Pith Number

pith:OT4YAD5E

pith:2014:OT4YAD5EXEUBF47RAHFTJZQXIL

not attested not anchored not stored refs pending

On the Sobolev and Hardy constants for the fractional Navier Laplacian

Alexander I. Nazarov, Roberta Musina

arxiv:1408.3946 v1 · 2014-08-18 · 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{OT4YAD5EXEUBF47RAHFTJZQXIL}

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	2026-05-18T02:44:57.539218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

74f9800fa4b92812f3f101cb34e61742e47f9ce901b7a7e89462ddb7a5a5ab3e

Aliases

arxiv: 1408.3946 · arxiv_version: 1408.3946v1 · doi: 10.48550/arxiv.1408.3946 · pith_short_12: OT4YAD5EXEUB · pith_short_16: OT4YAD5EXEUBF47R · pith_short_8: OT4YAD5E

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/OT4YAD5EXEUBF47RAHFTJZQXIL \
  | 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: 74f9800fa4b92812f3f101cb34e61742e47f9ce901b7a7e89462ddb7a5a5ab3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a50647a2415eab4d346a92f79b958b162f79aef374a367878b9adf14cb38741",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-08-18T09:24:45Z",
    "title_canon_sha256": "ad0daaf5b2b114b158930740e3927c9c1c4068c737cb1a4cb8391b74029418e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.3946",
    "kind": "arxiv",
    "version": 1
  }
}