Pith Number

pith:ZPAQ4UPU

pith:2012:ZPAQ4UPUOWIIWFY5TQSHBETJLX

not attested not anchored not stored refs pending

S-inequality for certain product measures

Piotr Nayar, Tomasz Tkocz

arxiv:1210.5546 v2 · 2012-10-19 · 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{ZPAQ4UPUOWIIWFY5TQSHBETJLX}

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	2026-05-18T02:48:47.226859Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbc10e51f475908b171d9c247092695dd36d42087954d0631ff148ce219510a8

Aliases

arxiv: 1210.5546 · arxiv_version: 1210.5546v2 · doi: 10.48550/arxiv.1210.5546 · pith_short_12: ZPAQ4UPUOWII · pith_short_16: ZPAQ4UPUOWIIWFY5 · pith_short_8: ZPAQ4UPU

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/ZPAQ4UPUOWIIWFY5TQSHBETJLX \
  | 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: cbc10e51f475908b171d9c247092695dd36d42087954d0631ff148ce219510a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57a758a96f9427548c6be10ff106a8c077ef59b42bce53b055bdeafaf5f3792a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-10-19T21:40:51Z",
    "title_canon_sha256": "85501bb325c699911df9aec66fa596bb1cc8144a8dcf798232e965d655138842"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.5546",
    "kind": "arxiv",
    "version": 2
  }
}