Pith Number

pith:5KNPELFC

pith:2000:5KNPELFC4JMGOSAJNAXT2JOKMT

not attested not anchored not stored refs pending

Vanishing cycles and mutation

Paul Seidel

arxiv:math/0007115 v3 · 2000-07-19 · math.SG · 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{5KNPELFC4JMGOSAJNAXT2JOKMT}

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	2026-07-04T14:34:36.524019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea9af22ca2e258674809682f3d25ca64d5b288ebd0055e1f0d36a6a37806b146

Aliases

arxiv: math/0007115 · arxiv_version: math/0007115v3 · doi: 10.48550/arxiv.math/0007115 · pith_short_12: 5KNPELFC4JMG · pith_short_16: 5KNPELFC4JMGOSAJ · pith_short_8: 5KNPELFC

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/5KNPELFC4JMGOSAJNAXT2JOKMT \
  | 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: ea9af22ca2e258674809682f3d25ca64d5b288ebd0055e1f0d36a6a37806b146

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab6ef685bc5d33d3f9cc167e8d0af2e7efdab7302c33eed3306a653e195a18b0",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.SG",
    "submitted_at": "2000-07-19T16:51:38Z",
    "title_canon_sha256": "937863d7dcab95c18f1d8088b1d3923bd72e3dbfa58260145646bf644f94d502"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0007115",
    "kind": "arxiv",
    "version": 3
  }
}