Pith Number

pith:HZIIE45F

pith:2012:HZIIE45FYWQEIDMU4JDVLHYK3X

not attested not anchored not stored refs pending

Frobenius categories, Gorenstein algebras and rational surface singularities

Dong Yang, Martin Kalck, Michael Wemyss, Osamu Iyama

arxiv:1209.4215 v3 · 2012-09-19 · math.RT · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HZIIE45FYWQEIDMU4JDVLHYK3X}

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	2026-05-17T23:53:36.063292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e508273a5c5a0440d94e247559f0addc5607cb05c42501c9a47d15bd044fbc9

Aliases

arxiv: 1209.4215 · arxiv_version: 1209.4215v3 · doi: 10.48550/arxiv.1209.4215 · pith_short_12: HZIIE45FYWQE · pith_short_16: HZIIE45FYWQEIDMU · pith_short_8: HZIIE45F

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/HZIIE45FYWQEIDMU4JDVLHYK3X \
  | 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: 3e508273a5c5a0440d94e247559f0addc5607cb05c42501c9a47d15bd044fbc9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5182c3903f767e69c39cc3a6f11681cb89535f28d4ff181019236ae2f2dd4aee",
    "cross_cats_sorted": [
      "math.AC",
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RT",
    "submitted_at": "2012-09-19T11:56:11Z",
    "title_canon_sha256": "226763886a56ff741336d526e51213fdcdc3402a815af564ffd629d5bd142814"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4215",
    "kind": "arxiv",
    "version": 3
  }
}