Pith Number

pith:B5WBP4UY

pith:2026:B5WBP4UYF7KIS62KV2753SFNXA

not attested not anchored not stored refs pending

The chromatic number of 3-stable Kneser graphs

Alex Parker, Shira Zerbib, Wei-Chia Chen

arxiv:2607.12912 v1 · 2026-07-14 · 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{B5WBP4UYF7KIS62KV2753SFNXA}

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	2026-07-15T01:22:24.805231Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f6c17f2982fd4897b4aaebfddc8adb82dc379d9a0a178afeffaccd189923b77

Aliases

arxiv: 2607.12912 · arxiv_version: 2607.12912v1 · doi: 10.48550/arxiv.2607.12912 · pith_short_12: B5WBP4UYF7KI · pith_short_16: B5WBP4UYF7KIS62K · pith_short_8: B5WBP4UY

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/B5WBP4UYF7KIS62KV2753SFNXA \
  | 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: 0f6c17f2982fd4897b4aaebfddc8adb82dc379d9a0a178afeffaccd189923b77

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8eafd82afdc63a5e357191035ec97afd3c7294b7f44067e75e051ba38d5e94bd",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-14T15:48:41Z",
    "title_canon_sha256": "6cb5daec473aa11656bac7bb72bbde62cf98844f3e38f2d1a4e4c94026660b2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12912",
    "kind": "arxiv",
    "version": 1
  }
}