Pith Number

pith:AF56K3TS

pith:2012:AF56K3TSCL3O2ITN2DKA5N2DHK

not attested not anchored not stored refs pending

$p^\ell$-Torsion Points In Finite Abelian Groups And Combinatorial Identities

Christophe Delaunay (LM-Besan\c{c}on), Fr\'ed\'eric Jouhet (ICJ)

arxiv:1208.6397 v2 · 2012-08-31 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AF56K3TSCL3O2ITN2DKA5N2DHK}

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	2026-05-18T03:29:27.252362Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

017be56e7212f6ed226dd0d40eb7433a9113b13876c83aa741b30f78cbb45f2c

Aliases

arxiv: 1208.6397 · arxiv_version: 1208.6397v2 · doi: 10.48550/arxiv.1208.6397 · pith_short_12: AF56K3TSCL3O · pith_short_16: AF56K3TSCL3O2ITN · pith_short_8: AF56K3TS

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/AF56K3TSCL3O2ITN2DKA5N2DHK \
  | 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: 017be56e7212f6ed226dd0d40eb7433a9113b13876c83aa741b30f78cbb45f2c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37642ac117196a3093279cf9e390c9b7241ab7b82ebef5d12db4e459fa4713f1",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-08-31T06:41:06Z",
    "title_canon_sha256": "f2607c9f76cfd79bfcb66438444b55cb95b2085198b8ae0a4f8a78c37d1d4ec8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.6397",
    "kind": "arxiv",
    "version": 2
  }
}