Pith Number

pith:PDQXRTCU

pith:2015:PDQXRTCUFRYLKHIF7MLA4HHQKN

not attested not anchored not stored refs pending

Estimating averages of order statistics of bivariate functions

Joscha Prochno, Markus Passenbrunner, Richard Lechner

arxiv:1507.06227 v1 · 2015-07-22 · math.PR · math.FA · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PDQXRTCUFRYLKHIF7MLA4HHQKN}

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	2026-05-18T00:04:24.435501Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78e178cc542c70b51d05fb160e1cf0535063c4ccc1d67b10a630a70d32578670

Aliases

arxiv: 1507.06227 · arxiv_version: 1507.06227v1 · doi: 10.48550/arxiv.1507.06227 · pith_short_12: PDQXRTCUFRYL · pith_short_16: PDQXRTCUFRYLKHIF · pith_short_8: PDQXRTCU

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/PDQXRTCUFRYLKHIF7MLA4HHQKN \
  | 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: 78e178cc542c70b51d05fb160e1cf0535063c4ccc1d67b10a630a70d32578670

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed1f40aee186b5f7c5d29393d7b1d0d1b57229019c77e04d618be0fed82d459e",
    "cross_cats_sorted": [
      "math.FA",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-07-22T15:25:12Z",
    "title_canon_sha256": "da82923dadf3d2b65884cfb3900db807bff83ab62c58342261f9a7b2287259c2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.06227",
    "kind": "arxiv",
    "version": 1
  }
}