Pith Number

pith:D2VLJGQ3

pith:2016:D2VLJGQ36DPV2252XVY4PQG6DF

not attested not anchored not stored refs pending

Geometry of the vacant set left by random walk on random graphs, Wright's constants, and critical random graphs with prescribed degrees

Sanchayan Sen, Shankar Bhamidi

arxiv:1608.07153 v3 · 2016-08-25 · math.PR · 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{D2VLJGQ36DPV2252XVY4PQG6DF}

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	2026-05-17T23:42:59.293745Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1eaab49a1bf0df5d6bbabd71c7c0de1962d90dc97e286b58a5aeefbfac97b581

Aliases

arxiv: 1608.07153 · arxiv_version: 1608.07153v3 · doi: 10.48550/arxiv.1608.07153 · pith_short_12: D2VLJGQ36DPV · pith_short_16: D2VLJGQ36DPV2252 · pith_short_8: D2VLJGQ3

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/D2VLJGQ36DPV2252XVY4PQG6DF \
  | 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: 1eaab49a1bf0df5d6bbabd71c7c0de1962d90dc97e286b58a5aeefbfac97b581

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05752636e1b31a4ff32083602405bc7a460857c8f6b0e06ddfeaab2d19fdbf97",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-08-25T14:02:00Z",
    "title_canon_sha256": "f9b36a5bb768342ede108cc8e5833cf9825940cd04db9fbbf7c992fd7c124b0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.07153",
    "kind": "arxiv",
    "version": 3
  }
}