Pith Number

pith:DT3EDKF3

pith:2012:DT3EDKF34KB7SDTVPOR3Z765GQ

not attested not anchored not stored refs pending

Characterizing $W^{2,p}$~submanifolds by $p$-integrability of global curvatures

Heiko von der Mosel, Pawe{\l} Strzelecki, S{\l}awomir Kolasi\'nski

arxiv:1203.4688 v2 · 2012-03-21 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DT3EDKF34KB7SDTVPOR3Z765GQ}

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	2026-05-18T03:00:59.318248Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1cf641a8bbe283f90e757ba3bcffdd341547c0376bfa295a0968542d0b1e00f6

Aliases

arxiv: 1203.4688 · arxiv_version: 1203.4688v2 · doi: 10.48550/arxiv.1203.4688 · pith_short_12: DT3EDKF34KB7 · pith_short_16: DT3EDKF34KB7SDTV · pith_short_8: DT3EDKF3

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/DT3EDKF34KB7SDTVPOR3Z765GQ \
  | 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: 1cf641a8bbe283f90e757ba3bcffdd341547c0376bfa295a0968542d0b1e00f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21f591ceaea39088c14b2cebfe7599742320981862d01e03636e3228d72d5d09",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-03-21T09:39:05Z",
    "title_canon_sha256": "fb39b4b213ca8de8b2da395727c6ad1c41de66343c23310382de4fe163f2dff7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.4688",
    "kind": "arxiv",
    "version": 2
  }
}