Pith Number

pith:5AEEJNDV

pith:2026:5AEEJNDV2MAASSONNODOUQPTW5

not attested not anchored not stored refs pending

Structural Results for 4 x n Chomp: Unique Extension, Bimodal Asymptotic Structure, and Period-112 Geometry

Arnav Garg

P-positions in 4 by n Chomp exhibit unique fourth-row extensions, converging ratios, period-112 structure, and linear cone geometry.

arxiv:2604.25952 v2 · 2026-04-24 · math.GM

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\usepackage{pith}
\pithnumber{5AEEJNDV2MAASSONNODOUQPTW5}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The analysis reveals four structural conjectures: (1) a Unique Extension property, stating that for any triple (a,b,c) of row lengths, there is at most one valid fourth-row length d completing a P-position; (2) convergence of row-length ratios to fixed asymptotic constants; (3) a period-112 modular structure governing the set of extendable triples; and (4) a linear cone geometry for the P-position set in (a,b,c)-space.

C2weakest assumption

That the four observed patterns in P-positions computed for n ≤ 500 will continue to hold for all larger n without exception or deviation.

C3one line summary

Large-scale computation of P-positions in 4xn Chomp yields conjectures on unique row-length extension, asymptotic ratio convergence, period-112 modularity, and linear cone geometry.

Cited by

1 paper in Pith

Unique Winning Opening Move in Three-Row Chomp

Receipt and verification

First computed	2026-05-22T02:04:41.360117Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e80844b475d3000949cd6b86ea41f3b777cd429ac063c47c01ceb823ab379068

Aliases

arxiv: 2604.25952 · arxiv_version: 2604.25952v2 · doi: 10.48550/arxiv.2604.25952 · pith_short_12: 5AEEJNDV2MAA · pith_short_16: 5AEEJNDV2MAASSON · pith_short_8: 5AEEJNDV

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5AEEJNDV2MAASSONNODOUQPTW5 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e80844b475d3000949cd6b86ea41f3b777cd429ac063c47c01ceb823ab379068

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a71be7afec30f4e1dbe200af9b4f6bf8d942bf471eac12085bb28ce338a24a2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GM",
    "submitted_at": "2026-04-24T14:43:31Z",
    "title_canon_sha256": "e6a9096e5b80e3c7d33ff9d0c2052fad4cc6e9ab6ada7af4e147975ca2ee2970"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25952",
    "kind": "arxiv",
    "version": 2
  }
}