Pith Number

pith:GKKAN76V

pith:2013:GKKAN76VXNOPOHAP52WMXVUU6O

not attested not anchored not stored refs pending

Statistical mechanics of permanents, real-Monge-Ampere equations and optimal transport

Robert J. Berman

arxiv:1302.4045 v1 · 2013-02-17 · math.AP · cond-mat.stat-mech · math-ph · math.DG · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GKKAN76VXNOPOHAP52WMXVUU6O}

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	2026-05-18T03:33:24.495903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

329406ffd5bb5cf71c0feeaccbd694f3aa22bdc8f4084d3ec07b61ed4b015776

Aliases

arxiv: 1302.4045 · arxiv_version: 1302.4045v1 · doi: 10.48550/arxiv.1302.4045 · pith_short_12: GKKAN76VXNOP · pith_short_16: GKKAN76VXNOPOHAP · pith_short_8: GKKAN76V

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/GKKAN76VXNOPOHAP52WMXVUU6O \
  | 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: 329406ffd5bb5cf71c0feeaccbd694f3aa22bdc8f4084d3ec07b61ed4b015776

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c3f9f51de86012108a16715aa3191fe194ffd2536442817924e469787dc28b4",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math-ph",
      "math.DG",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-02-17T09:30:46Z",
    "title_canon_sha256": "5b78f0624a094de8b822a9092f70be11e12a495ec5a67c52916014fb318729f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4045",
    "kind": "arxiv",
    "version": 1
  }
}