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SupportingRegistration Geometry

Canonical Complex Structure Without Canonical Orientation: Gauge-Equivalent Participant-Exchange Lifts in ACRF-4

Proves that canonical ACRF-4 derives a local complex structure but not a canonical complex orientation: gauge-equivalent lifts of the same participant exchange act with opposite signs on J, so only the unoriented class [J] = {J,-J} descends through the internal-label quotient.

2026-09-17v1.0DOI: 10.6084/m9.figshare.33916978View publication

Scope

Exact local tangent and quotient no-go result at the nonzero persistent closed registration. Participant block exchange P_SC is kept distinct from the internal relabeling gauge G = S2^(S) x S2^(C); the orientation ambiguity is derived from their interaction in the concrete finite model rather than assumed abstractly.

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Relevant research claims

Keywords

  • Registration Theory
  • Registration Theory (Physical Foundations)
  • Eugene Catrambone
  • ACRF-4
  • persistent registration closure
  • complex structure
  • complex orientation
  • gauge-equivalent lifts
  • participant exchange
  • bilateral registration
  • internal relabeling gauge
  • quotient symmetry
  • conjugate complex structure
  • orientation no-go theorem
  • unoriented complex structure
  • J squared equals minus I