Pith Number

pith:PUN6W46I

pith:2015:PUN6W46ID34TSGKZGKTICQDO7E

not attested not anchored not stored refs pending

The structure of graphs with Circular flow number 5 or more, and the complexity of their recognition problem

Giuseppe Mazzuoccolo, Louis Esperet, Michael Tarsi

arxiv:1501.03774 v2 · 2015-01-15 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PUN6W46ID34TSGKZGKTICQDO7E}

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	2026-05-18T01:20:03.762931Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d1beb73c81ef939195932a681406ef91b34bf070b076114c414cf5368e5bd32

Aliases

arxiv: 1501.03774 · arxiv_version: 1501.03774v2 · doi: 10.48550/arxiv.1501.03774 · pith_short_12: PUN6W46ID34T · pith_short_16: PUN6W46ID34TSGKZ · pith_short_8: PUN6W46I

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/PUN6W46ID34TSGKZGKTICQDO7E \
  | 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: 7d1beb73c81ef939195932a681406ef91b34bf070b076114c414cf5368e5bd32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "88ec4e988add739514e2ac6cb215b8b8df29700b4b75343d97891058bf43df31",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-01-15T18:47:55Z",
    "title_canon_sha256": "b14de72f292c9a8197402bbd42b87d5ee9d7b9f30aed9fc28cb1398822369934"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.03774",
    "kind": "arxiv",
    "version": 2
  }
}