Pith Number

pith:7CFBDDRR

pith:2025:7CFBDDRRBI6WAHBTYDM2LSQQIV

not attested not anchored not stored refs pending

H\"older extension for fractional Laplacian

Feng Li

arxiv:2508.12134 v1 · 2025-08-16 · 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{7CFBDDRRBI6WAHBTYDM2LSQQIV}

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

Substituting Proof of Work in Blockchain with Training-Verified Collaborative Model Computation

Receipt and verification

First computed	2026-07-05T11:55:00.662033Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f88a118e310a3d601c33c0d9a5ca104577e4014c049bdac32224513915692a16

Aliases

arxiv: 2508.12134 · arxiv_version: 2508.12134v1 · doi: 10.48550/arxiv.2508.12134 · pith_short_12: 7CFBDDRRBI6W · pith_short_16: 7CFBDDRRBI6WAHBT · pith_short_8: 7CFBDDRR

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/7CFBDDRRBI6WAHBTYDM2LSQQIV \
  | 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: f88a118e310a3d601c33c0d9a5ca104577e4014c049bdac32224513915692a16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a24ac1a534cdf8b2aab4077e57d6e7dcbc607d945bb51712650ae074d6270caa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-08-16T18:54:10Z",
    "title_canon_sha256": "71abc72466bd36b708cab360c7ae9a81998086e0561bf72bd6321f99140cb9a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.12134",
    "kind": "arxiv",
    "version": 1
  }
}