Pith Number

pith:H2U3O36F

pith:2017:H2U3O36FVULENTDXKEOLUUMDAJ

not attested not anchored not stored refs pending

Muckenhoupt $A_p$-properties of distance functions and applications to Hardy-Sobolev -type inequalities

Antti V. V\"ah\"akangas, Bart{\l}omiej Dyda, Heli Tuominen, Juha Lehrb\"ack, Lizaveta Ihnatsyeva

arxiv:1705.01360 v1 · 2017-05-03 · math.CA · 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{H2U3O36FVULENTDXKEOLUUMDAJ}

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	2026-05-18T00:45:05.330828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ea9b76fc5ad1646cc77511cba5183024fa0d94b279438247c16395bf28ac955

Aliases

arxiv: 1705.01360 · arxiv_version: 1705.01360v1 · doi: 10.48550/arxiv.1705.01360 · pith_short_12: H2U3O36FVULE · pith_short_16: H2U3O36FVULENTDX · pith_short_8: H2U3O36F

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/H2U3O36FVULENTDXKEOLUUMDAJ \
  | 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: 3ea9b76fc5ad1646cc77511cba5183024fa0d94b279438247c16395bf28ac955

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ef7c29362477b5a81dc62d048fa8a107d3b1cb63f543b5fbede2264fd97c83ee",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-05-03T11:13:19Z",
    "title_canon_sha256": "192a9a08538ba4d12c32a59f5257c11aabfb415917a4b0be6d8250562a7e5ca2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.01360",
    "kind": "arxiv",
    "version": 1
  }
}