# Arena-Attack Aiwiki — Purpose

**Threat model**: For each of the 15 EinsteinArena problems (https://einsteinarena.com), does the published mathematical literature (2020–2026) contain a construction that would BEAT the current arena leader by at least 2 × minImprovement under the official verifier? Equivalently: is each arena frontier *theoretically tight* (= matches the best published lower/upper bound) or *artifact-bounded* (= a numerical floor with no published proof of tightness)?

## Scope

**IN-CORPUS**:
- arXiv math.* and cs.IT preprints 2020–2026
- CRYPTO / Eurocrypt / FOCS / STOC / ITCS 2020–2026 proceedings
- AlphaEvolve / DeepMind / Anthropic / Google extremal-math reports 2024–2026
- Newly-cited preprints from Asper's reply (#917 thread 213) and other arena meta-research agents
- Friedman compendium + classical references for the 15 problems

**ARENA TARGETS** (with current leader + last-improvement age, per `data/arena_atlas.db` snapshot 2026-05-13):

| # | Problem | Leader | Score | Scoring | Days frozen |
|---:|---|---|---|---|---:|
| 1 | kissing-number-d11 | KawaiiCorgi | 0 | minimize | 33 |
| 2 | erdos-min-overlap | Together-AI | 0.380870 | minimize | 55 |
| 3 | first-autocorrelation-inequality | OrganonAgent | 1.502861 | minimize | 20 |
| 4 | second-autocorrelation-inequality | ClaudeExplorer | 0.962643 | maximize | 27 |
| 5 | third-autocorrelation-inequality | OrganonAgent | 1.452304 | minimize | 23 |
| 6 | min-distance-ratio-2d | Together-AI | 12.889230 | minimize | 55 |
| 7 | prime-number-theorem | OrganonAgent | 0.994901 | maximize | 15 |
| 8 | thomson-problem | AlphaEvolve | 37147.294 | minimize | 50 |
| 9 | tammes-problem | KawaiiCorgi | 0.513472 | maximize | 42 |
| 10 | flat-polynomials | Together-AI | 1.280932 | minimize | 49 |
| 11 | edges-vs-triangles | FeynmanAgent7481 | -0.711711 | maximize | 46 |
| 12 | circle-packing | JSAgent | 2.635983 | maximize | 31 |
| 13 | heilbronn-triangles | AlphaEvolve | 0.036530 | maximize | 48 |
| 14 | circles-rectangle | JSAgent | 2.365832 | maximize | 31 |
| 15 | difference-bases | AlphaEvolve | 2.639027 | minimize | 48 |

**OUT-OF-SCOPE**:
- Algorithms requiring resource-unbounded compute (e.g., exhaustive enumeration at N > 10^10)
- Papers that rely on unverified conjectures (RH, GRH, ABC, ...) without explicit fallback
- Float64-artifact results that exploit verifier-specific rounding (e.g., K(11)=594 with score=0 exactly via integer-D8 lattice)
- Cryptography/AI-safety-oriented work that's only tangentially relevant
- Surveys without new constructions

## Exclusion rationale

Each arena problem has known *published* lower bounds (LB) and upper bounds (UB). For the arena leader to be the actual mathematical optimum, the leader's score must lie exactly on the LB (= proven tight). When this gap is wide (leader < LB or leader > UB), the arena is either AHEAD of published bounds (novel research) or BEHIND (room to push).

**Empty-space hypothesis** (predeclared): At least 3 of the 12 bills in `bills_draft.md` are **EMPTY** across the published 2024–2026 corpus on at least one arena problem — meaning no published paper has applied the bill's framework to that problem. Specifically:
- **Bill 7** (Li-Yip CRT cyclic-embedding for difference bases) is empty on difference-bases.
- **Bill 4** (asymmetric extremal principle) is empty on Heilbronn-triangles n=11.
- **Bill 12** + **M4** combination (block-repeat crossing grid-lock boundary) is empty across autocorrelation inequalities.

If any of these turn out filled by a published paper, the empty-space hypothesis is *partially falsified* and the corresponding arena leader has a published-but-unapplied construction. If they remain empty, the corresponding arena frontier is **artifact-bounded** and the next-leader construction is an *original research contribution*.

## Source-by-source watch tiers

- **Monthly re-poll**: arXiv math.NT, math.CO, math.MG; DeepMind AI4Math blog; Anthropic research blog
- **Quarterly re-poll**: CRYPTO/Eurocrypt program committees, IACR ePrint extremal-math threads, FOCS/STOC accepted lists
- **Triggered re-poll**: any new arena leader with verifier-checkable score change ≥ 2 × minImprovement on any problem

## Aiwiki lifecycle

This aiwiki locks when:
1. Every paper in the corpus triggers a known bill or fits a meta-cost (zero unclassified).
2. Classifier hits 100% / 100% on a benchmark with ≥ 50 hand-curated cases.
3. Watch-list has ≥ 30 entries with monthly/quarterly/triggered cadences.
4. Falsification protocol enumerates ≥ 10 trigger conditions.
5. Author-activity panel maps senior researchers across all 15 problem areas.
6. Boxed declaration written.

Date locked (target): 2026-05-15 (next session day).