Methodology & status taxonomy

kerrproblems.com is edited as a curated research problem database. The old single “status” chip is split into orthogonal axes so “open” is not overloaded with “speculative,” “quantitative,” or “unverified import.”

Theorem status

Open

No theorem matching the stated conclusion is known to editors under the listed hypotheses.

Partial progress

Nontrivial proved subcases or restricted regimes exist; the page should list them under “What is already known.”

Conditional

The conclusion depends on an explicit extra hypothesis bridge (e.g. spectral-to-interior). The condition must appear in status_explanation.

Solved

Reserved for entries where known_results contains a statement that matches a cited theorem in the references. Do not use without that match.

Needs review

Bibliography or scope is not yet literature-anchored in-repo; may have empty references by policy.

Research state

Orthogonal to theorem status (what this site marks as proved, partial, or open on the page): where the target sits relative to published mathematics.

• Solved in literature (classical) — a classical theorem is understood to exist; this site still requires a solution_pointer and curated references before using theorem_status: solved.
• Open in literature — standard research question with identifiable paper trail (once references are attached).
• High-value / unformalized direction — synthesized targets, formalization-first packaging, or community-artifact roadmaps; the page should say so plainly in status_explanation or origin_type.

Problem type

• Classical frontier — community-scale conjectures or standard research targets.
• Literature reformulation — packaging or bridging statements built from published threads.
• Quantitative sharpening — effective constants, stability gaps, or remainders once a qualitative theorem exists.
• Formalization target — especially suitable for staged formal verification.
• Speculative direction — exploratory; should be rare and clearly scoped.

Maturity, evidence, verification

• Maturity — how complete the scoping block is (well_scoped / mostly_scoped / provisional).
• Evidence level — whether primary literature pointers are attached (primary_refs_present, secondary_refs_only, refs_missing).
• Verification state — editorial pipeline (verified_recently, imported_unverified, editorial_revision_needed).

Publication vs provisional

publish: false omits an entry from the main index, clusters, and RSS. YAML may still live under data/problems_provisional/ as a maintainer bucket (expansion batch); those rows can use publish: true so they appear on the index before files are moved into problems/. Provisional pipeline lists everything still in that directory.

A live public page needs theorem status, problem type, a filled scope block, at least two references with a primary pointer (unless theorem_status: needs_review under the editorial exception), and no placeholder language in public fields.

Reference policy (summary)

Public entries that are not needs_review should carry at least two references, including at least one primary pointer, and each reference needs a short relevance note. Do not ship TODO/FIXME language on public fields. Full maintainer text lives in the repository under docs/EDITORIAL_POLICY.md and docs/PROBLEM_SCHEMA.md.

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