Pith Number

pith:56NQHZ6I

pith:1999:56NQHZ6IK3ZKSHTUVY5KKSENXR

not attested not anchored not stored refs pending

Vanishing cycles and Hermitian duality

Claude Sabbah

arxiv:math/9910156 v1 · 1999-10-28 · math.AG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{56NQHZ6IK3ZKSHTUVY5KKSENXR}

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	2026-05-18T04:32:09.843780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef9b03e7c856f2a91e74ae3aa5488dbc763fe064df66e25527db41389fedb1a0

Aliases

arxiv: math/9910156 · arxiv_version: math/9910156v1 · doi: 10.48550/arxiv.math/9910156 · pith_short_12: 56NQHZ6IK3ZK · pith_short_16: 56NQHZ6IK3ZKSHTU · pith_short_8: 56NQHZ6I

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/56NQHZ6IK3ZKSHTUVY5KKSENXR \
  | 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: ef9b03e7c856f2a91e74ae3aa5488dbc763fe064df66e25527db41389fedb1a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4859efa6b150869e48c70289384019b4619910d4415e38169eb6e0258def7e12",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "1999-10-28T10:05:31Z",
    "title_canon_sha256": "700f59b0b0dc791f99957187d11121eb7495632ecdd21076c22e4776dd433abb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9910156",
    "kind": "arxiv",
    "version": 1
  }
}