Pith Number

pith:LNCYSCET

pith:2011:LNCYSCETURBCI6ACVWWM2Z63J3

not attested not anchored not stored refs pending

Concentration of measure for the number of isolated vertices in the Erd\H{o}s-R\'{e}nyi random graph by size bias couplings

Larry Goldstein, Martin Raic, Subhankar Ghosh

arxiv:1106.0048 v1 · 2011-05-31 · 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{LNCYSCETURBCI6ACVWWM2Z63J3}

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	2026-05-18T04:20:52.236886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b45890893a442247802adaccd67db4eeb7df6238bae177b9eaca04124b3a0ff

Aliases

arxiv: 1106.0048 · arxiv_version: 1106.0048v1 · doi: 10.48550/arxiv.1106.0048 · pith_short_12: LNCYSCETURBC · pith_short_16: LNCYSCETURBCI6AC · pith_short_8: LNCYSCET

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/LNCYSCETURBCI6ACVWWM2Z63J3 \
  | 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: 5b45890893a442247802adaccd67db4eeb7df6238bae177b9eaca04124b3a0ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96a1db3e21ea7429537fdfd25604c7b5333612e6eda04e9742d1249cb69ccc27",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-05-31T22:38:38Z",
    "title_canon_sha256": "890cb9f0668d8a8a02d5c5d3afc1f53f8b58f8a74fa9833f1549e061d68850d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0048",
    "kind": "arxiv",
    "version": 1
  }
}