Pith Number

pith:4HPMZ2PR

pith:2016:4HPMZ2PR26FXXNKQYMBPGNK47H

not attested not anchored not stored refs pending

Strict local martingales: examples

Xue-Mei Li

arxiv:1609.00935 v2 · 2016-09-04 · 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{4HPMZ2PR26FXXNKQYMBPGNK47H}

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	2026-05-18T00:43:09.197584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1decce9f1d78b7bb550c302f3355cf9cd25cc7638a4f28cd872278797ebe96c

Aliases

arxiv: 1609.00935 · arxiv_version: 1609.00935v2 · doi: 10.48550/arxiv.1609.00935 · pith_short_12: 4HPMZ2PR26FX · pith_short_16: 4HPMZ2PR26FXXNKQ · pith_short_8: 4HPMZ2PR

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/4HPMZ2PR26FXXNKQYMBPGNK47H \
  | 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: e1decce9f1d78b7bb550c302f3355cf9cd25cc7638a4f28cd872278797ebe96c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28c98dcfb135159e66246503c3c5658272d3821517282a8c14c582e017351019",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-09-04T13:49:29Z",
    "title_canon_sha256": "d7bd64b0d4518def4e182f179b0892bc65c014e003aad671fca0e0d2dd7ca690"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.00935",
    "kind": "arxiv",
    "version": 2
  }
}