Pith Number

pith:F7YSVGCP

pith:2011:F7YSVGCP33MVL2VRMVRDOGMTOQ

not attested not anchored not stored refs pending

The radius of a subcategory of modules

Hailong Dao, Ryo Takahashi

arxiv:1111.2902 v4 · 2011-11-12 · math.AC · math.CT · 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{F7YSVGCP33MVL2VRMVRDOGMTOQ}

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	2026-05-18T01:22:28.828723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ff12a984fded955eab16562371993741d1918474c0e1849d373391ab84feba5

Aliases

arxiv: 1111.2902 · arxiv_version: 1111.2902v4 · doi: 10.48550/arxiv.1111.2902 · pith_short_12: F7YSVGCP33MV · pith_short_16: F7YSVGCP33MVL2VR · pith_short_8: F7YSVGCP

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/F7YSVGCP33MVL2VRMVRDOGMTOQ \
  | 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: 2ff12a984fded955eab16562371993741d1918474c0e1849d373391ab84feba5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c6a92e5bdc796d1592a9f0d3a03f1a21f954f0e34a7c32a2219c823d4549ff4",
    "cross_cats_sorted": [
      "math.CT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-11-12T05:11:35Z",
    "title_canon_sha256": "e8a209c255e98c0a17a5a5a840c8b27daf580bc219f9d61a8af2c51d00c4fb2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2902",
    "kind": "arxiv",
    "version": 4
  }
}