Pith Number

pith:YA2IZMXL

pith:2012:YA2IZMXLWUYPZUGXS2RJVJNNPX

not attested not anchored not stored refs pending

On dynamic monopolies of graphs: the average and strict majority thresholds

Hossein Soltani, Kaveh Khoshkhah, Manouchehr Zaker

arxiv:1202.1146 v1 · 2012-02-06 · 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{YA2IZMXLWUYPZUGXS2RJVJNNPX}

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	2026-05-18T04:02:55.016257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c0348cb2ebb530fcd0d796a29aa5ad7dc39847ea314e6def60fa7dff9f54f883

Aliases

arxiv: 1202.1146 · arxiv_version: 1202.1146v1 · doi: 10.48550/arxiv.1202.1146 · pith_short_12: YA2IZMXLWUYP · pith_short_16: YA2IZMXLWUYPZUGX · pith_short_8: YA2IZMXL

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/YA2IZMXLWUYPZUGXS2RJVJNNPX \
  | 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: c0348cb2ebb530fcd0d796a29aa5ad7dc39847ea314e6def60fa7dff9f54f883

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5415736b2901717f8ac4f8e76bd2debbf5cc36219b1822611b3d18ef2072e9d5",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-02-06T14:17:57Z",
    "title_canon_sha256": "59c3b51dccc7736238d5d5db55393f1018bef8f4ce1d161df544b68beadff841"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.1146",
    "kind": "arxiv",
    "version": 1
  }
}