Pith Number

pith:7OZVJXMS

pith:2012:7OZVJXMSVREZ7QIYBGRQRSMDKB

not attested not anchored not stored refs pending

Transversally Lipschitz Harmonic Functions are Lipschitz

Sivaguru Ravisankar

arxiv:1203.4641 v1 · 2012-03-21 · math.AP · 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{7OZVJXMSVREZ7QIYBGRQRSMDKB}

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	2026-05-18T02:19:06.536475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbb354dd92ac499fc11809a308c983507027d71722c66544369b4e1221672257

Aliases

arxiv: 1203.4641 · arxiv_version: 1203.4641v1 · doi: 10.48550/arxiv.1203.4641 · pith_short_12: 7OZVJXMSVREZ · pith_short_16: 7OZVJXMSVREZ7QIY · pith_short_8: 7OZVJXMS

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/7OZVJXMSVREZ7QIYBGRQRSMDKB \
  | 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: fbb354dd92ac499fc11809a308c983507027d71722c66544369b4e1221672257

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0541e77136400ee365a4fa3b0f75586faa5da94b66da8528c545e883def005aa",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-03-21T02:48:28Z",
    "title_canon_sha256": "2f845a88ded595379d2c19bd25fbcd4c54f54782a7f576a159c6a6b2e6bdecaa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4641",
    "kind": "arxiv",
    "version": 1
  }
}