Complex Metrics and Swap-Attribution - Prepared for submission to Foundations of Physics

Boris Kriger

A monograph in sixteen articles by Boris Kriger (2026) This monograph presents ICAST — Imaginary Component Attribution Swaps Theory — a foundational programme in physics built on a single mathematical structure: an antilinear involution σ on a Hilbert space, generalised to a structural operation on the metric attribution of physical configurations. Sixteen articles develop the structure cumulatively, apply it systematically across the foundational domains of physics, and demonstrate convergence with the quantitative results of the αLGQV (Local Gravitation of Quantum Vacuum) programme. The mathematical core The structural primitive is an antilinear involution σ on a Hilbert space, satisfying σ² = 𝟙 and σ(αψ) = ᾱσ(ψ). Antilinearity is essential: it makes σ a swap of real and imaginary components of attribution, not a unitary rotation. Conjugate observables — position and momentum, mass and energy, electric and magnetic field, matter and antimatter, our metric and the swapped metric — are pairs of attributions connected by σ. Where standard physics treats real and imaginary as a mathematical convenience, ICAST treats them as a structural duality: both components are physically real, each in its own attribution. Applications across foundational physics The σ-operation is realised across sixteen articles as: measurement (σ-fixation event); mass-energy swap-attribution of the 4-momentum; energy as σ-invariant, entropy as σ-monotone; charge as local σ-fixation; Heaviside duality as σ-action on the EM 2-form (with magnetic monopoles structurally excluded); electron capture as σ₂-merger; β-decay, neutrino oscillations, W/Z, Higgs, and electroweak unification as σ-metric phenomena; CPT-exactness at the 10⁻¹⁸ level as the empirical signature of the complete σ-structural swap covering both Heegaard hemispheres simultaneously. Article 11 establishes that σ-fixation is structurally necessary: coherence and persistence constraints make σ-fixation required for the existence of σ-coherent configurations. Article 12 installs the Quark-Gluon-Vacuum Plasma (QGVP) as ontological substrate: matter and vacuum are not separately real; both are markings of one substance. Articles 13–14 extend the framework to nucleosynthesis (the chiral condensate as σ-metric mediator from BBN through the r-process) and to the full hadronic sector (DIS, spectroscopy, nuclear structure, the Δ-resonance, the QCD phase diagram, with the spin crisis dissolved structurally). The gravitational reformulation Article 15 reformulates gravity: it is not a fundamental interaction. Factual gravity in our metric requires confinement-induced coordinate fixation of vacuum quanta, manifesting as the spatial structure of vacuum perturbation by visible matter. Imaginary gravity is intrinsic to unperturbed vacuum and is factual in the swapped Heegaard hemisphere. The cosmological constant Λ₀ is the projection of imaginary gravity into our metric. Dark matter is locally perturbed vacuum; dark energy is unperturbed vacuum. The cosmological constant problem, the dark sector, the singularity problem, and the equivalence principle are unified through one Heegaard-symmetric ontology. Convergence with αLGQV ICAST is the ontological foundation; αLGQV is the quantitative companion. αLGQV derives α ≈ 0.005 from QCD sigma terms with no free parameters; reproduces 175 SPARC galactic rotation curves through vacuum capture without dark-matter particles; identifies the Kriger limit ρ_cd ≈ 5ρ₀ as the structural barrier to gravitational collapse, replacing singularities with vacuum-cored compact objects; derives Λ₀ from measured QCD quantities; reads the CMB as latent heat of vacuum birth with η_B = α⁴. ICAST gives these quantitative results their structural meaning; αLGQV gives ICAST its empirical anchoring. The two programmes are independent in derivation and complementary in joint reading. Reception The αLGQV programme has been engaged in documented correspondence with leading specialists: Stanley Brodsky (Stanford/SLAC), Alexandre Deur (JLab), Craig Roberts (Nanjing), Robert Shrock (Stony Brook), Thomas Cohen (Maryland), Mikhail Shifman (Minnesota), George Ellis (Cape Town), Joan Solà Peracaula (Barcelona), Frans Klinkhamer (Karlsruhe), Salvatore Capozziello (Naples), Andreas Burkert (Munich), Ahmed Ali (Physica Scripta editorial board), Ariel Zhitnitsky (UBC), and others. Across more than thirty substantive exchanges, no derivational error was identified; no hidden free parameter was identified. Full record: https://interdisciplinary-research.institute/reception/ Falsifiable predictions ICAST makes four central structurally-discriminating falsifiable predictions: (P1) no free coloured object exists as an asymptotic state; (P2) no magnetic monopole exists as a stable particle; (P3) no fundamental dark-matter particle exists; (P4) CPT is exact and the speed of gravitational waves equals c at all measurable precision. Discovery of any of (P1)–(P3), or significant violation of (P4), falsifies the programme. Technical details 780 pages. Sixteen articles plus front matter (synopsis, contents, preface). Each article is structurally self-contained with formal propositions, counter-arguments, empirical contact, limitations, and references. The monograph is intended for foundations of physics, theoretical physics, philosophy of physics, and cosmology. Suitable for sequential reading, pivot-first reading (Articles 1, 11, 12, 15, 16), or referential consultation. Related work αLGQV Volume I: A Dark-Sector-Free Cosmology (DOI: 10.5281/zenodo.19027460) αLGQV Volume II: The Consistent Universe (DOI: 10.13140/RG.2.2.29913.28002) IIIR corpus: Orders of Orthogonality (DOI: 10.5281/zenodo.20100022); Volumetric Duality (DOI: 10.5281/zenodo.20100782); Topological Duality (DOI: 10.5281/zenodo.20100879); Operational Synthesis (DOI: 10.5281/zenodo.20102399) Keywords σ-programme; ICAST; antilinear involution; complex algebra; attribution swap; metric attribution; Heegaard symmetry; QGVP; quark-gluon-vacuum plasma; chiral condensate; relational realism; structural realism; foundations of physics; quantum mechanics; special relativity; thermodynamics; electromagnetism; weak sector; CP/CPT; nucleosynthesis; hadronic sector; gravity; dark matter; dark energy; cosmological constant; αLGQV; Boris Kriger.

J. G. Provost, Gérard Vallée

John Robert Lamarr Greer

Project Title: The Topological Information-Energy (TIE) Framework: A Mechanical Solution to Metric Interaction and the 0.00137 Constant (Paper 1)Summary:This repository contains the foundational "Audit" for the TIE Framework, focusing on the mechanical resolution of the 1989 Hitachi electron interference experiment. By moving beyond probabilistic models, this paper identifies the physical "steering" mechanism of the vacuum metric.Key Findings:The Metric Constant: Identification of the 75nm (\lambda_{75}) spatial reach of the metric wake.Petahertz Resonance: Derivation of the 1.64 PHz (f_m) frequency, representing the internal "heartbeat" of the vacuum displacement.The 137 Solution: A mechanical derivation of the 0.00137 coupling constant (Fine-Structure Constant) as a function of metric tension rather than probability.Included Materials:Full Manuscript (PDF): Containing the formal math and the "Mechanical Manifesto" (Rhythmic Synthesis).Audit Logic: Metadata linking to the 5,000-event Python simulation log.Historical Record: Preliminary submission data (NPHYS-2026-03-01292) establishing chronological priority.Author Note:This work is the first in a 4-part series (Astra 1-4) designed to provide an engineering-grade roadmap of the metric. It replaces the "Spooky Action" of quantum mechanics with a high-frequency, fluid-dynamic mechanical model of the vacuum.

William M. Honig

Makoto Naruse, Song-Ju Kim, Masashi Aono +4 more

Decision making is a vital function in the age of machine learning and artificial intelligence; however, its physical realization and theoretical fundamentals are not yet well understood. In our former study, we demonstrated that single photons can be used to make decisions in uncertain, dynamically changing environments. The two-armed bandit problem was successfully solved using the dual probabilistic and particle attributes of single photons. In this study, we present a category theoretic modeling and analysis of single-photon-based decision making, including a quantitative analysis that agrees well with the experimental results. The category theoretic model unveils complex interdependencies of the entities of the subject matter in the most simplified manner, including a dynamically changing environment. In particular, the octahedral structure and the braid structure in triangulated categories provide better understandings and quantitative metrics of the underlying mechanisms for the single-photon decision maker. This study provides insight and a foundation for analyzing more complex and uncertain problems for machine learning and artificial intelligence.

Helmut Satz