Pith Number

pith:76PCV57R

pith:2015:76PCV57RINI7Q4TEISBRRA3G4T

not attested not anchored not stored refs pending

Gradient stability for the Sobolev inequality: the case $p\geq 2$

Alessio Figalli, Robin Neumayer

arxiv:1510.02119 v2 · 2015-10-07 · 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{76PCV57RINI7Q4TEISBRRA3G4T}

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	2026-05-18T01:03:31.045060Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff9e2af7f14351f872644483188366e4de5412e33a96f24341606408708f2dfc

Aliases

arxiv: 1510.02119 · arxiv_version: 1510.02119v2 · doi: 10.48550/arxiv.1510.02119 · pith_short_12: 76PCV57RINI7 · pith_short_16: 76PCV57RINI7Q4TE · pith_short_8: 76PCV57R

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/76PCV57RINI7Q4TEISBRRA3G4T \
  | 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: ff9e2af7f14351f872644483188366e4de5412e33a96f24341606408708f2dfc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "375501af5e75c95565c8357f1b1eef9a86b896c84dc102a6b69d35f13812ed65",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-10-07T20:30:23Z",
    "title_canon_sha256": "a355747250f170a3a5c5c745df4c35101d2df726130f7435b0b344438a5cf76a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.02119",
    "kind": "arxiv",
    "version": 2
  }
}