Research Refine
zjYao36/Auto-Research-Refine
Turns a vague research direction into a focused, problem-anchored method plan through up to five review rounds with a second model.
Design or audit a Jacobian operation’s mathematical contract, boundedness, exact results, and composition.
$ npx skills add morluto/jacobian --skill audit-public-operation-contracts -a claude-codeProject install by default; add -g for ~/.claude/skills/.
$ gh skill install morluto/jacobian audit-public-operation-contracts --agent claude-codeProject scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).
$ git clone --depth 1 https://github.com/morluto/jacobian.git skills-src && mkdir -p .claude/skills && cp -r skills-src/.agents/skills/audit-public-operation-contracts .claude/skills/audit-public-operation-contracts && rm -rf skills-srcUse ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.
Claude Code skills documentation · loads skills from .claude/skills/
Install the "audit-public-operation-contracts" agent skill from https://github.com/morluto/jacobian/tree/main/.agents/skills/audit-public-operation-contracts into .claude/skills/audit-public-operation-contracts/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "audit-public-operation-contracts", then confirm the skill loads.Claude Code copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$skill-installer install https://github.com/morluto/jacobian/tree/main/.agents/skills/audit-public-operation-contractsType this inside Codex. $skill-installer <name> installs a curated skill from openai/skills. The installer writes to $CODEX_HOME/skills (default ~/.codex/skills). Restart Codex if the skill does not show up.
$ npx skills add morluto/jacobian --skill audit-public-operation-contracts -a codexProject install goes to .agents/skills/; add -g for ~/.codex/skills/.
$ gh skill install morluto/jacobian audit-public-operation-contracts --agent codexProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/morluto/jacobian.git skills-src && mkdir -p .agents/skills && cp -r skills-src/.agents/skills/audit-public-operation-contracts .agents/skills/audit-public-operation-contracts && rm -rf skills-srcUse ~/.agents/skills/ instead of .agents/skills for a personal install.
Codex skills documentation · loads skills from .agents/skills/
Install the "audit-public-operation-contracts" agent skill from https://github.com/morluto/jacobian/tree/main/.agents/skills/audit-public-operation-contracts into .agents/skills/audit-public-operation-contracts/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "audit-public-operation-contracts", then confirm the skill loads.Codex copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ npx skills add morluto/jacobian --skill audit-public-operation-contracts -a cursorProject install goes to .agents/skills/; add -g for ~/.cursor/skills/.
$ gh skill install morluto/jacobian audit-public-operation-contracts --agent cursorProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/morluto/jacobian.git skills-src && mkdir -p .cursor/skills && cp -r skills-src/.agents/skills/audit-public-operation-contracts .cursor/skills/audit-public-operation-contracts && rm -rf skills-srcUse ~/.cursor/skills/ instead of .cursor/skills for a personal install.
Cursor skills documentation · loads skills from .cursor/skills/, .agents/skills/, .claude/skills/, .codex/skills/
Install the "audit-public-operation-contracts" agent skill from https://github.com/morluto/jacobian/tree/main/.agents/skills/audit-public-operation-contracts into .cursor/skills/audit-public-operation-contracts/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "audit-public-operation-contracts", then confirm the skill loads.Cursor copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ gemini skills install https://github.com/morluto/jacobian.git --path .agents/skills/audit-public-operation-contracts--scope user (default) or --scope workspace; --path is the subfolder of the repo that holds the skill; --consent skips the security confirmation prompt.
$ npx skills add morluto/jacobian --skill audit-public-operation-contracts -a gemini-cliProject install goes to .agents/skills/; add -g for ~/.gemini/skills/.
$ gh skill install morluto/jacobian audit-public-operation-contracts --agent gemini-cliProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/morluto/jacobian.git skills-src && mkdir -p .gemini/skills && cp -r skills-src/.agents/skills/audit-public-operation-contracts .gemini/skills/audit-public-operation-contracts && rm -rf skills-srcUse ~/.gemini/skills/ instead of .gemini/skills for a personal install, then run /skills reload.
Gemini CLI skills documentation · loads skills from .gemini/skills/, .agents/skills/
Install the "audit-public-operation-contracts" agent skill from https://github.com/morluto/jacobian/tree/main/.agents/skills/audit-public-operation-contracts into .gemini/skills/audit-public-operation-contracts/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "audit-public-operation-contracts", then confirm the skill loads.Gemini CLI copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ gh skill install morluto/jacobian audit-public-operation-contractsInstalls for Copilot at project scope by default; add --scope user for a personal install. Preview a skill first with gh skill preview. Needs GitHub CLI 2.90.0 or later (public preview).
$ npx skills add morluto/jacobian --skill audit-public-operation-contracts -a github-copilotProject install goes to .agents/skills/; add -g for ~/.copilot/skills/.
$ git clone --depth 1 https://github.com/morluto/jacobian.git skills-src && mkdir -p .github/skills && cp -r skills-src/.agents/skills/audit-public-operation-contracts .github/skills/audit-public-operation-contracts && rm -rf skills-srcUse ~/.copilot/skills/ instead of .github/skills for a personal install. Commit .github/skills so cloud agent and code review can use it.
GitHub Copilot skills documentation · loads skills from .github/skills/, .claude/skills/, .agents/skills/
Install the "audit-public-operation-contracts" agent skill from https://github.com/morluto/jacobian/tree/main/.agents/skills/audit-public-operation-contracts into .github/skills/audit-public-operation-contracts/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "audit-public-operation-contracts", then confirm the skill loads.GitHub Copilot copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
$ npx skills add morluto/jacobian --skill audit-public-operation-contracts -a opencodeOpenCode documents no install command of its own. Project install goes to .agents/skills/; add -g for ~/.config/opencode/skills/.
$ gh skill install morluto/jacobian audit-public-operation-contracts --agent opencodeProject scope by default (.agents/skills/); add --scope user for a personal install.
$ git clone --depth 1 https://github.com/morluto/jacobian.git skills-src && mkdir -p .opencode/skills && cp -r skills-src/.agents/skills/audit-public-operation-contracts .opencode/skills/audit-public-operation-contracts && rm -rf skills-srcUse ~/.config/opencode/skills/ instead of .opencode/skills for a personal install.
OpenCode skills documentation · loads skills from .opencode/skills/, .claude/skills/, .agents/skills/
Install the "audit-public-operation-contracts" agent skill from https://github.com/morluto/jacobian/tree/main/.agents/skills/audit-public-operation-contracts into .opencode/skills/audit-public-operation-contracts/ in this project. Copy the whole folder (SKILL.md and every file beside it), keep the folder name "audit-public-operation-contracts", then confirm the skill loads.OpenCode copies the folder itself, the same result as the manual copy. Check what it changed before you commit it.
audit-public-operation-contractsDesign or audit a Jacobian operation’s mathematical contract, boundedness, exact results, and composition.
Audit Public Operation Contracts is an agent skill from morluto/jacobian. Design or audit a Jacobian operation’s mathematical contract, boundedness, exact results, and composition.
Its SKILL.md is about 2k tokens, which your agent loads only when the skill is triggered. The skill folder holds 4 other files, including reference files (for example `agents/openai.yaml` and `references/scale-and-backends.md`).
It sits in Research & Science, covering Math and symbolic computation. It works with Model Context Protocol. The repository describes itself as: Composable mathematics tools for agents. The licence is MIT.
Read from SKILL.md and the folder at commit 9dc2aaf. It shows what the files ask for, not the result of running them.
Pre-approves nothing: there is no allowed-tools line, so your agent's usual permission prompts apply.
From allowed-tools in the SKILL.md frontmatter.
No scripts in the folder and no shell commands in SKILL.md.
From the folder's file list and the shell code blocks in SKILL.md.
No URLs in SKILL.md.
From URLs in SKILL.md, links to its own repository left out.
Names no API keys, tokens, secrets or passwords.
From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.
Audit Public Operation Contracts loads about 2k tokens when it runs, and up to ~3.7k if it reads all its reference files. Until then it costs about 35 tokens; SKILL.md has 965 words of instructions outside code blocks.
Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.
The automated check found no risky patterns in SKILL.md.
Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.
The full file from morluto/jacobian at commit 9dc2aaf, republished under its MIT licence (© morluto). 965 words, ~1,975 tokens.
.claude/skills/audit-public-operation-contracts/SKILL.md (or your agent's skills folder). This skill also uses 2 other files; get the full folder from GitHub.Determine whether an operation is a bounded, truthful, composable mathematical instrument. Record the revision, operation IDs, inspected scope, and whether the request includes implementation. Audit-only work does not authorize repository or external mutations.
Before adding a public operation or library abstraction, apply the vocabulary audit to the proposed boundary. Keep concise evidence in the existing issue or PR, reusing what is already established rather than creating a mandatory review form:
A justified boundary has one stable mathematical result, not a whole-proof API, assurance wrapper, workflow state, or compatibility metadata. Keep the existing composition and scale-first obligations below; a separating example motivates investigation but does not establish an admitted implementation.
Treat request representation, canonical values, semantic admission, kernel, trusted result construction, and downstream consumers as one execution path. Inspect schemas, declarations, examples, and MCP errors when public projection is in scope. The implementation alone does not define the advertised contract.
Use the applicable sections of the operation library. For public admission, consult the admission contract; for a backend boundary, consult the backend contract. Record applicable evidence in the requested audit or existing issue/PR description; do not create a universal review form.
When changing field/domain recognition, shape resolution, codec parsing or canonical conversion, identify the semantic owner and trace the actual callers that rely on its interpretation. Do not infer every possible producer-consumer pair from annotations. Similar-looking code may have different mathematical meanings: share an implementation when semantics are genuinely identical, or state and test a legitimate contextual difference instead of forcing reuse.
Run the same owner-local fixture through the relevant recognizer, resolver and consumer, with a useful accepted case and an invalid case that stays rejected. Cover alternate supported spellings, aliases/qualified forms, nesting and empty/zero/singleton cases only where they belong to that contract. For static checks, include binding and scope: unrelated guards, reassignment, destructured names and shadowing must not falsely establish the required property.
For example, the three-level annotation fixture in
tests/tooling/test_before_validator_containers.py checks container recognition,
nested shape resolution and the projection consumer together, including shallow
projection, unrelated-guard and destructured-rebinding controls. Keep this at the
owner boundary; add no duplicate runtime validation layer, generic ledger,
transport abstraction or catalog-wide generated matrix.
Use small deterministic reproductions to test the suspected mechanism:
Check serialized producer-consumer composition when relevant. Defining-invariant proof belongs in tests or an admitted caller-claim operation, not replay during ordinary result construction. Use current official backend documentation and the pinned implementation for consequential backend claims.
For a representation, performance, admission-limit, or backend-selection investigation, read scale and backends. Audit what the contract unnecessarily excludes as well as what it unsafely accepts. Preserve the motivating request and exact invariant; a fast but weaker result is not a scale improvement.
For a changed mathematical owner, choose a relevant invariant or equivariance and derive its expected effect before writing the test. Relabelling may preserve a scalar invariant while transporting indexed witnesses; row permutations must preserve the intended set or multiset semantics. Translation preserves planar squared circumradii, while scaling by nonzero c multiplies them by c². Translation preserves repeated differences; an invertible linear coordinate map transports their values and preserves their multiplicities. These are examples, not a requirement that every operation support every transformation. State when the transformation changes the problem or leaves the admitted domain.
Use the actual source and an independent defining-identity check, alongside the relation between transformed outputs. Include a negative control for an invalid invariance assumption or lost source indices/multiplicities. For a transformation or encoding operation, check that source identities, hypotheses and the intended relation survive the map: correct solver execution on the encoded problem does not establish that the mathematical model was valid.
Keep these tests with the affected owner. Do not introduce a catalog-wide matrix,
generic assurance fields, or repeated expensive verification during result
construction. A concrete example is
tests/math/combinatorics/additive/test_difference_profile_equivariance.py:
affine coordinate changes and source permutations are checked against exact
source subtraction, with stale-index and noninjective-map controls.
After proving a defect, inspect the owner, shared helper, and its callers for the same mechanism, keeping adjacent candidates confirmed, disproved, or untested. Choose a repair at the invariant's owning boundary. Preserve a regression that fails on the base for the intended reason when feasible, using an independent oracle, defining identity, or adversarial composition rather than source-text assertions. Select validation through the contributor guide's owning lanes.
Report the public claim, reproduction and observed result, violated invariant, affected scope, smallest repair, and meaningful proof gaps. If implementation was authorized, complete the focused repair and affected checks before handing back; existing authorization persists, but local investigation does not grant permission for external writes.
© morluto, MIT. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file
SKILL.md and 2 other files (references) in .agents/skills/audit-public-operation-contracts of morluto/jacobian.
Open the folder on GitHubat commit 9dc2aaf
Audit Public Operation Contracts next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.
| Skill | Stars | Used in | Tokens | Auto-check | Licence | Repo updated |
|---|---|---|---|---|---|---|
| Audit Public Operation Contracts this skillmorluto/jacobian | 220 | — | ~2k | Automated safety check: Pass | MIT | |
| Research RefinezjYao36/Auto-Research-Refine | 128 | 6 repos | ~6.9k | Automated safety check: Notes | None | |
| Read GitHubAgentTeam-TaichuAI/ScienceClaw | 671 | 2 repos | ~638 | Automated safety check: Pass | None | |
| Proof Run Orchestratorwanshuiyin/Auto-claude-code-research-in-sleep | 17k | 1 repos | ~4.7k | Automated safety check: Pass | MIT | |
| FirstdataMLT-OSS/FirstData | 184 | — | ~3.1k | Automated safety check: Pass | MIT | |
| Fin Generate Ideacsmar432/finai-research | 109 | — | ~2.5k | Automated safety check: Pass | MIT |
zjYao36/Auto-Research-Refine
Turns a vague research direction into a focused, problem-anchored method plan through up to five review rounds with a second model.
AgentTeam-TaichuAI/ScienceClaw
Read and search GitHub repository documentation via gitmcp.io MCP service.
wanshuiyin/Auto-claude-code-research-in-sleep
Runs a mathematical proof project as a stateful pipeline of run directories: a local attempt first, then a manual GPT Pro handoff package, with an optional DeepSeek audit.
MLT-OSS/FirstData
Find official portals, APIs, and download paths for authoritative primary data sources (governments, international organizations, research institutions, etc.).
csmar432/finai-research
针对经济金融研究方向的创意生成与评估。生成8-12个可发表的研究idea,过滤后在数据可行的情况下进行小规模实证验证,输出排序后的研究想法报告。
anthropics/claude-plugins-official
Solves one hard mathematics problem in a single session without subagents, keeping settled steps in a notes file and ending with a self-contained proof.md.
morluto/jacobian
Evaluate Jacobian reliability using recently resolved conjectures as held-out probes.
morluto/jacobian
Author, package, validate, or run mathematical evaluations as Jacobian Harbor datasets.
morluto/jacobian
Extract reusable Jacobian capabilities from a mathematical solution corpus, rather than one agent trajectory.
morluto/jacobian
Investigate MCP tool availability, discovery, and selection, including controlled adoption evaluations.
morluto/jacobian
Review mathematical agent trajectories for evidence-backed Jacobian improvements; do not resume solving.
morluto/jacobian
Design, audit, or repair mathematical benchmark verifiers, submission contracts, and scoring.
Works with
Categories
Design or audit a Jacobian operation’s mathematical contract, boundedness, exact results, and composition. Audit Public Operation Contracts is an agent skill from morluto/jacobian. Design or audit a Jacobian operation’s mathematical contract, boundedness, exact results, and composition.
Audit Public Operation Contracts fits situations like: tasks that involve Math and symbolic computation.
Run `npx skills add morluto/jacobian --skill audit-public-operation-contracts -a claude-code`. Or copy the skill folder (.agents/skills/audit-public-operation-contracts in morluto/jacobian) into .claude/skills/audit-public-operation-contracts in your project. Claude Code loads it when a task matches its description.
Run `npx skills add morluto/jacobian --skill audit-public-operation-contracts -a codex`. Or copy the skill folder (.agents/skills/audit-public-operation-contracts in morluto/jacobian) into .agents/skills/audit-public-operation-contracts in your project. Codex loads it when a task matches its description.
Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add morluto/jacobian --skill audit-public-operation-contracts -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/audit-public-operation-contracts, .gemini/skills/audit-public-operation-contracts, .github/skills/audit-public-operation-contracts and .opencode/skills/audit-public-operation-contracts in your project.
SKILL.md names no scripts, command-line tools or credentials: Audit Public Operation Contracts is instructions for the agent only.
SKILL.md contains no URLs. Any network use would come from the scripts or tools the agent runs. This is read from the text; nothing was executed.
Our automated static check of SKILL.md found no risky patterns, such as piping downloads into a shell, reading credential files or hidden Unicode. It is not a guarantee. Review the folder before installing.
Audit Public Operation Contracts is published under the MIT licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.
About 2k tokens (SKILL.md is roughly 7.9k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full. Its references folder adds about 1.7k tokens, read only when the agent opens those files.
Skills that share tags, products or a category with Audit Public Operation Contracts: Research Refine (zjYao36/Auto-Research-Refine, 128 stars), Read GitHub (AgentTeam-TaichuAI/ScienceClaw, 671 stars), Proof Run Orchestrator (wanshuiyin/Auto-claude-code-research-in-sleep, 17k stars) and Firstdata (MLT-OSS/FirstData, 184 stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.
morluto (a GitHub user) maintains it in morluto/jacobian, which has 220 GitHub stars. The repository holds 11 skills in this directory. The repository was last updated on October 5, 2026.
Source: morluto/jacobian on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.