Pith Number

pith:MMDJG3IU

pith:2013:MMDJG3IU4HS665RNX2AQCK3PQ3

not attested not anchored not stored refs pending

The probability that a random multigraph is simple, II

Svante Janson

arxiv:1307.6344 v1 · 2013-07-24 · 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{MMDJG3IU4HS665RNX2AQCK3PQ3}

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	2026-05-18T03:17:43.623442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6306936d14e1e5ef762dbe81012b6f86d6c33b89f5e58ecc8bf571c1b1eb9f78

Aliases

arxiv: 1307.6344 · arxiv_version: 1307.6344v1 · doi: 10.48550/arxiv.1307.6344 · pith_short_12: MMDJG3IU4HS6 · pith_short_16: MMDJG3IU4HS665RN · pith_short_8: MMDJG3IU

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/MMDJG3IU4HS665RNX2AQCK3PQ3 \
  | 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: 6306936d14e1e5ef762dbe81012b6f86d6c33b89f5e58ecc8bf571c1b1eb9f78

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7581a7f0873c015945189bc058dbe0e3e1359ce5ba9b92352210c0474b346a5",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-07-24T09:24:07Z",
    "title_canon_sha256": "f4e2e053055d1ce52c6c58f66b34224d2b9832473a280faed183b098411b4df0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.6344",
    "kind": "arxiv",
    "version": 1
  }
}