Pith Number

pith:YZD2HQF3

pith:2026:YZD2HQF3G2SQALARCEYFRUXKJQ

not attested not anchored not stored refs pending

On clique-to-clique densities

Jie Ma, Tianhen Wang, Tianming Zhu

arxiv:2606.31967 v1 · 2026-06-30 · 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{YZD2HQF3G2SQALARCEYFRUXKJQ}

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

1 paper in Pith

An edge-spectral supersaturation of Mubayi's theorem for color-critical graphs

Receipt and verification

First computed	2026-07-01T01:18:27.223860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c647a3c0bb36a5002c11113058d2ea4c25012e34d3d3eff461551db721678a27

Aliases

arxiv: 2606.31967 · arxiv_version: 2606.31967v1 · doi: 10.48550/arxiv.2606.31967 · pith_short_12: YZD2HQF3G2SQ · pith_short_16: YZD2HQF3G2SQALAR · pith_short_8: YZD2HQF3

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/YZD2HQF3G2SQALARCEYFRUXKJQ \
  | 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: c647a3c0bb36a5002c11113058d2ea4c25012e34d3d3eff461551db721678a27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46a334a5da40fb9bab8febadaeef5985cd5dc99ff250514bb45e7b4229c2fb9b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-30T17:10:55Z",
    "title_canon_sha256": "8e4dd8cfde7b11a3977dd4ea68042670364e26f7c1cc44a92b89b28b1f7773ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.31967",
    "kind": "arxiv",
    "version": 1
  }
}