Pith Number

pith:7MCCC3SI

pith:2010:7MCCC3SIMNNLECTMG6VRCBGNO7

not attested not anchored not stored refs pending

A Strong Abhyankar-Moh Theorem and Criterion of Embedded Line

Yansong Xu

arxiv:1012.3064 v2 · 2010-12-14 · 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{7MCCC3SIMNNLECTMG6VRCBGNO7}

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	2026-05-18T02:58:58.130368Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb04216e48635ab20a6c37ab1104cd77ede2ec32644f3c9ccdc5c0e8ee01f6e8

Aliases

arxiv: 1012.3064 · arxiv_version: 1012.3064v2 · doi: 10.48550/arxiv.1012.3064 · pith_short_12: 7MCCC3SIMNNL · pith_short_16: 7MCCC3SIMNNLECTM · pith_short_8: 7MCCC3SI

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/7MCCC3SIMNNLECTMG6VRCBGNO7 \
  | 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: fb04216e48635ab20a6c37ab1104cd77ede2ec32644f3c9ccdc5c0e8ee01f6e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1fd6571fa9f2c74a2a7d47665aa442c07628669ec59826f8df33688f2bda36cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-12-14T15:53:58Z",
    "title_canon_sha256": "d1e44e556ee0602a5ea86cda4eab28276948972e7ca01897f9752888259b41e3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3064",
    "kind": "arxiv",
    "version": 2
  }
}