Pith Number

pith:VTLEPFEF

pith:2008:VTLEPFEF4EQVWAMDJC76NHVVAL

not attested not anchored not stored refs pending

Aspects of area formulas by way of Luzin, Rad\'o, and Reichelderfer on metric measure spaces

Niko Marola, William P. Ziemer

arxiv:0807.2233 v4 · 2008-07-14 · math.CA · 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{VTLEPFEF4EQVWAMDJC76NHVVAL}

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	2026-05-18T02:26:23.967763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

acd6479485e1215b018348bfe69eb502e68c8aa5d4e31d82be9808f40c17c3e1

Aliases

arxiv: 0807.2233 · arxiv_version: 0807.2233v4 · doi: 10.48550/arxiv.0807.2233 · pith_short_12: VTLEPFEF4EQV · pith_short_16: VTLEPFEF4EQVWAMD · pith_short_8: VTLEPFEF

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/VTLEPFEF4EQVWAMDJC76NHVVAL \
  | 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: acd6479485e1215b018348bfe69eb502e68c8aa5d4e31d82be9808f40c17c3e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0330a83564e490f939a7c63e77fce5d1648928588e22f1b778cb00e0a5ebe823",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2008-07-14T19:40:57Z",
    "title_canon_sha256": "01aefe2cc6ce436b1c70669dd11f4284b4e4977d27de78b8513e44cd97d04324"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0807.2233",
    "kind": "arxiv",
    "version": 4
  }
}