Pith Number

pith:YT44KSMC

pith:2016:YT44KSMCP5SA6RCFQBSOTJPLQY

not attested not anchored not stored refs pending

Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces

Carlo Mercuri, Jacopo Bellazzini, Jean Van Schaftingen, Marco Ghimenti, Vitaly Moroz

arxiv:1612.00243 v2 · 2016-12-01 · math.FA · math-ph · math.AP · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YT44KSMCP5SA6RCFQBSOTJPLQY}

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	2026-05-18T00:05:19.908350Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4f9c549827f640f44458064e9a5eb86269802b0db4cc650a05bc676e204db16

Aliases

arxiv: 1612.00243 · arxiv_version: 1612.00243v2 · doi: 10.48550/arxiv.1612.00243 · pith_short_12: YT44KSMCP5SA · pith_short_16: YT44KSMCP5SA6RCF · pith_short_8: YT44KSMC

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/YT44KSMCP5SA6RCFQBSOTJPLQY \
  | 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: c4f9c549827f640f44458064e9a5eb86269802b0db4cc650a05bc676e204db16

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0171e25182268768011b848983206aa962079e47b2e04ac86e6e6b18caffc63b",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-12-01T13:46:45Z",
    "title_canon_sha256": "0385814d5206a1f5b8318f0aa3e260dc30371eb9d79c56ec772337af3041607c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.00243",
    "kind": "arxiv",
    "version": 2
  }
}