Pith Number

pith:NI4CALLZ

pith:2025:NI4CALLZIRNCODZLC3SXA3S3Z3

not attested not anchored not stored refs pending

Strong odd colorings in graph classes of bounded expansion

Micha{\l} Pilipczuk

arxiv:2505.15288 v1 · 2025-05-21 · 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{NI4CALLZIRNCODZLC3SXA3S3Z3}

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	2026-07-05T11:06:43.310367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a38202d79445a270f2b16e5706e5bcedc681eb9bab4daeed4100da664568e04

Aliases

arxiv: 2505.15288 · arxiv_version: 2505.15288v1 · doi: 10.48550/arxiv.2505.15288 · pith_short_12: NI4CALLZIRNC · pith_short_16: NI4CALLZIRNCODZL · pith_short_8: NI4CALLZ

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/NI4CALLZIRNCODZLC3SXA3S3Z3 \
  | 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: 6a38202d79445a270f2b16e5706e5bcedc681eb9bab4daeed4100da664568e04

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "740d6e60324b1f8f3267f6c6e7882aa640a36cddb96ce119839a19a4683bf1af",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-05-21T09:17:10Z",
    "title_canon_sha256": "3cd1085f5f7db04d881b3f2d5b323883e0fbc86940b22950414580c126a1b42e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.15288",
    "kind": "arxiv",
    "version": 1
  }
}