Pith Number

pith:BWDVCKKU

pith:2025:BWDVCKKU6HNS4HOALDDSJCMFSK

not attested not anchored not stored refs pending

Density of rainbow triangles and properly colored $K_4$'s

Bernard Lidick\'y, J\'ozsef Balogh, Peter Bradshaw, Ramon I. Garcia

arxiv:2511.21061 v3 · 2025-11-26 · 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{BWDVCKKU6HNS4HOALDDSJCMFSK}

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	2026-06-23T02:13:18.963130Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d87512954f1db2e1dc058c724898592b973c05de3bf8c1c2a5d8b4de3f82f42

Aliases

arxiv: 2511.21061 · arxiv_version: 2511.21061v3 · doi: 10.48550/arxiv.2511.21061 · pith_short_12: BWDVCKKU6HNS · pith_short_16: BWDVCKKU6HNS4HOA · pith_short_8: BWDVCKKU

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/BWDVCKKU6HNS4HOALDDSJCMFSK \
  | 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: 0d87512954f1db2e1dc058c724898592b973c05de3bf8c1c2a5d8b4de3f82f42

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd978422a4937bb59212c1c54c2f2e57c9ea2f22c4517f181a6c660a91f8a186",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-11-26T05:00:45Z",
    "title_canon_sha256": "a842f256ed6e1c35ac8808402b46a535f7ea87cc3f6b8025b5efe6da598ac7de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.21061",
    "kind": "arxiv",
    "version": 3
  }
}