MISSION — `wide_search`

Persona

A breadth-first search for one externally checkable mathematical contribution adjacent to the Riemann zeta function, run under the laboratory's standing controls. The operator's instruction was explicit: generate approaches in volume, allocate independent programmes, kill aggressively, search prior art, reproduce survivors independently, attempt formalization where feasible, and call nothing new without passing a novelty gate. A negative result is an acceptable outcome. A rediscovery is an acceptable outcome, provided it is labelled as one.

Scope

This hunt may write: hunts/wide_search/ and, if the run earns one, a single new docs/NN-*.md taken from the next free number, plus figures/.

This hunt may not write: zeta/, ontology/, harness/, lean/ without explicit permission, and may not write a verdict into README.md, ROADMAP.md or HANDOFF.md as an established finding. It may not promote its own claim. The routes that can say "yes" are the battery (docs/doors/refute.md) and the funnel (docs/doors/discover.md), and neither of them is this hunt.

Objective

Not RH. RH is allowed but deliberately not privileged, and every direct route to it carries a standing no-go result (docs/08). The target is adjacent: a precise statement about zeta or its neighbours — an identity, an inequality, a counterexample, an asymptotic, a bound, a negative result, or a machine-checked formalization — that is

1. precisely stateable, so it is either true or false;
2. externally checkable, so that somebody outside this tree can settle it without trusting this tree; and
3. not already in the literature, established by an operator-level search, because the offline knownness gate structurally cannot say that anything is new (ontology/knownness.py: Knownness has exactly two values, and establishes_novelty is hard-coded False).

Method

Breadth first, then adversarial narrowing. The generator of a claim never judges it — the rule the director run was built on.

1. Generate. Independent programmes across disjoint territories, each emitting candidate propositions in a fixed schema, each candidate carrying its own refutation condition and an honest prior-art risk.
2. Triage. A referee that did not generate the candidates kills against the standing walls (docs/08), the in-tree graveyard, and the rule that raw computational reach is a non-goal.
3. Prior art. A networked search on survivors. This is the step the offline gate refuses to fake.
4. Attempt. Compute. Most survivors are expected to die here.
5. Reproduce. Anything still standing is rebuilt by a replicator given the statement only and forbidden the first implementation, because a cross-check bounds only what is actually duplicated.
6. Formalize where the statement is small enough to be worth a kernel.

The standing checklist, answered in advance

1. Rival. Any structural claim about zeta goes through zeta.epstein.battery — zeta against Davenport–Heilbronn and both discriminant −23 Epstein forms. A claim a rival also satisfies distinguishes nothing. The trap is recorded: if the test set is the rival set, the measurement is of this laboratory's own admission criterion.
2. Decoy / surrogate. Any claimed effect is run against a matched null with no arithmetic in it. Davenport–Heilbronn sits at the 27th percentile of the random non-factoring null, so "it is unusual" has a denominator here.
3. Lesion. Any detector is shown a violation planted on purpose, and must distinguish the plant from the claimed signal.
4. Precision response. An artifact does not respond to added precision; a real quantity does. Every numerical survivor is re-run at strictly higher working precision before it is written down.

What would make this hunt a failure worth recording

Finding nothing is the expected outcome and is not a failure. The failure modes that would matter are: a claim recorded without its prior-art search; a numerical effect written down without a precision response; a structural claim written down without the battery; or a survivor whose generator also judged it. Each of those is a defect in this hunt, not a weak result.

Vocabulary

This directory says measured, observed, consistent with. It does not say verified, confirmed, definitively or proves, and it never uses the reserved word that zeta/rigor.py owns for enclosure-carrying quantities — a ban tests/test_hunt_probe_discipline.py enforces on the bytes of every file here.