Pith Number

pith:IBGS64MT

pith:2019:IBGS64MT2R4ACFGD3OS5YWBAH3

not attested not anchored not stored refs pending

A proof that square ice entropy is $\frac{3}{2} \log_2 (4/3)$

Silv\`ere Gangloff

arxiv:1902.09274 v5 · 2019-02-25 · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IBGS64MT2R4ACFGD3OS5YWBAH3}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-05-17T23:49:27.086253Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

404d2f7193d4780114c3dba5dc58203ef9a55b528a9122811906e221e0668704

Aliases

arxiv: 1902.09274 · arxiv_version: 1902.09274v5 · doi: 10.48550/arxiv.1902.09274 · pith_short_12: IBGS64MT2R4A · pith_short_16: IBGS64MT2R4ACFGD · pith_short_8: IBGS64MT

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/IBGS64MT2R4ACFGD3OS5YWBAH3 \
  | 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: 404d2f7193d4780114c3dba5dc58203ef9a55b528a9122811906e221e0668704

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a46390497cb2aba7fc5b69f348632f299948e80f402cc87e6d6fc3ff7e47ffd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2019-02-25T14:10:36Z",
    "title_canon_sha256": "6db5218e8222caed8773d84d9fb954af549c65ae7cada87f1ece2fc60efccc91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.09274",
    "kind": "arxiv",
    "version": 5
  }
}