Pith Number

pith:ZIPQSTSP

pith:2000:ZIPQSTSPIBSTQAHEMYN7QS7A6W

not attested not anchored not stored refs pending

Statistics of smoothed cosmic fields in perturbation theory I: Formulation and useful formulas in second-order perturbation theory

Takahiko Matsubara

arxiv:astro-ph/0006269 v2 · 2000-06-20 · astro-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZIPQSTSPIBSTQAHEMYN7QS7A6W}

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

Ensemble Average of Three-Dimensional Minkowski Tensors of a Gaussian Random Field in Redshift Space

Receipt and verification

First computed	2026-07-04T14:10:26.696029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca1f094e4f40653800e4661bf84be0f5821b8c745f9c9699da78918225cd1f15

Aliases

arxiv: astro-ph/0006269 · arxiv_version: astro-ph/0006269v2 · doi: 10.48550/arxiv.astro-ph/0006269 · pith_short_12: ZIPQSTSPIBST · pith_short_16: ZIPQSTSPIBSTQAHE · pith_short_8: ZIPQSTSP

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/ZIPQSTSPIBSTQAHEMYN7QS7A6W \
  | 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: ca1f094e4f40653800e4661bf84be0f5821b8c745f9c9699da78918225cd1f15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c94d8cad30e54b4dedfe14d14e70475c2186a132744440b392fd4fd8b2b384be",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2000-06-20T04:31:48Z",
    "title_canon_sha256": "813e93925c3b2fda46559e7029fdfa70d7aaad42e2009625c82c64f05661325d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0006269",
    "kind": "arxiv",
    "version": 2
  }
}