Pith Number

pith:WFFBQOG7

pith:2015:WFFBQOG7C4VRL4BJDVG7QET2SO

not attested not anchored not stored refs pending

The optimal constant in Hardy-type inequalities

Mu-Fa chen

arxiv:1501.03230 v1 · 2015-01-14 · math.PR · math.CA · 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{WFFBQOG7C4VRL4BJDVG7QET2SO}

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	2026-05-18T02:29:24.441198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b14a1838df172b15f0291d4df8127a93b87060a88dd956bc430dd8e5beb49c75

Aliases

arxiv: 1501.03230 · arxiv_version: 1501.03230v1 · doi: 10.48550/arxiv.1501.03230 · pith_short_12: WFFBQOG7C4VR · pith_short_16: WFFBQOG7C4VRL4BJ · pith_short_8: WFFBQOG7

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/WFFBQOG7C4VRL4BJDVG7QET2SO \
  | 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: b14a1838df172b15f0291d4df8127a93b87060a88dd956bc430dd8e5beb49c75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "295aaef57ee48199a0c3c09d5a604adef5d5adfdf99b37aead88b73a1eb79b0b",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-01-14T01:39:32Z",
    "title_canon_sha256": "f2e4bb0e0f23b82781e8e102908b33a3128f8d8debdd3c3f20527f0ba23ee373"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.03230",
    "kind": "arxiv",
    "version": 1
  }
}