Pith Number

pith:XUMSEBQO

pith:2026:XUMSEBQOJTVODWGUQSR736WS3C

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Convergence of Lorentzian spaces and curvature bounds for generalized cones

Christian Ketterer

Timelike curvature and curvature-dimension bounds are stable under ℓ-convergence for Lorentzian pre-length spaces, with sharp bounds holding for generalized cones.

arxiv:2605.11271 v2 · 2026-05-11 · math.DG · math-ph · math.MG · math.MP

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\pithnumber{XUMSEBQOJTVODWGUQSR736WS3C}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

timelike curvature and timelike curvature-dimension bounds are stable under (measured) ℓ-convergence; a sequence of generalized cones −I_i ×_{f_i} X_i converges in ℓ-sense if the base I_i and fiber X_i converge in GH sense and f_i converge uniformly; sharp timelike curvature and CD bounds hold for such cones; pre-compactness theorem for smooth generalized cones with uniform lower bound on full Ricci or Riemann curvature.

C2weakest assumption

The spaces under consideration are Lorentzian pre-length spaces for which the new ℓ-convergence can be defined and for which timelike curvature bounds make sense; the uniform convergence of warping functions f_i and GH convergence of bases and fibers are sufficient to control the Lorentzian distance and curvature in the cone construction.

C3one line summary

Introduces ℓ-convergence for Lorentzian pre-length spaces, establishes stability of timelike curvature and CD bounds under it, and derives sharp bounds plus precompactness for generalized cones via GH convergence of bases and fibers.

Receipt and verification

First computed	2026-06-09T02:07:28.917307Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd1922060e4ceae1d8d484a3fdfad2d8981dc7e122ec4699b4822a26ea44b2e7

Aliases

arxiv: 2605.11271 · arxiv_version: 2605.11271v2 · doi: 10.48550/arxiv.2605.11271 · pith_short_12: XUMSEBQOJTVO · pith_short_16: XUMSEBQOJTVODWGU · pith_short_8: XUMSEBQO

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XUMSEBQOJTVODWGUQSR736WS3C \
  | 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: bd1922060e4ceae1d8d484a3fdfad2d8981dc7e122ec4699b4822a26ea44b2e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d28460bd638255c0462d8d66c27201b2aad239433654b517eca8f2116e183397",
    "cross_cats_sorted": [
      "math-ph",
      "math.MG",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-05-11T21:50:56Z",
    "title_canon_sha256": "f9458d092efcae08fd32872672931ba86db7bb300c113e0b36598e2e7ff111c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.11271",
    "kind": "arxiv",
    "version": 2
  }
}