Pith Number

pith:VGS2IIP7

pith:2010:VGS2IIP7GT2UHMLPVUWPLFALUI

not attested not anchored not stored refs pending

Examples of degenerations of Cohen-Macaulay modules

Naoya Hiramatsu, Yuji Yoshino

arxiv:1012.5346 v1 · 2010-12-24 · math.AC · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VGS2IIP7GT2UHMLPVUWPLFALUI}

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	2026-05-18T04:32:35.059679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9a5a421ff34f543b16fad2cf5940ba21f41088fe62a1d329cac1f70bc0313c3

Aliases

arxiv: 1012.5346 · arxiv_version: 1012.5346v1 · doi: 10.48550/arxiv.1012.5346 · pith_short_12: VGS2IIP7GT2U · pith_short_16: VGS2IIP7GT2UHMLP · pith_short_8: VGS2IIP7

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/VGS2IIP7GT2UHMLPVUWPLFALUI \
  | 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: a9a5a421ff34f543b16fad2cf5940ba21f41088fe62a1d329cac1f70bc0313c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d957bef6fd15f0828e998bdfd8b37e279792a0b3866c8fd02cae476e14caa53c",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-12-24T06:52:25Z",
    "title_canon_sha256": "a39ab49c76bf6e15131d30a1e9286784355242e500df08f97a78b7f1674c9692"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5346",
    "kind": "arxiv",
    "version": 1
  }
}