Pith Number

pith:2N57KES6

pith:2006:2N57KES62XVRIS4PJLEMY4RQYY

not attested not anchored not stored refs pending

Decompositions of the free product of graphs

Luigi Accardi, Rafal Salapata, Romuald Lenczewski

arxiv:math/0609329 v1 · 2006-09-12 · math.CO · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2N57KES62XVRIS4PJLEMY4RQYY}

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	2026-05-18T02:46:38.120392Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d37bf5125ed5eb144b8f4ac8cc7230c628223fea4e89a6897ba2ca11606dde6f

Aliases

arxiv: math/0609329 · arxiv_version: math/0609329v1 · doi: 10.48550/arxiv.math/0609329 · pith_short_12: 2N57KES62XVR · pith_short_16: 2N57KES62XVRIS4P · pith_short_8: 2N57KES6

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/2N57KES62XVRIS4PJLEMY4RQYY \
  | 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: d37bf5125ed5eb144b8f4ac8cc7230c628223fea4e89a6897ba2ca11606dde6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbeb27538f760fdfed104e9717255b7addeb25801b403f5f73548b308ecebc9d",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2006-09-12T16:49:06Z",
    "title_canon_sha256": "576a1733b1abdfea31a8767a124bed2a20b099efa0fe9b99b8e4307a68155a8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609329",
    "kind": "arxiv",
    "version": 1
  }
}