Pith Number

pith:FFE5H2C4

pith:2015:FFE5H2C4C4MGT65CBYFSXF5ZKO

not attested not anchored not stored refs pending

Castelnuovo-Mumford regularity and Ratliff-Rush closure

Maria Evelina Rossi, Ngo Viet Trung, Trung Thanh Dinh

arxiv:1512.04372 v3 · 2015-12-14 · math.AC · 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{FFE5H2C4C4MGT65CBYFSXF5ZKO}

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	2026-05-18T00:24:31.930709Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2949d3e85c171869fba20e0b2b97b953a236a5b6bbe7116ac754ac4509172699

Aliases

arxiv: 1512.04372 · arxiv_version: 1512.04372v3 · doi: 10.48550/arxiv.1512.04372 · pith_short_12: FFE5H2C4C4MG · pith_short_16: FFE5H2C4C4MGT65C · pith_short_8: FFE5H2C4

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/FFE5H2C4C4MGT65CBYFSXF5ZKO \
  | 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: 2949d3e85c171869fba20e0b2b97b953a236a5b6bbe7116ac754ac4509172699

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e95f372fc6dd17c60c96a214e4a3473e528b149d9ea257dbbb52760a09b70b7",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-12-14T15:47:00Z",
    "title_canon_sha256": "98beb0f28ae7ef34cdc3cc7d3994f36434ad23108ba03cbd7914203e5d7abed1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04372",
    "kind": "arxiv",
    "version": 3
  }
}