Pith Number

pith:4V7RTMHA

pith:2015:4V7RTMHABQNKUB4YH7A3LNF3FR

not attested not anchored not stored refs pending

Monotone Increasing Properties and Their Phase Transitions in Uniform Random Intersection Graphs

Jun Zhao, Osman Ya\u{g}an, Virgil Gligor

arxiv:1502.00405 v1 · 2015-02-02 · physics.soc-ph · cs.DM · cs.SI · math.CO · 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{4V7RTMHABQNKUB4YH7A3LNF3FR}

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	2026-05-18T02:28:06.055439Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e57f19b0e00c1aaa07983fc1b5b4bb2c716fc9315e3e409e133b76e42017c72e

Aliases

arxiv: 1502.00405 · arxiv_version: 1502.00405v1 · doi: 10.48550/arxiv.1502.00405 · pith_short_12: 4V7RTMHABQNK · pith_short_16: 4V7RTMHABQNKUB4Y · pith_short_8: 4V7RTMHA

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/4V7RTMHABQNKUB4YH7A3LNF3FR \
  | 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: e57f19b0e00c1aaa07983fc1b5b4bb2c716fc9315e3e409e133b76e42017c72e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fecb86836dc86917932216499b36e19b581451bac7d2eed83d141b0396955e15",
    "cross_cats_sorted": [
      "cs.DM",
      "cs.SI",
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2015-02-02T09:04:51Z",
    "title_canon_sha256": "dcae88dd8f668ead6847fa1a6e6ad7bc038dccf0365226af1de1ec5fa91d7d13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.00405",
    "kind": "arxiv",
    "version": 1
  }
}