Pith Number

pith:5LQ63BH5

pith:2026:5LQ63BH5KTR4CECH6UNJAXF5YV

not attested not anchored not stored refs pending

Coloring sparse random Cayley graphs

Nathan Tung

arxiv:2606.23762 v1 · 2026-06-22 · 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{5LQ63BH5KTR4CECH6UNJAXF5YV}

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.

Cited by

2 papers in Pith

Linear equations and chromatic thresholds in $B_h$ sets

Receipt and verification

First computed	2026-06-24T00:14:25.319744Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eae1ed84fd54e3c11047f51a905cbdc56fc061c55e32ed690d46aac47cb05d9f

Aliases

arxiv: 2606.23762 · arxiv_version: 2606.23762v1 · doi: 10.48550/arxiv.2606.23762 · pith_short_12: 5LQ63BH5KTR4 · pith_short_16: 5LQ63BH5KTR4CECH · pith_short_8: 5LQ63BH5

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/5LQ63BH5KTR4CECH6UNJAXF5YV \
  | 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: eae1ed84fd54e3c11047f51a905cbdc56fc061c55e32ed690d46aac47cb05d9f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f298ea577fd14546b63adbf5bd60efcf342a4ef4aabb5eab9279a3fdc1a3efbe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-22T13:46:32Z",
    "title_canon_sha256": "f56ec0157174a712f1fdcc80a59648ab1ae1653af147805ce4e2addde13418c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23762",
    "kind": "arxiv",
    "version": 1
  }
}