Pith Number

pith:Z7L45SVA

pith:2011:Z7L45SVAGXHS323QU5QSO7VJO4

not attested not anchored not stored refs pending

Extension of Lyapunov's Convexity Theorem to Subranges

Eugene A. Feinberg, Peng Dai

arxiv:1102.2534 v1 · 2011-02-12 · 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{Z7L45SVAGXHS323QU5QSO7VJO4}

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	2026-05-18T04:28:47.153719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cfd7cecaa035cf2deb70a761277ea9772389a1d1127406c76efece1f922c32ab

Aliases

arxiv: 1102.2534 · arxiv_version: 1102.2534v1 · doi: 10.48550/arxiv.1102.2534 · pith_short_12: Z7L45SVAGXHS · pith_short_16: Z7L45SVAGXHS323Q · pith_short_8: Z7L45SVA

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/Z7L45SVAGXHS323QU5QSO7VJO4 \
  | 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: cfd7cecaa035cf2deb70a761277ea9772389a1d1127406c76efece1f922c32ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51b99340ff0910f53188718f697a5fd3571d6f2f7b819f73fd6a73e6c19dbff9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-02-12T19:27:10Z",
    "title_canon_sha256": "5f09b88abdd45507780be258aea5eb1fecc3b1de34f902310653f7b06c3b232d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.2534",
    "kind": "arxiv",
    "version": 1
  }
}