Pith Number

pith:LJ6USOI7

pith:2021:LJ6USOI7LIFXFZ5HLFODNSN57B

not attested not anchored not stored refs pending

From Modular Decomposition Trees to Level-1 Networks: Pseudo-Cographs, Polar-Cats and Prime Polar-Cats

Guillaume E. Scholz, Marc Hellmuth

arxiv:2112.05537 v3 · 2021-12-10 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LJ6USOI7LIFXFZ5HLFODNSN57B}

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	2026-07-05T04:31:58.336984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a7d49391f5a0b72e7a7595c36c9bdf86ce9defd4f623540509f7e69eec29e3c

Aliases

arxiv: 2112.05537 · arxiv_version: 2112.05537v3 · doi: 10.48550/arxiv.2112.05537 · pith_short_12: LJ6USOI7LIFX · pith_short_16: LJ6USOI7LIFXFZ5H · pith_short_8: LJ6USOI7

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/LJ6USOI7LIFXFZ5HLFODNSN57B \
  | 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: 5a7d49391f5a0b72e7a7595c36c9bdf86ce9defd4f623540509f7e69eec29e3c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8eddd90980dfa0ed5d7f1178d4275c2e3e9df9c7a9d5b204959300ef0bee5158",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-12-10T13:41:31Z",
    "title_canon_sha256": "5bc9d0f077ecc199cd142dc27ec74a70e54b77da73673e973cde24b115a526e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.05537",
    "kind": "arxiv",
    "version": 3
  }
}