Pith Number

pith:44LH6L7Q

pith:2026:44LH6L7QQGKLMGPPEBYIUNRPWS

not attested not anchored not stored refs pending

Proof of the Finiteness of the Chromatic Number of Two-Dimensional Lacunary Distance Graphs

Nabh Singh

arxiv:2606.22539 v1 · 2026-06-21 · 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{44LH6L7QQGKLMGPPEBYIUNRPWS}

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	2026-06-23T02:13:41.059987Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7167f2ff08194b619ef20708a362fb49fd1140245c848e21661aa29dbbd22b5

Aliases

arxiv: 2606.22539 · arxiv_version: 2606.22539v1 · doi: 10.48550/arxiv.2606.22539 · pith_short_12: 44LH6L7QQGKL · pith_short_16: 44LH6L7QQGKLMGPP · pith_short_8: 44LH6L7Q

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/44LH6L7QQGKLMGPPEBYIUNRPWS \
  | 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: e7167f2ff08194b619ef20708a362fb49fd1140245c848e21661aa29dbbd22b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e72bc28dc648901d56e3b8737462372f79a122796fb778bb67c1ac658455e87",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-21T14:54:03Z",
    "title_canon_sha256": "68a3820ba59ff6f9414ce06893c7a36b6f7628c6652b9327f7f2574f1e88fed5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.22539",
    "kind": "arxiv",
    "version": 1
  }
}