Pith Number

pith:XHTBLKKU

pith:2002:XHTBLKKUMKPY4NWNGJJUEM4OXW

not attested not anchored not stored refs pending

Crossing Probabilities and Modular Forms

Don Zagier, Peter Kleban

arxiv:math-ph/0209023 v2 · 2002-09-12 · math-ph · cond-mat.dis-nn · cond-mat.stat-mech · hep-th · math.MP · math.NT · 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{XHTBLKKUMKPY4NWNGJJUEM4OXW}

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	2026-05-18T01:05:31.925080Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9e615a954629f8e36cd325342338ebdb74014a9b15a9801b3ecf184ff31fbc7

Aliases

arxiv: math-ph/0209023 · arxiv_version: math-ph/0209023v2 · doi: 10.48550/arxiv.math-ph/0209023 · pith_short_12: XHTBLKKUMKPY · pith_short_16: XHTBLKKUMKPY4NWN · pith_short_8: XHTBLKKU

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/XHTBLKKUMKPY4NWNGJJUEM4OXW \
  | 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: b9e615a954629f8e36cd325342338ebdb74014a9b15a9801b3ecf184ff31fbc7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef7b2fc51f0aa7665cab367a9d66623a14a5de3f4754d4900e6a2089ff01db76",
    "cross_cats_sorted": [
      "cond-mat.dis-nn",
      "cond-mat.stat-mech",
      "hep-th",
      "math.MP",
      "math.NT",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2002-09-12T20:36:20Z",
    "title_canon_sha256": "a273019f335a225daea30fde99e7f784f2ad1efc4ef2c38c90b878366e5f9cc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0209023",
    "kind": "arxiv",
    "version": 2
  }
}