Pith Number

pith:2Y3JXFMY

pith:2026:2Y3JXFMYXCA3AKYLRX6E6IDFNX

not attested not anchored not stored refs pending

Vertex-critical co-gem-free graphs

Manoj Belavadi, T. Karthick

arxiv:2606.11757 v1 · 2026-06-10 · 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{2Y3JXFMYXCA3AKYLRX6E6IDFNX}

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	2026-06-11T01:10:06.389536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6369b9598b881b02b0b8dfc4f20656dcf85328755d021686eb595fd35c187ef

Aliases

arxiv: 2606.11757 · arxiv_version: 2606.11757v1 · doi: 10.48550/arxiv.2606.11757 · pith_short_12: 2Y3JXFMYXCA3 · pith_short_16: 2Y3JXFMYXCA3AKYL · pith_short_8: 2Y3JXFMY

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/2Y3JXFMYXCA3AKYLRX6E6IDFNX \
  | 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: d6369b9598b881b02b0b8dfc4f20656dcf85328755d021686eb595fd35c187ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6a01a08e05160878ca07eaafcaca72dc3dac588cf481c4a723eabd8ec4b86a49",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-10T07:31:54Z",
    "title_canon_sha256": "f6b86243db185c5c6cdfa9af0343cf97550432a5d3c70bbb38d8cc2be49ad0f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.11757",
    "kind": "arxiv",
    "version": 1
  }
}