Pith Number

pith:JRW2BXTH

pith:2023:JRW2BXTHASE254GX6YZVDMFKJR

not attested not anchored not stored refs pending

A Formalization of Martingales in Isabelle/HOL

Ata Keskin

arxiv:2311.06188 v1 · 2023-11-10 · cs.LO · 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{JRW2BXTHASE254GX6YZVDMFKJR}

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.

Cited by

2 papers in Pith

A Machine-Checked It\^o Calculus for Brownian Motion

The Fundamental Theorem of Asset Pricing, Formalized in Lean 4

Receipt and verification

First computed	2026-07-05T07:11:29.499274Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c6da0de670489aef0d7f63351b0aa4c7594e16eada1f4888d1d8ac9318bfcbe

Aliases

arxiv: 2311.06188 · arxiv_version: 2311.06188v1 · doi: 10.48550/arxiv.2311.06188 · pith_short_12: JRW2BXTHASE2 · pith_short_16: JRW2BXTHASE254GX · pith_short_8: JRW2BXTH

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/JRW2BXTHASE254GX6YZVDMFKJR \
  | 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: 4c6da0de670489aef0d7f63351b0aa4c7594e16eada1f4888d1d8ac9318bfcbe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d4bead4ced96ac8931fa6f2b386f2c10490bd37cfb0fe3db661672efa7be162",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2023-11-10T17:10:47Z",
    "title_canon_sha256": "63291c9f8d43553477a87b37f0913650574e403791f016763c3b838f4fde4c92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2311.06188",
    "kind": "arxiv",
    "version": 1
  }
}