Pith Number

pith:GR2Q7ZHD

pith:2026:GR2Q7ZHDZV65ZOSBMBGRQ5WDCR

not attested not anchored not stored refs pending

$L^2(\mathbb{R}^2)$ Well-Posedness and Logarithmic Lipschitz Regularity for the Density Patch Problem

Alessandro Violini

arxiv:2607.10676 v1 · 2026-07-12 · 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{GR2Q7ZHDZV65ZOSBMBGRQ5WDCR}

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	2026-07-14T01:21:34.336272Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34750fe4e3cd7ddcba41604d1876c314676cc72781ba66d2285397b461f39987

Aliases

arxiv: 2607.10676 · arxiv_version: 2607.10676v1 · doi: 10.48550/arxiv.2607.10676 · pith_short_12: GR2Q7ZHDZV65 · pith_short_16: GR2Q7ZHDZV65ZOSB · pith_short_8: GR2Q7ZHD

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/GR2Q7ZHDZV65ZOSBMBGRQ5WDCR \
  | 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: 34750fe4e3cd7ddcba41604d1876c314676cc72781ba66d2285397b461f39987

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7faccce883f2994c3620ec00725b885acc382025ffaa9829bce86697302208de",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-12T09:43:45Z",
    "title_canon_sha256": "d06367a7e46f5807ece8dd3b7051d62bcad2c734fbd35302a371a05cf8bc8211"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10676",
    "kind": "arxiv",
    "version": 1
  }
}