Pith Number

pith:HAUHP4LB

pith:2013:HAUHP4LBWXFCPDVDEU3BFDSMZF

not attested not anchored not stored refs pending

The four-in-a-tree problem in triangle-free graphs

Christophe Picouleau, Nicolas Derhy, Nicolas Trotignon

arxiv:1309.0978 v1 · 2013-09-04 · cs.DM · 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{HAUHP4LBWXFCPDVDEU3BFDSMZF}

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	2026-05-18T03:14:09.440715Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

382877f161b5ca278ea32536128e4cc942814443945b36a4288d71264bb6172d

Aliases

arxiv: 1309.0978 · arxiv_version: 1309.0978v1 · doi: 10.48550/arxiv.1309.0978 · pith_short_12: HAUHP4LBWXFC · pith_short_16: HAUHP4LBWXFCPDVD · pith_short_8: HAUHP4LB

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/HAUHP4LBWXFCPDVDEU3BFDSMZF \
  | 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: 382877f161b5ca278ea32536128e4cc942814443945b36a4288d71264bb6172d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e21880ddb089d4eea74651b362620293a5f7fb6ecc1603e98d91004c1b51f12a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2013-09-04T11:10:27Z",
    "title_canon_sha256": "12eb0592ec587de72192944c4ab6d415d3a672274e7c72f1bba91486a6425208"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.0978",
    "kind": "arxiv",
    "version": 1
  }
}