Pith Number

pith:ZGJ5JOXU

pith:2026:ZGJ5JOXUALU7NQONELOAIJZDVX

not attested not anchored not stored refs pending

Odd covers for complete graphs and complete 3-graphs

Jiabao Yang, Ting Huang, Yaojun Chen

arxiv:2607.07448 v1 · 2026-07-08 · 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{ZGJ5JOXUALU7NQONELOAIJZDVX}

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	2026-07-09T01:20:25.189990Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c993d4baf402e9f6c1cd22dc042723adc6fb5ddd936ed8dba824da7d7f252e3a

Aliases

arxiv: 2607.07448 · arxiv_version: 2607.07448v1 · doi: 10.48550/arxiv.2607.07448 · pith_short_12: ZGJ5JOXUALU7 · pith_short_16: ZGJ5JOXUALU7NQON · pith_short_8: ZGJ5JOXU

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/ZGJ5JOXUALU7NQONELOAIJZDVX \
  | 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: c993d4baf402e9f6c1cd22dc042723adc6fb5ddd936ed8dba824da7d7f252e3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f09356d91961e86b523412a4cbba6ad507c7041a5792c8c6c6145f399aebd64",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-08T14:18:36Z",
    "title_canon_sha256": "14bb475d98e18d0430a781487841010e9c08a6796cbbebefd8befd43fbc34c73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.07448",
    "kind": "arxiv",
    "version": 1
  }
}