Pith Number

pith:COGJTCC4

pith:2017:COGJTCC4JUAJBUDPDHSJFRRRN5

not attested not anchored not stored refs pending

The sharp Gagliardo--Nirenberg--Sobolev inequality in quantitative form

Van Hoang Nguyen

arxiv:1702.01039 v1 · 2017-02-03 · math.FA · 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{COGJTCC4JUAJBUDPDHSJFRRRN5}

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	2026-05-18T00:51:29.142942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

138c99885c4d0090d06f19e492c6316f7564d38403d0a0705d73baaf4e260946

Aliases

arxiv: 1702.01039 · arxiv_version: 1702.01039v1 · doi: 10.48550/arxiv.1702.01039 · pith_short_12: COGJTCC4JUAJ · pith_short_16: COGJTCC4JUAJBUDP · pith_short_8: COGJTCC4

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/COGJTCC4JUAJBUDPDHSJFRRRN5 \
  | 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: 138c99885c4d0090d06f19e492c6316f7564d38403d0a0705d73baaf4e260946

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e70eddfa63de6034a6e3db6de378bd5ae14ce7562f3a1a15ecdaa2a06a1d0336",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-02-03T15:08:49Z",
    "title_canon_sha256": "bdc1ea212d235ef775e841852a53ef6a61d2535783148ab858cc5d09cc7d4172"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.01039",
    "kind": "arxiv",
    "version": 1
  }
}