Pith Number

pith:CQ66RLIT

pith:2009:CQ66RLITSGCDAKTWKJN3DL2YKH

not attested not anchored not stored refs pending

The div-curl lemma for sequences whose divergence and curl are compact in W^{-1,1}

Georg Dolzmann, Sergio Conti, Stefan M\"uller

arxiv:0907.0397 v1 · 2009-07-02 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CQ66RLITSGCDAKTWKJN3DL2YKH}

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	2026-05-18T00:17:20.342415Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

143de8ad139184302a76525bb1af5851fae7463e0b1726dee98b06e10cda523f

Aliases

arxiv: 0907.0397 · arxiv_version: 0907.0397v1 · doi: 10.48550/arxiv.0907.0397 · pith_short_12: CQ66RLITSGCD · pith_short_16: CQ66RLITSGCDAKTW · pith_short_8: CQ66RLIT

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/CQ66RLITSGCDAKTWKJN3DL2YKH \
  | 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: 143de8ad139184302a76525bb1af5851fae7463e0b1726dee98b06e10cda523f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43232589c589932bf8d549bfe27138813519df919a2d374f5e90884ab00aca1e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-07-02T14:55:38Z",
    "title_canon_sha256": "af496431cdfcc24c972771a4e4a05870b09345d4aa2aeac3127ee8f451228b04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.0397",
    "kind": "arxiv",
    "version": 1
  }
}