Pith Number

pith:R43EMQK4

pith:2015:R43EMQK4HXJF2WNP6HRHUQHPCP

not attested not anchored not stored refs pending

Universal and complete sets in martingale theory

Dominique Lecomte, Miroslav Zeleny

arxiv:1512.05966 v1 · 2015-12-18 · math.LO · math.GN

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R43EMQK4HXJF2WNP6HRHUQHPCP}

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	2026-05-18T01:24:05.773779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f3646415c3dd25d59aff1e27a40ef13df1e84768bcdc3e44df7523331089f5e

Aliases

arxiv: 1512.05966 · arxiv_version: 1512.05966v1 · doi: 10.48550/arxiv.1512.05966 · pith_short_12: R43EMQK4HXJF · pith_short_16: R43EMQK4HXJF2WNP · pith_short_8: R43EMQK4

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/R43EMQK4HXJF2WNP6HRHUQHPCP \
  | 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: 8f3646415c3dd25d59aff1e27a40ef13df1e84768bcdc3e44df7523331089f5e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18f564ad2e5affc0bb62ad79d97042a8bb2c5e73fcbcc13b8870c507f26ac96d",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2015-12-18T14:10:55Z",
    "title_canon_sha256": "9642ed6083726338bdb95637c0d1a3c22d9d56a2c13cf26166779ae145665b55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.05966",
    "kind": "arxiv",
    "version": 1
  }
}