Pith Number

pith:5C7ICRGH

pith:2019:5C7ICRGHYAKIJF7RIVTQHRFNZM

not attested not anchored not stored refs pending

Extremal functions for a singular Hardy-Moser-Trudinger inequality

Songbo Hou

arxiv:1908.03982 v1 · 2019-08-12 · 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{5C7ICRGHYAKIJF7RIVTQHRFNZM}

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	2026-07-05T00:28:11.828136Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8be8144c7c0148497f1456703c4adcb3dbae72beae5065f41d39487af68ea59

Aliases

arxiv: 1908.03982 · arxiv_version: 1908.03982v1 · doi: 10.48550/arxiv.1908.03982 · pith_short_12: 5C7ICRGHYAKI · pith_short_16: 5C7ICRGHYAKIJF7R · pith_short_8: 5C7ICRGH

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/5C7ICRGHYAKIJF7RIVTQHRFNZM \
  | 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: e8be8144c7c0148497f1456703c4adcb3dbae72beae5065f41d39487af68ea59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4eda11105dd2e2dbe580c1090c78b6860547bb02f5afec1686c02a4f2c415f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-08-12T02:23:25Z",
    "title_canon_sha256": "d92b9b8c8d186e7fb7cb3b04e029b48087897f8d3aeec2be7f2027faa404566f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.03982",
    "kind": "arxiv",
    "version": 1
  }
}