Pith Number

pith:DW3WPJZX

pith:2026:DW3WPJZXRECV2FSYTZHFR7CVU5

not attested not anchored not stored refs pending

Positive Criticality and Optimal Hardy Inequality for Fractional Laplacians

Felix Pogorzelski, Matthias Keller, Philipp Hake

arxiv:2605.19423 v1 · 2026-05-19 · math-ph · math.AP · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DW3WPJZXRECV2FSYTZHFR7CVU5}

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	2026-05-20T01:05:44.962147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1db767a73789055d16589e4e58fc55a7674f0bdb24ab27937a77b6fc4faaf0d1

Aliases

arxiv: 2605.19423 · arxiv_version: 2605.19423v1 · doi: 10.48550/arxiv.2605.19423 · pith_short_12: DW3WPJZXRECV · pith_short_16: DW3WPJZXRECV2FSY · pith_short_8: DW3WPJZX

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/DW3WPJZXRECV2FSYTZHFR7CVU5 \
  | 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: 1db767a73789055d16589e4e58fc55a7674f0bdb24ab27937a77b6fc4faaf0d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6d9bbbcec8c88f133770576bc8851a2d46508ba9367433c38ca305d704a42ec",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-19T06:22:02Z",
    "title_canon_sha256": "624209eafcb31faa8ac2ccb1da20fdee137d14457607ed70872e73403bc9797b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.19423",
    "kind": "arxiv",
    "version": 1
  }
}