HLV-LAYER-ORIGIN-001–003: Locked Numerical Gates for Layer-Twist Observability, Emergent Spectral Fibres, and Intrinsic Projector Holonomy

This archive contains the complete locked numerical sequence HLV-LAYER-ORIGIN-001 through HLV-LAYER-ORIGIN-003, developed to test a prospective layered common-origin construction in the Helix–Light–Vortex (HLV) framework. The investigated hypothesis starts from a common six-dimensional cut-and-project source and asks whether target-independent, relatively rotated two-dimensional layer structures can generate both an effective stacked carrier and intrinsic transport structure without inserting a desired gauge group, fibre rank, or curvature by hand. The archive preserves all three locked Colab notebooks together with their corresponding result packages and SHA-256 checksums. HLV-LAYER-ORIGIN-001 -------------------- Gate 001 tested an initial spectral-sector construction across HLV-like irrational twist, zero twist, periodic twist, alternative irrational twist, shuffled, and random controls. Recorded verdict: NO_ROBUST_EMERGENT_FIBRE A subsequent mathematical audit identified an important observability limitation in this first implementation. The acceptance condition used a rotationally symmetric internal window. For an orthogonal internal rotation R, ||Y R^T||_2 = ||Y||_2, so the acceptance mask was invariant under the tested rotation. Consequently, the first observable could not distinguish the twist branches by construction. Gate 001 is retained unchanged as a negative and protocol-diagnostic result. It is not interpreted as a falsification of the complete layered hypothesis. HLV-LAYER-ORIGIN-002 -------------------- Gate 002 was defined as a new pre-result protocol rather than a retrospective modification of Gate 001. It introduced an anisotropic internal window and an order-sensitive coupled stack operator, making relative layer rotation observable while keeping the construction and controls frozen across branches. Recorded verdict: TWIST_COUPLING_OBSERVABLE__PROCEED_TO_PROJECTOR_TRANSPORT_GATE The frozen observability, order-sensitivity, and perturbation-robustness criteria passed. This establishes only a finite numerical result: relative twist and layer ordering can leave measurable signatures in the specified anisotropic layered construction. Golden-ratio physical specificity was NOT established. Alternative irrational, periodic, shuffled, random, and zero-twist branches remain essential controls. HLV-LAYER-ORIGIN-003 -------------------- Gate 003 tested the substantially stronger question of whether the observable layered construction generates a robust target-independent spectral fibre and projector-derived transport/holonomy structure. The gate examined spectral rank stability, overlap conditioning, admissible loop support, frame covariance, nontrivial holonomy, noncommutativity, control specificity, and perturbation robustness. Recorded verdict: NO_ROBUST_EMERGENT_FIBRE The HLV-IRR branch did not satisfy the frozen robust-fibre criterion. Adequate intrinsic loop support was not obtained, and no noncommuting projector holonomy was established. Frame-covariance residuals were nevertheless at numerical precision, supporting the internal consistency of the implemented projector/transport calculation. Finite nontrivial holonomy diagnostics appeared in some control branches, preventing an HLV-specific interpretation. Scientific interpretation ------------------------- The combined 001–003 sequence therefore supports the following restricted conclusion: 6D-derived anisotropic layered geometry → relative twist/order observability is numerically supported within the frozen finite Gate-002 construction. The stronger chain layered geometry → robust emergent spectral fibre → intrinsic nontrivial projector holonomy → noncommuting holonomy is NOT supported by Gate 003. The sequence therefore provides both a positive intermediate result and a subsequent falsification boundary rather than a monotonic sequence of positive tests. No result in this archive establishes a physical gauge field, U(1), SU(2), SU(3), Standard-Model gauge emergence, gravity, fermions, spacetime emergence, continuum quantum field theory, cosmological inflation, dark energy, or global cosmic rotation. Golden-ratio physical specificity is also not established. Any successor gate must be defined prospectively and must not obtain a positive result by retrospectively relaxing the rank-stability, overlap, loop-support, commutator, specificity, or perturbation thresholds used here. The archive is intended as a reproducible record of hypothesis formation, protocol locking, negative controls, successful finite observability, and subsequent failure of the stronger emergent-holonomy hypothesis. Author: Marcel Krüger HLV–RFP, Independent Researcher Meiningen, Germany ORCID: 0009-0002-5709-9729 Date: 17 August 2026