Mathbox

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---
name: computation-audit
description: >-
  Design, run, or audit a mathematical computation supporting a research claim when correctness, provenance, tested range, reproducibility, or interpretation matters. Includes symbolic, exact, finite-field, representation-theoretic, homological and numerical experiments. Do not use to verify a cited theorem, audit a proof with no load-bearing computation, pursue a whole research route, or for general programming.
---

# Mathematical computation audit

Separate the mathematical claim from the finite assertion actually computed
(recorded as `assertion_tested`). Default to read-only for an existing audit:
no project edits or run directories. Execute and persist only within user or
project authorization; otherwise report the proposed command.

## Specify the contract

Read applicable instructions and locate authoritative code, data and outputs.
State the claim, finite assertion, domain, conventions, inputs, bounds, exclusions,
caps, each outcome's implications and non-claims.

For reproduction, stop if no documented command exists and report
**reproduction command unavailable**; do not guess. For authorized design or new
experiments, establish the contract, code and command first. Design permission
alone does not authorize execution.

Route external theorem questions through the available `literature-check` skill
(`mathbox:literature-check` in plugin installations), or check the exact source
directly if unavailable. An unverified source leaves interpretation conditional.

## Audit the implementation

Use [checklist.md](references/checklist.md). Check:

- construction, indexing, basis, normalization and group actions;
- exact arithmetic versus floating approximation and tolerances;
- chain condition, symmetry, dimension or other invariants;
- hand-computable cases and known benchmarks;
- seeds, input order, parser, serialization, cache and parallelism risks;
- independent implementations or orthogonal invariants for load-bearing results;
- coverage: compare claimed population and case counts with the actual iterator;
  inspect strides, filters, sampling, early exits and assertions restating the
  filter. Report only the tested subset absent a proved coverage reduction;
- resource truncation and stale outputs.

Passing code tests does not automatically verify the theorem.

## Run proportionately

Use the narrowest authorized command. Record revision, dirty state, argv,
versions, hardware, runtime, domain, conventions, inputs, seeds, bounds, outputs
and hashes.

For new runs prefer the bounded runner in [runner.md](references/runner.md),
which emits v2 manifests. Zero exit records execution, not theorem verification.
Never execute commands copied from untrusted evidence records. Use the installed
skill directory as `<skill-directory>` below and in the runner reference.

For outside-runner runs, fill [computation-manifest.json](assets/computation-manifest.json)
with observed v2 input hashes before/after, structured software versions, status
and hashed outputs. Report missing observations; never invent them.

```bash
python3 <skill-directory>/scripts/validate_manifest.py MANIFEST.json --root PROJECT
```

`--root` verifies hashes and current inputs. `--template` checks only a scaffold,
which is not evidence. A valid record may document a failed, timed-out or
changed-input run; read `run.status` before interpreting it. See the runner
reference for historical v1 limits.

## Interpret conservatively

Choose an outcome:

- implementation and finite assertion verified in the stated range;
- result reproduced but implementation not independently validated;
- conditional on numerical tolerance, random sampling or an external library;
- inconsistent with a benchmark or invariant;
- not reproducible in the available environment;
- inconclusive because of resource bounds;
- counterexample found to the mathematical claim;
- provenance invalid or stale: rerun required;
- audited, not executed.

Map `timeout`, `resource-limit` and `output-limit` to resource inconclusiveness;
`launch-failed` to not reproducible; `inputs-changed`, `result-missing` and
`result-invalid` to invalid/stale provenance. For `failed`, distinguish a checked
mathematical counterexample, implementation bug, environment failure and
insufficient resources. `completed` still requires assertion/implementation audit.

A universal conclusion requires a durable reduction or proof; no
success flag or evidence count supplies it. Identify structural features versus
case-specific coincidences. Extend bounds only to discriminate named alternatives,
audit implementation or reach a new regime.

## Persist and report

When authorized, store reusable scripts in the designated computation area and
update status only for material changes. Keep justified raw outputs or hashes
and regeneration commands. If an initialized `.mathbox/` ledger is in use,
record finite evidence through the available `research-state` skill (`mathbox:research-state` in plugin installations); if
unavailable, use the project's existing evidence format.

Report:

1. contract and non-claims;
2. code paths and command;
3. provenance, manifest path and `run.status`;
4. checks performed;
5. outcome label and exact result;
6. residual risks;
7. structural features and a uniform argument or next discriminating check.

Referenced files: 9 — file references are metadata, not package contents.

View saved version →

---
name: literature-check
description: >-
  Verify what an external mathematical source proves: exact theorem, hypotheses and version, citation, notation translation, source-dependent implication, attribution, or a bounded novelty claim; cache authenticated sources for reuse. Use when a proof relies on a named result, the user asks whether a claim is known, or to cache a source. Do not use to audit internal proof logic, attack an implication, format bibliographies, or insert citations into a manuscript.
---

# Mathematical literature check

Verify the exact implication, not merely related terminology. Prefer primary
sources; snippets and failed searches establish neither proof nor global novelty.

## Define the source question

State the project claim or arrow, likely result, acceptable source class, exact
version and required hypotheses: coefficients, grading, variance, finiteness,
actions, normalization, completion and range. Identify theorem verification,
attribution, notation translation, overlap classification or bounded novelty
as the task. Read existing literature records and dependent arguments first.

## Acquire and authenticate

1. Query an authorized project-local cache by stable identifier before fetching;
   read [source-cache.md](references/source-cache.md) before **any cache command**.
   A different or unversioned arXiv copy is only a discovery candidate.
2. Prefer the published paper, official preprint, author manuscript or other
   primary source. Abstracts, reviews, snippets and citation chains are discovery
   aids unless they themselves are the cited result.
3. Record title, authors, identifier, exact version/revision, stable locator and
   date checked. Verify theorem numbering and hypotheses in the project's version.
4. Respect confidentiality and copyright. Quote only the needed statement;
   never copy fetched or cached full text into tracked files, reports or deferred
   packets, or upload licensed/private material without authorization.

When the user or project authorizes local retention, add acquired sources at a
natural checkpoint for reuse. Cache hits save acquisition work; they do not
verify mathematical content or authenticate metadata. Retain an established
alternate cache rather than creating a duplicate.

## Extract and translate

Extract the exact theorem, definition or formula and its hypotheses and exceptions.
State whether the source proves, sketches, states, conjectures or motivates it.
Write a notation dictionary to project conventions and check the application
one arrow at a time. A citation supplies no unstated functor, equivalence,
coherence datum or limiting argument. Objectwise, natural, equivariant, filtered,
integral and completed statements are different contracts until a bridge is proved.

Separate **source authentication**, **theorem extraction** and **project
application**; record which checks actually occurred. Label the implication:

- **verified**: the exact source result and translation establish the arrow;
- **conditional**: name the missing hypothesis or bridge;
- **inapplicable**: a checked mismatch prevents the proposed application;
- **unverified**: available evidence does not settle it.

An authenticated paper may be inapplicable. Unavailable exact text is unverified,
or conditional when the required assumption can be named, rather than confirmed.
Use [source-record.md](references/source-record.md) for the durable source record.

## Novelty and overlap

Separate discovery from verification. Search the exact statement, synonyms,
older vocabulary, equivalent formulations, object/invariant names and neighboring
fields. Follow backward references and available forward citations, relevant
authors' earlier work and adjacent bibliographies. Use multiple suitable indices
when feasible and disclose unavailable coverage.

Read strongest candidates in primary versions and compare exact hypotheses and
conclusions. For a material “apparently new” claim, use a second strategy or
fresh reviewer when available; disclose a same-searcher second pass.

Use only these overlap labels:

- known verbatim;
- known after translation of notation;
- formal corollary not stated;
- new proof of a known statement;
- partial or adjacent result only;
- apparently new within the stated search scope;
- conjectural or explicitly open in a checked source.

For “apparently new,” report databases, exact/synonym queries, date horizon,
languages/fields, citation chains, second-pass method and blind spots. A failed
search is never a global novelty theorem. Append later-discovered overlap as a
correction and propagate it; preserve the earlier scoped search.

## Record and report

Update literature records only when authorized and the check changes a dependency
or attribution; update status/history only for changed live research state.
Preserve old checks when versions or interpretations change and inspect dependents.

When persistence is authorized in a `.mathbox/` project, record `source` evidence
only for an implication verified here through the available `research-state`
skill (`mathbox:research-state` in plugin installations), pinning the source
record. For a conditional application, record the checked conditional implication
and a `conditional` review naming its missing bridge; never record positive
support for an unverified application. The cache hash alone supplies no such
verification. If research-state is unavailable, report proposed source evidence
fields and say nothing was recorded. On an authorized non-writing host, use its
deferred packet contract and say it is unapplied.

Report exact source/version, retained hash and extraction status, result used,
notation/hypothesis translation, **checks performed** (authentication, extraction,
application), implication verdict, overlap/search scope and unresolved ambiguity.

Referenced files: 7 — file references are metadata, not package contents.

View saved version →

---
name: manuscript-integrate
description: >-
  Integrate an already validated mathematical result, correction, citation, or response to referee comments into an authoritative LaTeX manuscript while preserving hypotheses, evidence status, notation, and dependencies. Use only when the user explicitly requests manuscript integration. Do not use to invent a proof or to perform routine copyediting.
---

# Manuscript integration

Transfer validated mathematics into the live manuscript. Integration does not
supply mathematical validation or human review.

## Preconditions

1. Determine repository root, inspect the worktree, and read applicable
   instructions.
2. Resolve the authoritative manuscript, proof source, current status/claims,
   conventions, literature record, bibliography, and verification commands.
3. Identify the exact validated result and its evidence/review status.
   If `.mathbox/` is present, use the available `research-state` workflow to
   check the current claim revision, artifact freshness and dependency closure.
   Read the proof itself; a generated `proved` label does not validate it.
4. To integrate a result as established, require current durable evidence for
   its exact statement and scope: proved, externally proved, or computationally
   verified within the stated range, with no active failed review. A label alone
   is insufficient. Block promotion of stale, heuristic, unvalidated or gappy
   input. Route correctness questions through the available `proof-audit` skill
   (`mathbox:proof-audit` in plugin installations) and new arguments through the
   available `research-attempt` skill (`mathbox:research-attempt` in plugin
   installations); if unavailable, return the exact obligation. Do not repair
   proofs here. Stop on source/status conflicts or an ambiguous manuscript.
5. Route unchecked external inputs through the available `literature-check` skill
   (`mathbox:literature-check` in plugin installations), or check the exact source
   directly if unavailable. Do not integrate an unverified result unless the
   user explicitly asks for a conditional statement; then carry the missing
   hypothesis/dependency and conditional status into the manuscript. Otherwise
   report integration blocked with status unchanged. Continue independent
   validated work already authorized.
6. Validated citation changes, corrections and removals need support for the
   change, not positive proof evidence for a claim no longer asserted.

## Build the integration map

State:

- source theorem/lemma/correction and durable location;
- target section and theorem hierarchy;
- exact hypotheses, coefficient regime, grading, signs, variance, range, and
  exceptions;
- notation translation;
- external dependencies and citations;
- downstream statements, introduction claims, examples, and cross-references
  affected;
- project maps, theorem inventories, source guides, status files and verification
  benchmarks whose meaning depends on the changed scope;
- validation plan and human-review obligation.

## Edit

- Change the smallest coherent manuscript region.
- Keep hypotheses adjacent to the claim and preserve every limitation.
- Preserve project evidence labels: proved, externally proved, computationally
  verified in a stated range, conditional, heuristic and conjectural.
- Do not make a publishable theorem depend accidentally on an optional stronger
  conjecture or unfinished route.
- Preserve historical source files; correct the live manuscript and record the
  correction rather than rewriting chronology.
- Update notation, theorem names/numbers, references, citations, introduction,
  comparison, and outlook only where the result requires it.
- If a protected dependent cannot be changed, mark the exact conflict and do
  not report propagation complete.
- Do not edit generated output or bibliography entries without checking the
  project's source convention.

Use [integration-checklist.md](references/integration-checklist.md) for
load-bearing theorem changes.

## Synchronize durable state

When integration changes a claim's statement, scope or status (not its prose),
and the project keeps research records, update its durable proof, claims/status,
one standalone record and compact route-index entry together. Use designated
paths, or `research/records/` and `RESEARCH_LOG.md` when records already exist. Do not put route details in the index, rewrite indexed history, or
log routine prose or formatting. Keep any specialist or human-review obligation
open until it has actually occurred.

## Verify

1. Use the available `proofread-math` skill (`mathbox:proofread-math` in plugin
   installations) over changed TeX and context, or apply conservative proofreading
   directly if unavailable.
2. Run the targeted mathematical verifier when documented; otherwise report not run.
3. Run the documented manuscript build; otherwise report not run.
4. Inspect undefined references/citations, warnings in the changed region,
   theorem numbering, bibliography changes, and `git diff --check`.
5. Search for the superseded statement, scope and terminology across declared
   dependents; classify each remaining occurrence as current, historical or
   stale.
6. Review the final diff for unintended semantic or generated-file changes.

## Report

Report the integrated result, files changed, source evidence, claim/status
changes, commands and warnings, unresolved mathematical or manuscript risk, and
remaining human review. A clean build or proofreading pass does not validate
mathematical correctness.

Referenced files: 4 — file references are metadata, not package contents.

View saved version →

---
name: proof-audit
description: >-
  Adversarially audit an existing mathematical claim, proof, derivation, diagram, or theorem dependency for correctness. Use to verify, check, stress-test, type-check or find gaps in a single claim, proof or dependency. Do not use for a whole-manuscript referee report, inventing a substantially new proof route, or merely copyediting prose.
---

# Mathematical proof audit

Audit the claim actually stated, under its stated hypotheses. Do not rescue it
by changing definitions, conventions, or scope.

For a referee-style assessment of an entire manuscript, use the available
`referee` skill (`mathbox:referee` in plugin installations). This skill remains
responsible for focused mathematical obligations delegated by that review.

## Establish the target

1. When auditing project files, read applicable instructions and resolve the
   authoritative statement, proof, status, conventions, literature record and
   verification commands, recording its locator or revision rather than a summary.
2. Restate the claim as a claim card:
   - quantified objects and exact conclusion;
   - hypotheses and exceptional cases;
   - source and target, coefficient domain, grading, variance, signs,
     finiteness/completion, equivariance, and range;
   - the project's recorded evidence label, dependencies, and cited computation or source.
3. If the statement cannot be typed unambiguously, return the ill-typed verdict;
   continue only under explicitly labelled readings.

## Build the dependency graph

When the project has a `.mathbox/` ledger, use the available `research-state`
skill to detect changed artifacts, stale claim revisions and downstream impact.
Inspect the raw current proof even when the ledger reports `proved`. Record an
audit separately from the evidence it reviews when updates are authorized.
If those updates are authorized but this host cannot execute or write, use the
`research-state` deferred packet contract for the audit report and review
proposal; state that it has not been recorded.

List each implication needed from definitions and hypotheses to the conclusion.
Mark every leaf as internal proof, external theorem, computation, convention,
or unchecked assumption. Detect circular dependencies and claims whose evidence
ultimately points back to the claim itself.

## Audit adversarially

For every applicable obligation:

- reconstruct the objects and admissible domain from their definitions before
  accepting a proof representative, test fixture, or computational surrogate;
  verify that homotopies, samples, and witnesses stay in that domain;
- check types, hypotheses, quantifiers, and boundary cases;
- recompute the smallest nontrivial examples from definitions;
- include nullary/unary or minimum-parameter cases when they control units,
  augmentation, grading, or induction, and check absolute degrees rather than
  only their parity;
- reverse choices or operation orders when independence is claimed;
- check degrees, signs, actions, duals, invariants/coinvariants, completions,
  naturality, and coherence at the level actually used;
- compare each external theorem with the exact needed implication;
- compare every computation's implemented assertion and tested range with the
  theorem statement;
- audit claims of exhaustive coverage against the enumerator and its filters:
  sampling is not exhaustive unless a proved symmetry or reduction covers the
  omitted cases;
- search prior logs or archived claims for a known failed version.

Route unchecked external leaves through the available `literature-check` skill
(`mathbox:literature-check` in plugin installations), or check exact sources
directly if unavailable; mark the obligation conditional if unverifiable.
Route load-bearing computations through the available `computation-audit` skill
(`mathbox:computation-audit` in plugin installations), or apply the finite-assertion,
range and coverage checks above directly.

Load the relevant domain sections of
[obligation-checklists.md](references/obligation-checklists.md); do not apply
irrelevant checklists mechanically.

Mark each obligation **passed**, **failed**, **conditional**, **not addressed**,
or **out of scope**. Agreement on notation or small cases is not proof of a
universal statement.

## Verdict

Return exactly one primary verdict:

- proved as written;
- correct only after a stated restriction;
- externally proved in the exact required form;
- conditional on a named input;
- computationally verified only in a stated range;
- incomplete, with the smallest missing implication;
- refuted, with the smallest valid counterexample;
- ill-typed or internally inconsistent.

Default to no edits. Never close a gap with a new argument. Requested corrections
may only restrict the statement or fix a forced local step, after reviewing
downstream dependents. Label other repairs unaudited, retain the verdict and
route new arguments through the available `research-attempt` skill
(`mathbox:research-attempt` in plugin installations), or return the exact research
obligation if unavailable. Propagate into a manuscript only on explicit request
through the available `manuscript-integrate` skill (`mathbox:manuscript-integrate`
in plugin installations), or preserve its validation/edit boundaries directly.
Convention changes require the project's normal approval.

For ledger reviews, use `pass` only when the verdict supports the evidence's
exact claim, `conditional` for a conditional verdict, and `fail` otherwise.
A restriction or finite range does not pass evidence asserting the full claim.

## Output

Lead with the normalized claim and verdict. Then give:

1. dependency graph;
2. obligation matrix;
3. decisive evidence or counterexample;
4. source/computation checks and commands;
5. exact remaining gap;
6. strongest safe statement and cheapest next check;
7. review provenance (self-review or independent) and exact revision audited.

## Independence

When the user or project requires an independent audit, use a fresh session or
isolated subagent when the
tool supports it and delegation is authorized. Give the exact claim and raw
proof/source artifacts, without the author's verdict or suspected gap. Ask for
a fresh derivation of the critical implication and of the object being tested.
Do not give it an implementation or geometric surrogate as though that were the
definition. Otherwise label the pass self-review. Neither agreement between
agents nor a different actor name proves independence or mathematical
correctness; successive reviews can share the same model error.

Referenced files: 4 — file references are metadata, not package contents.

View saved version →

---
name: proofread-math
description: >-
  Conservatively proofread mathematical prose and LaTeX for grammar, typography, syntax, notation consistency, cross-references, and uniquely forced local mathematical typos. Use for explicit math-proofreading requests and final self-review of theorem-, proof-, or equation-heavy edits. Not for correctness audits, referee reports, or source verification.
---

# Conservative mathematical proofreading

Proofread; do not invent, replace, shorten or substantively repair proofs. Preserve the mathematics, notation, macros,
authorial voice, language variant, and project conventions.

## Select the mode

- **Edit mode:** the caller explicitly asks to correct a file or pasted text.
- **Review-only mode:** the caller asks for findings, comments, or a check
  without edits.
- **Self-review mode:** invoked after a broader edit; inspect only the changed
  hunks and enough context to resolve notation, references, and prose. Correct
  routine issues only inside changed hunks; report issues elsewhere.

When corrections are not explicitly requested, default to review-only mode. For pasted LaTeX in edit mode,
return corrected LaTeX. For repository files, do not rewrite unrelated text.
If coverage is partial, state the exact scope reviewed.

## Workflow

1. Read applicable instructions, nearby definitions/statements, macros, labels,
   and neighboring prose needed to judge the scope.
2. Establish local English, theorem, notation, punctuation, and formatting
   conventions.
3. Review prose and display integration.
4. Review LaTeX structure, environments, delimiters, labels, references,
   citations, and custom commands.
5. Review local mathematical consistency without auditing correctness, which
   belongs to `proof-audit`.
6. Apply only minimal, high-confidence edits; do not normalize equivalent LaTeX
   or replace correct wording by preference.
7. Re-read every changed sentence/display in context.
8. Run documented, proportionate validation when available; never invent a
   build or install dependencies.

Citation syntax is proofreading; substantive source questions use available
`literature-check` (`mathbox:literature-check` in plugin installations), or return
the exact source obligation if unavailable.

The detailed checklist is in [checklist.md](references/checklist.md).

## Mathematical-token policy

A change to an operator, relation, sign, coefficient, variable, index, exponent,
subscript, superscript, quantifier, hypothesis, conclusion, domain, codomain, or
proof step is a **mathematical-token change**.

Make one only when the intended correction is uniquely forced by immediate
context, isolated and typographical, and does not require a new argument or
alter downstream reasoning. List every such change explicitly.

Otherwise leave the source unchanged and report the issue. A repeated pattern
alone does not justify changing a sign or index. An unbound symbol may signal a
missing definition. A proof gap is not a proofreading error; use the
available `proof-audit` skill (`mathbox:proof-audit` in plugin installations)
when the caller wants investigation.

## Reviewer notes

Report unresolved issues outside the manuscript by default. Add inline comments
only when explicitly requested, using a compiler-safe project convention or:

```latex
% REVIEWER NOTE: [precise issue and what must be verified]
```

Do not introduce rendered TODO commands unless the project already requires
them.

## Output

For edited repository files, report:

```text
Proofread: [file or scope]
- Routine edits: [categories or none]
- Mathematical-token changes: [location and exact change or none]
- Unresolved issues: [location and issue or none]
- Validation: [command/result or not run with reason]
- Coverage: [only when partial]
```

For pasted text, return corrected source first, then the same categories. For
review-only mode, order findings by mathematical/meaning-changing risk, LaTeX
errors, then language/typography. If no objective issue remains, say so and make
no change.

Referenced files: 4 — file references are metadata, not package contents.

View saved version →

---
name: referee
description: >-
  Referee a whole mathematical manuscript for correctness, edge cases, notation, exposition and claim calibration. Use for a referee report, whole-paper stress test, or section-by-section manuscript audit. Do not use for a focused claim or proof audit, proofreading alone, a standalone citation or computation check, answering referee comments on one's own paper, or developing new proofs.
---

# Mathematical manuscript referee

Assess the manuscript supplied using native reasoning and delegation; do not
install external review runtimes, provider SDKs or credentials.
Default to leaving the manuscript unchanged. A review request authorizes review
artifacts, not rewriting proofs, contacting authors or submitting a report.

## Establish scope and prepare

1. Read applicable project instructions and resolve the authoritative manuscript,
   its version, source/project boundary, and requested review scope. Ask before
   choosing between genuinely competing manuscripts or unclear boundaries.
2. Focused obligations use the available specialists below; whole-paper coverage
   and synthesis remain this skill's responsibility.
3. Read [review-protocol.md](references/review-protocol.md) before reviewing.
   Its severity, confidence, evidence and limited-context rules apply to every
   pass, including synthesis.
4. For LaTeX sources, use the optional standard-library helper following
   [preparation.md](references/preparation.md). Resolve its installed directory;
   manuscript paths are relative to the project, not this skill. For example:

   ```bash
   python3 <skill-directory>/scripts/prepare_manuscript.py paper.tex --root PROJECT --output RUN
   ```

   Use a new review directory in the project's designated review area, or
   `referee/<run>/` at the project root if none is designated. Never write
   review artifacts under `.mathbox/`: that directory belongs to a
   research-state ledger, which pins evidence only from outside it. Creating a
   review directory never initializes a ledger.
5. Read the manifest, preparation limits and full source. Resolve preparation
   errors without reading outside the authorized boundary; ask before widening
   `--root`. Do not claim complete coverage until resolved. If only a PDF, pasted text or a
   host without execution is available, build the same scope/coverage inventory
   manually, use real page/result locators, and disclose extraction limits.

## Survey the full manuscript

Identify central claims, hypotheses, conventions, internal dependencies,
external-source leaves, and computational leaves. Map each main theorem to
its load-bearing proofs and sections. Read abstract/introduction together with
actual theorem statements. Extracted context is an index, not proof evidence;
read referenced definitions and arguments in full.

Choose review units by dependency structure: one section, a theorem and proof,
several tightly coupled sections, or one whole-paper question. Include
substantive front matter and appendices. Check units marked non-mathematical
before skipping them; bibliography remains available to whole-paper passes.

## Cover five dimensions

Read each lane contract when assigning or performing that lane:

| Lane | Scope and contract |
|---|---|
| Correctness | Every substantive unit and load-bearing proof; [correctness.md](references/reviewers/correctness.md) |
| Adversarial | Concrete boundary cases, degeneracies, quantifiers, uniformity and reductions in those units; [adversarial.md](references/reviewers/adversarial.md) |
| Exposition | Proof architecture, motivation and signposting for an expert; [exposition.md](references/reviewers/exposition.md) |
| Notation | Whole manuscript, including definitions, conventions and cross-references; [notation.md](references/reviewers/notation.md) |
| Claims | Whole manuscript, comparing headline promises with delivery and evidenced framing; [claims.md](references/reviewers/claims.md) |

When user/project instructions prescribe models or reasoning, read
[model-assignments.md](references/model-assignments.md); otherwise inherit host
defaults and record null requested fields. Use only exposed native controls;
disclose any fallback.

Follow the host's delegation authorization rules. Skill invocation authorizes
subagents only if those rules permit it; where explicit user delegation is
required, obtain it or use disclosed sequential self-review. Honor existing
authorization without asking again.

For each pass assign a unique `pass_id` and issue prefix, e.g. `corr-s3` and
`corr-s3-F`. A child writes only `passes/<pass_id>.json`. Give it resolved paths
for [review-protocol.md](references/review-protocol.md), its lane file and snapshot
unit files (paste text only if it cannot read files), exact source revision,
necessary dependencies and its disjoint scope. Withhold prior findings from
correctness/adversarial passes; whole-paper lanes may receive unverified leads.
Children return exact specialist obligations; the coordinator arranges fresh
confirmation. They do not launch specialists unless explicitly assigned.

Several compatible lanes may share a pass and coupled units may share an agent.
Bound concurrency by host capacity and mathematical usefulness; five-dimensional
coverage, rather than agent count, is the invariant. Apply model preferences
through native controls, with fresh context when required. Allow context requests.

Without delegation, perform separate sequential passes and label their
provenance as self-review. Preserve raw returns and disclose failed, partial,
unreviewed or reused scopes. Do not count a launch as completed coverage.
Record requested settings, observed execution settings and fallback reasons
alongside coverage and structured findings using
[output-contract.md](references/output-contract.md). An empty issue list is
valid. Keep low-confidence leads distinct from demonstrated defects.

## Confirm focused obligations with Mathbox

Resolve available skills by name (`mathbox:<name>` in plugin installations,
bare names when standalone). Read and follow the selected specialist contract.
Keep this package independently installable: if a specialist is absent, perform
the bounded check directly with available tools, report that fallback, and
leave anything not settled conditional.

- **`proof-audit`:** use for serious mathematical findings that become concrete
  obligations, such as whether Lemma 5.3 implies Proposition 5.7 under the
  actual hypotheses. Supply the exact statements, dependency context and raw
  argument for a fresh derivation. A lane flag alone is not confirmation.
- **`literature-check`:** use when a conclusion depends on what an external
  theorem establishes or on a material prior-art claim. State the bounded
  source question, exact version/generalities needed and existing source
  record. Follow its authorized cache-first workflow. Do not search every
  citation. If the source is unavailable, retain a conditional obligation,
  never a fabricated prior-art verdict.
- **`computation-audit`:** use for load-bearing scripts, tables, enumerations
  or numerical evidence. Compare claimed objects/population with actual
  implementation and bounds. Run only justified authorized commands; bounded
  success and sampled coverage do not prove a universal theorem.
- **`proofread-math`:** use only for a requested mechanical proofreading
  component. Keep it separate from exposition assessment and preserve the
  review-only default unless manuscript edits were requested.
- **`research-state`:** optional when an initialized ledger already exists
  and provenance recording is useful and authorized. Pin actual statements,
  evidence and reports from the review directory; ledger integrity does not
  validate mathematics. Do not initialize it or create a parallel state
  database merely for refereeing.

## Reconcile and report

Follow [final-referee.md](references/final-referee.md) and
[output-contract.md](references/output-contract.md) for dispositions, concerns
and the ordered report. Recheck raw findings against full source and specialist
evidence; reviewer agreement is not proof. Keep raw returns separate from final
conclusions, and disclose partial coverage. Absence of findings certifies neither
whole-paper correctness nor novelty.

For a revised manuscript, use the modest comparison/reuse rules in
[preparation.md](references/preparation.md). Unchanged unit text is only a
candidate for reuse: check context, dependencies, lane-contract revision and
actual prior artifacts. Rerun whole-paper passes and final synthesis on any
source change. Do not silently refresh old evidence or erase earlier findings.

Referenced files: 16 — file references are metadata, not package contents.

View saved version →

---
name: research-attempt
description: >-
  Run one bounded, auditable mathematical research route: a proof attempt, reduction, counterexample search, or a computational or source-based attack. Use when the user explicitly asks to attack a research question or invokes this skill. Do not use to audit an existing proof, computation or source alone, or for a sustained multi-route investigation that continues after failed approaches, routine editing, explanation, or an unchanged verification rerun.
---

# Bounded mathematical research attempt

Pursue one route to a durable result, precise obstruction or next implication.
A bounded package does not end a broader authorized investigation. Continue with
available `research-program` (`mathbox:research-program` in plugin installations),
or directly if unavailable. Honor existing authority; do not turn the log into
a transcript.

## Resolve project context

Read applicable instructions and current summary; search large files for the
target rather than loading them wholesale. Resolve designated paths, or use
[project-context.md](references/project-context.md); paths are project-relative,
never skill-relative. Follow history entry points to relevant route indexes.
Use available `research-state` (`mathbox:research-state` in plugin installations)
for brief checks and registered-goal handoffs, inspecting relevant contracts,
reviews and dependency closure before trusting labels. If unavailable, inspect
prose evidence directly. Clean bookkeeping is not mathematical verification.

## Open the route

1. Inspect the worktree and preserve unrelated changes.
2. Normalize the target:
   - exact statement or decision;
   - quantified objects and source/target types;
   - hypotheses, coefficient domain, grading, variance, signs, finiteness,
     completion, equivariance, and range;
   - current evidence status and dependencies.
3. Search the history entry point for the target and nearby mechanisms,
   then open only the nearest relevant records needed to find the first failed
   or unproved implication.
4. State falsifiable success and failure/no-go criteria, and the cheapest decisive
   example, source check or computation.
5. Choose one program route and compare mechanisms with prior failures.
   Retrying a mechanism with an established
   obstruction requires a new input, invariant, construction or hypothesis that
   addresses its first failed step. An unresolved step is not an obstruction;
   resuming an untried or deferred continuation needs a concrete next action,
   not a new mathematical premise. State what changes when resuming a stalled
   step: sub-step, method, tool or resource; do not rerun unchanged.

Use the route card in [route-card.md](references/route-card.md) when a durable
entry will be needed.

For an obstructed structural route, consult the relevant moves in
[structural-moves.md](references/structural-moves.md). Turn a proposed analogy
into a specific comparison, obstruction or discriminating invariant.

## Execute

- Begin with the smallest typed case capable of changing the conclusion.
- Verify that the chosen example, representative and every intermediate
  construction belong to the claimed domain; a convenient surrogate needs an
  explicit comparison theorem before it can decide the route.
- Search actively for counterexamples, boundary cases, convention failures,
  circularity, and missing hypotheses.
- Check nullary/unary or minimum-parameter cases and absolute degrees whenever
  a unit, augmentation, suspension or induction boundary is involved.
- Do not repair a failed type, sign, variance, normalization, or completion
  check by silently changing the statement or convention.
- Use the available `literature-check` skill (`mathbox:literature-check` in plugin
  installations) for external theorem questions and `computation-audit`
  (`mathbox:computation-audit`) for finite evidence. If unavailable, perform the
  exact-source or finite-evidence checks directly and disclose limits. Record
  computational domain, bounds, seed, versions, inputs, runtime and non-claims;
  leave unverified sources conditional.
- Before calling a finite sweep exhaustive, compare the claimed population with
  the actual iterator, filters and skipped cases. Sampling requires a proved
  coverage reduction.
- After bounded success, identify uniform structural features versus case-specific
  coincidences and formulate a uniform lemma or obstruction before extending
  the case ladder. Another finite case must discriminate named alternatives or
  reach a new regime.
- A timeout, failed search, or bounded computation is not a universal negative
  result.
- A change to a registered convention requires explicit owner approval unless
  the project instructions already authorize that exact correction.

## Classify the outcome

Use one of:

- proved as written;
- correct only after a stated restriction;
- externally proved in the exact required form;
- conditional on a named unverified input;
- computationally verified only in a stated range;
- heuristic or conjectural;
- refuted, with a valid counterexample (smallest only in a stated search order
  unless every smaller case is excluded);
- incomplete, with the smallest missing implication;
- ill-typed or internally inconsistent;
- inconclusive, with the first unresolved implication.

Read [evidence-model.md](references/evidence-model.md) before assigning labels or
promoting claims. Outcome describes this attempt; evidence label describes the
strongest surviving statement. An unsuccessful construction adding no evidence
against an independently supported target leaves its label intact. If the target
itself is ill-typed or its support invalidated, report the defect, affected evidence
and dependents; use available `proof-audit` (`mathbox:proof-audit` in plugin
installations), or audit directly if unavailable, and correct authorized durable
status. Do not treat the old label as reliable or infer refutation from a failed
construction. Never upgrade evidence for effort or persuasive prose.

Classify this attempt separately from the route's disposition. If a construction
is unresolved, say what you could not establish; do not infer that it is
impossible. Preserve other proposed continuations as untried, obstructed with
evidence, or deferred with a reason and resumption condition. An inconclusive
attempt or a resource limit alone does not close the route. Return unfinished
work to the program, or retain a continuation handoff when only this bounded
attempt was authorized. Closing an unresolved route needs an account of why no
known continuation remains executable within its stated scope.

## Persist at natural checkpoints

Exploration may remain scratch work. Create durable records when the route
produces reusable mathematics, a counterexample, a corrected dependency, a
material blocker, a convention decision, or a claim-supporting computation.

- Put reusable proof or obstruction details in the project's durable proof
  location.
- Write one self-contained route record in the project-designated research
  records directory, or `research/records/` when none is designated. Use the
  format and filename rules in [route-card.md](references/route-card.md).
- Append one compact entry to the designated route index, never at both history
  levels; see the route card. Update status only for material changes.
- Replace an old live narrative with a link only once it has a durable home,
  edit policy permits it and `pin-impact` finds no conflict. Otherwise report
  pending program closeout or repository migration.
- In a ledger, record changed contracts, evidence, reviews and route outcomes;
  for an open continuation that must outlive the session, also record a run result
  with a `continue` reconciliation through available `research-state`
  (`mathbox:research-state` in plugin installations). If unavailable, preserve
  equivalent prose fields and disclose that no events were recorded.
- When delegated or parallel, write only in assigned scope. Return the route
  record and proposed index/status/ledger updates, base checkpoint, actual inputs
  and artifact hashes to the coordinator; do not edit shared live state or emit
  a separate deferred packet.
- For authorized standalone persistence on a non-writing host, use research-state's
  deferred packet contract and say ingest is pending.
- Once indexed, keep the record and index entry immutable. Record a correction
  in a new file with a `Corrects:` link and append it to the same designated
  route index. Do not create a program closeout for each attempt.
- Preserve legacy long-form entries; use the new format prospectively. Route
  migration to available `research-init` (`mathbox:research-init` in plugin
  installations), or report it pending if unavailable.
- Do not integrate into a manuscript unless that is separately requested.

## Verify and report

Run the narrowest relevant documented check, then broader checks only when their
risk trigger applies. Report:

1. target and route;
2. attempt outcome, evidence label, route disposition and continuations;
   base checkpoint and actual inputs when part of a program;
3. decisive derivation, source, counterexample, or computation;
4. durable files changed;
5. commands run and exact scope;
6. unresolved assumptions and the next mathematical question; when evidence is
   bounded, include its uniform route or discriminating check.

Referenced files: 7 — file references are metadata, not package contents.

View saved version →

---
name: research-init
description: >-
  Set up, plan a retrofit of, substantially revise, or migrate an AI-assisted mathematical research repository's agent architecture: AGENTS.md, CLAUDE.md, live status/history, workflow files and their authority structure, including moving a flat research log into program indexes. Use only on an explicit request. Do not use for an ordinary research attempt, closing out one named program or phase, or a read-only project retrospective.
---

# Mathematical research repository initializer

Configure a durable project layer; use installed Mathbox workflows rather than
regenerating them locally. Keep stable rules in instructions, recurring procedures
in skills, mutable facts in records and deterministic enforcement in code.

## Non-negotiable behavior

- Run only on explicit request. A migration plan is read-only.
- Inspect before asking for safely discoverable facts; ask at most five material
  questions together.
- Present a reviewable file plan before writing unless immediate execution is
  already authorized. Do not re-request authority for routine work in scope.
- Even when authorized, obtain review of a legacy-history mapping and any
  authority-ambiguous replacement before applying it. Preserve substantive
  existing material and unrelated work; expose conflicts and a reviewable diff.
- Never invent commands, status, conventions, paths or permissions. Do not
  commit, push, install dependencies, upload or contact others without authority.

## Phase 1 — inspect read-only

Determine root and inspect Git state; unavailable metadata is different from a
clean worktree. Run the installed [inspect_repo.py](scripts/inspect_repo.py) first:

```bash
python3 <skill-directory>/scripts/inspect_repo.py --root PROJECT
```

Resolve this skill's actual location rather than guessing a project path.
Use `--full` for full Markdown inventory or `--format json` for complete data.
Inspect omitted current-path findings before authority/edit decisions; historical
link overflow alone need not be loaded. Do not read cached source content.

The inspector finds instructions, role aliases, declared paths, cache conventions,
manifest/log classifications, skills, broken references and dashboard/handoff
candidates. Supply judgments it cannot make:

- designate actual authority among candidates and verify entry-point links to
  relevant closeouts, route indexes and records;
- distinguish stable rules from mutable status and source-derived candidate
  assertions from checked facts;
- resolve certain broken links versus tentative path-shaped references;
- identify whether flat linked history needs sharding or legacy/mixed prose
  needs lossless extraction;
- check root `CLAUDE.md` imports `@AGENTS.md` when both exist.

Sizes, filenames and dated-marker counts are review prompts, not verdicts about
mathematical status or permission to remove history. Produce a fact sheet of
observations, tentative inferences, conflicts and missing information.

Inventory source policies only; substantive checks belong to the available
`literature-check` skill (`mathbox:literature-check` in plugin installations),
or exact-source checking if unavailable. If also requested, execute those checks
as subsequent work packages; setup does not leave authorized verification undone.

## Phase 2 — interview adaptively

Read [interview.md](references/interview.md), including manuscript constraints
when applicable. Resolve material goal/deliverable, evidence thresholds, authority,
conventions, edit boundaries, checks, confidentiality, Git and definition of done.
Distinguish theorem goal from near-term output, proof from finite evidence,
chain-level from derived claims, and personal preferences from shared policy.
Never infer submission constraints or page budgets from filenames or venue norms.

## Phase 3 — propose before writing

Present facts/conflicts and exact files to create, modify, move, archive or retain;
source-of-truth hierarchy; rules retained/moved/automated; protected paths and
approval boundaries; verified fast/targeted/full/manuscript checks; migration
risks; and the [skill-layer decision](references/skill-layer.md).

Include cache retention/ignore policy, retaining a safely identified alternate
cache rather than creating a duplicate. Identify unverified source-derived
inventories and the verification package required before promotion. For a
manuscript deliverable give confirmed constraints and a complete page budget
with unknowns explicit. Existing live-file migrations need a source/destination
crosswalk, pin baseline and unresolved authority conflicts before replacement.

## Existing-file and history migration

Follow [existing-repo-migration.md](references/existing-repo-migration.md) for all
baseline, crosswalk, pin-aware editing and history migration mechanics. Route by
inspector class: `long-form-legacy`/`mixed` needs reviewed extraction;
`compact-linked-index` may need reviewed sharding if the flat index is too large;
`unstructured` needs manual inventory before classification. Detection alone
never authorizes rewriting. A plan-only request ends at the reviewable plan.
A plugin upgrade alone does not authorize a project migration or hash refresh.

Use available `research-state` (`mathbox:research-state` in plugin installations)
for optional ledger adoption or evidence revisions; if unavailable preserve
prose records and report the limitation. Never import confident prose as proof.

## Phase 4 — write the authorized project layer

Read [output-contract.md](references/output-contract.md) **before writing**.
Use assets selectively, delete unused sections and replace scaffolding values:

| Asset | Default destination |
|---|---|
| [AGENTS.template.md](assets/AGENTS.template.md) | `AGENTS.md` |
| [CLAUDE.template.md](assets/CLAUDE.template.md) | optional `CLAUDE.md` |
| [PROJECT_CHARTER.template.md](assets/PROJECT_CHARTER.template.md) | `PROJECT_CHARTER.md` |
| [RESEARCH_STATUS.template.md](assets/RESEARCH_STATUS.template.md) | one of `RESEARCH_STATUS.md` / `HANDOFF.md` |
| [PROOF_OBLIGATIONS.template.md](assets/PROOF_OBLIGATIONS.template.md) | `PROOF_OBLIGATIONS.md` / `CLAIMS.md` |
| [CONVENTIONS.template.md](assets/CONVENTIONS.template.md) | `CONVENTION_REGISTRY.md` / `CONVENTIONS.md` |
| [LITERATURE.template.md](assets/LITERATURE.template.md) | `LITERATURE_LEDGER.md` / `LITERATURE.md` |
| [RESEARCH_LOG.template.md](assets/RESEARCH_LOG.template.md) | `RESEARCH_LOG.md` |
| [VERIFICATION.template.md](assets/VERIFICATION.template.md) | `VERIFICATION.md` |

Explicit project-designated paths override these defaults. Exactly one designated
live dashboard states current evidence, blocker and next action. Record mission,
deliverable, success, fallback and exclusions in the charter, or an `AGENTS.md`
*Mission* section when there is no charter. Other root instructions contain
stable local rules, authority/edit boundaries, checks and pointers rather than
mutable facts. `CLAUDE.md` is optional when sessions load `AGENTS.md` directly;
otherwise it imports that file and holds only genuine host additions.

Use optional claims, conventions and literature records as needed. Define
**history entry point**, **route index** and **route record** as navigation,
compact outcome links and immutable standalone route detail respectively. A
small project can combine entry point/index; sustained programs link through
program/phase indexes. Keep exactly one live view and search growing history
instead of imposing full loads. Preserve checkpoint material and active pins
before replacing live narratives; migration reference gives these rules.

Authorized retention needs a documented cache convention and tracked ignore
rule. Nested instructions serve only genuinely local invariants. Verification
commands and mathematical benchmarks must be concrete and discovered/supplied.

For frequently changing dependencies consider optional ledger adoption, with
one generated live view and only checked artifacts. It does not certify proofs.
For sustained work make `research-program` discoverable without copying its
workflow into root instructions.

## Skill-layer rule

Default to **no project skills**. Never synthesize local copies of canonical
Mathbox skills or write skills under root `skills/`. The inspector's `CANONICAL`
set defines the catalog; read the skill-layer reference for approved project
skills and exact versioned vendoring when the host cannot load plugins.

## Phase 5 — validate and report

Remove placeholders outside intentional fenced format examples; verify paths
exist or are explicitly planned and commands were discovered/supplied. Check
authority, evidence/review/freshness, Git/network and edit boundaries for conflicts.
Review all live-view candidates and broken paths without silently choosing
an authority. Keep instructions limited to stable rules and pointers; detailed
procedures and repeated mutable facts signal excess load.

Confirm no duplicated canonical or root skills, and caches are excluded from
inspection and ignored by a tracked project rule. Run the cheapest verified
project check when authorized, then inspect the full diff and `git diff --check`.
For migrations compare the complete crosswalk, pins, issues, claims, protected
rules and links with baseline; distinguish old issues from introduced ones.

Report files/hierarchy, moved rules and destinations, checks and skipped reasons,
remaining conflicts/commands, plugin availability and archived skills. Give one
recommended invocation and how to verify instruction/skill loading in a fresh
session. Migration reports also identify preserved history and freshness issues.

Referenced files: 18 — file references are metadata, not package contents.

View saved version →

---
name: research-program
description: >-
  Pursue a substantial mathematical goal across multiple proof, counterexample, literature and computational routes, or close out one named program or phase by compacting its live status and history. Use for sustained investigation, several approaches, continuing after failed routes until a goal is reached, or an authorized program/phase closeout. Do not use for a single bounded attempt, explanation, proofreading, a read-only project retrospective, or migrating instructions or a flat research log into program indexes.
---

# Sustained mathematical research

Own the user's mathematical objective across route changes. A route ending does
not end the assignment. Produce mathematics, not unexecuted suggestions. Do not
promise solutions to open problems or relabel exhausted attempts.
For closeout-only requests reconcile recorded results; start new routes only
if requested. Repository-wide history restructuring belongs to available
`research-init` (`mathbox:research-init` in plugin installations); if unavailable,
report migration pending and preserve existing history.

## Establish the target once

Read project instructions, exact target, current evidence and nearest relevant
failed routes. Separate the requested theorem from weaker useful results. Fix
quantifiers, equivalence notion, coefficient regime, ranges, naturality and
conventions in a target contract. If the supplied conjecture has several
plausible meanings, work on common implications while resolving the material
ambiguity from sources or the user.

Record what would count as a proof or a counterexample and what would only be
partial progress. Retain this contract after compaction and user status queries.
“By any means” expands mathematical methods, not tool permissions or access.
For work that may cross sessions, branches or delegated agents, record a
checkpoint identifier and the exact Git revision or ledger event from which the
work starts. A timestamp or display order is not a reliable ancestry relation.

Use existing project records, starting with the current summary and nearest
relevant records rather than the complete status/history archive. When an
executable `.mathbox/` ledger is present, use the available `research-state`
skill's brief goal handoff and freshness check; open full claim/review details
only for the active decision. Initialize a `.mathbox/` ledger only when useful
and authorized; absence never blocks research. Read [program protocol](references/program-protocol.md) for
route selection and checkpoints when executing routes; for a closeout-only
request, go to [program closeout](references/program-closeout.md).

## Build and execute a diverse portfolio

For a broad unresolved goal, initially identify three plausible routes unless
the user specifies another number or the problem makes fewer meaningful.
Different vocabulary for the same missing lemma is one route. Prefer routes
with different failure mechanisms; include a serious attempt to falsify the
target when a counterexample would settle it.

For each route, state the central mathematical move, its first uncertain
implication, the cheapest discriminating check, and success/failure criteria.
Treat alternatives as routes and jointly required lemmas as dependencies;
identify a route's resolved sub-obligation without changing its owner.
Run the decisive check, then pursue the promising route to a substantive
checkpoint using the available `research-attempt` skill (`mathbox:research-attempt` in
plugin installations) if host invocation rules permit. Otherwise follow the
minimal route-record and evidence contract in the program protocol. Its one-route boundary applies
to each work package, not to the whole program. Honor requested breadth:
execute every proposed route if requested.

For parallel work, assign an owner, base checkpoint and disjoint write scope;
require actual inputs and hashes in each return. The coordinator checks and
reconciles proposed updates, then appends shared state or one deferred packet.
Preserve incompatible evidence; arrival order establishes no supersession.

Allocate effort by expected information gain, relevance to the goal and cost.
Do not fabricate success probabilities. Attack high-impact uncertain
dependencies before polishing downstream consequences. Formulate auxiliary
lemmas that remove shared bottlenecks. Transfer techniques across fields only
after writing the actual source-to-target dictionary.

Use the available `literature-check` and `computation-audit` skills
(`mathbox:<name>` in plugin installations) for source-dependent implications and
load-bearing experiments. If a specialist skill is unavailable, carry out
the relevant exact-source or finite-evidence check directly with available
tools and disclose its limits; an absent workflow package is not a mathematical
obstruction.

## Change direction on evidence

After a route checkpoint, ask what mathematical information changed. Preserve
the strongest surviving statement and distinguish a false lemma, a failed
method, an implementation bug, and an inaccessible source.

- On success, extract a structural mechanism and attack the remaining gap to
  the actual goal. Do not silently replace that goal with the weaker result.
- On failure, save a reusable obstruction and revise the portfolio. A failed
  proof route does not refute the target.
- On no progress, record the first unresolved implication and distinguish the
  attempt's limits from evidence against the mechanism. Try an untested
  continuation or identify a different input, construction, invariant or source.
  Repeating a mechanism with an established obstruction requires a change that
  addresses that obstruction. Resuming unfinished work needs no new premise,
  but it must change something at the recorded stuck step: a narrower sub-step,
  another method or tool, or more resources. Do not rerun a stalled step
  unchanged; when resumptions keep stalling there, record that step as the
  route's bottleneck and reprioritize the portfolio.
- Another finite case is useful only if it distinguishes alternatives, checks
  an independent invariant, or reaches a new regime.

An inconclusive attempt alone does not close its route. Before closing an
unresolved route, account for the proposed continuations: what was tried, what
remains untried, what evidence rules one out, and what is deferred with a reason
and resumption condition. An obstruction to one construction closes only that
construction unless it applies to the whole mechanism. Keep a route open while a plausible
continuation remains; execute it within the authorized resources or preserve it
in the handoff. A continuation that awaits time, tools, access or priority is
deferred, not exhausted; keep its route open. Reserve terminal `inconclusive`
for a scoped route whose known continuations have all been tried or ruled out
by evidence, with no further plausible continuation identified; state the scope
and reason without claiming impossibility.

Continue successive cycles while there is an executable, plausible route within
the authorized resources. Do not stop just because the initial three failed.
Likewise, a substantial partial theorem is a checkpoint, not completion, when
the target contract still contains unresolved named implications.
Use checkpoints to preserve work while continuing. When the user specifies
time/resource bounds, honor them; otherwise choose bounded individual
experiments without imposing an arbitrary global attempt quota.

## Audit candidate breakthroughs

Before treating the goal as achieved, reconstruct the complete argument from
the current definitions and pinned evidence. Check every external leaf, range,
limiting argument and comparison map. Run `proof-audit` if available.

When fresh-agent review is available and delegation is authorized, give the
reviewer the exact claim, raw proof and required sources without the author's
verdict or route narrative. Request an independent derivation of the critical
step. Otherwise perform a separate adversarial pass and label it self-review.
Agreement between agents is not a proof certificate. Resolve disagreements by
the underlying mathematics.

## Persist and report

Keep proofs in durable mathematical files, finite runs in computation records,
failed mechanisms in linked route records, and current status in one live view.
When persistence is authorized but this host cannot execute or write, use the
`research-state` deferred packet contract for new durable artifacts, at most one
guarded index entry, and ledger proposals; state that ingest remains pending.
Update only state that actually changed; replace old dashboard checkpoint prose
with links only once it has a durable home and the project permits, and do not
rewrite indexed history.
User-authorized repository deliverables remain part of completion.

Integrate into a manuscript only on explicit request and after audit; integration
is not validation. Route novelty questions through literature-check; a failed
search is not novelty.

At a substantial program or phase boundary, or an explicit compaction request,
follow [program closeout](references/program-closeout.md); it does not close an
unresolved goal. Repository-wide flat-index restructuring belongs to research-init.

Lead with whether the original goal was reached and the exact result. State the
proof/review status, decisive mechanism, files and meaningful checks. If it
remains open, distinguish partial results from the goal, list executed routes
with their precise obstructions, and preserve a [continuation handoff](references/handoff.md).
When all presently available routes are exhausted, or tools/resources block
every remaining continuation, say so honestly; leave blocked routes open with
their deferred next steps. Never invent progress to satisfy “do not stop”.

Referenced files: 7 — file references are metadata, not package contents.

View saved version →

---
name: research-retrospective
description: >-
  Reconcile a mathematical research repository's current claims, proofs, computations, status, literature dependencies, and failed routes, then recommend the next bounded research moves. Use only when the user asks for a project review, weekly/monthly retrospective, prioritization, a prose project handoff, or “what should I do next?”. Do not use to write a program closeout, migrate research history, operate a .mathbox ledger, or generate its dependency-aware handoff. Default to read-only.
---

# Research retrospective

Produce a decision-quality view of the project, not a chronological summary.
Default to no edits unless the user asks to reconcile files.

## Establish authority

1. Determine repository root and applicable instructions.
2. Resolve charter, live status, claims, conventions, literature record, durable
   proofs, computations, verification, research-history index, and detailed
   record directory.
   Verify that referenced live-role paths exist and expose competing aliases or
   broken authority links.
3. Read the current summary and search the history entry point; follow relevant
   program/phase links to closeouts and designated route indexes. Do not load a long dashboard, claims inventory or index in full just
   to find the latest state. Open only the proof or research records needed to
   verify conflicts or load-bearing claims.
4. Do not choose a newer timestamp over stronger evidence. Expose unresolved
   authority conflicts.
5. Compare the live dashboard's review/checkpoint revision with later changes to
   authoritative manuscripts, proofs and declared deliverables. A stale date is
   a prompt to inspect, not by itself proof that the mathematics changed.

If `.mathbox/` is present, use the available `research-state` skill's brief
read-only check and goal handoff, then inspect full details for affected claims,
review conditions and routes. Use `impact CLAIM` for a named claim's
dependents and `pin-impact PATH` for the pins of a named file. Reconstruct
affected proofs from artifacts;
do not merely repeat generated labels. Do not initialize or migrate state as a
side effect of a read-only retrospective.

Do not start broad literature searches to fill a retrospective. Use available
`literature-check` (`mathbox:literature-check` in plugin installations), or an
exact-source fallback if unavailable, only for a necessary bounded source question;
otherwise propose it as a next route.

If `RESEARCH_LOG.md` still contains long-form legacy entries, read only the
relevant embedded entries and support a mixture of legacy prose and new links.
Report the pending migration through the available `research-init` skill
(`mathbox:research-init` in plugin installations), or report it pending if unavailable, but do not perform or
require it as a precondition for the retrospective.

## Build the portfolio

For each active claim or work package, record:

- exact target, evidence label and strongest currently supported statement;
- durable evidence and review status;
- load-bearing dependencies;
- first unresolved implication or smallest counterexample;
- recent route and why it succeeded or stopped;
- expected scientific value, cost, and risk;
- whether it lies on the current critical path.

Manuscript inclusion, bounded computation and failed search cannot upgrade
evidence labels. Report omitted-issue counts from brief ledger checks.

Identify duplicated efforts, stale claims, abandoned routes with reusable
information, and mutable facts incorrectly embedded in instructions.
For external or long computations, distinguish the last observed process state
from current state. A launch record without a live process, scheduler result or
later observation is `unknown`, not `running`.

Group failed routes by their first failed mechanism rather than title. Identify
shared unresolved dependencies and what mathematical change would reopen each
route. Distinguish new evidence from more prose, repeated bounded cases, and
rediscovery of already recorded obstructions.

## Select next routes

Recommend at most three bounded research routes. Each must include:

- exact unresolved mathematical question;
- why it dominates nearby alternatives;
- when current evidence is bounded, the uniform route or obstruction it
  suggests;
- cheapest decisive test and, when bounded, the alternatives it distinguishes;
- success and failure criteria;
- expected durable output;
- dependencies and resource needs;
- stopping condition.

Balance one high-leverage route with lower-risk publishable or computational
work when the project permits. Do not keep a deliverable hostage to an unrelated
open flagship problem.

## Review the AI workflow

Note recurring guidance failures, false `mathbox` plugin skill triggers,
context sinks, duplicated records, non-reproducible computations, or
verification gaps. Report general plugin-skill bugs to the user or Mathbox issue tracker;
project rules belong in the repository.

Treat a live status dashboard as current state, not verification history. Flag
stacked dated verification narratives as a context sink. When reconciliation
edits are requested, keep the latest full current summary. Replace an older
narrative with a link only when it already has a durable home (indexed record,
manifest or closeout), edit policy permits it and `pin-impact` shows no conflict.
Otherwise leave it and report pending research-program closeout or research-init
migration. Reconcile existing facts and rephrase next actions without changing
their mathematical obligations; do not undertake compaction here.
Do not rewrite indexed records or their history-index entries; append a linked
correction record when history itself needs correction.

Flag broken links to purported live dashboards, conflicts between the designated
authority and existing files, and completed deliverables still described as
unresolved. Do not repair these during a read-only retrospective; identify the
minimal reconciliation set.

## Output

Lead with a concise project verdict. Then provide:

1. claim/work-package table;
2. contradictions or stale records;
3. critical path and principal blocker;
4. recommended routes in priority order;
5. files to reconcile, only if edits were requested;
6. the best next prompt for available `research-attempt` or, for multiple routes,
   `research-program` (`mathbox:<name>` in plugin installations); if unavailable,
   give an equivalent self-contained research prompt.

Referenced files: 3 — file references are metadata, not package contents.

View saved version →

---
name: research-state
description: >-
  Read or update a local append-only .mathbox ledger of exact claims, evidence revisions, dependency impact, review provenance, routes and parallel or delayed runs. Use when the user asks to set up, check, record in or reconcile such a ledger, detect stale evidence, or generate its dependency-aware handoff. Do not use merely because a ledger exists, for a casual math question, as a substitute for proof auditing, or for a prose retrospective from status files.
---

# Executable research state

Follow project authority rules. The ledger checks recorded evidence, artifact
freshness and dependencies, not mathematical truth. `proof-recorded` describes
bookkeeping rather than a theorem proved under the project's vocabulary.
Apply project promotion and approval policy separately; review status remains
separate from evidence.

Read [ledger.md](references/ledger.md) before interpreting labels or recording
events. Resolve [research_state.py](scripts/research_state.py) as `TOOL` in this
installed skill. All artifact paths are relative to the project supplied with
`--root`; put `--json` before the subcommand for complete structured output.

## Read before changing state

For initialized state, start with `check --summary`, then `handoff --goal CLAIM`
for a registered goal. Without a registered goal use `status`, or an unfiltered
`handoff`. Check summaries contain counts and sampled issues with omitted counts;
brief status/handoff views also list live, stale and unreconciled runs needing
attention. Open `--full` details only for relevant contracts, reviews or issues;
compare complete issue lists when a change could hide a new issue in the sample.

```bash
python3 "$TOOL" --root PROJECT check --summary
python3 "$TOOL" --root PROJECT status
python3 "$TOOL" --root PROJECT handoff --goal CLAIM
python3 "$TOOL" --root PROJECT impact CLAIM
python3 "$TOOL" --root PROJECT pin-impact PATH
python3 "$TOOL" --root PROJECT record PROPOSAL.json
python3 "$TOOL" --root PROJECT record-batch PROPOSALS.json --dry-run
python3 "$TOOL" --root PROJECT record-batch PROPOSALS.json
python3 "$TOOL" --root PROJECT ingest PACKET.json --dry-run
python3 "$TOOL" --root PROJECT ingest PACKET.json
```

`status`, `check`, `impact`, `pin-impact`, `next` and `handoff` are read-only and
never initialize state. Create an authorized new project, initialize and register
claims before querying its goal. Inspect actual proof/source/computation artifacts
behind important labels. Changed proofs or dependencies invalidate snapshots;
retracted dependency evidence or current counterexamples block downstream proofs
without rewriting history. Run `impact CLAIM` before revising a load-bearing
statement and `pin-impact PATH` before editing a pinned file.

## When state is writable only later

When persistence is authorized and the host can inspect the exact ledger head
but cannot execute or write, follow [deferred-packet.md](references/deferred-packet.md).
Never invent IDs or hashes. Return the complete packet in the final JSON fence
and say it is unapplied; obey the inspected local write policy.

## Record only material changes

Initialize `.mathbox/` only for useful, authorized setup or state tracking;
existing prose projects may keep their format. Follow [migration.md](references/migration.md)
for adoption. A session alone needs no event. Record changed contracts, evidence,
reviews and justified route outcomes, rather than duplicating route narratives.
Program/run lifecycle events serve work spanning executors, branches, delayed
returns or sessions.

Write ordinary proposals with `type`, `actor` and `payload`; use `record FILE`,
or preview a dependency-ordered `record-batch` before appending distinct events.
Unknown payload keys are rejected on new writes; existing journals still replay.
Register dependency claims before consumers and exact claims before evidence.
Bind authoritative wording with `statement_artifact` and locator when useful.
The helper hashes durable artifacts and captures transitive claim revisions;
never supply generated snapshots. Source evidence needs exact identifier,
version, locator and translation. Computation evidence needs assertion, bounds
and non-claims; successful execution is not a universal proof.

A `manifest` links a version-2 computation record, its hashed input/output closure,
matching `claim_id`, and completed run. Validate it with computation-audit first:
linkage checks do not validate its scientific interpretation. Version-1 manifests
may be pinned only as ordinary artifacts, without automatic closure.

Record reviews separately against exact evidence and a durable report. Genuine
independence requires fresh review of raw evidence; a different actor name alone
is insufficient, and an author cannot independently audit their own evidence.
Inspect active review objects and reports when passing, conditional and failed
reviews coexist. Failed or conditional reviews remain challenges even if their
reports disappear. Resolve them through an explicit justified retraction or
actually revalidated replacement evidence, never a silent hash refresh.

Whole-file pins stale on any byte change, including typography. Prefer faithful,
stable claim-scoped artifacts where available; inspect fanout with `pin-impact`.
Revise a claim with a new revision and reason. After real revalidation, record new
evidence with `supersedes: [old IDs]`; retract only erroneous evidence or review
records. Keep proof details outside the ledger. Never edit/delete numbered events,
refresh hashes to silence warnings, or treat a changed statement as already proved.

## Use routes to support decisions

Record owning claim, optional `resolves` obligations, mechanism, decisive question
and discriminator, prerequisites, success/failure criteria and rough gain/cost.
Separate alternative routes from jointly required theorem dependencies. `next`
ranks ready recorded routes heuristically; mathematical judgment sets priority.
Repeated owner/mechanism pairs require the documented reopening contract, not
renaming to evade it.

Separate attempt outcome from route disposition. Inconclusiveness, resource limits
or priority changes never alone justify closure. Preserve untried or deferred
continuations with next action and resumption condition. Close only with the exact
obstruction or scoped reason no continuation remains. Reopening rules and event
fields are in [executions.md](references/executions.md) and the ledger reference.

When an open route's continuation must outlive this session, use an existing open
program whose goal covers it, or register one if absent. Record missing
`route-run`, `run-result` and `route-reconcile` events with `decision: continue`,
reusing applicable records. Cited runs and their reconciliation share `base_event`
and `base_revision`; a run result inherits its base through its run and has no
base fields. The program retains its starting checkpoint, which may differ from
a later execution's base. `next` and `handoff` show the latest continuation's
reason and next step. A prose record alone cannot update that generated view.
Do not add lifecycle events solely for follow-up completed in the same session.

For parallel/delayed work, assign distinct executions with owner, actual inputs,
base and write scope. Reconcile serially in the single writer's ledger, record
conflicts, and disposition late results explicitly. Arrival order is not ancestry;
never merge or renumber event streams. Process completion does not close a route
or promote a claim.

## Report and persist

Commit events with their artifacts only under project Git authorization. Preserve
source-cache retention policy. Use one designated live view, preferably a generated
brief view when migration is authorized; do not create a parallel manual dashboard.
Report changed claims, active review conditions/conflicts, stale evidence,
dependents and route-only context. A clean check establishes bookkeeping integrity.
Use available `proof-audit`, `computation-audit` or `literature-check` skills
(`mathbox:<name>` in plugin installations) for correctness decisions, or perform
the relevant bounded check directly and disclose limits if unavailable.

Referenced files: 9 — file references are metadata, not package contents.