Pith Number

pith:AC5XU5LX

pith:2017:AC5XU5LXFY2JBXMVM6LPXVBX3Q

not attested not anchored not stored refs pending

A stochastic maximal inequality, strict countability, and infinite-dimensional martingales

Yoichi Nishiyama

arxiv:1707.08829 v2 · 2017-07-27 · 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{AC5XU5LXFY2JBXMVM6LPXVBX3Q}

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	2026-05-18T00:38:01.657292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00bb7a75772e3490dd956796fbd437dc0e05f55c40ebed674ef068a1a09ed8aa

Aliases

arxiv: 1707.08829 · arxiv_version: 1707.08829v2 · doi: 10.48550/arxiv.1707.08829 · pith_short_12: AC5XU5LXFY2J · pith_short_16: AC5XU5LXFY2JBXMV · pith_short_8: AC5XU5LX

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/AC5XU5LXFY2JBXMVM6LPXVBX3Q \
  | 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: 00bb7a75772e3490dd956796fbd437dc0e05f55c40ebed674ef068a1a09ed8aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46d08ddcb259c9226319dae9219408364e740be4e1ce0c2a86951e555c314969",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-07-27T12:22:14Z",
    "title_canon_sha256": "85318d067d73b45a6d286f05bcbf6b13afe49b20df4f25f4c62266cb1cc1e582"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.08829",
    "kind": "arxiv",
    "version": 2
  }
}