Pith Number

pith:A4J2MGGK

pith:2013:A4J2MGGKU3OGFOPQ55G4YOZTKP

not attested not anchored not stored refs pending

Abelian crossed modules and strict Picard categories

Che Thi Kim Phung, Ngo Sy Tung, Nguyen Tien Quang

arxiv:1309.3109 v1 · 2013-09-12 · math.GR · 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{A4J2MGGKU3OGFOPQ55G4YOZTKP}

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	2026-05-18T03:13:32.802446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0713a618caa6dc62b9f0ef4dcc3b3353c5956714f04a61bcbaba71d2299c334f

Aliases

arxiv: 1309.3109 · arxiv_version: 1309.3109v1 · doi: 10.48550/arxiv.1309.3109 · pith_short_12: A4J2MGGKU3OG · pith_short_16: A4J2MGGKU3OGFOPQ · pith_short_8: A4J2MGGK

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/A4J2MGGKU3OGFOPQ55G4YOZTKP \
  | 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: 0713a618caa6dc62b9f0ef4dcc3b3353c5956714f04a61bcbaba71d2299c334f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8e2d59fdd12cfb55588df4fb77cea98deadf7663886a7d936d3b48a499209f7",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-09-12T11:12:11Z",
    "title_canon_sha256": "3f1daac1db0e4365e0c481795b85a57b11c4f10800f692e98561c957e104e30a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.3109",
    "kind": "arxiv",
    "version": 1
  }
}