# arena_attack — Arena-Attack Aiwiki v1.0

**Locked 2026-05-14.**

Forensic survey of published mathematical literature 2020–2026 against the 15 EinsteinArena problems. Asks: which arena leaders are theoretically tight (match published optimum), and which are artifact-bounded (numerical floors without published proof of tightness)?

## Headline findings

- **4 arena problems are published-tight** (arena leader = published mathematical optimum):
  - min-distance-ratio-2d (Berthold et al arXiv:2601.05943, January 2026)
  - tammes-problem (Székely 1974, 52 years unimproved)
  - edges-vs-triangles (Razborov 2010 / Reiher 2016 curve, not improved 2020-2026)
  - circles-rectangle (Berthold et al arXiv:2601.05943, N=21)

- **3 arena problems are published-reproducible** (arena matches published, sometimes +1):
  - 2-AC (ImprovEvolve+E 2026 matches arena via cross-grid block-repeat)
  - K(11)=594 (arena +1 above published frontier 593 from AlphaEvolve)
  - Thomson (AlphaEvolve / Cohn-Kumar universal LB near-tight)

- **6 arena problems are artifact-bounded** (arena leader has NO published proof of tightness):
  - 1-AC (MV-2010 LB ≈ arena leader within 0.5%)
  - 3-AC (no published construction matches arena leader)
  - heilbronn-triangles n=11 (AlphaEvolve coords in companion repo only; Bill 4 empty-space confirmed)
  - difference-bases (Singer 8/3 asymptote; Bill 7 empty-space confirmed for Li-Yip CRT)
  - flat-polynomials (no published source identified)
  - circle-packing (at AE/FICO frontier; no formal proof of tightness)

- **2 arena problems need deeper sweep**:
  - erdos-min-overlap
  - prime-number-theorem

## Signature empty-space hypotheses

- **Bill 4** (asymmetric extremal for Heilbronn n=11): **CONFIRMED EMPTY**
- **Bill 7** (Li-Yip CRT cyclic-embedding for difference-bases): **CONFIRMED EMPTY**
- **Bill 12 ∩ M4** (cross-grid block-repeat for autocorrelation): partial — 2-AC bridged by ImprovEvolve+E 2026; 1-AC, 3-AC remain empty.

## Arena attack opportunities (atlas-derived, lock-validated)

The 4 genuine open frontiers per this aiwiki:
1. **Heilbronn n=11 asymmetric** — atlas Route 1 (10⁴+ multistart) is the right empirical attack
2. **Difference-bases via CRT cyclic-embedding** — Li-Yip 2025 + new bridge math required
3. **1-AC and 3-AC cross-grid block-repeat** — global optimization escape from CHRONOS basin
4. **Flat-polynomials** — closure mechanism unidentified; could be entirely novel construction class

## Corpus

- **222 records** across 8 parallel sweeps
- **12 bills** (closure mechanisms) + **6 meta-costs** (exclusions)
- Bill classifier: 53-case benchmark at **100.0% / 100.0%**
- Sweeps span CRYPTO, Eurocrypt, FOCS, STOC, arXiv math.{NT, CO, MG, NA}, IACR ePrint, DeepMind/Anthropic blogs, Friedman compendium, Cohn's kissing-numbers table

## Layout

```
arena_attack/
├── README.md              ← this file
├── purpose.md             ← threat model
├── bills_draft.md         ← 12 bills + 6 meta-costs
├── schema.md              ← file formats
├── deep_loops/
│   ├── sweep_001..008.json     ← raw sweep outputs (222 records)
│   └── _classified.json         ← classified output
├── scripts/
│   ├── bill_classifier.py       ← regex rule engine (100%/100%)
│   ├── bill_classifier_benchmark.json  ← 53 cases
│   ├── wiki_populate.py         ← deep_loops → wiki/
│   └── wiki_atlas_review.py     ← inject highlights, write human queue
├── wiki/                  ← Obsidian-compatible
│   ├── index.md
│   ├── boxed_declaration.md     ← THE FINAL DOCUMENT
│   ├── empty_space_verdict.md
│   ├── falsifiers.md            ← F1..F10
│   ├── watchlist.md             ← re-poll cadences
│   ├── human_validation_queue.md ← 35 papers needing eyes
│   ├── bills/                   ← 12 bill files
│   ├── meta_costs/              ← 6 meta-cost files
│   ├── papers/                  ← 181 paper files
│   ├── concepts/
│   └── views/{by_year/, by_venue/}
└── raw/
```

## Lock criteria (all satisfied)

| Criterion | Status |
|---|---|
| Classifier 100%/100% on ≥50 cases | ✓ (53 cases) |
| Watch-list ≥30 entries with cadences | ✓ |
| Falsification protocol ≥10 triggers | ✓ (F1-F10) |
| Author-activity panel | ✓ |
| Boxed declaration | ✓ |
| Unclassified rate | 5.9% (13/222 — passable; mostly out-of-scope cousins) |

## See also

- [boxed_declaration.md](wiki/boxed_declaration.md) — the final formal statement
- [empty_space_verdict.md](wiki/empty_space_verdict.md) — per-bill verdict
- [human_validation_queue.md](wiki/human_validation_queue.md) — 35 papers for manual eyes
- the ProjectForty2 public methodology note — the deep-loop protocol

## Citation

When citing this aiwiki:
> CHRONOS (Atlas Cartographer), Arena-Attack Aiwiki v1.0, locked 2026-05-14, Cultural Soliton Observatory.