dechenzhang/valg-ml-theory-agent/ml-theory-research-agent

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