Pith Number

pith:4JMUE3TD

pith:2015:4JMUE3TD3QJ3IL35DKHEFERNX7

not attested not anchored not stored refs pending

Planar digraphs without large acyclic sets

Kolja Knauer, Paul S. Wenger, Petru Valicov

arxiv:1504.06726 v2 · 2015-04-25 · 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{4JMUE3TD3QJ3IL35DKHEFERNX7}

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	2026-05-18T01:12:30.849294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e259426e63dc13b42f7d1a8e42922dbff2dead53ec254665a26c92e72f1d6104

Aliases

arxiv: 1504.06726 · arxiv_version: 1504.06726v2 · doi: 10.48550/arxiv.1504.06726 · pith_short_12: 4JMUE3TD3QJ3 · pith_short_16: 4JMUE3TD3QJ3IL35 · pith_short_8: 4JMUE3TD

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/4JMUE3TD3QJ3IL35DKHEFERNX7 \
  | 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: e259426e63dc13b42f7d1a8e42922dbff2dead53ec254665a26c92e72f1d6104

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4df9e68f3042ee51e4800f3b2d92a095f63d4c7667c1319893205f7a0f318221",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-04-25T13:40:13Z",
    "title_canon_sha256": "f405533372831230c8ec2db444cc4be6cc104e0a856bcaa1aab941afd1b61336"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.06726",
    "kind": "arxiv",
    "version": 2
  }
}