Pith Number

pith:3TK5FI7T

pith:2012:3TK5FI7TWZDATV7DT5RDI6DNZH

not attested not anchored not stored refs pending

Strong Bounds for Evolution in Undirected Graphs

George B. Mertzios, Paul G. Spirakis

arxiv:1211.2384 v2 · 2012-11-11 · cs.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3TK5FI7TWZDATV7DT5RDI6DNZH}

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	2026-05-18T00:17:13.827257Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dcd5d2a3f3b64609d7e39f6234786dc9e181a0c8eab2d766fdbdf17fcbb38805

Aliases

arxiv: 1211.2384 · arxiv_version: 1211.2384v2 · doi: 10.48550/arxiv.1211.2384 · pith_short_12: 3TK5FI7TWZDA · pith_short_16: 3TK5FI7TWZDATV7D · pith_short_8: 3TK5FI7T

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/3TK5FI7TWZDATV7DT5RDI6DNZH \
  | 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: dcd5d2a3f3b64609d7e39f6234786dc9e181a0c8eab2d766fdbdf17fcbb38805

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6df7a5cc9ea3d4782b29b668e67f43587c528d00a77811292153c20670ff3bc",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2012-11-11T08:04:50Z",
    "title_canon_sha256": "47f06cdbf9f4e5f8b5737b3113f31f198a5d69bfca81fd4c9b2b7c54dca2d03d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2384",
    "kind": "arxiv",
    "version": 2
  }
}