Pith Number

pith:BCQ45VEG

pith:2017:BCQ45VEGQQFWWCYKZP2LMPE6UN

not attested not anchored not stored refs pending

Ulrich modules over Cohen-Macaulay local rings with minimal multiplicity

Ryo Takahashi, Toshinori Kobayashi

arxiv:1711.00652 v1 · 2017-11-02 · 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{BCQ45VEGQQFWWCYKZP2LMPE6UN}

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	2026-05-18T00:31:29.891828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08a1ced486840b6b0b0acbf4b63c9ea36a97158b2130d26cd50a886de0b0ec13

Aliases

arxiv: 1711.00652 · arxiv_version: 1711.00652v1 · doi: 10.48550/arxiv.1711.00652 · pith_short_12: BCQ45VEGQQFW · pith_short_16: BCQ45VEGQQFWWCYK · pith_short_8: BCQ45VEG

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/BCQ45VEGQQFWWCYKZP2LMPE6UN \
  | 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: 08a1ced486840b6b0b0acbf4b63c9ea36a97158b2130d26cd50a886de0b0ec13

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "700964d61d0196072bd7693d859688117f2130c50899ba905f009584b51284b3",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2017-11-02T08:56:02Z",
    "title_canon_sha256": "19b89fe8cea015c07ddead5d192a35b168b6afa05cbab30f3d37d4c620022dd9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.00652",
    "kind": "arxiv",
    "version": 1
  }
}