Pith Number

pith:CBT2REIB

pith:2005:CBT2REIBJARUMME3TC6FBM254Q

not attested not anchored not stored refs pending

Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables

Sergio Albeverio, Song Liang

arxiv:math/0503601 v1 · 2005-03-25 · math.PR

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CBT2REIBJARUMME3TC6FBM254Q}

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.

Cited by

1 paper in Pith

A Shared Observation Shields Collective Fluctuations while Preserving Local Independence

Receipt and verification

First computed	2026-07-04T14:39:50.299928Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1067a89101482346309b98bc50b35de41ec3d5f68b577a5ea9a93a32dca30edd

Aliases

arxiv: math/0503601 · arxiv_version: math/0503601v1 · doi: 10.48550/arxiv.math/0503601 · pith_short_12: CBT2REIBJARU · pith_short_16: CBT2REIBJARUMME3 · pith_short_8: CBT2REIB

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/CBT2REIBJARUMME3TC6FBM254Q \
  | 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: 1067a89101482346309b98bc50b35de41ec3d5f68b577a5ea9a93a32dca30edd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f1f4021fd1b7c39d696416ad6ddf0a1e42f05a701fd0df663364ca4c3410da9",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2005-03-25T14:37:45Z",
    "title_canon_sha256": "d31c2558dd460325249ac69f8a31afee153897cc2e1c9fe2a1b67d1f3e09876c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0503601",
    "kind": "arxiv",
    "version": 1
  }
}