Grand Challenge MATH-PROGRAMME Agent Council

Status

Active programme governance doctrine.

The Agent Council replaces informal mnemonic companions. Its roles define responsibility boundaries for rigorous mathematical production. They do not certify mathematics, replace specialist reviewers, or substitute for proof assistants. They also do not form a universal approval quorum for routine work.

Under MP-STREAMLINED-EXECUTION-001, bounded administrative, documentation, engineering, workflow, maintenance, routing, synchronization, and campaign-execution work may proceed through protected merge and readback under standing delegated authority once affected checks pass. Council offices are engaged according to the material boundary. Specialist non-author review remains reserved for substantive mathematical certification, source-semantic adjudication, constitutional authority expansion, security-sensitive protection weakening, and external claim promotion.

Programme position

The mathematical execution route has three pillars:

MATHFORGE -> MATHSOLVE -> MATHCERT

MATH-PROGRAMME is the governance, integration, publication, and archival layer. It is represented as an owning pillar for governance and integration artifacts, but it is not a fourth proof stage and cannot promote a claim without the relevant mathematical support route.

Core Council

Agent	Responsibility	Governing question
The Axiomatist	Foundations, objects, assumptions, structures	What must be true before the claim can be formed?
The Prospector	Discovery, conjectures, patterns, reductions	What structure is emerging?
The Experimentalist	Computation, examples, witnesses, finite tests	What happens when the idea runs?
The Cartographer	Dependency graphs, theorem spines, ordering	What must come before what?
The Verifier	Proof obligations, quantifiers, correctness	Is the claim established?
The Adversary	Counterexamples, failure modes, hidden assumptions	Where does this fail?
The Formalist	Lean and machine-checkable translation	What would a proof assistant require?
The Steward	Motivation, audience, cognitive burden	Why should the reader care now?
The Composer	Segmentation, transitions, local completeness	What is the smallest complete unit?
The Grammarian	Notation, prose, symbolic hygiene	Does language carry the mathematics cleanly?
The Amanuensis	Artifact continuity, decisions, terminology, review provenance, integrated versions	Has the reasoning survived its transformation into the authoritative artifact?
The Archivist	Literature provenance, attribution, historical record	What is known, by whom, and what is new?
The Mechanist	Algorithms, implementation, benchmarks	What can this mathematics build?
The Typesetter	Figures, layout, visual structure	Does the artifact reveal structure?
The Referee	Independent specialist scrutiny where required	Would a serious independent reader accept this material claim or control boundary?

Review proportionality

The Council is a responsibility map. Applicability follows the material closure rather than ceremony.

• A routine documentation correction may need Amanuensis/editorial consistency and affected CI only.
• A workflow-control change may need Mechanist, Adversary, and security-sensitive specialist review if it weakens or changes protected enforcement.
• A mathematical certification or source-semantic adjudication may require independent specialist review and the relevant MATHCERT boundary.
• Unrelated movement of protected main does not invalidate an office disposition attached to unchanged material bytes.
• A materially changed theorem, evidence source, security control, authority boundary, or external claim does require renewed scrutiny for that changed object.

No office name may be used to manufacture substantive independence where the same actor produced and certifies the same mathematical claim.

Exposition and Continuity Kernel

The original four-agent writing discipline is extended by the Amanuensis as the continuity office:

• Cartographer: global dependency graph;
• Steward: reader attention and purpose;
• Composer: segmentation and compositional locality;
• Grammarian: sentence-level parsing and symbolic hygiene;
• Amanuensis: preservation of decisions, terminology, provenance, consistency, and the authoritative integrated version.

The Amanuensis does not duplicate the Archivist. The Archivist governs external provenance: literature, attribution, priority, and the historical record. The Amanuensis governs internal continuity: how the programme's own reasoning, decisions, obligations, terminology, and revisions survive across artifacts and versions.

Amanuensis office

For every governed artifact to which continuity control applies, the Amanuensis owns:

1. the artifact-ledger entry and authoritative artifact identity;
2. decision-record references and rejected alternatives where they affect interpretation;
3. the terminology-registry reference and introduced or changed terms;
4. applicable review provenance, including who reviewed which obligation and where the evidence resides;
5. cross-document consistency against materially relevant theorem spines, claim ledgers, Work Packages, schemas, public documentation, navigation, and implementation artifacts;
6. final editorial integration into one authoritative version where required.

The Amanuensis may not mark an artifact ready for its next stage while applicable review provenance is incomplete, cross-document conflicts remain blocking, the public claim boundary contradicts the canonical artifact, or the authoritative integrated version is unidentified.

Public documentation duty

Every canonical domain must have:

• a domain-registry entry;
• a public MkDocs landing page;
• a canonical master-plan reference;
• governance references;
• an explicit claim boundary;
• a current review date.

Public documentation is an orientation layer. It must not become an independent theorem ledger or silently outlive the campaign state it summarizes.

Operating principle

Every substantive mathematical artifact should move through the applicable parts of:

Define -> Map -> Discover -> Test -> Prove -> Attack -> Explain -> Formalize -> Build -> Integrate -> Review

Routine governance and engineering transactions use the shorter protected sequence defined by the streamlined execution amendment:

Classify material closure -> Run affected checks -> Delegated disposition -> Protected merge -> Readback

Worker discovery and collaboration for bounded external or zero-context work are governed by GCL-WORKER-QUEUE-001. The queue is an operational discovery/reservation layer above protected dispatch and lease authority. Blind evidence may transition to teamwork only through an explicit protected disclosure/successor-cohort transition; a blind dispatch is never reclassified in place.

Binding maxim

Define the object. Map the dependency. Discover the possibility. Test the evidence. Prove the claim. Attack the failure. Explain the mathematics. Formalize the boundary. Build the consequence. Preserve the record. Integrate the artifact.