Pith Number

pith:45HWE32B

pith:2016:45HWE32BJFJVFOAQ4LKUHDV54K

not attested not anchored not stored refs pending

Extremal Functions for Singular Moser-Trudinger Embeddings

Gabriele Mancini, Stefano Iula

arxiv:1601.05666 v1 · 2016-01-21 · 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{45HWE32BJFJVFOAQ4LKUHDV54K}

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.

Cited by

1 paper in Pith

Extremal functions for a singular Hardy-Moser-Trudinger inequality

Receipt and verification

First computed	2026-07-05T01:10:09.765329Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e74f626f41495352b810e2d5438ebde280560b3181bf6426cec160a5ed527833

Aliases

arxiv: 1601.05666 · arxiv_version: 1601.05666v1 · doi: 10.48550/arxiv.1601.05666 · pith_short_12: 45HWE32BJFJV · pith_short_16: 45HWE32BJFJVFOAQ · pith_short_8: 45HWE32B

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/45HWE32BJFJVFOAQ4LKUHDV54K \
  | 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: e74f626f41495352b810e2d5438ebde280560b3181bf6426cec160a5ed527833

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a0d31b755c036d52d05032e36d1a9fc5c39133b5f17deaf1be49171070900a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-01-21T15:00:39Z",
    "title_canon_sha256": "ed6d51e22c0d5b3964955132a4174ac8e7114a8ece409b77c3db31c0b4e5cc21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.05666",
    "kind": "arxiv",
    "version": 1
  }
}