Pith Number

pith:KQFLPI3P

pith:2000:KQFLPI3PMS4NHZZORQGYBGPGTB

not attested not anchored not stored refs pending

Painlev\'e equations and deformations of rational surfaces with rational double points

Hiroshi Umemura, Masa-Hiko Saito

arxiv:math/0007156 v1 · 2000-07-26 · 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{KQFLPI3PMS4NHZZORQGYBGPGTB}

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	2026-05-18T00:32:26.402085Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

540ab7a36f64b8d3e72e8c0d8099e69867df0df959e7c23c7bdf3e06cc8f421f

Aliases

arxiv: math/0007156 · arxiv_version: math/0007156v1 · doi: 10.48550/arxiv.math/0007156 · pith_short_12: KQFLPI3PMS4N · pith_short_16: KQFLPI3PMS4NHZZO · pith_short_8: KQFLPI3P

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/KQFLPI3PMS4NHZZORQGYBGPGTB \
  | 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: 540ab7a36f64b8d3e72e8c0d8099e69867df0df959e7c23c7bdf3e06cc8f421f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "949ab58b692d08629aa5075003df30c813fb65bf2118af4d9f448d3664f59143",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2000-07-26T12:34:42Z",
    "title_canon_sha256": "3b03591a1f523dabdf2dfd341ed7968b926738ca4e2592350fa591d537835583"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0007156",
    "kind": "arxiv",
    "version": 1
  }
}