Pith Number

pith:M72WDL4E

pith:2013:M72WDL4ER37WLZ45J2PG2OLFUW

not attested not anchored not stored refs pending

Supermartingales as Radon-Nikodym densities and related measure extensions

Johannes Ruf, Nicolas Perkowski

arxiv:1309.4623 v2 · 2013-09-18 · 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{M72WDL4ER37WLZ45J2PG2OLFUW}

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	2026-05-18T01:23:59.052644Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67f561af848eff65e79d4e9e6d3965a588c953c49992ebdea7c4efd7001ccfe1

Aliases

arxiv: 1309.4623 · arxiv_version: 1309.4623v2 · doi: 10.48550/arxiv.1309.4623 · pith_short_12: M72WDL4ER37W · pith_short_16: M72WDL4ER37WLZ45 · pith_short_8: M72WDL4E

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/M72WDL4ER37WLZ45J2PG2OLFUW \
  | 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: 67f561af848eff65e79d4e9e6d3965a588c953c49992ebdea7c4efd7001ccfe1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0e0ce6652a70cb6b024d3b45d09c31de4ff4ccde558936b4e5e51fbf2581e4e2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-09-18T12:14:52Z",
    "title_canon_sha256": "896063186a3f673e6ab249fd2d32d605b114c58b495e22944aac1b5c6566ddd7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.4623",
    "kind": "arxiv",
    "version": 2
  }
}