Pith Number

pith:WBTBDX74

pith:2015:WBTBDX74UJSNLC2N2SG62UJPGO

not attested not anchored not stored refs pending

Spectral multipliers for sub-Laplacians on solvable extensions of stratified groups

Alessandro Ottazzi, Alessio Martini, Maria Vallarino

arxiv:1504.03862 v2 · 2015-04-15 · 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{WBTBDX74UJSNLC2N2SG62UJPGO}

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	2026-05-17T23:58:15.326133Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b06611dffca264d58b4dd48ded512f33b66be62957cc83231597a7a8b18a131f

Aliases

arxiv: 1504.03862 · arxiv_version: 1504.03862v2 · doi: 10.48550/arxiv.1504.03862 · pith_short_12: WBTBDX74UJSN · pith_short_16: WBTBDX74UJSNLC2N · pith_short_8: WBTBDX74

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/WBTBDX74UJSNLC2N2SG62UJPGO \
  | 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: b06611dffca264d58b4dd48ded512f33b66be62957cc83231597a7a8b18a131f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a49dbfa97949d37b2d75d7c3d557727b9e23a778289f33acaf09dec082b372c3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-04-15T11:24:28Z",
    "title_canon_sha256": "295dbc52606d3f968a141f00f9f6cadeca4f5fc8aa98d3711444860a571be80f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.03862",
    "kind": "arxiv",
    "version": 2
  }
}