Pith Number

pith:5UBM3QPZ

pith:2026:5UBM3QPZAXHDB7Y7SRQO2HFWAX

not attested not anchored not stored refs pending

From Lecture Notes to Lean: Formalizing a Textbook on Probability Theory

Kenneth W. Shum, Shuo Deng

arxiv:2607.27298 v1 · 2026-07-29 · cs.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5UBM3QPZAXHDB7Y7SRQO2HFWAX}

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	2026-07-31T00:10:32.300741Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

ed02cdc1f905ce30ff1f9460ed1cb605c4526c1f72f7e9bd37ea8f94e8660413

Aliases

arxiv: 2607.27298 · arxiv_version: 2607.27298v1 · doi: 10.48550/arxiv.2607.27298 · pith_short_12: 5UBM3QPZAXHD · pith_short_16: 5UBM3QPZAXHDB7Y7 · pith_short_8: 5UBM3QPZ

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/5UBM3QPZAXHDB7Y7SRQO2HFWAX \
  | 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: ed02cdc1f905ce30ff1f9460ed1cb605c4526c1f72f7e9bd37ea8f94e8660413

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fded3d6d88cc52d2968b194dcb4b3f2339b1cd318991d47989de778facb5edba",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2026-07-29T16:15:08Z",
    "title_canon_sha256": "95c6d3c4c98feaac2c7c9bfdedf0bea07e02b69a6aa61074c0eacd11404592ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.27298",
    "kind": "arxiv",
    "version": 1
  }
}