Pith Number

pith:WLCKG63E

pith:2007:WLCKG63EKFDF2GJXURCBGHXRHC

not attested not anchored not stored refs pending

Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere

Carlo Morpurgo, Luigi Fontana, Thomas P. Branson

arxiv:0712.3905 v5 · 2007-12-23 · math.AP · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WLCKG63EKFDF2GJXURCBGHXRHC}

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	2026-05-18T03:41:59.155384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2c4a37b6451465d1937a444131ef138a9869680c72e1b3ffbc7f06795e4e549

Aliases

arxiv: 0712.3905 · arxiv_version: 0712.3905v5 · doi: 10.48550/arxiv.0712.3905 · pith_short_12: WLCKG63EKFDF · pith_short_16: WLCKG63EKFDF2GJX · pith_short_8: WLCKG63E

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/WLCKG63EKFDF2GJXURCBGHXRHC \
  | 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: b2c4a37b6451465d1937a444131ef138a9869680c72e1b3ffbc7f06795e4e549

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a00578a0e594e54d05493195b24a05e6de7ab162ba7e911155b33c1211d2bcd",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2007-12-23T10:00:34Z",
    "title_canon_sha256": "8ee82cfd6b510b89b0f5f388b54fb5e0b468f20098f5af06069b7ec401b3acdb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.3905",
    "kind": "arxiv",
    "version": 5
  }
}