Pith Number

pith:4NO7GHFH

pith:2011:4NO7GHFHMQDVSWSI2H3J7BFJJX

not attested not anchored not stored refs pending

Factoring threefold divisorial contractions to points

Jungkai Alfred Chen

arxiv:1106.1705 v1 · 2011-06-09 · 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{4NO7GHFHMQDVSWSI2H3J7BFJJX}

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	2026-05-18T04:20:15.293226Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e35df31ca76407595a48d1f69f84a94de757ab82f566c4340372d8f0eef8b5e7

Aliases

arxiv: 1106.1705 · arxiv_version: 1106.1705v1 · doi: 10.48550/arxiv.1106.1705 · pith_short_12: 4NO7GHFHMQDV · pith_short_16: 4NO7GHFHMQDVSWSI · pith_short_8: 4NO7GHFH

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/4NO7GHFHMQDVSWSI2H3J7BFJJX \
  | 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: e35df31ca76407595a48d1f69f84a94de757ab82f566c4340372d8f0eef8b5e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b764fcf132808a55b205ee492916b57658fa4f03ce05f9af5dc28f280ad359af",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-06-09T05:29:04Z",
    "title_canon_sha256": "b7fd5b0f9c6d2485e03fd50341a0d4fb2d2defda66ab1b7145a6d061149cd0df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.1705",
    "kind": "arxiv",
    "version": 1
  }
}