Pith Number

pith:E2N2APH3

pith:2018:E2N2APH3X7XXJKQ4AXQEXO6PKM

not attested not anchored not stored refs pending

Spectral multipliers and wave equation for sub-Laplacians: lower regularity bounds of Euclidean type

Alessio Martini, Detlef M\"uller, Sebastiano Nicolussi Golo

arxiv:1812.02671 v2 · 2018-12-06 · math.AP · math.CA · 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{E2N2APH3X7XXJKQ4AXQEXO6PKM}

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.

Cited by

1 paper in Pith

Almost everywhere convergence of Bochner-Riesz means on Heisenberg-type groups

Receipt and verification

First computed	2026-07-05T08:28:30.405966Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

269ba03cfbbfef74aa1c05e04bbbcf5330c5d409ba412b7ada5171c9ac5198cf

Aliases

arxiv: 1812.02671 · arxiv_version: 1812.02671v2 · doi: 10.48550/arxiv.1812.02671 · pith_short_12: E2N2APH3X7XX · pith_short_16: E2N2APH3X7XXJKQ4 · pith_short_8: E2N2APH3

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/E2N2APH3X7XXJKQ4AXQEXO6PKM \
  | 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: 269ba03cfbbfef74aa1c05e04bbbcf5330c5d409ba412b7ada5171c9ac5198cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a44724349d10762b454e20c57ae377cbf276ab8a8a69447836a69547d17a4dc",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-12-06T17:13:53Z",
    "title_canon_sha256": "8abc70d3c8dfbd18697dc39360274168d2a3e133e002bfad74995ecc23ea651f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.02671",
    "kind": "arxiv",
    "version": 2
  }
}