Pith Number

pith:4YV76DJF

pith:2015:4YV76DJF7XBAMUEMESTW4JLZQU

not attested not anchored not stored refs pending

Interpolation inequalities on the sphere: linear vs. nonlinear flows

Jean Dolbeault (CEREMADE), Maria J. Esteban (CEREMADE), Michael Loss

arxiv:1509.09099 v2 · 2015-09-30 · 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{4YV76DJF7XBAMUEMESTW4JLZQU}

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	2026-05-18T01:29:20.391248Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e62bff0d25fdc206508c24a76e257985073268cab7fc2d8f8246702a9928dfff

Aliases

arxiv: 1509.09099 · arxiv_version: 1509.09099v2 · doi: 10.48550/arxiv.1509.09099 · pith_short_12: 4YV76DJF7XBA · pith_short_16: 4YV76DJF7XBAMUEM · pith_short_8: 4YV76DJF

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/4YV76DJF7XBAMUEMESTW4JLZQU \
  | 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: e62bff0d25fdc206508c24a76e257985073268cab7fc2d8f8246702a9928dfff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51032a4bb924316e60a8381e2ac9b18d6c4b70e597e5d25c083ada4f4114c8d9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-30T09:40:47Z",
    "title_canon_sha256": "d47c80f0b95ee501ce3f6e243ea81f4e082ded83f6fbfa3dbc70810974029295"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.09099",
    "kind": "arxiv",
    "version": 2
  }
}