Pith Number

pith:L75DWOGY

pith:2014:L75DWOGYRQGHNJ7KFIWJFZBS3K

not attested not anchored not stored refs pending

A Gaussian upper bound for martingale small-ball probabilities

Charles K. Smart, James R. Lee, Yuval Peres

arxiv:1405.5980 v3 · 2014-05-23 · 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{L75DWOGYRQGHNJ7KFIWJFZBS3K}

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	2026-05-18T01:33:35.304292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ffa3b38d88c0c76a7ea2a2c92e432da9836f16a231d605a1e0b5154e373cf9a

Aliases

arxiv: 1405.5980 · arxiv_version: 1405.5980v3 · doi: 10.48550/arxiv.1405.5980 · pith_short_12: L75DWOGYRQGH · pith_short_16: L75DWOGYRQGHNJ7K · pith_short_8: L75DWOGY

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/L75DWOGYRQGHNJ7KFIWJFZBS3K \
  | 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: 5ffa3b38d88c0c76a7ea2a2c92e432da9836f16a231d605a1e0b5154e373cf9a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7cc5dbb710efeee3230a4e8a0815c7d8a7c117e4f0d72af9da46af122b78d8f6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2014-05-23T07:46:41Z",
    "title_canon_sha256": "213974b99bf9cfacc4783a4f7563b3cd82b18e365b9e7a471126ff8fce434cda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.5980",
    "kind": "arxiv",
    "version": 3
  }
}