Pith Number

pith:VY3SUOSR

pith:2000:VY3SUOSRVMNMIKQL5QNGOHGUZ5

not attested not anchored not stored refs pending

A degeneration of stable morphisms and relative stable morphisms

Jun Li

arxiv:math/0009097 v2 · 2000-09-09 · math.AG · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VY3SUOSRVMNMIKQL5QNGOHGUZ5}

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	2026-07-04T14:49:40.496738Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae372a3a51ab1ac42a0bec1a671cd4cf5c048ed2b08edd730a81db06bb60761b

Aliases

arxiv: math/0009097 · arxiv_version: math/0009097v2 · doi: 10.48550/arxiv.math/0009097 · pith_short_12: VY3SUOSRVMNM · pith_short_16: VY3SUOSRVMNMIKQL · pith_short_8: VY3SUOSR

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/VY3SUOSRVMNMIKQL5QNGOHGUZ5 \
  | 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: ae372a3a51ab1ac42a0bec1a671cd4cf5c048ed2b08edd730a81db06bb60761b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c99532ea034dd928447ee0162a3cf4d6fc2c5b1edb2553ad7091a4989c74a696",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2000-09-09T21:14:53Z",
    "title_canon_sha256": "e2e8d0e4b435718146ac24b281521ef43c192cbb7a982342e17c80012b26fdb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0009097",
    "kind": "arxiv",
    "version": 2
  }
}