Pith Number

pith:YOWAXHAF

pith:2013:YOWAXHAFWRGCTKWIGOHY45HSQH

not attested not anchored not stored refs pending

Results on independent sets in categorical products of graphs, the ultimate categorical independence ratio and the ultimate categorical independent domination ratio

Hsiang-Hsuan Liu, Sheung-Hung Poon, Ton Kloks, Wing-Kai Hon, Yue-Li Wang

arxiv:1306.1656 v1 · 2013-06-07 · cs.DM · 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{YOWAXHAFWRGCTKWIGOHY45HSQH}

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	2026-05-18T03:21:32.774181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3ac0b9c05b44c29aac8338f8e74f281e145e4a5bb0ceaae3f803df5eeddcd5b

Aliases

arxiv: 1306.1656 · arxiv_version: 1306.1656v1 · doi: 10.48550/arxiv.1306.1656 · pith_short_12: YOWAXHAFWRGC · pith_short_16: YOWAXHAFWRGCTKWI · pith_short_8: YOWAXHAF

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/YOWAXHAFWRGCTKWIGOHY45HSQH \
  | 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: c3ac0b9c05b44c29aac8338f8e74f281e145e4a5bb0ceaae3f803df5eeddcd5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca55d69ba0b05c810efb365e588fcf6b4d287e2f21cc2d6fa3db0f9a7ada3e7f",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2013-06-07T08:59:26Z",
    "title_canon_sha256": "dce1abe508667e57c41958276635b945dcc9b7a5e66aa98460a5513111abfc1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1656",
    "kind": "arxiv",
    "version": 1
  }
}