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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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.

Cited by

1 paper in Pith

Null distance on cosmological spacetimes and monotone convergence

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

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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
  }
}