name: ml-theory-research-agent description: Orchestrate the full ML theory research workflow, including idea discovery, upgraded split proof workflow with global proof diagnostics and review, specialized final reviewers, checkpoints, tracker lifecycle, branch routing, and accepted-result copying. metadata: version: "1.0.0"

ML Theory Research Agent

Use this public controller skill for the full ML-theory research workflow. The controller owns workflow order, checkpoints, tracker lifecycle, worker provenance, retry routing, and accepted-result copying. Internal research and proof rubrics live in the producing or reviewing skills.

Responsibilities

• Orchestrate Workflow 1: literature survey, perspective selection, idea generation, and formalization.
• Orchestrate Workflow 2: split proof sketch, sketch review, global proof diagnostics, global proof review, step proof, step review, proof assembly, specialized final review, and aggregate final review.
• Enforce RUN_MODE, defaulting to interactive; RUN_MODE = autopilot approves checkpoints by default but does not change perspective coverage.
• Maintain theory_tracker.md, proof_tracker.md, IDEA_REPORT.md, workflow_feedback.md, and worker_log.md.
• Route local and final review outcomes to the smallest retry point.
• Copy accepted final artifacts into results/perspective_M/idea_N/theory.

Inputs And Outputs

Required input:

• $ARGUMENT

Optional input:

• RESEARCH_BRIEF.md

RESEARCH_BRIEF.md refines or overrides $ARGUMENT; after the Workflow 1 merge, $ARGUMENT in this controller means the merged effective research direction. The merged effective research direction is subject to the Source-Direction Fidelity Contract in ../_shared/checklists/artifact-contracts.md; downstream workers must extract only constraints that are present or clearly implied, without assuming fixed brief headings.

Controller-owned outputs:

• LITERATURE_SURVEY.md
• Perspective_Selection.md
• IDEA_REPORT.md
• theory_tracker.md
• workflow_feedback.md
• worker_log.md
• perspective_M/idea_N/proof_tracker.md
• perspective_M/idea_N/proof_history/ for non-binding archival copies of overwritten proof-stage artifacts
• accepted artifacts under results/perspective_M/idea_N/theory

Internal Skill Calls

• /research-lit "$ARGUMENT" -> writes LITERATURE_SURVEY.md
• /perspective-select "$ARGUMENT" -> writes Perspective_Selection.md
• /subagent-idea-generator "$ARGUMENT" -> writes perspective_M/idea_N/idea.md, or returns NO_VIABLE_IDEA without finalizing an idea when all candidates fail hard gates
• /idea-formalizer -> writes perspective_M/idea_N/setting.md
• /proof-sketch -> writes perspective_M/idea_N/proof_sketch.md
• /proof-sketch-review -> writes perspective_M/idea_N/proof_sketch_review.md
• /global-proof -> writes perspective_M/idea_N/global_proof.md
• /global-proof-review -> writes perspective_M/idea_N/global_proof_review.md
• /proof-step <Step ID> -> writes perspective_M/idea_N/proof_steps/<Step ID>/proof.md
• /proof-step-review <Step ID> -> writes perspective_M/idea_N/proof_steps/<Step ID>/review.md
• /proof-assembly -> writes perspective_M/idea_N/latex_template/ and perspective_M/idea_N/assembly_report.md
• /proof-review-structural -> writes perspective_M/idea_N/proof_review_structural.md
• /proof-review-rigor -> writes perspective_M/idea_N/proof_review_rigor.md
• /proof-review-citation -> writes perspective_M/idea_N/proof_review_citation.md
• /proof-review-adversarial -> writes perspective_M/idea_N/proof_review_adversarial.md
• /proof-review-aggregate -> writes perspective_M/idea_N/proof_review.md

Slash-style calls are symbolic skill invocations. To invoke a skill, load its SKILL.md, provide the listed inputs through the assigned subagent, and verify the expected artifact.

Split Subagent Model

Before perspective branches, spawn or resume two distinct run-scoped subagents:

• literature-worker for /research-lit "$ARGUMENT"
• perspective-selector for /perspective-select "$ARGUMENT"

These run-scoped handles are required worker provenance for the full workflow, but they are not counted in the per-perspective 12 + 2k proof/idea distinctness gate.

For each approved perspective, spawn twelve distinct perspective-scoped subagents:

• idea-worker for /subagent-idea-generator
• formalizer for /idea-formalizer
• sketch-worker for /proof-sketch
• sketch-reviewer for /proof-sketch-review
• global-proof-worker for /global-proof
• global-proof-reviewer for /global-proof-review
• assembler for /proof-assembly
• structural-reviewer for /proof-review-structural
• rigor-reviewer for /proof-review-rigor
• citation-reviewer for /proof-review-citation
• adversarial-reviewer for /proof-review-adversarial
• review-aggregator for /proof-review-aggregate

For each accepted sketch step, spawn two additional distinct step-scoped subagents:

• step-worker for /proof-step <Step ID>
• step-reviewer for /proof-step-review <Step ID>

If an approved perspective has k sketch steps, the controller requires 12 + 2k distinct runtime-visible subagent handles for that perspective. Step-scoped handles are tied to one Step ID; do not reuse them for another step in the same sketch. Reruns may resume the same handle for the same role and step when available; otherwise spawn a replacement and record a handoff.

Before each delegated stage, append a row to worker_log.md using ../_shared/templates/worker-log.md. Do not run a delegated stage with an empty or invented handle.

Resolve ../_shared/... references relative to this skill directory (skills/ml-theory-research-agent/ in source form or the installed skill directory), not relative to the active run root.

Artifact Gates

Before consuming an artifact for routing, tracker updates, acceptance, or copying, validate it against ../_shared/checklists/artifact-contracts.md.

Required checks:

• LITERATURE_SURVEY.md keeps the required literature-survey structure and does not contradict extracted source-direction constraints; when source-relevant constraints matter downstream, the survey keeps them visible in relation and gap prose.
• Perspective_Selection.md contains complete normalized perspective tuples and does not contradict extracted source-direction constraints; if normalization drops source-critical details, its gap or focus prose preserves them as residual context for idea generation.
• idea.md preserves required headings, concrete lineage notes, and support provenance in existing Notes fields; theorem-critical assumptions, procedures, protocols, and mechanisms are standard/literature-derived or novel example-verified, and every novel component names several branch-specific concrete verification examples. When source-direction constraints are present, idea.md records source alignment, progress type, and materiality, and does not pass an unmarked weakening or non_material candidate.
• setting.md preserves required headings, assigns a stable ASCII assumption id such as assump:smoothness to every technical assumption, contains exactly one goal statement, preserves idea-level assumption-support provenance in # Note / Rigor, and preserves source-alignment and progress-type metadata when present.
• proof_sketch.md exposes stable steps, exact claims, dependencies, assumptions, proof tools, theorem-critical mechanism-witness entries, exported-interface feasibility for downstream-facing theorem-critical outputs, including source-convention compatibility, object-target compatibility for theorem-critical entry/reference/baseline objects, same-target bridges with residual-to-target adequacy when the produced object is transformed, weighted, preconditioned, whitened, reference-operator-modified, or otherwise surrogate relative to the consumed target, and raw-assumption-to-interface feasibility for direct derivations, standard facts or tools, current-notation wrappers, and primitive-source derivations when applicable, baseline invariance obligations when present, obligation locality classification when theorem-critical hard obligations are visible, noncircular closure status when applicable, entry-state / first-update stress results when applicable, generated-output flow entries when theorem-facing generated outputs are consumed, and blockers.
• proof_sketch_review.md contains a controlled sketch-review status, integer sketch viability score, smallest retry target, retry mode, audit summary, early obstruction audit including the theorem-critical mechanism-witness gate, Exported Interface Feasibility Gate, Residual-To-Target Adequacy Gate when applicable, Baseline Invariance Obligation when applicable, Step-Locality And Theorem-Contract Gate, Noncircular Closure Gate, Entry-State / Activation Trace Gate, source-interface feasibility including source-convention compatibility and object-target compatibility for direct derivations, standard facts or tools, current-notation wrappers, and primitive-source derivations when applicable, same-target bridge checks with residual-to-target adequacy for transformed or surrogate produced objects, and generated-output flow when applicable, a Gate Evidence Table satisfying the shared Gate Evidence Row Contract, blocking issues, required repair bundle, and rationale.
• global_proof.md contains a controlled global proof status, reviewed sketch identity, attempted theorem claim, detailed whole-proof draft, theorem-level block map, sketch-step coverage, dependency and assumption audit, citation and tool audit, quantitative dependence audit including baseline invariance obligations when present, scope and closure certificate covering theorem-critical mechanism witnesses, exported-interface feasibility for downstream-facing theorem-critical outputs, including source-convention compatibility, object-target compatibility for theorem-critical entry/reference/baseline objects, same-target bridges with residual-to-target adequacy for transformed or surrogate produced objects, and raw-assumption-to-interface feasibility for direct derivations, standard facts or tools, current-notation wrappers, and primitive-source derivations when applicable, obligation locality classification using only step-local, sketch/interface defect, or idea/theorem-contract defect, noncircular closure status when applicable, entry-state / first-update stress results when applicable, generated-output flow when applicable, early obstruction and repair-plausibility audit, global gaps and hard steps, diagnostic boundary note, and suggested routing.
• global_proof_review.md contains a controlled global-proof review status, smallest retry target, blocking issues, required repair bundle, contract and status audit, claim and sketch fidelity audit, theorem-level structure audit, dependency and assumption audit, citation and tool audit, quantitative dependence audit, scope and closure review with an independent theorem-critical mechanism-witness gate, Exported Interface Feasibility Gate, Residual-To-Target Adequacy Gate when applicable, source-interface feasibility including source-convention compatibility and object-target compatibility for direct derivations, standard facts or tools, current-notation wrappers, and primitive-source derivations when applicable, same-target bridge checks with residual-to-target adequacy for transformed or surrogate produced objects, and Baseline Invariance Obligation when applicable, a Gate Evidence Table satisfying the shared Gate Evidence Row Contract, row-level obligation locality classification review, Noncircular Closure Gate, Entry-State / Activation Trace Gate, Step-Locality And Theorem-Contract Gate, and generated-output flow when applicable, hard-step localization audit, early idea-failure screen, and rationale.
• every step proof and review artifact contains the required local proof and local review sections.
• latex_template/ contains the required content and support files and passes the self-contained paper-ready TeX gate.
• assembly_report.md contains a controlled assembly status, attempted claim, blockers, and notes.
• the Assumption Provenance Contract passes for sketch, global proof, step, assembly, and final review artifacts.
• every specialized review artifact contains Reviewer Verdict, Blocking Issues, Nonblocking Concerns, Suggested Repair Depth, and Smallest Candidate Repair Target.
• aggregated proof_review.md contains Score, Failure Type, Critical Issues, Suggested Next Action, and Retry Mode.
• accepted-result copying copies only setting.md, latex_template/, and proof_review.md.

Hard controller gates:

• MAX_* budgets are total allowed producer attempts, not retry counts. Do not run or accept attempt MAX + 1 for any idea, sketch, global proof, step, or assembly producer.
• Before any rerun overwrites a branch artifact path that has already been consumed for routing, tracker updates, acceptance checks, or accepted-result copying, copy the previous consumed file or directory into branch-local proof_history/sketch_XXX/... under a stage-and-attempt-specific path. Preserve enough path structure to identify the original artifact, including proof_steps/<Step ID>/... and latex_template/ when applicable.
• proof_history/ is archival history only. It is never current proof evidence, never satisfies an artifact gate, and is never copied to accepted results.
• Specialized final reviewers are diagnostic. After a specialized reviewer reports a blocker in a contract-valid artifact, any producer repair must be routed by /proof-review-aggregate; the controller may rerun or hand off a specialized reviewer directly only when that diagnostic review artifact is missing or contract-invalid.
• Finalization must fail if any budget gate, worker-provenance gate, artifact gate, or accepted-copy verification gate fails.

Initialization

Treat the current directory as the run root unless the user explicitly names another root.

Before running /research-lit:

• If worker_log.md is missing at the run root, initialize it with the table structure from ../_shared/templates/worker-log.md.
• If workflow_feedback.md is missing at the run root, initialize it from ../_shared/templates/workflow-feedback.md.
• If theory_tracker.md is missing at the run root, initialize it from ../_shared/templates/theory-tracker.md.
• If IDEA_REPORT.md is missing at the run root, initialize it from ../_shared/templates/idea-report.md.
• Preserve existing controller-owned files when present; do not rewrite or truncate prior run history during initialization.
• Do not append a theory_tracker.md branch row during initialization. Append a normal viable-idea branch row only after idea.md passes its checkpoint and the cross-perspective duplicate gate. Exception: if /subagent-idea-generator returns NO_VIABLE_IDEA or the approved idea.md fails the cross-perspective duplicate gate, append the corresponding failed row for that consumed idea_N slot immediately before routing to the next idea slot or marking the perspective exhausted.

Existing proof-stage artifacts are branch history. Do not delete them unless the user asks. On a rerun, use the latest relevant review or final review artifact as the triggering repair artifact.

Before a rerun overwrites any latest proof-stage artifact path that was previously consumed, archive that consumed artifact under proof_history/sketch_XXX/.... Do not archive by moving the live artifact; copy it, then let the producer overwrite the fixed path.

Control Parameters

• RUN_MODE: interactive or autopilot; default interactive and requires explicit user approval at checkpoints
• MAX_PERSPECTIVES = 3
• MAX_IDEA_VARIANTS_PER_PERSPECTIVE = 8
• MAX_SKETCH_ATTEMPTS_PER_IDEA = 6
• MAX_GLOBAL_PROOF_ATTEMPTS_PER_SKETCH = 3
• MAX_STEP_ATTEMPTS_PER_STEP = 3
• MAX_ASSEMBLY_ATTEMPTS_PER_SKETCH = 8
• ACCEPT_THRESHOLD = 7

Retry Mode is recorded only in proof_sketch_review.md and aggregated proof_review.md, and may be summarized in proof_tracker.md Reasons; do not add a proof-tracker column for it. global_proof.md records Status and Suggested Routing, not retry mode. global_proof_review.md records Global-Proof Review Status and Smallest Retry Target, not retry mode or a numeric score. Step-review and specialized review artifacts do not include Retry Mode: proof_steps/<Step ID>/review.md records Step-Review Status and Smallest Retry Target, and the controller derives step repair routing from those fields; specialized review artifacts provide diagnostic repair depth and candidate target for the aggregator only.

Retry Budget Rules

The controller owns retry budgets. Reviewer skills diagnose outcomes and retry targets but do not consume or update budgets.

• Each MAX_* value is the total number of allowed producer attempts. Attempt 1 consumes the first budget slot; the controller must stop before dispatching attempt MAX + 1. Budget state is invalid if one perspective has more than MAX_IDEA_VARIANTS_PER_PERSPECTIVE consumed idea slots, or if any accepted proof-tracker row has Sketch attempt > MAX_SKETCH_ATTEMPTS_PER_IDEA, global Unit attempt > MAX_GLOBAL_PROOF_ATTEMPTS_PER_SKETCH, step Unit attempt > MAX_STEP_ATTEMPTS_PER_STEP, or assembly Unit attempt > MAX_ASSEMBLY_ATTEMPTS_PER_SKETCH.
• MAX_IDEA_VARIANTS_PER_PERSPECTIVE limits idea-generation slots under one approved perspective. IDEA_FAIL consumes this budget by creating the next idea_N; NO_VIABLE_IDEA consumes the current idea_N slot without creating or accepting an idea.md; cross-perspective duplicate rejection consumes the current idea_N slot after idea.md checkpoint approval but before formalization. Enforce the budget by counting all theory_tracker.md rows for that perspective with Idea attempt = idea_N, including failed NO_VIABLE_IDEA and DUPLICATE_IDEA rows. Exhaustion ends the perspective branch.
• MAX_SKETCH_ATTEMPTS_PER_IDEA limits proof-roadmap and decomposition attempts for one idea. Sketch attempt starts at 1; sketch-review REVISE_SKETCH, global-proof-review REVISE_SKETCH, and final PROOF_SKETCH_FLAW consume this budget by incrementing Sketch attempt.
• MAX_GLOBAL_PROOF_ATTEMPTS_PER_SKETCH limits /global-proof producer attempts under the current accepted sketch. The first global diagnostic uses Unit attempt = 1; global-proof-review REVISE_GLOBAL consumes this budget by rerunning /global-proof with the next global Unit attempt under the same Sketch attempt.
• MAX_STEP_ATTEMPTS_PER_STEP limits attempts for one Step ID under the current sketch attempt. REVISE_STEP and final PROOF_STEP_FLAW consume the affected step's Unit attempt budget.
• BLOCKED_BY_DEPENDENCY consumes the blocking dependency step's MAX_STEP_ATTEMPTS_PER_STEP budget, not the downstream step that reported the dependency block.
• MAX_ASSEMBLY_ATTEMPTS_PER_SKETCH limits assembly attempts under the current accepted sketch. Final PROOF_ASSEMBLY_FLAW consumes the assembly Unit attempt budget.
• /global-proof-review consumes no producer budget itself. REVISE_GLOBAL consumes the global-proof attempt budget by rerunning /global-proof under the same accepted sketch and same Sketch attempt. REVISE_SKETCH consumes the sketch retry budget by rerunning /proof-sketch. IDEA_FAIL consumes the idea-generation budget by creating the next idea slot.
• After any sketch revision, previous step proof/review and assembly artifacts from an earlier Sketch attempt are stale for binding purposes. The controller must rerun /proof-step and /proof-step-review for every required step in the newly accepted sketch, in dependency order, before assembly. The only prior proof material that may be consulted is the latest prior relevant artifact for the same branch and same step or dependency, such as the latest previous same-step proof/review, latest previous dependency proof/review, or latest aggregate review that triggered repair. These artifacts may be used only as diagnostic or repair references when their claims, assumptions, and dependencies still match the current accepted sketch. Do not scan or rely on the full historical archive; acceptance requires fresh artifacts under the current Sketch attempt.
• After any /proof-step <Step ID> producer rerun, the previous accepted proof_steps/<Step ID>/review.md is stale unless its Sketch attempt, Step ID, Unit attempt, and Reviewed proof artifact identify the current proof_steps/<Step ID>/proof.md produced by that rerun. The repaired step proof must pass a fresh /proof-step-review <Step ID> with Step-Review Status = ACCEPTED before it can be consumed by downstream step reviews, assembly, specialized final reviews, aggregate review, or accepted-result copying.
• The specialized final reviewer ensemble consumes no producer budget and does not route retries directly.
• Final /proof-review-aggregate consumes no budget itself. Its Suggested Next Action consumes the controller-supported repair target's budget.
• When a local step or assembly budget is exhausted, escalate to sketch revision. When sketch attempts are exhausted, escalate to a new idea. When idea-generation slots are exhausted, mark the branch failed.
• Before any IDEA_FAIL or retry-exhaustion route creates a fresh idea_N, perform a minimal-delta check: identify the failed needed property, any failed baseline invariance obligation, and which prior primitive assumption, algorithm/model/procedure, theorem scope/mode/metric, exposed dependence, success criterion, or mechanism source, including any theorem-facing mechanism source not supported by the setting, is implicated, or whether weakening the conclusion is implicated. Prefer the smallest idea/formalization repair that keeps unaffected idea structure intact, including inherited baseline/recovery conclusions unless the triggering failure explicitly made their weakening target-changing. First preserve any review-allowed same-setting sketch repair when the route is not a valid IDEA_FAIL; after a valid IDEA_FAIL, treat primitive-assumption, theorem-contract, or target changes as idea repair rather than as repair of the existing proof artifacts, and create a materially new idea only when the implicated repair cannot preserve the prior branch structure. A target-changing drift after IDEA_FAIL, retry exhaustion, or explicit checkpoint feedback must remain the smallest change justified by the failure record and must preserve source-direction metadata and remaining-gap labeling.

Workflow 1: Idea Discovery

1. Read $ARGUMENT; if RESEARCH_BRIEF.md exists, merge it with $ARGUMENT, with the brief taking priority. All later /research-lit "$ARGUMENT", /perspective-select "$ARGUMENT", and /subagent-idea-generator "$ARGUMENT" calls use this merged effective argument. Apply the Source-Direction Fidelity Contract to downstream Workflow 1 artifacts: extract constraints from available prose only when present or clearly implied, and do not assume fixed RESEARCH_BRIEF.md headings.
2. Spawn or resume the run-scoped literature-worker, append a worker_log.md row with Branch Path = run, Stage = literature-survey, and Notes containing scope=run, then run /research-lit "$ARGUMENT" and checkpoint LITERATURE_SURVEY.md.
3. Spawn or resume the run-scoped perspective-selector, append a worker_log.md row with Branch Path = run, Stage = perspective-selection, and Notes containing scope=run, then run /perspective-select "$ARGUMENT" and checkpoint Perspective_Selection.md.
4. Launch all approved perspectives as active branches before proof work monopolizes any one branch: create every approved perspective_M/, allocate each initial idea_1 slot, spawn each distinct idea-worker, and dispatch /subagent-idea-generator "$ARGUMENT" for all approved perspectives when the runtime supports parallel delegation. If true parallel delegation is unavailable, use fair round-robin scheduling across active perspectives and do not run one perspective to acceptance, exhaustion, or hard-gate termination before launching or advancing the others.
5. As each active perspective branch's idea worker returns NO_VIABLE_IDEA, do not checkpoint that branch's idea.md and do not run /idea-formalizer for that branch. Append exactly one failed theory_tracker.md row for the consumed branch-local idea_N slot with Setting = N/A, Goal = N/A, Setting Signature = N/A, Goal Signature = N/A, Status = Fail, Best Score empty or 0, and Reasons = NO_VIABLE_IDEA: <compact gate-failure reasons>; if that perspective's idea budget remains, route that branch to the next idea_N using those compact gate-failure reasons as feedback, otherwise mark only that perspective branch exhausted.
6. For each active perspective branch whose worker produces an idea.md, checkpoint that branch-local idea.md; on approval, run the cross-perspective duplicate gate for that branch.
7. If the cross-perspective duplicate gate rejects an approved branch-local idea.md, do not run /idea-formalizer for that branch and do not include that branch in IDEA_REPORT.md. Append exactly one failed theory_tracker.md row for the consumed branch-local idea_N slot with Setting, Goal, Setting Signature, and Goal Signature filled from the generated idea.md using the same normalized summaries used for viable idea rows, Status = Fail, Best Score empty or 0, and Reasons = DUPLICATE_IDEA: matches <perspective_M/idea_N>; <compact duplicate reason>; if that perspective's idea budget remains, route that branch to the next idea_N using that duplicate reason as feedback, otherwise mark only that perspective branch exhausted.
8. For each viable non-duplicate branch-local idea, append the normal theory_tracker.md row only after that branch's idea.md passes checkpoint and duplicate gate.
9. Keep IDEA_REPORT.md as a current snapshot of active non-duplicate branches.

Checkpoint actions:

• In RUN_MODE = interactive or when RUN_MODE is unspecified, stop at each checkpoint and ask the user for approve/proceed, edit, or re-generate/re-search.
• approve or proceed: continue.
• edit: apply the requested edits to the current artifact, then checkpoint again.
• re-generate or re-search: persist feedback in workflow_feedback.md, rerun the producing skill, then clear the feedback section.
• RUN_MODE = autopilot: choose approve/proceed. Autopilot approval does not authorize first-attempt target weakening or source-scope drift; first ideas still follow the Source-Direction Fidelity Contract, and later drift requires valid failure evidence, retry exhaustion, or explicit checkpoint feedback. Autopilot also does not stop the run after the first accepted branch; launch all approved perspectives as active branches and continue them unless the user explicitly requested a first-success search.

Workflow 2: Split Theory Proof

Workflow 2 runs one active proof branch per approved perspective whose current idea passed duplicate checks. Keep these perspective branches active in parallel when the runtime supports it; otherwise advance them by fair round-robin scheduling. Branch-local retries consume only that branch's budgets. Acceptance and finalization are branch-local: after one branch is accepted and copied, continue every remaining approved perspective until that perspective is accepted, exhausted, or blocked by a hard gate, unless the user explicitly requested a first-success search.

Phase 1: Formalization

Spawn or resume the perspective's distinct formalizer, then invoke:

/idea-formalizer

Inputs:

• perspective_M/idea_N/idea.md that has passed the support-provenance artifact gate
• optional LITERATURE_SURVEY.md
• optional branch-local files under perspective_M/

Output:

• perspective_M/idea_N/setting.md

Checkpoint setting.md, including the compact assumption-support summary in # Note / Rigor. When accepted, initialize perspective_M/idea_N/proof_tracker.md from the shared proof-tracker template.

Phase 2: Proof Sketch

Spawn or resume the perspective's distinct sketch-worker, append a proof-tracker row with Sketch attempt = current sketch attempt, Unit type = sketch, Unit id = sketch, Unit attempt = 1, and Score = N/A, then invoke:

/proof-sketch

Inputs:

• perspective_M/idea_N/setting.md
• perspective_M/idea_N/proof_tracker.md
• optional idea.md, LITERATURE_SURVEY.md, theory_tracker.md, technical_survey.md, and prior same-perspective artifacts
• on reruns, the triggering proof_sketch_review.md, global_proof.md, global_proof_review.md, proof_steps/<Step ID>/review.md, or aggregated proof_review.md
• on reruns, controller-provided Retry Mode: revise_sketch

Outputs:

• perspective_M/idea_N/proof_sketch.md
• optional perspective_M/idea_N/technical_survey.md

The sketch must expose stable step IDs, intended claims, dependencies, assumptions, proof tools or cited results, theorem-critical mechanism-witness entries, exported-interface feasibility for downstream-facing theorem-critical outputs, source-convention compatibility, object-target compatibility for theorem-critical entry/reference/baseline objects, same-target bridges with residual-to-target adequacy when the produced object is transformed, weighted, preconditioned, whitened, reference-operator-modified, or otherwise surrogate relative to the consumed target, and raw-assumption-to-interface feasibility for direct derivations, standard facts or tools, current-notation wrappers, and primitive-source derivations when applicable, obligation locality classification when theorem-critical hard obligations are visible, noncircular closure status when applicable, entry-state / first-update stress results when applicable, generated-output flow entries when theorem-facing generated outputs are consumed, and blockers.

Phase 3: Proof Sketch Review

Spawn or resume the perspective's distinct sketch-reviewer, then invoke:

/proof-sketch-review

Inputs:

• perspective_M/idea_N/setting.md
• perspective_M/idea_N/proof_sketch.md
• optional lineage, tracker, and technical-survey artifacts

Output:

• perspective_M/idea_N/proof_sketch_review.md

After proof_sketch_review.md passes its artifact gate, fill the open sketch proof-tracker row with Score = N/A, Review outcome = <sketch review status>, Retry target = <Smallest Retry Target>, and Status = Accept only for ACCEPTED; otherwise set Status = Fail.

Route sketch-review status:

• ACCEPTED: count sketch steps as k, prepare the 12 + 2k worker-provenance plan, then proceed to global proof.
• REVISE_SKETCH: require Retry Mode = revise_sketch; if MAX_SKETCH_ATTEMPTS_PER_IDEA remains, increment Sketch attempt and rerun /proof-sketch; otherwise route to idea revision or branch exhaustion.
• IDEA_FAIL: require Smallest Retry Target = /subagent-idea-generator, Retry Mode = new_idea, and an explicit rationale explaining why same-setting sketch repair cannot preserve the current formalized setting and goal and identifying the required theorem-contract change: changed primitive assumptions, changed algorithm/model/procedure, changed theorem scope/mode/metric, changed exposed dependence, changed success criterion, adding a theorem-facing mechanism source not supported by the setting, or weakening the conclusion. If that rationale is missing, treat the review artifact as contract-invalid and rerun or hand off /proof-sketch-review. If valid and MAX_IDEA_VARIANTS_PER_PERSPECTIVE remains, route to idea revision with the triggering proof_sketch_review.md as prior failure evidence; otherwise mark branch exhaustion.

Phase 4: Global Proof

After the sketch review is accepted, spawn or resume the perspective's distinct global-proof-worker, append a proof-tracker row with Sketch attempt = current sketch attempt, Unit type = global, Unit id = global, Unit attempt = next global proof attempt under the current sketch attempt starting at 1, and Score = N/A, then invoke:

/global-proof

Inputs:

• setting.md
• accepted proof_sketch.md
• accepted proof_sketch_review.md
• optional prior failures and tracker history

Output:

• perspective_M/idea_N/global_proof.md

The global proof artifact must be a detailed theorem-level diagnostic draft, not a short sketch summary. It must expose the attempted claim, theorem-level block map, step coverage, dependency and assumption audit, cited-tool obligations, source-convention compatibility, object-target compatibility for theorem-critical entry/reference/baseline objects, same-target bridges with residual-to-target adequacy when the produced object is transformed, weighted, preconditioned, whitened, reference-operator-modified, or otherwise surrogate relative to the consumed target, and raw-assumption-to-interface feasibility for direct derivations, standard facts or tools, current-notation wrappers, and primitive-source derivations when applicable, quantitative-dependence obligations when relevant, scope-and-closure certificate for all entries covered by the Theorem-Critical Mechanism Witness Gate, exported-interface feasibility and raw-control-to-exported-interface paths for downstream-facing theorem-critical outputs, obligation locality classification for theorem-critical hard obligations, noncircular closure status when applicable, entry-state / first-update stress results when applicable, generated-output flow when applicable, and diagnostic boundary note required by the shared artifact contract. global_proof.md may label candidate idea-level evidence, but only global_proof_review.md can route that evidence to /subagent-idea-generator.

After global_proof.md passes its artifact gate, spawn or resume the perspective's distinct global-proof-reviewer, append a worker-log row, then invoke:

/global-proof-review

Inputs:

• setting.md
• accepted proof_sketch.md
• accepted proof_sketch_review.md
• global_proof.md
• optional prior failures and tracker history

Output:

• perspective_M/idea_N/global_proof_review.md

After global_proof_review.md passes its artifact gate, fill the open global proof-tracker row with Score = N/A, Review outcome = <Global-Proof Review Status>, Retry target = <Smallest Retry Target>, and Status = Accept only for ACCEPTED; otherwise set Status = Fail. Do not copy any global-proof or global-proof-review diagnostic score into the tracker.

Route global-proof-review status:

• ACCEPTED: require Smallest Retry Target = None, then continue to step proof using global_proof.md only as accepted diagnostic context.
• REVISE_GLOBAL: require Smallest Retry Target = /global-proof; if MAX_GLOBAL_PROOF_ATTEMPTS_PER_SKETCH remains, append a new global proof-tracker row with the next global Unit attempt, rerun /global-proof under the same accepted sketch and same Sketch attempt, then rerun /global-proof-review. If the global proof budget is exhausted, escalate to /proof-sketch with Retry Mode = revise_sketch if the sketch budget remains; otherwise route to idea revision or branch exhaustion.
• REVISE_SKETCH: require Smallest Retry Target = /proof-sketch; if MAX_SKETCH_ATTEMPTS_PER_IDEA remains, increment Sketch attempt and rerun /proof-sketch with Retry Mode = revise_sketch and the triggering global_proof_review.md; otherwise route to idea revision or branch exhaustion.
• IDEA_FAIL: require Smallest Retry Target = /subagent-idea-generator and an explicit rationale explaining why same-setting sketch repair cannot preserve the current formalized setting and goal and identifying the required theorem-contract change: changed primitive assumptions, changed algorithm/model/procedure, changed theorem scope/mode/metric, changed exposed dependence, changed success criterion, adding a theorem-facing mechanism source not supported by the setting, or weakening the conclusion. If that rationale is missing, treat the review artifact as contract-invalid and rerun or hand off /global-proof-review. If valid and MAX_IDEA_VARIANTS_PER_PERSPECTIVE remains, route to idea revision with the triggering global_proof_review.md as prior failure evidence; otherwise mark branch exhaustion.

global_proof.md is diagnostic. It must not replace accepted step proofs, justify assembly acceptance, or change sketch-step claims without routing back through accepted global_proof_review.md and then /proof-sketch.

Phase 5: Step Proof And Step Review

Run steps in dependency order. A step may start only after all listed dependencies have accepted reviews.

For each Step ID, spawn or resume the distinct step-scoped step-worker, append a proof-tracker row with Sketch attempt = current sketch attempt, Unit type = step, Unit id = <Step ID>, Unit attempt = next attempt for this Step ID under the current sketch attempt, and Score = N/A, then invoke:

/proof-step <Step ID>

Inputs:

• setting.md
• proof_sketch.md
• accepted proof_sketch_review.md
• optional accepted diagnostic global_proof.md when paired with accepted global_proof_review.md
• accepted global_proof_review.md when global_proof.md is provided
• target Step ID
• accepted dependency step proof/review artifacts, when dependencies exist
• on reruns, triggering same-step proof_steps/<Step ID>/review.md, downstream proof_steps/<Downstream Step ID>/review.md naming this step as the failed dependency, or aggregated proof_review.md when repairing a step

Output:

• proof_steps/<Step ID>/proof.md

Then spawn or resume the distinct step-scoped step-reviewer and invoke:

/proof-step-review <Step ID>

Inputs:

• setting.md
• proof_sketch.md
• accepted proof_sketch_review.md
• target Step ID
• proof_steps/<Step ID>/proof.md
• accepted dependency step proof/review artifacts, when dependencies exist

Output:

• proof_steps/<Step ID>/review.md

After proof_steps/<Step ID>/review.md passes its artifact gate, fill the open step proof-tracker row with Score = N/A, Review outcome = <Step-Review Status>, Retry target = <Smallest Retry Target>, and Status = Accept only for ACCEPTED; otherwise set Status = Fail.

Route step-review status:

• ACCEPTED: continue to downstream steps or assembly.
• REVISE_STEP: if MAX_STEP_ATTEMPTS_PER_STEP remains for this Step ID, rerun /proof-step <Step ID> with the same-step review as the triggering repair artifact, then rerun /proof-step-review <Step ID> against the repaired proof and proceed only if that same-step review returns ACCEPTED; otherwise route by the new step-review status. If the step budget is exhausted, escalate to sketch revision.
• REVISE_SKETCH: if MAX_SKETCH_ATTEMPTS_PER_IDEA remains, rerun /proof-sketch with Retry Mode = revise_sketch and an incremented sketch attempt; otherwise route to idea revision or branch exhaustion.
• BLOCKED_BY_DEPENDENCY: if MAX_STEP_ATTEMPTS_PER_STEP remains for the named dependency, rerun /proof-step <dependency Step ID> with the downstream review as the triggering repair artifact, then rerun /proof-step-review <dependency Step ID> against the repaired dependency proof and proceed only if that dependency review returns ACCEPTED; after that, rerun affected downstream step reviews or step proofs as needed in dependency order. If the dependency review is not ACCEPTED, route by its step-review status. If the dependency step budget is exhausted, escalate to sketch revision.

Phase 6: Proof Assembly

After all required steps are accepted, spawn or resume the perspective's distinct assembler, append a proof-tracker row with Sketch attempt = current sketch attempt, Unit type = assembly, Unit id = assembly, and Unit attempt = next assembly attempt under the current sketch attempt, then invoke:

/proof-assembly

Inputs:

• setting.md
• accepted proof_sketch.md
• accepted proof_sketch_review.md
• accepted proof/review artifacts for every required step
• optional aggregated proof_review.md when repairing PROOF_ASSEMBLY_FLAW

Outputs:

• perspective_M/idea_N/latex_template/
• perspective_M/idea_N/assembly_report.md

Assembly may combine accepted step claims and reconcile notation, but it must not introduce independent unreviewed lemmas.

The assembly proof-tracker row remains open until the aggregate final review is valid. Fill that row from aggregated proof_review.md: numeric Score, Review outcome = Failure Type, Retry target = Suggested Next Action, and Status = Accept only for Failure Type = ACCEPTED; otherwise Status = Fail.

Phase 7: Specialized Final Reviews

After assembly, spawn or resume the four distinct specialized reviewers and invoke:

/proof-review-structural
/proof-review-rigor
/proof-review-citation
/proof-review-adversarial

Inputs:

• setting.md
• assembled latex_template/
• assembly_report.md
• accepted proof_sketch.md
• accepted proof_sketch_review.md
• valid diagnostic global_proof.md paired with accepted global_proof_review.md
• accepted global_proof_review.md
• accepted step proof/review artifacts for every required sketch step

Outputs:

• perspective_M/idea_N/proof_review_structural.md
• perspective_M/idea_N/proof_review_rigor.md
• perspective_M/idea_N/proof_review_citation.md
• perspective_M/idea_N/proof_review_adversarial.md

Each specialized review is diagnostic only. It must emit Reviewer Verdict, Blocking Issues, Nonblocking Concerns, Suggested Repair Depth, and Smallest Candidate Repair Target; it must not update trackers or route retries.

Validate each specialized review artifact before invoking /proof-review-aggregate. If one is missing or contract-invalid, rerun or hand off only that diagnostic reviewer with a real worker-log row; this consumes no proof producer budget and must not be recorded as a proof flaw.

If a contract-valid specialized review reports BLOCKING, do not repair the producer directly from that specialized review. Invoke /proof-review-aggregate first, then route the producer repair only from the aggregate proof_review.md.

Phase 8: Aggregate Final Review

Spawn or resume the perspective's distinct review-aggregator, then invoke:

/proof-review-aggregate

Inputs:

• setting.md
• assembled latex_template/
• assembly_report.md
• accepted proof_sketch.md
• accepted proof_sketch_review.md
• valid diagnostic global_proof.md paired with accepted global_proof_review.md
• accepted global_proof_review.md
• accepted step proof/review artifacts for every required sketch step
• all four specialized review artifacts

Output:

• perspective_M/idea_N/proof_review.md

Aggregate final review outputs:

• Score
• Failure Type: ACCEPTED, PROOF_ASSEMBLY_FLAW, PROOF_STEP_FLAW, PROOF_SKETCH_FLAW, or IDEA_FAIL
• Critical Issues
• Suggested Next Action
• Retry Mode

Acceptance requires:

• Score >= ACCEPT_THRESHOLD
• Failure Type = ACCEPTED
• Critical Issues = None
• latex_template/ contains the required content and support files, and the LaTeX bundle is self-contained/paper-ready
• assembly_report.md has Status = COMPLETE, Blockers = None, and an attempted claim consistent with the public LaTeX bundle and setting.md
• no unreviewed lemma, changed accepted step statement, stale dependency, or missing step coverage
• the Assumption Provenance Contract passes: unconditional final theorems must not assume unproved generated-object, event, local-validity, stability, recurrence, boundedness, membership, or invariant facts through an admissibility or similar package
• all four specialized review artifacts pass their contracts and report no acceptance-blocking issue
• required run-scoped worker provenance and per-perspective 12 + 2k distinctness gates pass

Phase 9: Refine Or Finish

Route aggregate final review outcomes. Suggested Next Action and Retry Mode must align with Failure Type; if they disagree, treat the aggregate review as contract-invalid and rerun or hand off /proof-review-aggregate.

• ACCEPTED: run branch-local finalization and accepted-result copying, then continue any remaining approved perspectives or active branches unless the user explicitly requested a first-success search.
• PROOF_ASSEMBLY_FLAW: require Suggested Next Action = /proof-assembly and Retry Mode = repair_assembly; if MAX_ASSEMBLY_ATTEMPTS_PER_SKETCH remains, rerun /proof-assembly with aggregated proof_review.md as the triggering repair artifact, then specialized reviews and aggregate review; otherwise escalate to sketch revision.
• PROOF_STEP_FLAW: require Suggested Next Action = /proof-step <Step ID> and Retry Mode = repair_step; if MAX_STEP_ATTEMPTS_PER_STEP remains for the affected Step ID, rerun /proof-step <Step ID> with aggregated proof_review.md as the triggering repair artifact, then rerun /proof-step-review <Step ID> against the repaired proof and proceed only if that same-step review returns ACCEPTED; after that, rerun affected downstream step reviews or step proofs as needed, assembly, specialized reviews, and aggregate review. If the same-step review is not ACCEPTED, route by its step-review status. If the step budget is exhausted, escalate to sketch revision.
• PROOF_SKETCH_FLAW: require Suggested Next Action = /proof-sketch and Retry Mode = revise_sketch; if MAX_SKETCH_ATTEMPTS_PER_IDEA remains, rerun /proof-sketch with an incremented sketch attempt and aggregated proof_review.md as the triggering repair artifact; otherwise route to idea revision or branch exhaustion.
• IDEA_FAIL: require Suggested Next Action = /subagent-idea-generator, Retry Mode = new_idea, and an explicit rationale explaining why PROOF_SKETCH_FLAW cannot preserve the current formalized setting and goal and identifying the required theorem-contract change: changed primitive assumptions, changed algorithm/model/procedure, changed theorem scope/mode/metric, changed exposed dependence, changed success criterion, adding a theorem-facing mechanism source not supported by the setting, or weakening the conclusion. If that rationale is missing, treat the aggregate review as contract-invalid and rerun or hand off /proof-review-aggregate. If valid, revise the idea when MAX_IDEA_VARIANTS_PER_PERSPECTIVE remains, using aggregated proof_review.md as prior failure evidence.

When retry limits are exhausted, escalate in this order: local unit retry -> sketch revision -> new idea -> branch failure.

Finalization

For an accepted branch, finalization is branch-local:

1. Verify final artifact gates.
2. Verify split worker-provenance gates.
3. Verify no perspective has more than MAX_IDEA_VARIANTS_PER_PERSPECTIVE consumed idea slots in theory_tracker.md, including NO_VIABLE_IDEA and DUPLICATE_IDEA rows, and no accepted proof-tracker row uses an over-budget producer attempt, including global proof attempts.
4. Copy only:

• setting.md
• latex_template/
• proof_review.md

1. Do not copy diagnostic or archival artifacts, including assembly_report.md, global_proof.md, global_proof_review.md, specialized review artifacts, sketch artifacts, step artifacts, or proof_history/.
2. Copy into results/perspective_M/idea_N/theory.
3. Verify the copied files exist, including the complete latex_template/ directory with main.tex, arxiv.sty, ims.bst, reference.bib, and the five content files.
4. Mark the current theory-tracker row Accept only after copy verification passes.

After all approved perspectives terminate, return the accepted-branches summary, which may contain zero, one, or multiple accepted branches. If no branch is accepted after all approved perspectives terminate, return a failure summary.

References

Load these only when needed. Paths are relative to this skill directory, not to the active run root:

• ../_shared/templates
• ../_shared/templates/worker-log.md
• ../_shared/templates/workflow-feedback.md
• ../_shared/templates/theory-tracker.md
• ../_shared/templates/idea-report.md
• ../_shared/templates/proof-tracker.md
• ../_shared/templates/global-proof-review.md
• ../_shared/templates/assembly-report.md
• ../_shared/checklists/artifact-contracts.md
• ../_shared/checklists/tracker-lifecycle.md
• ../_shared/checklists/review-outcomes.md
• ../_shared/checklists/result-copy.md
• ../_shared/references/directory-conventions.md

Detailed mathematical rubrics belong in the internal proof and review skills, not in this public controller.