Pith Number

pith:VWKBI3GL

pith:2011:VWKBI3GL2PE42ZSTBXJCBX7H6Y

not attested not anchored not stored refs pending

Castelnuovo-Mumford regularity and the discreteness of $F$-jumping coefficients in graded rings

Mordechai Katzman, Wenliang Zhang

arxiv:1110.2093 v3 · 2011-10-10 · 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{VWKBI3GL2PE42ZSTBXJCBX7H6Y}

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	2026-05-18T03:51:14.363926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad94146ccbd3c9cd66530dd220dfe7f63b9bab9e0714ea6daa5a8872a21e5752

Aliases

arxiv: 1110.2093 · arxiv_version: 1110.2093v3 · doi: 10.48550/arxiv.1110.2093 · pith_short_12: VWKBI3GL2PE4 · pith_short_16: VWKBI3GL2PE42ZST · pith_short_8: VWKBI3GL

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/VWKBI3GL2PE42ZSTBXJCBX7H6Y \
  | 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: ad94146ccbd3c9cd66530dd220dfe7f63b9bab9e0714ea6daa5a8872a21e5752

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f62b651b35cb8e798f65a8a8830e95b784e940c16562b67c63268101875197b1",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-10-10T16:15:22Z",
    "title_canon_sha256": "2b980a94f5b5c59e505f4659a66a7d7d9bc27fb1b4de3790c3b7efbbde72c5dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.2093",
    "kind": "arxiv",
    "version": 3
  }
}