Pith Number

pith:23R4JOLW

pith:2022:23R4JOLWHJ3JVIQRHK2PAMT5N5

not attested not anchored not stored refs pending

Spectral asymptotics for sub-Riemannian Laplacians

CaGE ), Emmanuel Tr\'elat (LJLL (UMR\_7598), Luc Hillairet (IDP), Yves Colin de Verd\`i\`ere (IF)

arxiv:2212.02920 v1 · 2022-12-06 · math.DG · math.MG · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{23R4JOLWHJ3JVIQRHK2PAMT5N5}

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

5 papers in Pith

Pleijel's theorem for a class of degenerate elliptic operators

Nonclassical Weyl laws and Connes' Integration for weak Lorentz ideals, I

Quantum ergodicity for contact metric structures

Noncommutative Geometry, Spectral Asymptotics, and Semiclassical Analysis

Receipt and verification

First computed	2026-07-05T05:22:35.821062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6e3c4b9763a769aa2113ab4f0327d6f7c24c08e44b981e7cdad73d74c44c260

Aliases

arxiv: 2212.02920 · arxiv_version: 2212.02920v1 · doi: 10.48550/arxiv.2212.02920 · pith_short_12: 23R4JOLWHJ3J · pith_short_16: 23R4JOLWHJ3JVIQR · pith_short_8: 23R4JOLW

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/23R4JOLWHJ3JVIQRHK2PAMT5N5 \
  | 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: d6e3c4b9763a769aa2113ab4f0327d6f7c24c08e44b981e7cdad73d74c44c260

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f2e16f4a2031f49618ee29d03e4ac24ba7a4044cfbac8253dbce69bbee273f03",
    "cross_cats_sorted": [
      "math.MG",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2022-12-06T12:20:13Z",
    "title_canon_sha256": "cfd6913f57c6ed3376b5ff682bd7a0b456bfa79c8f54fd7a71441c8d10ff3b19"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.02920",
    "kind": "arxiv",
    "version": 1
  }
}