# Jacobian MCP Server

Executable mathematics and independent verification for AI agents.

**Publisher claimed.** No tool list reported, and Pod has not connected to this server.

## Status

Pod has not dialled Jacobian yet, so everything on this page is what its publisher reported rather than what we observed. Registries describe servers; they do not connect to them. Until a check runs, treat the tool list below as a claim.

## Connect

Published as `jacobian` on npm. Runs locally.

## Known issues

**208 problems reported by people outside the maintainer team.** Issues filed by the project's own owners, members and collaborators are excluded — those are release checklists and internal refactors, not things that will go wrong for you. Showing 12.

### Most discussed

### [Evaluation]: Jacobian is available but unused across a four-case conjecture canary

## Area

Agent evaluation, MCP tool discovery, recently solved conjecture reliability.

## Reproduction

A frozen four-case canary was run with `gpt-5.6-terra` at low reasoning under three conditions:

1. no Jacobian;
2. ordinary Jacobian availability;
3. the same Jacobian surface plus a frozen 99-word selective operation-grounding card.

Prompts, sandbox, unified-exec mode, timeouts, and model configuration were otherwise held fixed.

Jacobian treatment fixture:

- revision: `fb33f6f471ab804418

[Read the thread](https://github.com/morluto/jacobian/issues/845) · 2026-08-08 · closed · 37 comments

### [Design]: Evaluate native resource-link handoffs for durable capability results

## Decision

Should `capability.invoke` return native MCP resource links for durable result and
episode artifacts, alongside its compact text projection, after a model-in-the-loop
evaluation shows that supported hosts reliably follow those links with
`resources/read`?

## Context

Jacobian already has the important architectural pieces:

- immutable artifacts are readable through the
  `artifact://sha256/{digest}` resource template;
- `capability.invoke` keeps the canonical `CapabilityResult` in

[Read the thread](https://github.com/morluto/jacobian/issues/195) · 2026-07-29 · closed · 8 comments

### [Feature]: Make capability contracts easier for agents to discover and compose

**Priority**

P2 (medium)

**Area**

mcp, kernel

**Problem**

Agents can call `capability.describe` and `capability.invoke`, but successful mathematical composition still depends on understanding exact scope, evidence type, artifact flow, and failure recovery from compact tool descriptions. The initial paired transcripts show that opaque artifact outputs and weak provenance cues can cause an agent to reconstruct or relabel an object instead of using the exact returned artifact.

Adding more cap

[Read the thread](https://github.com/morluto/jacobian/issues/28) · 2026-07-25 · closed · 7 comments

### [Security][Reproducibility]: Adversarially validate per-checker identity, dependency closure, and non-interference

## Priority

P1 checker-identity and operability bug: every bundled Python checker currently inherits one coarse package-wide implementation digest, and that digest also includes the entire `jacobian` product package because the checker worker lives inside it. Unrelated source changes can invalidate all checker authorizations, while some actual runtime dependencies are not represented by the digest at all.

## Area

Checker authorization, implementation identity, worker runtime, packaging, provi

[Read the thread](https://github.com/morluto/jacobian/issues/1228) · 2026-08-11 · closed · 5 comments

### [Experiment][MCP]: Evaluate schema-bearing direct operation tools against the fixed two-tool contract

## Summary

Jacobian currently represents hundreds of mathematical operations as data behind one MCP meta-tool:

```json
{
  "name": "math.run",
  "arguments": {
    "capability_id": "matrix.rank.compute",
    "payload": {}
  }
}
```

The selected operation’s actual input/output schemas, effects, execution behavior, and value type are not the schema of the tool the model calls. They were returned earlier by `math.find` as data. This erases the strongest native affordance MCP provides: every tool

[Read the thread](https://github.com/morluto/jacobian/issues/1218) · 2026-08-11 · closed · 5 comments

### Most recent

### Expose admitted operations directly for client-managed discovery and composition

## Decision

Should Jacobian replace its mandatory `math.find` -> `math.run` execution path with directly exposed typed MCP operations, allowing clients with deferred tool search and code mode to discover and compose those operations themselves?

This issue proposes that direct operation tools become the only execution surface. `math.find` may remain only if it provides measurable mathematical vocabulary discovery beyond client tool search. `math.run` would be removed rather than retained as a c

[Read the thread](https://github.com/morluto/jacobian/issues/2982) · 2026-08-28 · closed · 3 comments

### [Discovery] Separate math.find namespace filtering from descriptive tags

## Current limitation

`math.find` exposes an optional `domain` filter, but its implementation does not have one stable meaning. A value matches either the first segment of an operation ID or any descriptive tag:

```python
return (
    normalized_domain == normalize_domain(operation_domain(operation))
    or normalized_domain in normalized_tags
)
```

Consequently an agent can reasonably use `domain="polynomial"` expecting the `polynomial.*` operation family, while the result also contains grap

[Read the thread](https://github.com/morluto/jacobian/issues/2918) · 2026-08-27 · closed · 0 comments

### [Graphs] Construct bounded rooted-tree fine partitions

## Parent gap / RFC

Erdős Problem 550 was resolved in [Li, *A Resolution of Erdős Problem 550 on Tree versus Complete Multipartite Ramsey Numbers* (arXiv:2606.23659v2)](https://arxiv.org/html/2606.23659v2).  Its off-Turán embedding argument repeatedly needs a finite rooted-tree decomposition before any regularity, Ramsey, or compactness reasoning: choose a small seed set and expose the bounded rooted components (``shrubs``) with their boundary/parity data.

Jacobian has graph and tree-decomposi

[Read the thread](https://github.com/morluto/jacobian/issues/2912) · 2026-08-27 · closed · 0 comments

### [Coding theory]: Construct the exact selected-distance graph of an explicit binary code

## Parent gap / RFC

Follow-up to closed [#1785](https://github.com/morluto/jacobian/issues/1785). Its proposed `code.binary.constant_weight.distance_graph.compute` was an explicit acceptance criterion, but the landed `code_nonlinear` domain currently exposes only word distance, compact explicit/constant-weight profiles, and a support-set conversion.

## Public mathematical postcondition

For a bounded explicit binary code and selected Hamming distance, return the complete indexed simple graph w

[Read the thread](https://github.com/morluto/jacobian/issues/2910) · 2026-08-27 · closed · 0 comments

### [Rigidity] Compute exact planar framework rigidity-matrix profiles

## Current limitation

Jacobian can compute pairwise distances of a labelled rational planar configuration and the exact rank of a caller-authored rational matrix. It has no operation that binds a realised graph to its planar rigidity matrix: callers must independently align graph vertices with point labels, lay out the two coordinate columns per vertex, construct one row per edge, and interpret the rank.

That is a reusable finite geometry postcondition, not a unit-distance or rigidity-conjectu

[Read the thread](https://github.com/morluto/jacobian/issues/2905) · 2026-08-27 · closed · 1 comment

### [Matrix permanent] Bind admission to Ryser work and correct the public order limit

## Confirmed contract failure

`matrix.permanent.compute` has the right stable mathematical postcondition, but
its admitted envelope does not bound the work of its pinned backend.

`SquareRationalMatrixRequest` accepts every dense rational square matrix of
order at most 32 with 256-digit scalar components.  The permanent operation
calls `sympy.Matrix.per()` directly.  In the pinned SymPy 1.14.0, `_per` uses
Ryser's formula by materializing every nonempty subset of the matrix columns
and then for

[Read the thread](https://github.com/morluto/jacobian/issues/2902) · 2026-08-27 · closed · 1 comment

### [Differential geometry] Compute exact Laplace–Beltrami values on rational coordinate metrics

## Parent gap / RFC

This is a focused follow-up to [#2877](https://github.com/morluto/jacobian/issues/2877), [#2878](https://github.com/morluto/jacobian/issues/2878), and [#2885](https://github.com/morluto/jacobian/issues/2885).  Those issues establish the exact coordinate metric, rational partial derivatives, and covariant derivative, but none returns the scalar second-order operator determined by a supplied metric.  Existing `polynomial_field.scalar.laplacian.compute` is the Euclidean, polyno

[Read the thread](https://github.com/morluto/jacobian/issues/2897) · 2026-08-27 · open · 0 comments

[See all 24 reports Pod holds for Jacobian](/mcp/jacobian/issues) — of 208 qualified upstream.

## Firsthand observations

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