Pith Number

pith:TQS7TT2H

pith:2026:TQS7TT2HZEK522IOLIH425EJFU

not attested not anchored not stored refs pending

Normal approximation of the numbers of isolated edges and isolated 2-stars in uniform simple graphs with given vertex degrees

Ryo Imai

New Stein couplings deliver the first finite-sample normal approximation bounds for isolated edges and isolated 2-stars in uniform simple graphs with prescribed degrees.

arxiv:2605.08706 v3 · 2026-05-09 · math.PR · math.CO

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\usepackage{pith}
\pithnumber{TQS7TT2HZEK522IOLIH425EJFU}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

The latter provides the first finite sample normal approximation results for the uniform simple graph with given vertex degrees.

C2weakest assumption

The degree sequence satisfies the (unspecified in abstract) regularity conditions under which the configuration model is simple with high probability and the new Stein couplings yield the stated quantitative error bounds.

C3one line summary

The paper establishes the first finite-sample normal approximation bounds for the numbers of isolated edges and isolated 2-stars in uniform simple graphs with prescribed degrees, via new joint normal-Poisson Stein's method and indicator coupling.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-28T02:04:49.065378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c25f9cf47c915dd690e5a0fcd74892d1be908a87bb50f50ca3c45ce870caa7e

Aliases

arxiv: 2605.08706 · arxiv_version: 2605.08706v3 · doi: 10.48550/arxiv.2605.08706 · pith_short_12: TQS7TT2HZEK5 · pith_short_16: TQS7TT2HZEK522IO · pith_short_8: TQS7TT2H

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/TQS7TT2HZEK522IOLIH425EJFU \
  | 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: 9c25f9cf47c915dd690e5a0fcd74892d1be908a87bb50f50ca3c45ce870caa7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13727dfb1e99bdb87e89e1dc4cb59f9357a881f4ba982459c82e465361b3ab38",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-09T05:41:38Z",
    "title_canon_sha256": "d115d8d9089e0cd1cff98c22d139fb83f25eb4efded8a6017ce674dac2b34843"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.08706",
    "kind": "arxiv",
    "version": 3
  }
}