Pith Number

pith:U3G4ZMG5

pith:2009:U3G4ZMG5YIKPWL2KF6RXDML2HG

not attested not anchored not stored refs pending

Equivalence of the random intersection graph and G(n,p)

Katarzyna Rybarczyk

arxiv:0910.5311 v2 · 2009-10-28 · 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{U3G4ZMG5YIKPWL2KF6RXDML2HG}

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	2026-05-18T02:29:44.496255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6cdccb0ddc214fb2f4a2fa371b17a39826828bc3dde4c2476d9268f1aef7c22

Aliases

arxiv: 0910.5311 · arxiv_version: 0910.5311v2 · doi: 10.48550/arxiv.0910.5311 · pith_short_12: U3G4ZMG5YIKP · pith_short_16: U3G4ZMG5YIKPWL2K · pith_short_8: U3G4ZMG5

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/U3G4ZMG5YIKPWL2KF6RXDML2HG \
  | 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: a6cdccb0ddc214fb2f4a2fa371b17a39826828bc3dde4c2476d9268f1aef7c22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1ffb380188818889edb9b78fe7d89665c1d3ef76e8ae079c10f4641e528a7c34",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-10-28T09:21:52Z",
    "title_canon_sha256": "1e79c44aef801fdb600116711ebc634166431ab3cc9cfe0ba629d6152e6a915b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.5311",
    "kind": "arxiv",
    "version": 2
  }
}