Pith Number

pith:LPL7ASNE

pith:2025:LPL7ASNEHEM2RI7V3TRZYUJWAE

not attested not anchored not stored refs pending

Robustness of the Sauer-Spencer Theorem

Julia B\"ottcher, Mihir Neve, Peter Allen, Yoshiharu Kohayakawa

arxiv:2507.03676 v1 · 2025-07-04 · 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{LPL7ASNEHEM2RI7V3TRZYUJWAE}

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	2026-07-05T11:32:03.524233Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bd7f049a43919a8a3f5dce39c51360116a369bdb2eb3d2050fc7f4ee56960a9

Aliases

arxiv: 2507.03676 · arxiv_version: 2507.03676v1 · doi: 10.48550/arxiv.2507.03676 · pith_short_12: LPL7ASNEHEM2 · pith_short_16: LPL7ASNEHEM2RI7V · pith_short_8: LPL7ASNE

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/LPL7ASNEHEM2RI7V3TRZYUJWAE \
  | 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: 5bd7f049a43919a8a3f5dce39c51360116a369bdb2eb3d2050fc7f4ee56960a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8013cc63f399d3201c9902d8540491c5cb72134bd4eb79729a90f1967ec79f7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-04T15:51:52Z",
    "title_canon_sha256": "861c253b45925d63c142145df11cee1056fb103f39e033a35e9c0612ec44c3cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.03676",
    "kind": "arxiv",
    "version": 1
  }
}