Pith Number

pith:ZOCG5IZX

pith:2000:ZOCG5IZXATKACUNVU4XXFZY2CL

not attested not anchored not stored refs pending

A Little Microlocal Morse Theory

David B. Massey

arxiv:math/0006185 v2 · 2000-06-24 · 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{ZOCG5IZXATKACUNVU4XXFZY2CL}

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.

Cited by

1 paper in Pith

Using Large Language Models to Study Mathematical Practice

Receipt and verification

First computed	2026-07-04T14:34:34.810285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb846ea33704d40151b5a72f72e71a12d38b949d0dc92934919eb686e3adbff9

Aliases

arxiv: math/0006185 · arxiv_version: math/0006185v2 · doi: 10.48550/arxiv.math/0006185 · pith_short_12: ZOCG5IZXATKA · pith_short_16: ZOCG5IZXATKACUNV · pith_short_8: ZOCG5IZX

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/ZOCG5IZXATKACUNVU4XXFZY2CL \
  | 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: cb846ea33704d40151b5a72f72e71a12d38b949d0dc92934919eb686e3adbff9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d2302032740390b700abc40f3312314cf2640bf9423190f7064d0131bd6cf7d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2000-06-24T18:35:34Z",
    "title_canon_sha256": "52508bb5dde7efdb4ec489b519c3d5639dce8403f7414d01bfe31ba1bf3c11ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0006185",
    "kind": "arxiv",
    "version": 2
  }
}