Pith Number

pith:B7Q4FPI2

pith:2025:B7Q4FPI2L2XO23BJUV4WOAWYK3

not attested not anchored not stored refs pending

A critical Hardy-Rellich inequality

Hern\'an Castro

arxiv:2511.16537 v3 · 2025-11-20 · math.AP · 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{B7Q4FPI2L2XO23BJUV4WOAWYK3}

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	2026-05-20T00:00:28.240699Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fe1c2bd1a5eaeed6c29a5796702d856d65ecf52acd565f636a58e136f5af4e3

Aliases

arxiv: 2511.16537 · arxiv_version: 2511.16537v3 · doi: 10.48550/arxiv.2511.16537 · pith_short_12: B7Q4FPI2L2XO · pith_short_16: B7Q4FPI2L2XO23BJ · pith_short_8: B7Q4FPI2

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/B7Q4FPI2L2XO23BJUV4WOAWYK3 \
  | 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: 0fe1c2bd1a5eaeed6c29a5796702d856d65ecf52acd565f636a58e136f5af4e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "664aff97f8c8cff912a12bf49344339b914eb479b9fb03a9b3c163cc29be48a2",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-11-20T16:52:15Z",
    "title_canon_sha256": "d122278038892b5b1d08b6b2816a9075434267faddcd1f8c84cbb9ed387951e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.16537",
    "kind": "arxiv",
    "version": 3
  }
}