Pith Number

pith:RUMN5SFJ

pith:2011:RUMN5SFJSZ2TM4FVGYGTJ5DJSE

not attested not anchored not stored refs pending

Divisorial algebras and modules on schemes

Caucher Birkar

arxiv:1105.0441 v2 · 2011-05-02 · 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{RUMN5SFJSZ2TM4FVGYGTJ5DJSE}

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	2026-05-18T04:23:02.092742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8d18dec8a996753670b5360d34f4699105a11f412ad3e84014e8ae460d99b0db

Aliases

arxiv: 1105.0441 · arxiv_version: 1105.0441v2 · doi: 10.48550/arxiv.1105.0441 · pith_short_12: RUMN5SFJSZ2T · pith_short_16: RUMN5SFJSZ2TM4FV · pith_short_8: RUMN5SFJ

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/RUMN5SFJSZ2TM4FVGYGTJ5DJSE \
  | 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: 8d18dec8a996753670b5360d34f4699105a11f412ad3e84014e8ae460d99b0db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ddac41f4485f453354c1ec4c08303e73844d1f5027f5dae432250888939a6905",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-05-02T21:22:11Z",
    "title_canon_sha256": "5d584753aee956be2c5a6f99b977c4f040019f3172702a379132ac8bcd564b46"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.0441",
    "kind": "arxiv",
    "version": 2
  }
}