Pith Number

pith:SDWA23UQ

pith:2003:SDWA23UQXULLQZICO7L73EALVV

not attested not anchored not stored refs pending

Birational morphisms of the plane

Jie-Tai Yu, Vladimir Shpilrain

arxiv:math/0309125 v1 · 2003-09-07 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SDWA23UQXULLQZICO7L73EALVV}

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	2026-05-18T01:05:28.649041Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90ec0d6e90bd16b8650277d7fd900bad5b9ff43a8f92b83acebbc20bc9c8c96f

Aliases

arxiv: math/0309125 · arxiv_version: math/0309125v1 · doi: 10.48550/arxiv.math/0309125 · pith_short_12: SDWA23UQXULL · pith_short_16: SDWA23UQXULLQZIC · pith_short_8: SDWA23UQ

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/SDWA23UQXULLQZICO7L73EALVV \
  | 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: 90ec0d6e90bd16b8650277d7fd900bad5b9ff43a8f92b83acebbc20bc9c8c96f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5086ef072d86645f92fc44b123a54aa9f3b6b0278f9640b0e1ee9d92c078c424",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2003-09-07T01:04:46Z",
    "title_canon_sha256": "736878c69a8fb74b90082f3c3c04c4e7ee2b69f7c83a09157c9f04dff7a19333"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0309125",
    "kind": "arxiv",
    "version": 1
  }
}