Pith Number

pith:ZNKZPUWE

pith:2013:ZNKZPUWEJHN6D6SURHPZI2X74O

not attested not anchored not stored refs pending

Degenerations of graded Cohen-Macaulay modules

Naoya Hiramatsu

arxiv:1302.1643 v1 · 2013-02-07 · 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{ZNKZPUWEJHN6D6SURHPZI2X74O}

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	2026-05-18T03:34:15.192350Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb5597d2c449dbe1fa5489df946affe38dcc9c2406bf26c8933aaca62cde6473

Aliases

arxiv: 1302.1643 · arxiv_version: 1302.1643v1 · doi: 10.48550/arxiv.1302.1643 · pith_short_12: ZNKZPUWEJHN6 · pith_short_16: ZNKZPUWEJHN6D6SU · pith_short_8: ZNKZPUWE

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/ZNKZPUWEJHN6D6SURHPZI2X74O \
  | 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: cb5597d2c449dbe1fa5489df946affe38dcc9c2406bf26c8933aaca62cde6473

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdfdbc94a67b926d7b2f8de15c5802fccfc63254d9385c9faa944bf19e6f0feb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-02-07T05:11:13Z",
    "title_canon_sha256": "c0f37e2602afb3c8d98ec2368107c8dfd1b29b590d97f953de4aa64676710279"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.1643",
    "kind": "arxiv",
    "version": 1
  }
}