Pith Number

pith:RGI3Z72S

pith:2026:RGI3Z72SET6VK7MZCJ42WU7L6V

not attested not anchored not stored refs pending

A spectral threshold for triangle counting

Mingqing Zhai, Yuhan Zhang

arxiv:2606.08163 v1 · 2026-06-06 · 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{RGI3Z72SET6VK7MZCJ42WU7L6V}

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	2026-06-09T01:05:28.667001Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8991bcff5224fd557d991279ab53ebf577ee46e993f5fca256ff92d78ab7f86b

Aliases

arxiv: 2606.08163 · arxiv_version: 2606.08163v1 · doi: 10.48550/arxiv.2606.08163 · pith_short_12: RGI3Z72SET6V · pith_short_16: RGI3Z72SET6VK7MZ · pith_short_8: RGI3Z72S

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/RGI3Z72SET6VK7MZCJ42WU7L6V \
  | 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: 8991bcff5224fd557d991279ab53ebf577ee46e993f5fca256ff92d78ab7f86b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c74c90939e4cfb6a73e89758709cd60045e436b2b396bc4e06a5429728cfd8c3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-06T13:25:58Z",
    "title_canon_sha256": "4eacd46a10d36ed44a8b3216449d368c59f3188a27d8e35986b4dc18f38e5ff0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08163",
    "kind": "arxiv",
    "version": 1
  }
}