Pith Number

pith:WCM5ZJPY

pith:2016:WCM5ZJPYXYB5IBVYB3VJU4LVJS

not attested not anchored not stored refs pending

A bridge between Sobolev and Escobar inequalities and beyond

Francesco Maggi, Robin Neumayer

arxiv:1609.02346 v3 · 2016-09-08 · math.AP · math.FA · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WCM5ZJPYXYB5IBVYB3VJU4LVJS}

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	2026-05-18T00:58:03.820020Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b099dca5f8be03d406b80eea9a71754ca9b5c8921d7d15bb7e6cd33ef0f22ff9

Aliases

arxiv: 1609.02346 · arxiv_version: 1609.02346v3 · doi: 10.48550/arxiv.1609.02346 · pith_short_12: WCM5ZJPYXYB5 · pith_short_16: WCM5ZJPYXYB5IBVY · pith_short_8: WCM5ZJPY

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/WCM5ZJPYXYB5IBVYB3VJU4LVJS \
  | 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: b099dca5f8be03d406b80eea9a71754ca9b5c8921d7d15bb7e6cd33ef0f22ff9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a50a405cab768a012304668a33d38b6ac28da06ba6dfe402d925473733e5065c",
    "cross_cats_sorted": [
      "math.FA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-09-08T09:29:51Z",
    "title_canon_sha256": "98f0ff99bea68be731c3d6fda513cfcf06ff53b6f464d9016a61aebf3fa5eace"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.02346",
    "kind": "arxiv",
    "version": 3
  }
}