Pith Number

pith:4JCFJF5Q

pith:2026:4JCFJF5QWB3L7OM7BOVSKJJDSS

not attested not anchored not stored refs pending

Decomposing tournaments into comparability graphs

Benjamin Moore, Hidde Koerts, Hugo Jacob, Julien Duron, Logan Crew, Pierre Aboulker, R\'emy Kimbrough, Sophie Spirkl, St\'ephan Thomass\'e, Xinyue Fan

arxiv:2606.07748 v1 · 2026-06-05 · 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{4JCFJF5QWB3L7OM7BOVSKJJDSS}

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	2026-06-09T01:04:51.026350Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2445497b0b076bfb99f0bab25252394bc96a533c337b5231d94f4d02d41da21

Aliases

arxiv: 2606.07748 · arxiv_version: 2606.07748v1 · doi: 10.48550/arxiv.2606.07748 · pith_short_12: 4JCFJF5QWB3L · pith_short_16: 4JCFJF5QWB3L7OM7 · pith_short_8: 4JCFJF5Q

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/4JCFJF5QWB3L7OM7BOVSKJJDSS \
  | 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: e2445497b0b076bfb99f0bab25252394bc96a533c337b5231d94f4d02d41da21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa3901caa6b492b5e303b86f63dd14c3114c205ed8e3a15da275cf3f807de20f",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-05T18:00:36Z",
    "title_canon_sha256": "ef4dd08584f7d84fe34d04cb73e5f729f7a1be297e1eb78f2f98983d3386ebc5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.07748",
    "kind": "arxiv",
    "version": 1
  }
}