Pith Number

pith:SODZP3WS

pith:2012:SODZP3WSFKKDYB4OZRJKV5A55B

not attested not anchored not stored refs pending

Gradings, smash products and Galois coverings of a small category

Claude Cibils, John MacQuarrie

arxiv:1203.5905 v1 · 2012-03-27 · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SODZP3WSFKKDYB4OZRJKV5A55B}

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	2026-05-18T03:59:13.106241Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

938797eed22a943c078ecc52aaf41de84d4a7b0c61417d53251f5cd58b8ef75f

Aliases

arxiv: 1203.5905 · arxiv_version: 1203.5905v1 · doi: 10.48550/arxiv.1203.5905 · pith_short_12: SODZP3WSFKKD · pith_short_16: SODZP3WSFKKDYB4O · pith_short_8: SODZP3WS

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/SODZP3WSFKKDYB4OZRJKV5A55B \
  | 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: 938797eed22a943c078ecc52aaf41de84d4a7b0c61417d53251f5cd58b8ef75f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "59dd0d585046af49eb4b45fbaca4c05b988ec0e67649e1164f098b6259178679",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2012-03-27T09:28:29Z",
    "title_canon_sha256": "ea7b4030cf37ca4fcd16bb08b690f30eb404dc600686734ee87a6938f4912f61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.5905",
    "kind": "arxiv",
    "version": 1
  }
}