Pith Number

pith:KF3CDN7Q

pith:2018:KF3CDN7QBE4F3PPCP3XV47R3XD

not attested not anchored not stored refs pending

The $p$-CurlCurl : Spaces, traces, coercivity and a Helmholtz decomposition in $L^p$

Marc Laforest

arxiv:1808.05976 v1 · 2018-08-17 · 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{KF3CDN7QBE4F3PPCP3XV47R3XD}

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.

Cited by

1 paper in Pith

Gradient estimates for $p\left(\cdot\right)$-harmonic differential forms

Receipt and verification

First computed	2026-05-18T00:07:46.576240Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

517621b7f009385dbde27eef5e7e3bb8f0cc8b9b37a83334d6172384c70ec40a

Aliases

arxiv: 1808.05976 · arxiv_version: 1808.05976v1 · doi: 10.48550/arxiv.1808.05976 · pith_short_12: KF3CDN7QBE4F · pith_short_16: KF3CDN7QBE4F3PPC · pith_short_8: KF3CDN7Q

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/KF3CDN7QBE4F3PPCP3XV47R3XD \
  | 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: 517621b7f009385dbde27eef5e7e3bb8f0cc8b9b37a83334d6172384c70ec40a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2532f8ddcfbb99ea2352279e22b7b9f5f41473663515d68e65893bac1ffc620b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-08-17T19:54:44Z",
    "title_canon_sha256": "d9e788a09055919d613ac241bf1d03ad84e3e8f3ca19c0eb2aed032a15c8a40f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.05976",
    "kind": "arxiv",
    "version": 1
  }
}