Pith Number

pith:ILWFJTCT

pith:2012:ILWFJTCTLI2CBVIQ2EO2QDPE2S

not attested not anchored not stored refs pending

A Simple Proof of Vitali's Theorem for Signed Measures

Tony Samuel

arxiv:1202.2106 v2 · 2012-02-09 · math.DS · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ILWFJTCTLI2CBVIQ2EO2QDPE2S}

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	2026-05-18T00:32:24.213278Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42ec54cc535a3420d510d11da80de4d4b1fe500a5ca369dcaa437a6aeddefc73

Aliases

arxiv: 1202.2106 · arxiv_version: 1202.2106v2 · doi: 10.48550/arxiv.1202.2106 · pith_short_12: ILWFJTCTLI2C · pith_short_16: ILWFJTCTLI2CBVIQ · pith_short_8: ILWFJTCT

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/ILWFJTCTLI2CBVIQ2EO2QDPE2S \
  | 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: 42ec54cc535a3420d510d11da80de4d4b1fe500a5ca369dcaa437a6aeddefc73

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b395654f86672c73f8cbe0846d42714ae3b1693c4c5220cb6ee5484a4dcebfd",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-02-09T20:35:36Z",
    "title_canon_sha256": "f88ed4becceda90e555d30bff64b3adbbcfa998243f78b9543fccf38b6a43bb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.2106",
    "kind": "arxiv",
    "version": 2
  }
}