Pith Number

pith:K3IACMS3

pith:2021:K3IACMS3KQAKHEWLRYHUUN7D77

not attested not anchored not stored refs pending

The ratio of the numbers of odd and even cycles in outerplanar graphs

Akihiro Higashitani, Naoki Matsumoto

arxiv:2105.02361 v1 · 2021-05-05 · 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{K3IACMS3KQAKHEWLRYHUUN7D77}

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	2026-07-05T02:38:00.539283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56d001325b5400a392cb8e0f4a37e3ffc4f6b7ea9cec9b96c4f207320ab8663d

Aliases

arxiv: 2105.02361 · arxiv_version: 2105.02361v1 · doi: 10.48550/arxiv.2105.02361 · pith_short_12: K3IACMS3KQAK · pith_short_16: K3IACMS3KQAKHEWL · pith_short_8: K3IACMS3

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/K3IACMS3KQAKHEWLRYHUUN7D77 \
  | 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: 56d001325b5400a392cb8e0f4a37e3ffc4f6b7ea9cec9b96c4f207320ab8663d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c4ef4ec5a3546b95982f40f894681b959fd73aa99f794e9bc85c7d6027846b4",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-05-05T22:44:50Z",
    "title_canon_sha256": "86ef408fafc6017ff75ed07a36aafc5657802a40ec96640197c03e43c3e7b06c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.02361",
    "kind": "arxiv",
    "version": 1
  }
}