Pith Number

pith:KO7X7IJK

pith:2001:KO7X7IJKKZOXRHCNPSIYNIV23A

not attested not anchored not stored refs pending

Covering theorems and Lebesgue integration

Erik Talvila, Peter A. Loeb

arxiv:math/0101014 v1 · 2001-01-02 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KO7X7IJKKZOXRHCNPSIYNIV23A}

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

1 paper in Pith

Using Large Language Models to Study Mathematical Practice

Receipt and verification

First computed	2026-07-04T14:35:00.414538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53bf7fa12a565d789c4d7c9186a2bad81bad421ab192df3ad35ea44ec06d0e1b

Aliases

arxiv: math/0101014 · arxiv_version: math/0101014v1 · doi: 10.48550/arxiv.math/0101014 · pith_short_12: KO7X7IJKKZOX · pith_short_16: KO7X7IJKKZOXRHCN · pith_short_8: KO7X7IJK

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/KO7X7IJKKZOXRHCNPSIYNIV23A \
  | 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: 53bf7fa12a565d789c4d7c9186a2bad81bad421ab192df3ad35ea44ec06d0e1b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4760763bee3f02d42cbd3dce866935ff1495a6bdc18c16c15f360e4d5d3c6a9",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2001-01-02T19:09:48Z",
    "title_canon_sha256": "f6049ed4cd856cb897ba3d9041392a8fc575349132dd35b8f6c8367973136a7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0101014",
    "kind": "arxiv",
    "version": 1
  }
}