P0-pilot/results/simplex-schema-index.json`: 65 item IDs, schema keys,
+  role counts, coverage status and reference-candidate counts.
+- `experiments/P0-pilot/results/simplex-schema-summary.json`: coverage, limitations and hashes.
+- [65-item schema review](reviews/simplex-schemas.html): an owner-approved, self-contained
+  HTML view of all 65 source/Lean pairs. It includes schema role descriptions and Lean
+  signature expressions, but no textbook paragraphs or full assistant judgment explanations.
+  Open the file in a browser after cloning, or download it from the repository; the Git web
+  interface may display HTML source instead of rendering it. The JSON indexes above remain
+  text-free counts/keys. Full source-inclusive inputs and assessment files remain gitignored.
+
+Replay from the repository root with private inputs present:
+
+```sh
+PYTHONPATH=. python3 experiments/P0-pilot/build_schemas.py \
+  --items experiments/P0-pilot/data/simplex-schemas-v1/items.jsonl \
+  --assessments experiments/P0-pilot/data/simplex-schemas-v1/assistant-assessments.json \
+  --key experiments/P0-pilot/labels/key.json \
+  --private-out experiments/P0-pilot/data/simplex-schemas-v1 \
+  --index experiments/P0-pilot/results/simplex-schema-index.json \
+  --summary experiments/P0-pilot/results/simplex-schema-summary.json \
+  --review-page docs/reviews/simplex-schemas.html
+```
+
+The original annotations, judgments, Qwen results and matcher thresholds remain unchanged.
+The registry is a usable schema foundation, not evidence of a validated theorem, a working
+prover, independently measured faithfulness, or a completed Phase 1 experiment.

examples/simplex_registry.py

@@ -0,0 +1,35 @@
+"""Synthetic example: one isomorphism schema relates two groups and a map."""
+from __future__ import annotations
+
+import json
+
+from leanbench.schema import KIND_FACT, KIND_GOAL, Role, Simplex, SimplexInstance
+from leanbench.schema_registry import SchemaRegistry, slot_key
+
+
+def example():
+    group = Role("group", type_text="group carrier", context="Reusable group role definition")
+    schema = Simplex("group_isomorphism", {
+        "left": group,
+        "right": group,
+        "map": Role("homomorphism", type_text="left →* right",
+                    attrs={"references": ["left", "right"]}),
+        "bijective": Role("bijective", KIND_FACT, type_text="Bijective map",
+                          attrs={"references": ["map"]}),
+        "goal": Role("isomorphic", KIND_GOAL, type_text="Nonempty (left ≃* right)",
+                     attrs={"references": ["left", "right"]}),
+    }, context="A bijective homomorphism supplies a group isomorphism")
+    with SchemaRegistry() as registry:
+        registry.set_role(group, "role:group")
+        key = registry.set_simplex(schema, role_keys={"left": "role:group", "right": "role:group"})
+        instance = SimplexInstance(schema, facts={
+            "left": "group A", "right": "group B", "map": "f", "bijective": "supplied evidence"})
+        candidates = registry.find_solvable([slot_key(key, alias) for alias in instance.facts])
+        return {"schema": registry.get_simplex(key).as_dict(), "definition_keys": registry.slots(key),
+                "bindings": {alias: fact.value for alias, fact in instance.facts.items()},
+                "structural_candidates": candidates, "completed": instance.is_completed(),
+                "note": "Evidence is symbolic user input; this example does not run a Lean proof."}
+
+
+if __name__ == "__main__":
+    print(json.dumps(example(), indent=2, ensure_ascii=False))

experiments/P0-pilot/README.md

@@ -44,6 +44,9 @@ Labeling must be finished before anyone opens `results.jsonl`.
 - Metadata is stored beside the output as `results.meta.json`. Model, endpoint, temperature,
   input hash, frozen-label hash and prompt hashes must match on resume. Usage is cumulative.
   A file lock prevents concurrent writers. A budget stop returns exit status 2.
+- Billing/authentication failures stop immediately. Resume retries only missing detector components,
+  keeping both complete items and the successful side of partial items. Rows are replaced atomically.
+  `--audit-only` reconciles saved completion counts and status without any API request.
 - The nominal successful path uses 130 calls (one source extraction and one judge per item);
   malformed replies and network retries may increase the actual count.
 - Scoring requires complete labels and results and no unresolved detector errors. The primary
@@ -51,7 +54,16 @@ Labeling must be finished before anyone opens `results.jsonl`.
   The complementary-signal PARTIAL rule counts wrong items flagged by role alignment but missed
   by the judge. No threshold, concept table or detector prompt was tuned for these labels.
 - Raw passages, labeling HTML and model responses remain in the ignored `data/` directory.
-  Only verdicts, abstract annotation notes, hashes and text-free summaries belong in Git.
+  Verdicts, abstract annotation notes, hashes and text-free summaries belong in Git;
+  the owner-approved schema-only HTML review is also tracked separately under docs/reviews/.
+
+## Qwen execution snapshot
+
+The 2026-10-28 run was blocked by DashScope `Arrearage`: 42 items are complete, 23 need
+42 detector components, and 131 of the 400 request reservations have been consumed.
+The owner requested fixes and a report now, with paid resumption deferred.
+See `docs/experiments/P0-execution-2026-10-28.md` and `results/execution.json`.
+No gate decision has been issued. Restore provider billing before resuming the same run.
 
 ## Separate GPT-assisted diagnostic
 
@@ -65,3 +77,17 @@ See `docs/experiments/P0-gpt-diagnostic.md` for all counts, limitations, artifac
 and the offline replay command. The tracked `results/gpt-diagnostic-*.json` files contain
 only categorical/numeric outputs and audit metadata. The authored source structures,
 reasons and full review page stay in the ignored `data/gpt-diagnostic/` directory.
+
+## Semantic simplex registry
+
+The current 65-item annotation cohort is materialized as multi-role relation schemas:
+65 source seeds, 50 Lean signature seeds and 15 explicitly incomplete Lean projections.
+See `docs/simplex-schema.md` for the data model, scoped identities, explicit role reuse,
+structural candidate queries, bindings and replay command. Private SQLite/JSON/HTML outputs
+stay under `data/simplex-schemas-v1/`; tracked `results/simplex-schema-*.json` files contain
+only counts, opaque keys, provenance hashes and coverage status. This does not change the
+frozen diagnostic or claim complete semantic extraction or proof verification.
+
+The owner-approved schema-only HTML review is tracked at
+`docs/reviews/simplex-schemas.html`. Regenerate it with the builder's `--review-page` option;
+the raw inputs, full assessment explanations and SQLite snapshot remain gitignored.

experiments/P0-pilot/build_schemas.py

@@ -0,0 +1,193 @@
+"""Materialize scoped multi-role relation schemas from the frozen 65-item review.
+
+The schema is the relation joining its slots. No geometric faces, inferred proof
+links or cross-theorem object identities are constructed.
+"""
+from __future__ import annotations
+
+import argparse
+import hashlib
+import html
+import json
+import re
+from collections import Counter
+from pathlib import Path
+
+from leanbench.project import project
+from leanbench.schema import KIND_OBJECT, Role, Simplex, role_from_dict
+from leanbench.schema_registry import SchemaRegistry, slot_key
+from leanbench.srcsimplex import parse_source_simplex
+
+
+def digest(path):
+    return hashlib.sha256(path.read_bytes()).hexdigest()
+
+
+def source_schema(name, payload):
+    source = parse_source_simplex(payload)
+    symbol_slots = {}
+    for role in source.roles:
+        if role.kind == KIND_OBJECT:
+            for symbol in role.symbols:
+                symbol_slots.setdefault(symbol, []).append(role.alias)
+    roles = {}
+    for role in source.roles:
+        references = sorted({alias for symbol in role.symbols for alias in symbol_slots.get(symbol, [])
+                             if alias != role.alias and len(symbol_slots[symbol]) == 1})
+        roles[role.alias] = Role(
+            role.symbols[0] if len(role.symbols) == 1 else role.alias,
+            role.kind, context=role.description,
+            attrs={"symbols": role.symbols, "keywords": role.keywords,
+                   "introduced": role.introduced, "quantifier_status": "unreviewed",
+                   "references": references,
+                   "reference_status": "explicit_symbol_candidates" if references else "unknown",
+                   "origin": "frozen_current_chat_annotation"})
+    return Simplex(name, roles, attrs={"side": "source", "goal_has_exists": source.goal_has_exists,
+                                      "reference_completeness": "partial"})
+
+
+def lean_schema(name, code):
+    projection = project(code)
+    if projection.simplex is None:
+        return None, projection
+    originals = projection.simplex.roles
+    by_name = {}
+    for alias, role in originals.items():
+        by_name.setdefault(role.name, []).append(alias)
+    roles = {}
+    for alias, role in originals.items():
+        identifiers = set(re.findall(r"[^\W\d]\w*'?", role.type_text, flags=re.UNICODE))
+        references = sorted({target for symbol in identifiers for target in by_name.get(symbol, [])
+                             if len(by_name[symbol]) == 1 and target != alias})
+        roles[alias] = Role(role.name, role.kind, type_text=role.type_text, context=role.context,
+                           choices=role.choices, attrs={**role.attrs, "references": references,
+                           "reference_status": "syntactic_candidates",
+                           "origin": "deterministic_signature_projection"})
+    return Simplex(name, roles, attrs={"side": "lean", "reference_completeness": "syntactic_only"}), projection
+
+
+def build(items, assessment, key, registry, namespace="p0-v1"):
+    by_id = {item["id"]: item for item in items}
+    records = {row["blind_id"]: row for row in assessment["records"]}
+    if (not key or len(by_id) != len(items) or len(records) != len(assessment["records"])
+            or len(set(key.values())) != len(key) or set(by_id) != set(key.values())
+            or set(records) != set(key)):
+        raise ValueError("Items, assessments and blind key must match exactly once")
+    index, snapshots = [], []
+    for blind, item_id in key.items():
+        record = records[blind]
+        if record["id"] != item_id:
+            raise ValueError("Assessment identity mismatch")
+        source_key = f"schema:{namespace}:{item_id}:source:v1"
+        lean_key = f"schema:{namespace}:{item_id}:lean:v1"
+        source = source_schema(source_key, record["source"])
+        lean, projection = lean_schema(lean_key, by_id[item_id]["lean_code"])
+        registry.set_simplex(source, source_key)
+        if lean is not None:
+            registry.set_simplex(lean, lean_key)
+        source_restored = registry.get_simplex(source_key)
+        if source_restored.as_dict() != source.as_dict():
+            raise ValueError("Source schema persistence roundtrip failed")
+        if lean is not None and registry.get_simplex(lean_key).as_dict() != lean.as_dict():
+            raise ValueError("Lean schema persistence roundtrip failed")
+        index.append({"blind_id": blind, "source_schema": source_key,
+                      "source_status": "unreviewed_annotation_seed",
+                      "source_slots": len(source.roles),
+                      "lean_schema": lean_key if lean is not None else None,
+                      "lean_slots": len(projection.roles),
+                      "lean_status": "materialized" if lean is not None else "insufficient_projected_roles",
+                      "source_role_counts": dict(Counter(r.kind for r in source.roles.values())),
+                      "lean_role_counts": dict(Counter(r.kind for r in projection.roles)),
+                      "source_slots_with_reference_candidates": sum(bool(r.attrs["references"]) for r in source.roles.values())})
+        snapshots.append({"blind_id": blind, "source": source.as_dict(),
+                          "lean": lean.as_dict() if lean is not None else None,
+                          "lean_projection": projection.as_dict(),
+                          "source_slot_keys": [slot_key(source_key, alias) for alias in source.roles]})
+    return index, snapshots
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--items", required=True, type=Path)
+    parser.add_argument("--assessments", required=True, type=Path)
+    parser.add_argument("--key", required=True, type=Path)
+    parser.add_argument("--private-out", required=True, type=Path)
+    parser.add_argument("--index", required=True, type=Path)
+    parser.add_argument("--summary", required=True, type=Path)
+    parser.add_argument("--review-page", type=Path,
+                        help="Also export the owner-approved schema-only HTML review into the project")
+    args = parser.parse_args()
+    if "data" not in args.private_out.parts:
+        parser.error("Private schemas must remain in the gitignored data/ directory")
+    assessment = json.loads(args.assessments.read_text())
+    key = json.loads(args.key.read_text())["key"]
+    if (assessment["provenance"]["items_sha256"] != digest(args.items)
+            or assessment["provenance"]["key_sha256"] != digest(args.key)):
+        parser.error("Frozen assessment hashes do not match inputs/key")
+    items = [json.loads(line) for line in args.items.read_text().splitlines() if line.strip()]
+    args.private_out.mkdir(parents=True, exist_ok=True)
+    identity = {"items": digest(args.items), "assessments": digest(args.assessments),
+                "key": digest(args.key)}
+    manifest = args.private_out / "schema-inputs.json"
+    if manifest.exists() and json.loads(manifest.read_text()) != identity:
+        parser.error("Existing schema output belongs to different inputs; choose a new directory")
+    temporary = args.private_out / "registry.sqlite.tmp"
+    if temporary.exists():
+        temporary.unlink()
+    with SchemaRegistry(temporary) as registry:
+        index, snapshots = build(items, assessment, key, registry,
+                                 namespace=f"p0-{identity['assessments'][:12]}")
+        info = registry.info()
+    temporary.replace(args.private_out / "registry.sqlite")
+    manifest.write_text(json.dumps(identity, indent=2) + "\n")
+    (args.private_out / "schemas.json").write_text(json.dumps(snapshots, indent=2, ensure_ascii=False) + "\n")
+    sections = []
+    for row in snapshots:
+        sides = []
+        for side in ["source", "lean"]:
+            value = row[side]
+            content = (json.dumps(value, indent=2, ensure_ascii=False) if value is not None
+                       else "Insufficient projected roles; no object roles were invented.")
+            sides.append(f'<h3>{side}</h3><pre>{html.escape(content)}</pre>')
+        sections.append(f'<section id="{row["blind_id"]}"><h2>{row["blind_id"]}</h2>'
+                        + ''.join(sides) + '</section>')
+    review_page = (
+        '<!doctype html><html lang="en"><meta charset="utf-8"><title>P0 semantic simplex schemas</title>'
+        '<style>body{font:16px/1.5 system-ui;max-width:1050px;margin:32px auto;padding:16px}'
+        'pre{white-space:pre-wrap;background:#f5f5f5;padding:16px}section{border-top:1px solid #ccc}</style>'
+        '<h1>65 semantic multi-role relation schemas</h1>'
+        '<p>Schema annotation seeds, not independently validated mathematical statements. '
+        'A simplex joins the objects, assumptions and conclusion in its slots. '
+        'References are partial symbol/syntax candidates. '
+        'This review contains schema annotations and Lean signature text, not textbook passages '
+        'or full assistant judgment explanations.</p>' + ''.join(sections) + '</html>')
+    (args.private_out / "schemas.html").write_text(review_page, encoding="utf-8")
+    if args.review_page is not None:
+        args.review_page.parent.mkdir(parents=True, exist_ok=True)
+        args.review_page.write_text(review_page, encoding="utf-8")
+    # JSON-only reload is independently checked; it does not use pickle.
+    for row in snapshots:
+        for side in ["source", "lean"]:
+            if row[side] is not None:
+                if role_from_dict(row[side]).as_dict() != row[side]:
+                    raise ValueError("JSON schema roundtrip failed")
+    summary = {"representation": "semantic_multi_role_relation_schema_v1", "items": len(items),
+               "source_schemas": len(index), "lean_schemas": sum(r["lean_schema"] is not None for r in index),
+               "lean_incomplete": sum(r["lean_schema"] is None for r in index), "registry": info,
+               "hashes": {"items": digest(args.items), "assessments": digest(args.assessments),
+                          "key": digest(args.key), "builder": digest(Path(__file__)),
+                          "schema_module": digest(Path(__file__).resolve().parents[2] / "leanbench/schema.py"),
+                          "registry_module": digest(Path(__file__).resolve().parents[2] / "leanbench/schema_registry.py")},
+               "limitations": ["Source annotations come from a non-independent current-chat diagnostic.",
+                               "Source quantifiers are preserved as unreviewed; existing given tags are not repaired.",
+                               "References are symbol/syntax candidates, not complete semantic dependencies.",
+                               "No cross-theorem identity or proof dependency is inferred.",
+                               "Fewer than two projected Lean roles is a projection limitation, not proof that objects are absent."]}
+    for path, value in [(args.index, index), (args.summary, summary)]:
+        path.parent.mkdir(parents=True, exist_ok=True)
+        path.write_text(json.dumps(value, indent=2, allow_nan=False) + "\n")
+    print(json.dumps({k: summary[k] for k in ["items", "source_schemas", "lean_schemas", "lean_incomplete", "registry"]}))
+
+
+if __name__ == "__main__":
+    main()

experiments/P0-pilot/results/execution.json

@@ -0,0 +1,72 @@
+{
+  "experiment": "P0",
+  "status": "provider_blocked",
+  "decision": null,
+  "decision_withheld_reason": "Incomplete detector outputs after DashScope Arrearage; no GO/PARTIAL/NO-GO is valid.",
+  "cohort_size": 65,
+  "completed_items": 42,
+  "items_with_failures": 23,
+  "missing_components": {
+    "judge": 22,
+    "role": 20
+  },
+  "request_attempts": 131,
+  "max_calls": 400,
+  "remaining_request_budget": 269,
+  "usage": {
+    "calls": 89,
+    "prompt_tokens": 37699,
+    "completion_tokens": 7790
+  },
+  "model": "qwen-max",
+  "temperature": 0.0,
+  "items_sha256": "487ecd22919a5e3b0174a2846ab8fe7c0daf4d3feccccf8ea6571aec04c41bed",
+  "labels_sha256": "1552dba85e75426799151384e7e28c9a0b1072ed4c862df0876df89920d2a638",
+  "results_sha256": "fce402e6eab460a48bb9a8e94140bb23f305843ab46d227bbffa5100d7de69e5",
+  "prompt_hashes": {
+    "source": "382f9a7b5a0cfb2d50d525f884dc806f45adaa59bcc45e388920c4759db1546f",
+    "judge": "7ab92682bd71d78a212471289f0f01db39d6b68f49d44df65d7b1c9e34ebb5e2"
+  },
+  "labels": {
+    "type": "single AI annotator; not human gold",
+    "frozen": true,
+    "count": 65
+  },
+  "affected_blind_ids": [
+    "P02",
+    "P04",
+    "P09",
+    "P18",
+    "P19",
+    "P20",
+    "P21",
+    "P22",
+    "P24",
+    "P27",
+    "P29",
+    "P30",
+    "P33",
+    "P36",
+    "P37",
+    "P38",
+    "P42",
+    "P43",
+    "P45",
+    "P47",
+    "P54",
+    "P59",
+    "P62"
+  ],
+  "successful_components_preserved": 88,
+  "resume_policy": "After owner confirms billing recovery, retry missing components only using the same run files, frozen labels, model, prompts and cumulative 400-request ceiling.",
+  "owner_instruction": "2026-10-28: complete fixes and the execution report now; resume paid calls later.",
+  "validation": {
+    "offline_unit_tests": 149,
+    "ruff": "passed",
+    "remote_runner_tag": "ubuntu24.04-x64-lean4.35",
+    "initial_remote_ci": "https://gitea.entroia.com/Zayden-Jung/lean-bench/actions/runs/427",
+    "initial_remote_ci_status": "success; image job skipped for PR",
+    "recovery_remote_ci": "https://gitea.entroia.com/Zayden-Jung/lean-bench/actions/runs/433",
+    "consolidated_pull_request": "https://gitea.entroia.com/Zayden-Jung/lean-bench/pulls/9"
+  }
+}

experiments/P0-pilot/results/simplex-schema-summary.json

@@ -0,0 +1,27 @@
+{
+  "representation": "semantic_multi_role_relation_schema_v1",
+  "items": 65,
+  "source_schemas": 65,
+  "lean_schemas": 50,
+  "lean_incomplete": 15,
+  "registry": {
+    "roles": 483,
+    "simplices": 115,
+    "slots": 483
+  },
+  "hashes": {
+    "items": "487ecd22919a5e3b0174a2846ab8fe7c0daf4d3feccccf8ea6571aec04c41bed",
+    "assessments": "f12735802ba0d4d94b776a91581a13a508eab0ce90ba8973a6c9c4e4d1390272",
+    "key": "f827cac92ee4e907554fadcc7c0e006ef2b829350f74e7f8b54ca11945e62836",
+    "builder": "7b3a982101f620c1480d95b5e483ca6186a7e9c32ce587fb132a90bfb38a01bc",
+    "schema_module": "958b81e89c0befeb32d24036c130f2b37bd2e881bd5b009acf873cbcdada50ae",
+    "registry_module": "7b434b1eb178f597d4f60591a5ab74eff0c96a40fa751cb0ba75589b52e56271"
+  },
+  "limitations": [
+    "Source annotations come from a non-independent current-chat diagnostic.",
+    "Source quantifiers are preserved as unreviewed; existing given tags are not repaired.",
+    "References are symbol/syntax candidates, not complete semantic dependencies.",
+    "No cross-theorem identity or proof dependency is inferred.",
+    "Fewer than two projected Lean roles is a projection limitation, not proof that objects are absent."
+  ]
+}

experiments/P0-pilot/run_pilot.py

@@ -50,37 +50,64 @@ def judge(client, passage: str, lean: str) -> dict:
             "reason": str(reply.get("reason", ""))[:300]}
 
 
-def run_item(client, item: dict) -> dict:
+def provider_blocked(error: Exception) -> bool:
-    if not item.get("source_text", "").strip():
+    text = str(error).lower()
-        raise ValueError("Missing source_text; use a private source-inclusive export")
+    return any(code in text for code in ("arrearage", "overdue-payment", "invalid_api_key", "http 401", "http 403"))
-    code = item.get("lean_code") or ""
+
-    row: dict = {"id": item["id"], "compiled": bool(item.get("verified")), "errors": {}}
+
-    proj = project(code)
+def complete_row(row: dict) -> bool:
-    row["projection"] = proj.as_dict()
+    return not row.get("errors") and "role" in row and "judge" in row
-    row["lint"] = lint(proj)
+
-    try:
+
-        src = srcsimplex.extract_source_simplex(client, item.get("source_text", ""),
+class ProviderBlocked(RuntimeError):
-                                                item.get("label", ""))
+    """A billing or authentication failure requires external recovery before resuming."""
-        al = align(src, proj)
+
-        row["source"] = [r.__dict__ for r in src.roles]
+    def __init__(self, row):
-        row["role"] = al.as_dict()
+        super().__init__("Provider billing/authentication blocked; partial results were preserved")
-    except CallBudgetExceeded:
+        self.row = row
-        raise
-    except Exception as error:  # a failed extraction is data, not a crash
-        row["errors"]["role"] = str(error)[:300]
-    try:
-        row["judge"] = judge(client, item.get("source_text", ""), code)
-    except CallBudgetExceeded:
-        raise
-    except Exception as error:
-        row["errors"]["judge"] = str(error)[:300]
-    return row
 
 
 class CallBudgetExceeded(RuntimeError):
     """Stop before issuing a request that would exceed the cumulative budget."""
 
 
+def run_item(client, item: dict, previous: dict | None = None) -> dict:
+    if not item.get("source_text", "").strip():
+        raise ValueError("Missing source_text; use a private source-inclusive export")
+    code = item.get("lean_code") or ""
+    row: dict = {**(previous or {}), "id": item["id"], "compiled": bool(item.get("verified"))}
+    row["errors"] = dict(row.get("errors", {}))
+    proj = project(code)
+    row["projection"] = proj.as_dict()
+    row["lint"] = lint(proj)
+    if "role" not in row:
+        try:
+            src = srcsimplex.extract_source_simplex(client, item["source_text"], item.get("label", ""))
+            al = align(src, proj)
+            row["source"] = [r.__dict__ for r in src.roles]
+            row["role"] = al.as_dict()
+            row["errors"].pop("role", None)
+        except CallBudgetExceeded as error:
+            error.row = row
+            raise
+        except Exception as error:
+            row["errors"]["role"] = str(error)[:300]
+            if provider_blocked(error):
+                raise ProviderBlocked(row) from error
+    if "judge" not in row:
+        try:
+            row["judge"] = judge(client, item["source_text"], code)
+            row["errors"].pop("judge", None)
+        except CallBudgetExceeded as error:
+            error.row = row
+            raise
+        except Exception as error:
+            row["errors"]["judge"] = str(error)[:300]
+            if provider_blocked(error):
+                raise ProviderBlocked(row) from error
+    return row
+
+
 def digest(path: Path) -> str:
     return hashlib.sha256(path.read_bytes()).hexdigest()
 
@@ -106,8 +133,9 @@ def execute(args, items, settings) -> int:
     if args.out.exists():
         rows = [json.loads(x) for x in args.out.read_text(encoding="utf-8").splitlines() if x.strip()]
     ids = {item["id"] for item in items}
-    done = {row["id"] for row in rows}
+    by_id = {row["id"]: row for row in rows}
-    if len(done) != len(rows) or not done <= ids:
+    done = {row["id"] for row in rows if complete_row(row)}
+    if len(by_id) != len(rows) or not set(by_id) <= ids:
         raise ValueError("Results have duplicate or unknown item IDs")
     hashes = {
         "source": hashlib.sha256((srcsimplex.SYSTEM_PROMPT + inspect.getsource(srcsimplex.passage_prompt)).encode()).hexdigest(),
@@ -129,11 +157,24 @@ def execute(args, items, settings) -> int:
     elif rows:
         raise ValueError("Cannot resume results without their audit metadata")
     todo = [item for item in items if item["id"] not in done]
+    missing = sum(2 - int("role" in by_id.get(i["id"], {}))
+                  - int("judge" in by_id.get(i["id"], {})) for i in todo)
     print(f"items={len(items)} done={len(done)} todo={len(todo)} model={settings.llm.model} "
-          f"nominal_calls={len(todo) * 2} request_attempts={meta['request_attempts']} cap={args.max_calls}")
+          f"missing_components={missing} request_attempts={meta['request_attempts']} cap={args.max_calls}")
     print("prompt_hashes:", json.dumps(hashes))
     if args.dry_run:
         return 0
+    if getattr(args, "audit_only", False):
+        meta["completed_items"] = len(done)
+        meta["processed_items"] = len(rows)
+        meta["status"] = ("provider_blocked" if any(provider_blocked(RuntimeError(message))
+                          for row in rows for message in row.get("errors", {}).values())
+                          else "detector_errors" if todo else "complete")
+        if args.out.exists():
+            meta["results_sha256"] = digest(args.out)
+        atomic_json(meta_path, meta)
+        print(json.dumps(meta))
+        return 0 if meta["status"] == "complete" else 2
     if settings.llm.model != "qwen-max" or settings.llm.temperature != 0:
         raise ValueError("P0 is preregistered for qwen-max at temperature 0")
     client = AuditedClient.from_settings(settings.llm)
@@ -142,6 +183,7 @@ def execute(args, items, settings) -> int:
     def checkpoint():
         meta["usage"] = client.usage.as_dict()
         meta["completed_items"] = len(done)
+        meta["processed_items"] = len(by_id)
         atomic_json(meta_path, meta)
 
     def reserve():
@@ -155,19 +197,30 @@ def execute(args, items, settings) -> int:
     meta["max_calls"] = args.max_calls
     meta["status"] = "running"
     checkpoint()
+    def save_row(row):
+        by_id[row["id"]] = row
+        if complete_row(row):
+            done.add(row["id"])
+        temporary = args.out.with_suffix(args.out.suffix + ".tmp")
+        with temporary.open("w", encoding="utf-8") as stream:
+            for item in items:
+                if item["id"] in by_id:
+                    stream.write(json.dumps(by_id[item["id"]], ensure_ascii=False) + "\n")
+            stream.flush()
+            os.fsync(stream.fileno())
+        os.replace(temporary, args.out)
+        checkpoint()
+
     try:
-        with args.out.open("a", encoding="utf-8") as stream:
+        for item in todo:
-            for item in todo:
+            row = run_item(client, item, by_id.get(item["id"]))
-                row = run_item(client, item)
+            save_row(row)
-                stream.write(json.dumps(row, ensure_ascii=False) + "\n")
+            print(f"completed={len(done)}/{len(items)} requests={meta['request_attempts']}", flush=True)
-                stream.flush()
+        meta["status"] = "complete" if len(done) == len(items) else "detector_errors"
-                os.fsync(stream.fileno())
+    except (CallBudgetExceeded, ProviderBlocked) as error:
-                done.add(item["id"])
+        if getattr(error, "row", None) is not None:
-                checkpoint()
+            save_row(error.row)
-                print(f"completed={len(done)}/{len(items)} requests={meta['request_attempts']}", flush=True)
+        meta["status"] = "provider_blocked" if isinstance(error, ProviderBlocked) else "budget_exhausted"
-        meta["status"] = "complete"
-    except CallBudgetExceeded as error:
-        meta["status"] = "budget_exhausted"
         print(str(error), file=sys.stderr)
     except BaseException:
         meta["status"] = "interrupted"
@@ -186,6 +239,7 @@ def main() -> int:
     ap.add_argument("--out", required=True, type=Path)
     ap.add_argument("--max-calls", type=int, default=400)
     ap.add_argument("--dry-run", action="store_true")
+    ap.add_argument("--audit-only", action="store_true", help="Reconcile saved state without making API calls")
     ap.add_argument("--labels", type=Path, help="Frozen labels; their hash is bound to the run")
     args = ap.parse_args()
     if not 1 <= args.max_calls <= 400:

leanbench/schema.py

@@ -1,4 +1,4 @@
-"""Roles and simplices: the parameters of a declaration as a small typed schema.
+"""Semantic multi-role relation schemas, not geometric simplices.
 
 A Lean declaration is a bundle of roles: the objects it is about (``(G : Type*)``),
 the facts it assumes (``(h : a ∣ b)``), and the goal it asserts or the thing it
@@ -8,8 +8,8 @@ be read off the prose of a book, so the two can be compared role by role.
 Design notes (from the archived ``schema-simplex`` prototype):
 
 * a role may be *constrained* to a closed set of allowed values (``choices``);
-* a simplex is itself a role, so simplices nest (a lemma used by another is a role
+* a simplex is itself a role, so explicitly supplied schemas can be composed;
-  of it), which is how a dependency structure appears;
+  nesting does not discover a proof dependency;
 * validation lives in ``__init__``. The prototype put it in a dataclass
   ``__post_init__`` next to a hand-written ``__init__``, where it never ran.
 """
@@ -41,7 +41,7 @@ class Role:
         choices: Sequence[Any] | None = None,
         attrs: dict[str, Any] | None = None,
     ) -> None:
-        if not name:
+        if not isinstance(name, str) or not name.strip():
             raise ValueError("a role needs a name")
         if kind not in KINDS:
             raise ValueError(f"unknown role kind {kind!r}; expected one of {KINDS}")
@@ -49,6 +49,8 @@ class Role:
         self.kind = kind
         self.type_text = type_text
         self.context = context
+        if isinstance(choices, (str, bytes)):
+            raise ValueError("choices must be a value sequence, not a string")
         self.choices: list[Any] | None = list(choices) if choices is not None else None
         self.attrs: dict[str, Any] = dict(attrs or {})
 
@@ -83,12 +85,21 @@ class Role:
 class Simplex(Role):
     """A reusable bundle of at least two roles, keyed by alias. Itself a role."""
 
-    def __init__(self, name: str, roles: dict[str, Role], *, context: str = "") -> None:
+    def __init__(self, name: str, roles: dict[str, Role], *, context: str = "",
-        super().__init__(name, KIND_SIMPLEX, context=context)
+                 attrs: dict[str, Any] | None = None) -> None:
+        super().__init__(name, KIND_SIMPLEX, context=context, attrs=attrs)
         if len(roles) < MIN_ROLES:
             raise ValueError(
                 f"simplex {name!r} needs at least {MIN_ROLES} roles, got {len(roles)}"
             )
+        if any(not isinstance(alias, str) or not alias or not isinstance(role, Role)
+               for alias, role in roles.items()):
+            raise ValueError("simplex slots need nonempty aliases and Role values")
+        for role in roles.values():
+            references = role.attrs.get("references", [])
+            if (not isinstance(references, list)
+                    or any(not isinstance(alias, str) or alias not in roles for alias in references)):
+                raise ValueError("role references must name slots in this simplex")
         self.roles = dict(roles)
 
     def by_kind(self, kind: str) -> list[Role]:
@@ -105,16 +116,16 @@ class Simplex(Role):
         return out
 
     def as_dict(self) -> dict[str, Any]:
-        return {
+        return {**super().as_dict(),
-            "name": self.name,
+                "roles": {alias: role.as_dict() for alias, role in self.roles.items()}}
-            "roles": {alias: role.as_dict() for alias, role in self.roles.items()},
-        }
 
 
 class State:
     """A role together with a value; unresolved until it has one."""
 
     def __init__(self, role: Role, value: Any = None) -> None:
+        if value is not None:
+            role.check_value(value)
         self.role = role
         self.value = value
 
@@ -133,3 +144,41 @@ class Fact(State):
 
 class Goal(State):
     """To be resolved."""
+
+
+def role_from_dict(data: dict[str, Any]) -> Role:
+    """Restore JSON role/schema data without executing code or loading pickle."""
+    kind = data.get("kind", KIND_SIMPLEX if "roles" in data else KIND_OBJECT)
+    if kind == KIND_SIMPLEX:
+        return Simplex(data["name"], {alias: role_from_dict(role)
+                                   for alias, role in data["roles"].items()},
+                       context=data.get("context", ""), attrs=data.get("attrs"))
+    return Role(data["name"], kind, type_text=data.get("type", ""),
+                context=data.get("context", ""), choices=data.get("choices"),
+                attrs=data.get("attrs"))
+
+
+class SimplexInstance:
+    """Values bind local slot aliases; a resolved goal is supplied, not proved here."""
+
+    def __init__(self, schema: Simplex, facts: dict[str, Any] | None = None,
+                 goals: Sequence[str] | None = None) -> None:
+        self.schema = schema
+        facts = facts or {}
+        goal_aliases = list(goals) if goals is not None else [
+            alias for alias, role in schema.roles.items() if role.kind in (KIND_GOAL, KIND_OWN)]
+        if (len(set(goal_aliases)) != len(goal_aliases)
+                or not (set(facts) | set(goal_aliases)) <= set(schema.roles)
+                or set(facts) & set(goal_aliases)):
+            raise ValueError("facts/goals need distinct, declared slot aliases")
+        self.facts = {alias: Fact(schema.roles[alias], value) for alias, value in facts.items()}
+        self.goals = {alias: Goal(schema.roles[alias]) for alias in goal_aliases}
+
+    def resolve(self, alias: str, value: Any) -> None:
+        if alias not in self.goals or value is None:
+            raise ValueError("resolve needs a declared goal and a non-None value")
+        self.goals[alias].role.check_value(value)
+        self.goals[alias].value = value
+
+    def is_completed(self) -> bool:
+        return bool(self.goals) and all(goal.is_resolved() for goal in self.goals.values())

leanbench/schema_registry.py

@@ -0,0 +1,208 @@
+"""JSON/SQLite registry of semantic relation schemas and scoped slot occurrences.
+
+A role definition may be reused deliberately. Occurrences remain local to a
+simplex: sharing a role definition never equates the objects bound to its aliases.
+"""
+from __future__ import annotations
+
+import fnmatch
+import json
+import sqlite3
+from collections.abc import Iterable, Mapping
+from pathlib import Path
+from urllib.parse import quote
+
+from .schema import KIND_GOAL, KIND_OWN, KIND_SIMPLEX, Role, Simplex, role_from_dict
+
+
+def slot_key(parent: str, alias: str) -> str:
+    """An occurrence identity, distinct even when two slots reuse one definition."""
+    return f"{parent}/slot/{quote(alias, safe='')}"
+
+
+class SchemaRegistry:
+    """Immutable versioned records; reusing a key with changed content is rejected."""
+
+    def __init__(self, path: str | Path = ":memory:") -> None:
+        self.connection = sqlite3.connect(str(path))
+        self.connection.execute("PRAGMA foreign_keys = ON")
+        self.connection.executescript("""
+            CREATE TABLE IF NOT EXISTS schema_nodes (
+                key TEXT PRIMARY KEY,
+                kind TEXT NOT NULL CHECK(kind IN ('role', 'simplex')),
+                payload TEXT NOT NULL
+            );
+            CREATE TABLE IF NOT EXISTS schema_slots (
+                parent TEXT NOT NULL REFERENCES schema_nodes(key) ON DELETE CASCADE,
+                alias TEXT NOT NULL,
+                child TEXT NOT NULL REFERENCES schema_nodes(key) ON DELETE RESTRICT,
+                position INTEGER NOT NULL,
+                PRIMARY KEY(parent, alias),
+                UNIQUE(parent, position)
+            );
+            CREATE INDEX IF NOT EXISTS schema_slots_child ON schema_slots(child);
+        """)
+
+    def __enter__(self):
+        return self
+
+    def __exit__(self, *_):
+        self.close()
+
+    def close(self) -> None:
+        self.connection.close()
+
+    def _insert(self, key: str, kind: str, payload: dict) -> None:
+        if not isinstance(key, str) or not key:
+            raise ValueError("a registry key must be nonempty")
+        if (kind == "simplex") != (payload.get("kind") == KIND_SIMPLEX):
+            raise ValueError("nested simplex roles must use a Simplex object")
+        encoded = json.dumps(payload, sort_keys=True, ensure_ascii=False, allow_nan=False)
+        existing = self.connection.execute(
+            "SELECT kind, payload FROM schema_nodes WHERE key = ?", (key,)).fetchone()
+        if existing is not None and existing != (kind, encoded):
+            raise ValueError(f"key {key!r} already has different content; use a new version key")
+        self.connection.execute("INSERT OR IGNORE INTO schema_nodes VALUES (?, ?, ?)",
+                                (key, kind, encoded))
+
+    def set_role(self, role: Role, key: str | None = None) -> str:
+        if isinstance(role, Simplex):
+            raise ValueError("use set_simplex for nested schemas")
+        key = key or f"role:{role.name}"
+        with self.connection:
+            self._insert(key, "role", role.as_dict())
+        return key
+
+    def set_simplex(self, simplex: Simplex, key: str | None = None,
+                    role_keys: Mapping[str, str] | None = None) -> str:
+        """Default children are scoped. role_keys explicitly opts into definition reuse."""
+        key = key or f"schema:{simplex.name}"
+        role_keys = dict(role_keys or {})
+        if not set(role_keys) <= set(simplex.roles):
+            raise ValueError("reuse map has an unknown alias")
+        with self.connection:
+            self._put_simplex(simplex, key, role_keys, set())
+        return key
+
+    def _put_simplex(self, simplex: Simplex, key: str, reuse: dict[str, str],
+                     active: set[int]) -> None:
+        if id(simplex) in active:
+            raise ValueError("cyclic simplex nesting")
+        active = active | {id(simplex)}
+        # Metadata only; children live in a relational slot table, not pickle blobs.
+        payload = Role.as_dict(simplex)
+        existing = self.connection.execute(
+            "SELECT key FROM schema_nodes WHERE key = ?", (key,)).fetchone()
+        if existing:
+            restored = self.get_simplex(key)
+            if restored is None or restored.as_dict() != simplex.as_dict():
+                raise ValueError(f"key {key!r} already has different content; use a new version key")
+            expected = {alias: reuse.get(alias, slot_key(key, alias)) for alias in simplex.roles}
+            if self.slots(key) != expected:
+                raise ValueError("same schema key cannot change its role-definition references")
+            return
+        self._insert(key, "simplex", payload)
+        for position, (alias, child) in enumerate(simplex.roles.items()):
+            child_key = reuse.get(alias, slot_key(key, alias))
+            if alias in reuse:
+                restored = self.get(child_key)
+                if restored is None or restored.as_dict() != child.as_dict():
+                    raise ValueError(f"reused role definition does not match slot {alias!r}")
+            elif isinstance(child, Simplex):
+                self._put_simplex(child, child_key, {}, active)
+            else:
+                self._insert(child_key, "role", child.as_dict())
+            self.connection.execute("INSERT INTO schema_slots VALUES (?, ?, ?, ?)",
+                                    (key, alias, child_key, position))
+
+    def get(self, key: str) -> Role | None:
+        return self._get(key, set())
+
+    def _get(self, key: str, active: set[str]) -> Role | None:
+        if key in active:
+            raise ValueError("cyclic schema references in registry")
+        row = self.connection.execute(
+            "SELECT kind, payload FROM schema_nodes WHERE key = ?", (key,)).fetchone()
+        if row is None:
+            return None
+        kind, encoded = row
+        payload = json.loads(encoded)
+        if kind == "role":
+            return role_from_dict(payload)
+        slots = self.slots(key)
+        children = {alias: self._get(child, active | {key}) for alias, child in slots.items()}
+        return Simplex(payload["name"], children, context=payload.get("context", ""),
+                       attrs=payload.get("attrs"))
+
+    def get_role(self, key: str) -> Role | None:
+        value = self.get(key)
+        return value if not isinstance(value, Simplex) else None
+
+    def get_simplex(self, key: str) -> Simplex | None:
+        value = self.get(key)
+        return value if isinstance(value, Simplex) else None
+
+    def slots(self, key: str) -> dict[str, str]:
+        return dict(self.connection.execute(
+            "SELECT alias, child FROM schema_slots WHERE parent = ? ORDER BY position", (key,)))
+
+    def keys(self, pattern: str = "*") -> list[str]:
+        return [key for (key,) in self.connection.execute("SELECT key FROM schema_nodes ORDER BY key")
+                if fnmatch.fnmatchcase(key, pattern)]
+
+    def search_roles(self, query: str, limit: int = 10) -> list[dict]:
+        """Literal substring candidates; search does not authorize semantic reuse."""
+        if not query.strip() or limit < 1:
+            return []
+        found = []
+        for key, payload in self.connection.execute(
+                "SELECT key, payload FROM schema_nodes WHERE kind = 'role' ORDER BY key"):
+            if query.casefold() in (key + payload).casefold():
+                found.append({"key": key, "role": json.loads(payload)})
+                if len(found) == limit:
+                    break
+        return found
+
+    def find_by_roles(self, role_keys: Iterable[str], match_all: bool = False) -> list[str]:
+        """Find schema keys containing definition keys, including nested descendants."""
+        wanted = set(role_keys)
+        if not wanted:
+            return []
+        found = []
+        for key in self._simplex_keys():
+            descendants = {row[0] for row in self.connection.execute("""
+                WITH RECURSIVE descendants(child) AS (
+                    SELECT child FROM schema_slots WHERE parent = ?
+                    UNION
+                    SELECT slots.child FROM schema_slots slots JOIN descendants d ON slots.parent = d.child
+                ) SELECT child FROM descendants
+            """, (key,))}
+            matches = wanted <= descendants if match_all else bool(wanted & descendants)
+            if matches:
+                found.append(key)
+        return found
+
+    def find_solvable(self, known_slots: Iterable[str]) -> list[dict]:
+        """Structural readiness by scoped occurrences, not proof or value unification."""
+        known = set(known_slots)
+        candidates = []
+        for key in self._simplex_keys():
+            schema = self.get_simplex(key)
+            inputs, outputs = [], []
+            for alias, role in schema.roles.items():
+                target = outputs if role.kind in (KIND_GOAL, KIND_OWN) else inputs
+                target.append(slot_key(key, alias))
+            missing_outputs = [output for output in outputs if output not in known]
+            if missing_outputs and set(inputs) <= known:
+                candidates.append({"schema_key": key, "input_slots": inputs,
+                                   "target_slots": missing_outputs, "structural_candidate_only": True})
+        return candidates
+
+    def _simplex_keys(self) -> list[str]:
+        return [row[0] for row in self.connection.execute(
+            "SELECT key FROM schema_nodes WHERE kind = 'simplex' ORDER BY key")]
+
+    def info(self) -> dict[str, int]:
+        counts = dict(self.connection.execute("SELECT kind, count(*) FROM schema_nodes GROUP BY kind"))
+        return {"roles": counts.get("role", 0), "simplices": counts.get("simplex", 0),
+                "slots": self.connection.execute("SELECT count(*) FROM schema_slots").fetchone()[0]}

tests/test_pilot_scripts.py

@@ -141,3 +141,82 @@ def test_judge_rejects_string_boolean():
     rp = load("run_pilot")
     with pytest.raises(ValueError, match="unusable judge"):
         rp.judge(ScriptedClient(['{"faithful": "false"}']), "passage", "code")
+
+
+def test_partial_resume_keeps_successful_detector_output():
+    rp = load("run_pilot")
+    row = rp.run_item(Stub(), ITEM)
+    expected_role = row["role"]
+    row.pop("judge")
+    row["errors"]["judge"] = "temporary failure"
+
+    class JudgeOnly:
+        calls = 0
+
+        def complete_json(self, messages):
+            self.calls += 1
+            assert "faithful" in messages[0]["content"]
+            return {"faithful": True}
+
+    client = JudgeOnly()
+    resumed = rp.run_item(client, ITEM, row)
+    assert client.calls == 1
+    assert resumed["role"] == expected_role
+    assert rp.complete_row(resumed)
+    assert row["errors"] == {"judge": "temporary failure"}
+
+
+def test_billing_failure_stops_before_next_detector():
+    import pytest
+
+    from leanbench.llm import LLMError
+
+    rp = load("run_pilot")
+
+    class Blocked:
+        calls = 0
+
+        def complete_json(self, messages):
+            self.calls += 1
+            raise LLMError("HTTP 400: Arrearage overdue-payment")
+
+    client = Blocked()
+    with pytest.raises(rp.ProviderBlocked) as caught:
+        rp.run_item(client, ITEM)
+    assert client.calls == 1
+    assert "role" in caught.value.row["errors"]
+    assert "judge" not in caught.value.row["errors"]
+
+
+def test_blocked_run_preserves_and_replaces_partial_row(tmp_path, monkeypatch):
+    import argparse
+    import json
+
+    from leanbench.config import Settings
+
+    rp = load("run_pilot")
+    args = argparse.Namespace(items=tmp_path / "items.jsonl", out=tmp_path / "results.jsonl",
+                              max_calls=400, dry_run=False)
+    args.items.write_text(json.dumps(ITEM) + "\n")
+    partial = {"id": "x1", "compiled": True, "role": {"flagged": False},
+               "errors": {"judge": "Arrearage"}}
+
+    def blocked(client, item, previous):
+        raise rp.ProviderBlocked(partial)
+
+    monkeypatch.setattr(rp, "run_item", blocked)
+    assert rp.execute(args, [ITEM], Settings()) == 2
+    meta = json.loads(args.out.with_suffix(".meta.json").read_text())
+    assert meta["status"] == "provider_blocked"
+    assert meta["completed_items"] == 0
+
+    def recover(client, item, previous):
+        assert previous["role"] == partial["role"]
+        return {**previous, "judge": {"faithful": True}, "errors": {}}
+
+    monkeypatch.setattr(rp, "run_item", recover)
+    assert rp.execute(args, [ITEM], Settings()) == 0
+    rows = [json.loads(line) for line in args.out.read_text().splitlines()]
+    assert len(rows) == 1 and rp.complete_row(rows[0])
+    meta = json.loads(args.out.with_suffix(".meta.json").read_text())
+    assert meta["completed_items"] == 1 and meta["status"] == "complete"

tests/test_schema_registry.py

@@ -0,0 +1,162 @@
+"""Semantic role definitions, scoped occurrences and structural candidate retrieval."""
+import json
+
+import pytest
+
+from leanbench.schema import (
+    KIND_FACT,
+    KIND_GOAL,
+    Fact,
+    Role,
+    Simplex,
+    SimplexInstance,
+    role_from_dict,
+)
+from leanbench.schema_registry import SchemaRegistry, slot_key
+
+
+def theorem(name="t"):
+    return Simplex(name, {"G": Role("group", context="A group carrier"),
+                          "g": Role("element", type_text="G", attrs={"references": ["G"]}),
+                          "finite": Role("finite", KIND_FACT, type_text="Finite G",
+                                         attrs={"references": ["G"]}),
+                          "goal": Role("claim", KIND_GOAL, type_text="P G g",
+                                       attrs={"references": ["G", "g"]})},
+                   context="A multi-object claim", attrs={"provenance": "synthetic"})
+
+
+def test_json_roundtrip_keeps_metadata_and_nesting():
+    outer = Simplex("outer", {"lemma": theorem(), "goal": Role("result", KIND_GOAL)},
+                    context="Composed relation", attrs={"version": 1})
+    encoded = json.loads(json.dumps(outer.as_dict()))
+    restored = role_from_dict(encoded)
+    assert restored.as_dict() == outer.as_dict()
+    assert restored.roles["lemma"].roles["g"].attrs["references"] == ["G"]
+
+
+def test_registry_persists_nested_schemas_in_one_transaction(tmp_path):
+    path = tmp_path / "registry.sqlite"
+    outer = Simplex("outer", {"lemma": theorem(), "goal": Role("result", KIND_GOAL)})
+    with SchemaRegistry(path) as registry:
+        registry.set_simplex(outer)
+        registry.set_simplex(outer)
+        assert registry.info() == {"roles": 5, "simplices": 2, "slots": 6}
+    with SchemaRegistry(path) as registry:
+        assert registry.get_simplex("schema:outer").as_dict() == outer.as_dict()
+        leaf = slot_key(slot_key("schema:outer", "lemma"), "g")
+        assert registry.find_by_roles([leaf], match_all=True) == [
+            "schema:outer", slot_key("schema:outer", "lemma")]
+
+
+def test_same_names_in_different_theorems_are_scoped():
+    with SchemaRegistry() as registry:
+        registry.set_simplex(theorem("first"))
+        registry.set_simplex(theorem("second"))
+        first_group = slot_key("schema:first", "G")
+        assert registry.find_by_roles([first_group]) == ["schema:first"]
+        assert registry.get_role(first_group).name == "group"
+        assert registry.slots("schema:first")["G"] != registry.slots("schema:second")["G"]
+
+
+def test_explicit_reuse_does_not_equate_local_bindings_or_multiplicity():
+    group = Role("group")
+    schema = Simplex("isomorphism", {"left": group, "right": group,
+                                    "goal": Role("equivalence", KIND_GOAL)})
+    with SchemaRegistry() as registry:
+        registry.set_role(group, "role:group")
+        registry.set_simplex(schema, role_keys={"left": "role:group", "right": "role:group"})
+        assert registry.slots("schema:isomorphism")["left"] == "role:group"
+        assert registry.find_solvable(["role:group"]) == []
+        assert registry.find_solvable([slot_key("schema:isomorphism", "left")]) == []
+        candidate = registry.find_solvable([slot_key("schema:isomorphism", x) for x in ["left", "right"]])
+        assert candidate[0]["target_slots"] == [slot_key("schema:isomorphism", "goal")]
+    instance = SimplexInstance(schema, {"left": "C2", "right": "C3"})
+    assert instance.facts["left"].value != instance.facts["right"].value
+    assert not instance.is_completed()
+    instance.resolve("goal", "a supplied result, not checked by the registry")
+    assert instance.is_completed()
+
+
+def test_premise_is_required_and_known_goal_is_not_a_missing_target():
+    with SchemaRegistry() as registry:
+        registry.set_simplex(theorem())
+        inputs = [slot_key("schema:t", alias) for alias in ["G", "g", "finite"]]
+        assert registry.find_solvable(inputs[:-1]) == []
+        assert registry.find_solvable(inputs)[0]["structural_candidate_only"]
+        assert registry.find_solvable(inputs + [slot_key("schema:t", "goal")]) == []
+
+
+def test_failed_write_rolls_back_every_child():
+    with SchemaRegistry() as registry:
+        registry.set_role(Role("incompatible"), "role:shared")
+        before = registry.info()
+        with pytest.raises(ValueError, match="does not match"):
+            registry.set_simplex(theorem(), role_keys={"goal": "role:shared"})
+        assert registry.info() == before
+        assert registry.get_simplex("schema:t") is None
+
+
+def test_cyclic_nesting_is_rejected_without_partial_write():
+    schema = Simplex("cycle", {"a": Role("a"), "b": Role("b")})
+    schema.roles["b"] = schema
+    with SchemaRegistry() as registry:
+        with pytest.raises(ValueError, match="cyclic"):
+            registry.set_simplex(schema)
+        assert registry.info() == {"roles": 0, "simplices": 0, "slots": 0}
+
+
+def test_keys_are_immutable_and_reuse_map_cannot_silently_change():
+    with SchemaRegistry() as registry:
+        registry.set_role(Role("G"), "role:G")
+        with pytest.raises(ValueError, match="different content"):
+            registry.set_role(Role("H"), "role:G")
+        schema = theorem()
+        registry.set_simplex(schema)
+        registry.set_role(schema.roles["G"], "role:shared")
+        with pytest.raises(ValueError, match="cannot change"):
+            registry.set_simplex(schema, role_keys={"G": "role:shared"})
+        assert registry.search_roles("%") == []
+        assert registry.search_roles("group", limit=1)[0]["role"]["name"] == "group"
+
+
+def test_instance_constraints_unknown_slots_and_invalid_references():
+    role = Role("parity", choices=["even", "odd"])
+    with pytest.raises(ValueError, match="not allowed"):
+        Fact(role, "prime")
+    schema = Simplex("pair", {"input": role, "goal": Role("result", KIND_GOAL, choices=[True])})
+    instance = SimplexInstance(schema, {"input": "even"})
+    with pytest.raises(ValueError, match="not allowed"):
+        instance.resolve("goal", False)
+    with pytest.raises(ValueError, match="declared"):
+        SimplexInstance(schema, {"unknown": "value"})
+    with pytest.raises(ValueError, match="references"):
+        Simplex("invalid", {"x": Role("x", attrs={"references": ["missing"]}), "y": Role("y")})
+    with pytest.raises(ValueError, match="name"):
+        Role(" ")
+    with pytest.raises(ValueError, match="sequence"):
+        Role("choice", choices="even")
+    with SchemaRegistry() as registry, pytest.raises(ValueError, match="Simplex object"):
+        registry.set_role(Role("fake", "simplex"))
+
+
+def test_pilot_materialization_keeps_partial_lean_projection_explicit():
+    import importlib.util
+    from pathlib import Path
+
+    path = Path(__file__).resolve().parents[1] / "experiments/P0-pilot/build_schemas.py"
+    spec = importlib.util.spec_from_file_location("build_schemas", path)
+    builder = importlib.util.module_from_spec(spec)
+    spec.loader.exec_module(builder)
+    items = [{"id": "closed", "lean_code": "theorem t : True := trivial"}]
+    assessment = {"records": [{"id": "closed", "blind_id": "P01", "source": {
+        "roles": [{"kind": "object", "symbols": ["G"], "description": "group"},
+                  {"kind": "goal", "description": "A synthetic claim"}]}}]}
+    with SchemaRegistry() as registry:
+        index, snapshots = builder.build(items, assessment, {"P01": "closed"}, registry)
+        assert registry.info()["simplices"] == 1
+        assert index[0]["source_status"] == "unreviewed_annotation_seed"
+        assert index[0]["lean_schema"] is None
+        assert index[0]["lean_status"] == "insufficient_projected_roles"
+        assert snapshots[0]["lean_projection"]["roles"][0]["kind"] == "goal"
+        with pytest.raises(ValueError, match="exactly once"):
+            builder.build(items, {"records": []}, {"P01": "closed"}, registry)