Pith Number

pith:72DYT3P5

pith:2009:72DYT3P5ZWFK2TKFVEYSZMLSDK

not attested not anchored not stored refs pending

Wall Crossing and M-theory

Cumrun Vafa, Hirosi Ooguri, Masahito Yamazaki, Mina Aganagic

arxiv:0908.1194 v1 · 2009-08-08 · hep-th · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{72DYT3P5ZWFK2TKFVEYSZMLSDK}

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	2026-05-18T04:18:23.821547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe8789edfdcd8aad4d45a9312cb1721ab8be6e0a8902286092dffff0ffa075f1

Aliases

arxiv: 0908.1194 · arxiv_version: 0908.1194v1 · doi: 10.48550/arxiv.0908.1194 · pith_short_12: 72DYT3P5ZWFK · pith_short_16: 72DYT3P5ZWFK2TKF · pith_short_8: 72DYT3P5

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/72DYT3P5ZWFK2TKFVEYSZMLSDK \
  | 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: fe8789edfdcd8aad4d45a9312cb1721ab8be6e0a8902286092dffff0ffa075f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a61b3af14de2d173e13c0c62ba4ee7055d3927299e83bac6dcb5ebe150b52c45",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2009-08-08T21:32:54Z",
    "title_canon_sha256": "03f50ce3e7a1b1b6bf7c93ba0868b9f3ca9ee886f2ece4447881a8f9812bf017"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.1194",
    "kind": "arxiv",
    "version": 1
  }
}