Pith Number

pith:HO56H4SK

pith:2016:HO56H4SKXXW4ENOHDMCDO7DPUC

not attested not anchored not stored refs pending

Fractional operators on weighted Morrey spaces

Hitoshi Tanaka, Shohei Nakamura, Yoshihiro Sawano

arxiv:1612.00663 v1 · 2016-12-02 · 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{HO56H4SKXXW4ENOHDMCDO7DPUC}

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	2026-05-18T00:55:59.365731Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bbbe3f24abdedc235c71b04377c6fa0be44aba38bc259818523499b91584d35

Aliases

arxiv: 1612.00663 · arxiv_version: 1612.00663v1 · doi: 10.48550/arxiv.1612.00663 · pith_short_12: HO56H4SKXXW4 · pith_short_16: HO56H4SKXXW4ENOH · pith_short_8: HO56H4SK

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/HO56H4SKXXW4ENOHDMCDO7DPUC \
  | 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: 3bbbe3f24abdedc235c71b04377c6fa0be44aba38bc259818523499b91584d35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b862457e3d705c4c7613ec4132f4adb03ff291387516d6016701f3412f8c2c5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-12-02T12:49:07Z",
    "title_canon_sha256": "b7a012900dae814abcaa0c0f635d193e9f88afff53955440af4d0899c232cdb8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.00663",
    "kind": "arxiv",
    "version": 1
  }
}