Pith Number

pith:XZEURTQP

pith:2026:XZEURTQPYKBIUEAI52XB47BC3J

not attested not anchored not stored refs pending

A Comprehensive Study of Clique Graphs and Clique Regular Graphs

Connor Phillips

arxiv:2605.22867 v1 · 2026-05-19 · 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{XZEURTQPYKBIUEAI52XB47BC3J}

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	2026-05-25T02:01:27.735945Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be4948ce0fc2828a1008eeae1e7c22da42938d85d94964c03cb843703813745f

Aliases

arxiv: 2605.22867 · arxiv_version: 2605.22867v1 · doi: 10.48550/arxiv.2605.22867 · pith_short_12: XZEURTQPYKBI · pith_short_16: XZEURTQPYKBIUEAI · pith_short_8: XZEURTQP

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/XZEURTQPYKBIUEAI52XB47BC3J \
  | 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: be4948ce0fc2828a1008eeae1e7c22da42938d85d94964c03cb843703813745f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "937113c465e845dc431714f232b0aff87e9459a4567e710453d6dd30bb448cea",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-19T20:49:26Z",
    "title_canon_sha256": "8fe197e00e7703c954fc9efbc444e6f69e0681736111858c855a1771ca4ca65e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.22867",
    "kind": "arxiv",
    "version": 1
  }
}