Pith Number

pith:VOMQHTHD

pith:2016:VOMQHTHDXRP4ELQNO4FZMO4EQY

not attested not anchored not stored refs pending

Asymptotic for optimizers of the fractional Hardy-Sobolev inequality

Salvatore Marano, Sunra Mosconi

arxiv:1609.01869 v3 · 2016-09-07 · 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{VOMQHTHDXRP4ELQNO4FZMO4EQY}

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	2026-05-18T00:36:09.596864Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab9903cce3bc5fc22e0d770b963b848621795685da33d65ad8b6777ee1d84fdc

Aliases

arxiv: 1609.01869 · arxiv_version: 1609.01869v3 · doi: 10.48550/arxiv.1609.01869 · pith_short_12: VOMQHTHDXRP4 · pith_short_16: VOMQHTHDXRP4ELQN · pith_short_8: VOMQHTHD

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/VOMQHTHDXRP4ELQNO4FZMO4EQY \
  | 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: ab9903cce3bc5fc22e0d770b963b848621795685da33d65ad8b6777ee1d84fdc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ee25ccca96537ef2183b60f794c568270ba271f4e19df539947f868011ffd86",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-09-07T08:16:24Z",
    "title_canon_sha256": "e01bfe7ddc08003b1fc9d6adfedbcb6648dfe11028683870d7c147b798e95c2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.01869",
    "kind": "arxiv",
    "version": 3
  }
}