Pith Number

pith:YFUNT3DR

pith:2012:YFUNT3DR7E2DTDQTWNEHN7Z77H

not attested not anchored not stored refs pending

Restricted volumes of effective divisors

Gianluca Pacienza, Lorenzo Di Biagio

arxiv:1207.1204 v1 · 2012-07-05 · 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{YFUNT3DR7E2DTDQTWNEHN7Z77H}

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	2026-05-18T03:51:46.629867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c168d9ec71f934398e13b34876ff3ff9cb8bb7b76ac6333c417981d8c834ab5e

Aliases

arxiv: 1207.1204 · arxiv_version: 1207.1204v1 · doi: 10.48550/arxiv.1207.1204 · pith_short_12: YFUNT3DR7E2D · pith_short_16: YFUNT3DR7E2DTDQT · pith_short_8: YFUNT3DR

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/YFUNT3DR7E2DTDQTWNEHN7Z77H \
  | 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: c168d9ec71f934398e13b34876ff3ff9cb8bb7b76ac6333c417981d8c834ab5e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "adb5af773eacfff4d66405be43fff6f076be437dce0fc5d473651a565d358f5f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-07-05T09:36:19Z",
    "title_canon_sha256": "b85bd040303f4fdfab24d75e3f2e02445c6f65aceda6a97164839c9d7fbd55ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.1204",
    "kind": "arxiv",
    "version": 1
  }
}