Pith Number

pith:TUS4OVDQ

pith:2011:TUS4OVDQP5DI6REDOA7GFK5GE5

not attested not anchored not stored refs pending

Necessary Conditions for Fractional Hardy-Sobolev's Inequalities

E. Ostrovsky, L. Sirota

arxiv:1108.1387 v1 · 2011-08-05 · 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{TUS4OVDQP5DI6REDOA7GFK5GE5}

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	2026-05-18T04:16:11.066245Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d25c754707f468f4483703e62aba62756602366d7faee5c56196f7f5f1d81b6

Aliases

arxiv: 1108.1387 · arxiv_version: 1108.1387v1 · doi: 10.48550/arxiv.1108.1387 · pith_short_12: TUS4OVDQP5DI · pith_short_16: TUS4OVDQP5DI6RED · pith_short_8: TUS4OVDQ

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/TUS4OVDQP5DI6REDOA7GFK5GE5 \
  | 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: 9d25c754707f468f4483703e62aba62756602366d7faee5c56196f7f5f1d81b6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b064b30a1bb31815dcff31da2cadd641342ce15de4cc0458787cce0af723c91d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-08-05T19:20:10Z",
    "title_canon_sha256": "220af393e8c554236c50bce489b0bc1cf8df4035afa930a4ac7177510a8fbe4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1387",
    "kind": "arxiv",
    "version": 1
  }
}