Pith Number

pith:HFWL224F

pith:2016:HFWL224FYWRJNENEKZ2DYYQIW6

not attested not anchored not stored refs pending

The probability of nonexistence of a subgraph in a moderately sparse random graph

Dudley Stark, Nick Wormald

arxiv:1608.05193 v1 · 2016-08-18 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HFWL224FYWRJNENEKZ2DYYQIW6}

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	2026-05-18T01:08:31.647919Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

396cbd6b85c5a29691a456743c6208b7a7218600591fe94c886f9d9da35ea496

Aliases

arxiv: 1608.05193 · arxiv_version: 1608.05193v1 · doi: 10.48550/arxiv.1608.05193 · pith_short_12: HFWL224FYWRJ · pith_short_16: HFWL224FYWRJNENE · pith_short_8: HFWL224F

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/HFWL224FYWRJNENEKZ2DYYQIW6 \
  | 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: 396cbd6b85c5a29691a456743c6208b7a7218600591fe94c886f9d9da35ea496

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5110679ebaaced47fdef59fe6831a6054684dd5a9576f8479d3fad2989773d11",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-08-18T07:22:03Z",
    "title_canon_sha256": "7f55dd81efb5e83fe3dae6572dd413cc89e07469057bd07337c9ef77017fe663"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.05193",
    "kind": "arxiv",
    "version": 1
  }
}