Pith Number

pith:L3C4K7DK

pith:2011:L3C4K7DKBVOZ2YAHGAFFUN6AKF

not attested not anchored not stored refs pending

On dynamic monopolies of graphs with general thresholds

Manouchehr Zaker

arxiv:1103.1112 v1 · 2011-03-06 · math.CO · cs.DM

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{L3C4K7DKBVOZ2YAHGAFFUN6AKF}

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	2026-05-18T04:27:17.099512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ec5c57c6a0d5d9d6007300a5a37c05160a8bf40db390e98e321bfc24b696a7c

Aliases

arxiv: 1103.1112 · arxiv_version: 1103.1112v1 · doi: 10.48550/arxiv.1103.1112 · pith_short_12: L3C4K7DKBVOZ · pith_short_16: L3C4K7DKBVOZ2YAH · pith_short_8: L3C4K7DK

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/L3C4K7DKBVOZ2YAHGAFFUN6AKF \
  | 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: 5ec5c57c6a0d5d9d6007300a5a37c05160a8bf40db390e98e321bfc24b696a7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31bb00e1170ffae028a4a9b65df71c4fc847339a9ac34b4c0fae8fe4c7ad7c46",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-03-06T10:20:44Z",
    "title_canon_sha256": "cd76ec93cf5784ff7efe40f4ef0b62d4c6f9ec43bf707602e8edf3b7831f7d91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.1112",
    "kind": "arxiv",
    "version": 1
  }
}