Pith Number

pith:D23XM6WY

pith:2012:D23XM6WYVJ2JV6M4IXLJEW3ETH

not attested not anchored not stored refs pending

Moment and tail estimates for martingales and martingale transform, with application to the martingale limit theorem in Banach spaces

E. Ostrovsky, L.Sirota

arxiv:1206.4964 v1 · 2012-06-21 · 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{D23XM6WYVJ2JV6M4IXLJEW3ETH}

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	2026-05-18T03:52:53.766763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1eb7767ad8aa749af99c45d6925b6499e325e8267e929d64a6652892fc9d0bf8

Aliases

arxiv: 1206.4964 · arxiv_version: 1206.4964v1 · doi: 10.48550/arxiv.1206.4964 · pith_short_12: D23XM6WYVJ2J · pith_short_16: D23XM6WYVJ2JV6M4 · pith_short_8: D23XM6WY

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/D23XM6WYVJ2JV6M4IXLJEW3ETH \
  | 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: 1eb7767ad8aa749af99c45d6925b6499e325e8267e929d64a6652892fc9d0bf8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87c59a7dc723e946e5e3336f4ccbe0ec84de4354df484c123c471e0434e40217",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-06-21T18:34:10Z",
    "title_canon_sha256": "78b56bd1d869dc2bb1816d21e03c7866152754607b1126724ce0b0bdcfa2bcf7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.4964",
    "kind": "arxiv",
    "version": 1
  }
}