Archived: the original frontier-math site, kept as it was on 14 October 2026, when the repository became Foundation0. Its data is frozen; see the current method page for the current version.

Method

Back to dashboard.

What “conditional κ” means

Upstream CrocSwap/integer-mult-bounds races an asymptotic integer-multiplication bound of the shape T(n) = O(n (log n)^(1−κ)). Every κ published there is conditional: it holds only given the retained interfaces the construction inherits (all-size compiler, weighted/common-ancestor chart, restored rows, selectors/routing, prime supply, precision/recovery, complex symbolic correctness, analytic transfer). A larger κ is better. It is not an unconditional multiplication-exponent theorem, and this dashboard never presents it as one.

Tiers

• claimed — default. Any open upstream PR whose title/body carries a parseable κ value (exact fraction and/or decimal). Draft PRs stay claimed and render hollow-grey; they are never promoted.
• human-verified — only when a PR’s exact (κ fraction, κ decimal) matches upstream certificates/selected-result.json on main (maintainer-reviewed checkpoint, bound by its certificate_sha256). v1 expects exactly one such point.
• lean-verified — reserved; requires a Lean formalization artifact. No upstream PR has one today, so v1 ships this set empty (schema support only).

Quarantine policy

A record is quarantined (stale: true) when its stated fraction and decimal disagree beyond 15 significant digits, when a κ-looking claim is unparseable, or when its head SHA changed without a successful re-fetch. Quarantined records stay in data/records.json and under feed.json’s quarantined[] (never silently deleted) but are excluded from the chart step-line until re-resolved.

Record key and staleness

One record per (PR × head SHA): any force-push creates a new record; old rows are retained append-only. fetched_at and pr_updated_at drive the age display; the red banner is always-on because the race moves roughly every ten minutes and nothing served here is a live quote.

Pipeline

A 15-minute GitHub Actions cron (.github/workflows/update.yml) runs scripts/fetch.py (upstream REST, conditional ETag requests) then scripts/gate.py: schema validation, byte-determinism re-emit, selected-result binding, and claimed/verified separation. Only if all four pass does the workflow commit the regenerated docs/feed.json and docs/chart-data.json; a failed run changes nothing and the last good state stays live. Parser behaviour is golden-file-gated on PRs #419/#425/#431/#433 (tests/golden_kappa_parse.json, tests/run_golden.py).

Schema reservations (v2, additive)

feed.schema.json already permits project_id, claim_id, machine_checked, ai_refereed_count and feed_version: 2 for the planned multi-project feed (integer-mult-kappa, threesum-derand, mobius-x1). v1 producers emit none of them.