Pith Number

pith:5P63RZ4O

pith:2019:5P63RZ4OFSLFD4K5WXR7OIFKJR

not attested not anchored not stored refs pending

Extremals for fractional Moser-Trudinger inequalities in dimension 1 via harmonic extensions and commutator estimates

Gabriele Mancini, Luca Martinazzi

arxiv:1904.10267 v1 · 2019-04-23 · 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{5P63RZ4OFSLFD4K5WXR7OIFKJR}

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	2026-05-17T23:47:54.629479Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebfdb8e78e2c9651f15db5e3f720aa4c687313cf3404ff8188d279bbb5441c69

Aliases

arxiv: 1904.10267 · arxiv_version: 1904.10267v1 · doi: 10.48550/arxiv.1904.10267 · pith_short_12: 5P63RZ4OFSLF · pith_short_16: 5P63RZ4OFSLFD4K5 · pith_short_8: 5P63RZ4O

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/5P63RZ4OFSLFD4K5WXR7OIFKJR \
  | 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: ebfdb8e78e2c9651f15db5e3f720aa4c687313cf3404ff8188d279bbb5441c69

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "543f1a994056bc340b7e63bbd498ff9580dd54ace232a2d33dd8e29c4597b1e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-04-23T12:08:21Z",
    "title_canon_sha256": "39a162ddfb72cc29c536f5aa4a27e315570b9d7ecdd3abdc75de6eea768f5336"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.10267",
    "kind": "arxiv",
    "version": 1
  }
}