Pith Number

pith:Y4IQUEBT

pith:2010:Y4IQUEBTZGODF3LGHPTRWH3UWH

not attested not anchored not stored refs pending

Stable degenerations of Cohen-Macaulay modules

Yuji Yoshino

arxiv:1012.4531 v1 · 2010-12-21 · math.AC · math.RT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y4IQUEBTZGODF3LGHPTRWH3UWH}

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	2026-05-18T04:32:54.166033Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7110a1033c99c32ed663be71b1f74b1f0afc481eb59c0637717ef652c0aaf89

Aliases

arxiv: 1012.4531 · arxiv_version: 1012.4531v1 · doi: 10.48550/arxiv.1012.4531 · pith_short_12: Y4IQUEBTZGOD · pith_short_16: Y4IQUEBTZGODF3LG · pith_short_8: Y4IQUEBT

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/Y4IQUEBTZGODF3LGHPTRWH3UWH \
  | 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: c7110a1033c99c32ed663be71b1f74b1f0afc481eb59c0637717ef652c0aaf89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "16b8f1ac2220769be0895f6afd9f8e3b1529e91820d5bfb8c540daaea6de4e70",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-12-21T02:04:41Z",
    "title_canon_sha256": "4be8ff2dc2fcde1d5672fd3fe5ceace1481eeacaebcbbe445785c62e281a113e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4531",
    "kind": "arxiv",
    "version": 1
  }
}