# problems.science

> Open scientific problems, and exactly what has been established about each one.
> The site publishes a read-only projection of scientific state held in Vela
> Repository Git repositories: Claims, the Verifications that checked them, the
> attributed Decisions that accepted them, and the Standing that follows. A
> source's report and this site's own state are separate facts and are always
> labelled as such.

Most Problems hold no accepted Result. That is the honest state of the
catalogue, not a gap in the page: 1,215 of 1,217 published Problems are held by
identity and source locator alone, and their pages say so rather than inferring
a status.

## Reading state correctly

- A **Claim** is an assertion recorded against a Problem.
- A **Verification** is one scoped check. It reports what it covered and what it
  explicitly does not establish. A passing check is not acceptance.
- A **Decision** is an attributed act by one Repository authority.
- **Standing** is what that Repository currently admits, after replaying its
  Decisions. It is always Repository-local — never "true".
- A source's `declared_status` ("solved", "proved") is the source's word, shown
  under "Source says". It is not this site's state.

## Agent interface

Problem pages register typed tools on `document.modelContext` (WebMCP). An agent
driving the page gets a bounded context packet (`vela.webmcp-problem-context.v1`)
and these operations:

- `inspect_problem` — the Problem's current state, Claims, sources, and the exact
  projection roots those facts came from. Call first; other tools take its ids. Read-only.
- `inspect_claim` — one Claim in full, with the lineage behind its Standing and what
  each Verification did *not* establish. Read-only.
- `inspect_history` — the ordered Proposals, Verifications and Decisions, plus
  correction and supersession relations. Read-only.
- `search_problems` — locate related or comparable Problems before proposing
  anything. Read-only.
- `open_approach` — begin an attributed line of work. Writes hosted Work, which
  carries no scientific authority. Requires sign-in.
- `attach_evidence` — attach an artifact by its exact content root with a written
  rationale. Bytes are not uploaded. Requires sign-in.
- `prepare_submission` — draft a Submission and leave it **unsigned**. Requires sign-in.
- `inspect_candidate` — read the unsigned drafts prepared in this Workspace.

### The boundary, which is enforced rather than promised

`prepare_submission` is the furthest an agent in a browser can go. This
application holds no signing key and cannot sign for anyone. An agent can never
issue a Decision, change a Standing, or sign a Submission — a test reads the
agent interface as bytes and fails the build on any shape that would.

A human takes the unsigned draft to a local tool, signs it with a key only they
hold, and submits it to the Repository. Verification and an attributed Decision
there decide whether Standing moves.

There is no remote MCP server. An agent that is not driving a page can read the
machine-readable documents below, but has no write path.

## Machine-readable

- [/problems.json](https://problems.science/problems.json): published Problems, root-labelled
- [/sources.json](https://problems.science/sources.json): source records, root-labelled
- [/.well-known/vela-site.json](https://problems.science/.well-known/vela-site.json): deployment manifest and exact release root
- [/sitemap.xml](https://problems.science/sitemap.xml)

Every projection read is pinned to an exact release root and fails closed on an
incompatible manifest. Responses carry `X-Vela-Projection-Root`.

## Routes

- [/problems](https://problems.science/problems): collections and directory
- [/problems/erdos-problems/94](https://problems.science/problems/erdos-problems/94): a Problem with an accepted Result whose scope does not reach the question
- [/problems/erdos-problems/2](https://problems.science/problems/erdos-problems/2): the dominant case — identity and source locator, nothing established here
- [/decisions](https://problems.science/decisions): attributed Repository Decisions
- [/repositories/math/reproduce](https://problems.science/repositories/math/reproduce): pinned commands to replay Repository state, and what success does not prove
- [/contribute](https://problems.science/contribute): how work returns
- [/accessibility](https://problems.science/accessibility): conformance and known limits