Pith Number

pith:X2IVFRG5

pith:2015:X2IVFRG5XFQORP4DMK5WHANFR4

not attested not anchored not stored refs pending

Besicovitch Covering Property on graded groups and applications to measure differentiation

Enrico Le Donne, Severine Rigot

arxiv:1512.04936 v1 · 2015-12-15 · math.MG · math.FA · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X2IVFRG5XFQORP4DMK5WHANFR4}

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	2026-05-18T01:24:15.100730Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

be9152c4ddb960e8bf8362bb6381a58f291126a47fdff5627b1f4c57884b118b

Aliases

arxiv: 1512.04936 · arxiv_version: 1512.04936v1 · doi: 10.48550/arxiv.1512.04936 · pith_short_12: X2IVFRG5XFQO · pith_short_16: X2IVFRG5XFQORP4D · pith_short_8: X2IVFRG5

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/X2IVFRG5XFQORP4DMK5WHANFR4 \
  | 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: be9152c4ddb960e8bf8362bb6381a58f291126a47fdff5627b1f4c57884b118b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "090628b44b3d1020064277ed74771b91b54f7882967cee13ebd1cda42a511468",
    "cross_cats_sorted": [
      "math.FA",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-12-15T20:56:40Z",
    "title_canon_sha256": "85ed938d3a55b2a25fcff654d2dd85bf23828e16755d1e63529713682ab476f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04936",
    "kind": "arxiv",
    "version": 1
  }
}