Protocol

Portable evidence without platform dependence.

Applications may depend on the protocol. The protocol does not depend on MathGraph.org, Metalogic-hosted services, LLMs, or Discover, Check, Resolve, or Develop services.

Dependency direction

One protocol, separately usable functions

Independent producers can publish declared receipts and snapshots; independent consumers can validate and replay them without this website. The website is one static publisher and reader. It is not a required runtime, a certificate authority, or the source of the protocol’s validity.

Implemented
Check — Implemented at the qualified record-001 boundary

The source-check record supports an exact record, version, source commit, suite commit, and goal match. It does not generalize beyond that tuple.

Bounded-qualified
Resolve — Bounded-qualified offline for record 002

The standard-library consumer replays one pinned historical dependency graph with a separately supplied trust-policy pin. The browser explorer only displays precomputed scenarios.

Local advisory
Discover — local advisory contract

The deterministic request/result contract allocates attention and cannot promote truth. The real example is PARTIAL with full replay unavailable. Hosted service: NOT_DEPLOYED.

QUALIFIED_BOUNDED
Develop — QUALIFIED_BOUNDED for one exact finite profile

Independent replay covers exactly eight ordered 3-bit states. The Capability Family Compiler is NOT_IMPLEMENTED; VDN / Lean remains EXPERIMENTAL. Hosted service: NOT_DEPLOYED.

Static registry
Capabilities — one qualified finite entry

The exact descriptor, evaluation, receipt, and policy are pinned separately. Experimental candidates remain outside the qualified index. Reading an entry grants no trust or authorization.

The conceptual Discover → Check → Resolve → Develop loop is optional, not a compulsory runtime pipeline. No autonomous loop is implemented. Capability qualification adds no mathematical terminal form: accepted claims still end in exactly one VERIFIED_PROOF, FINITE_COUNTERMODEL, or NAMED_OBSTRUCTION.

Proposed The Lean evidence profile remains a draft; native replay and independent statement correspondence are separate admission requirements.

Views over existing contracts

Five responsibilities, not a new universal ontology.

Object responsibility
Preserve the exact identity, type, version, source occurrence, attribution, and history already declared by each supported contract.
Relation responsibility
Carry only typed dependencies, evidence support, provenance, withdrawal, or other relations explicitly declared by a qualified source contract. Names and layout create no relation.
Evidence responsibility
Bind a claim to exact sources, verifier results, assumptions, toolchains, scope, and replay boundaries without promoting signatures or hashes into truth.
Resolution responsibility
Let a receiving consumer apply its own pinned policy and distinguish historic warrant, lifecycle, freshness, applicability, and authorization.
Transition responsibility
Represent a separately evidenced lifecycle or developmental change while preserving the byte-identical historical state that preceded it.

These responsibilities organize the current record, Resolve, Discover, capability, and interoperability contracts. They do not replace those contracts with a new serialized Unit type.

Separate operations

CLOSE, ACT, and REFINE do different work.

CLOSE
Bounded support closure over exact admitted roots and declared routes. Unsupported cycles and scope changes remain UNKNOWN.
ACT
Caller policy, viability, and permission. Action authorization remains NONE in every published static consumer and projection here.
REFINE
A separately qualified evidence or lifecycle change. It emits a new event or state and never rewrites historic bytes.

A proof does not authorize an action. A display projection cannot refine evidence. A new distinction requires its own appropriate qualification.

Minimum implemented substrate

Objects required by the bounded replay

ObjectImplemented meaning in P0
Typed claimAn exact identity, kind, and scope. A changed kind or scope is a different request.
Evidence receiptA typed, scoped evidence identity admitted only under a declared verifier and trust policy.
Dependency routeA conclusion with explicit premise and evidence identities.
ResolutionThe deterministic before/after result computed from admitted roots and routes.
Trust policyThe separately pinned authority profile that admits exact source bytes, verifier identities, assumptions, and scopes.
Immutable snapshotThe byte-preserved historical claims, receipts, routes, withdrawals, and reported outcomes.
Temporal/lifecycle axesHistorical qualification, historical resolution, current applicability, freshness, revocation or supersession, lifecycle, and action authorization remain distinct.

This is the minimum common model exercised by record 002, not a claim that every proposed MathGraph semantic object has a stable public contract.

Rooted, exact-scope resolution

Each dependency route is conjunctive: every named premise and evidence receipt must be supported. Separate routes to the same conclusion are alternatives, so one route can disappear while another preserves support.

Resolution computes a least fixed point from admitted qualified roots. A dependency cycle without such a root remains UNKNOWN; cycles cannot manufacture support or create circular self-justification.

Claims, receipts, premises, verifier identities, assumptions, source pins, and scopes are exact. An unsupported semantic transport, implication, equivalence, kind change, or scope generalization returns UNKNOWN or an explicit validation error. Similar names, shapes, and hashes establish no correspondence.

UNKNOWN

Unknown is neither false nor malformed. It says the admitted evidence cannot warrant the requested interpretation.

Content identity is not claim truth

Canonical content identities make exact objects addressable. Source pins name repositories, commits, files, and toolchains. A content hash proves byte identity relative to an expected digest; it does not authenticate its own publisher or establish that the represented claim is correct.

The historical Crystal/MGSO envelope remains an experimental semantic transport candidate. Its MGSO magic prefix and canonical encoding are not the deployed P0 record format, and unfamiliar object types must be preserved or declined—not coerced into known semantics.

Verification receipts therefore keep native-verifier authority, source identity, assumptions, and result separate. External proof assistants and finite checkers retain their own semantics; MathGraph does not replace them.

Historical qualification is not current applicability

An immutable snapshot can establish what qualified evidence supported at a pinned historical point. Historical qualification and historical support resolution remain distinct from current applicability, freshness, lifecycle, revocation or supersession, and action authorization.

The offline record-002 replay reports current applicability as UNKNOWN, freshness as NOT_CHECKED, revocation or supersession as NOT_CHECKED, and action authorization as NONE. A withdrawal can make documentary support STALE without making a mathematical proposition REFUTED.

Authenticity is not semantic correctness

A signature authenticates a signed statement under a key policy; it does not establish the truth of that statement. A cryptographic commitment likewise binds bytes without proving their mathematical or semantic meaning.

Experimental
Bounded ML-DSA-65 warrant experiment

A finite Boolean witness protocol passed 23/23 research tests using ML-DSA-65 and SHA3-512 evidence binding. It has no independent security audit, implementation diversity, or production trust policy.

The local in-toto profile implements unsigned correspondence only for one exact capability descriptor. The wrapper does not import qualification: signature is UNSIGNED, authenticity and freshness are NOT_CHECKED, qualification and current applicability are UNKNOWN, and action authorization is NONE. Inspect the exact binding contract.

Sigstore, SCITT, and RATS remain deferred extension boundaries. No signing, transparency verification, partnership, or endorsement is established. Full interoperability boundary ↗

The experiment is evidence that a bounded warrant can be signed and replayed—not a claim of general security, universal verification, production post-quantum security, or semantic truth.