Pith Number

pith:7KUH3C2E

pith:2015:7KUH3C2EH3Z57LNMZPIHTARURG

not attested not anchored not stored refs pending

In between the inequalities of Sobolev and Hardy

Antti V. V\"ah\"akangas, Juha Lehrb\"ack

arxiv:1502.01190 v1 · 2015-02-04 · 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{7KUH3C2EH3Z57LNMZPIHTARURG}

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	2026-05-18T00:57:44.451568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

faa87d8b443ef3dfadaccbd079823489ae299640e0b9c7611f5794fa5102a6fe

Aliases

arxiv: 1502.01190 · arxiv_version: 1502.01190v1 · doi: 10.48550/arxiv.1502.01190 · pith_short_12: 7KUH3C2EH3Z5 · pith_short_16: 7KUH3C2EH3Z57LNM · pith_short_8: 7KUH3C2E

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/7KUH3C2EH3Z57LNMZPIHTARURG \
  | 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: faa87d8b443ef3dfadaccbd079823489ae299640e0b9c7611f5794fa5102a6fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d73ab643394b316116cc03602f76e27d25c03617d8e0aba5cbaf9533c6d3c14",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-02-04T13:27:17Z",
    "title_canon_sha256": "0413d31dd98bd23236cf05e202aa4d61c42398dc2e781427b38f07a578605a5e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.01190",
    "kind": "arxiv",
    "version": 1
  }
}