Pith Number

pith:WREEB5KL

pith:2021:WREEB5KLPW6GYPEZF7AVFSW4AL

not attested not anchored not stored refs pending

Symmetric radial decreasing rearrangement can increase the fractional Gagliardo norm in domains

Dong Li, Ke Wang

arxiv:2106.12504 v1 · 2021-06-23 · 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{WREEB5KLPW6GYPEZF7AVFSW4AL}

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	2026-07-05T02:51:56.362519Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b44840f54b7dbc6c3c992fc152cadc02dd2cf24aea49514110b7865cb4a7296f

Aliases

arxiv: 2106.12504 · arxiv_version: 2106.12504v1 · doi: 10.48550/arxiv.2106.12504 · pith_short_12: WREEB5KLPW6G · pith_short_16: WREEB5KLPW6GYPEZ · pith_short_8: WREEB5KL

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/WREEB5KLPW6GYPEZF7AVFSW4AL \
  | 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: b44840f54b7dbc6c3c992fc152cadc02dd2cf24aea49514110b7865cb4a7296f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ec8d0ae91a8e6b2c0c123f59959d0d86bb71c71a905a6e5f8c06df7c292f77d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-06-23T16:22:22Z",
    "title_canon_sha256": "38141173ccf84ef64a119d154be4af5256b7118659b13f774c4693e19b7f402c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.12504",
    "kind": "arxiv",
    "version": 1
  }
}