Pith Number

pith:AZIPCDPB

pith:2012:AZIPCDPBJXE4HESKO6OYUIYTMK

not attested not anchored not stored refs pending

Sharp maximal inequalities for the moments of martingales and non-negative submartingales

Adam Os\c{e}kowski

arxiv:1201.1089 v1 · 2012-01-05 · 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{AZIPCDPBJXE4HESKO6OYUIYTMK}

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	2026-05-18T04:05:06.209585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0650f10de14dc9c3924a779d8a231362a8cee2c05e738190e8c68c9d5d3db809

Aliases

arxiv: 1201.1089 · arxiv_version: 1201.1089v1 · doi: 10.48550/arxiv.1201.1089 · pith_short_12: AZIPCDPBJXE4 · pith_short_16: AZIPCDPBJXE4HESK · pith_short_8: AZIPCDPB

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/AZIPCDPBJXE4HESKO6OYUIYTMK \
  | 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: 0650f10de14dc9c3924a779d8a231362a8cee2c05e738190e8c68c9d5d3db809

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ba06e91300e4a40896da804ffbfb73cdd0e769fffd63fe24d617abee6befaac",
    "cross_cats_sorted": [
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2012-01-05T09:18:24Z",
    "title_canon_sha256": "3b55567a24a988ba54c87bfd874d188564ae14686c26495398c8f20928c15c6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.1089",
    "kind": "arxiv",
    "version": 1
  }
}