Pith Number

pith:AN6CPAGS

pith:2010:AN6CPAGSE7MPJASQMKQGBIMZHA

not attested not anchored not stored refs pending

Bounds on the Rubbling and Optimal Rubbling Numbers of Graphs

Gyula Y. Katona, Nandor Sieben

arxiv:1009.5162 v1 · 2010-09-27 · 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{AN6CPAGSE7MPJASQMKQGBIMZHA}

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	2026-05-18T04:40:19.086423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

037c2780d227d8f4825062a060a1993813b427d24dd8938c99295ca484813177

Aliases

arxiv: 1009.5162 · arxiv_version: 1009.5162v1 · doi: 10.48550/arxiv.1009.5162 · pith_short_12: AN6CPAGSE7MP · pith_short_16: AN6CPAGSE7MPJASQ · pith_short_8: AN6CPAGS

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/AN6CPAGSE7MPJASQMKQGBIMZHA \
  | 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: 037c2780d227d8f4825062a060a1993813b427d24dd8938c99295ca484813177

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43c3a868f86c7d35925d4d8739e09a5165854b3a144a124b3017e82232fd24ed",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-09-27T05:36:01Z",
    "title_canon_sha256": "51fe835416eb13636af47756ae255282f4bcda328e2505d224fc6af83bb923d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5162",
    "kind": "arxiv",
    "version": 1
  }
}