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June 21, 20260 citationsOpen Access

Exact Dynamical Identifiability of Full Torsion

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HSHiroyuki Shioiri

Key Points

  • The aim is to demonstrate that the full torsion tensor can be precisely reconstructed from time-resolved twistor transport.
  • Utilized four probe directions spanning spacetime for pointwise reconstruction.
  • Employ two full-spinor jets or three projective-ray jets to determine the generator.
  • Ensured gauge-covariant and metric-free reconstruction through Levi-Civita subtraction.
  • Proved that the full 24-component torsion tensor is exactly recoverable.
  • Established that all-null tetrahedral probes are sufficient for the reconstruction process.
  • Showed that finite holonomy samples cannot identify an arbitrary torsion history.

Abstract

This paper proves that the full 24‑component torsion tensor is exactly recoverable from time‑resolved twistor transport. The logarithmic derivative of each propagator returns the instantaneous chiral generator, and the torsion map factorises as a tensor‑product DV=(EV⊗ϕ)∘C, giving rank 6 rank V. Four probe directions spanning spacetime are necessary and sufficient for pointwise reconstruction, including all‑null tetrahedral probes. Two full‑spinor jets or three projective-ray jets determine the generator, while finite holonomy samples never identify an arbitrary torsion history. The reconstruction is gauge‑covariant and metric‑free after Levi‑Civita subtraction.

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Cite This Study

Hiroyuki Shioiri (2026) studied this question.

synapsesocial.com/papers/6a37813124f042ddf4c5b1dbhttps://doi.org/10.5281/zenodo.20766076
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