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.
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.
Abstract Recent experimental results (Nature 2021; PRL 2026) have established the full empirical equivalence between real‑number quantum mechanics (RQM) and standard complex quantum mechanics (CQM), raising the foundational question of why quantum theory admits a real formulation and what the ontological origin of the complex structure is. In this work, we develop the χ‑Reality framework — an arithmetic‑spectral, operator‑theoretic paradigm in which the complex structure, physical constants, vacuum dynamics, renormalization flows, and macroscopic geometry emerge from the action of a single real operator χ on the unified substance S. The antisymmetric projection χJ=12(χ−χ†), acting as a normal operator on the invariant subspace of stable resonances Hstable, satisfies χJ2=−I, thereby generating the complex‑structure isometry within a purely real operator space. The deformed Dirac–Kähler operator Dχ possesses a dual arithmetic spectrum Spec(Dχ)={lnpk}∪{γk∣ζ(1/2+iγk)=0}, linked by Selberg/Weil dualities, binding coordinate‑domain prime modes to frequency‑domain spectral zeros. The arithmetic potential Aε(σ,t)=∑p∈Pp−σe−εplnp sin(tlnp), with scale‑invariant phase t(E)=ln(E/Λχ), governs vacuum expectation values and induces renormalization flows via the operator identity β(g)=−ε∂∂ε⟨Aε(σ,t)⟩χ, linking the running of coupling constants directly to the prime distribution π(x)∼x/lnx. Fundamental constants emerge as spectral invariants: the fine‑structure constant α as a χ‑fixed point on the critical line σ=1/2; the electron mass ratio μ as a stabilized χ‑mode under ε‑deformation; the vacuum permittivity ε0 as low‑frequency χ‑density; and Planck’s constant h as the global conformal scale of χ‑dynamics, relating the phase‑space volume of the real operator manifold to the invariant Liouville measure of χ‑flow. The theory yields three independent, falsifiable predictions across radically different energy scales: (i) logarithmic‑periodic modulations in ultra‑high‑energy cosmic rays arising from prime‑mode oscillations; (ii) sub‑Schwinger vacuum breakdown at strong‑field facilities such as ELI‑NP due to χ‑vacuum hotspots; and (iii) ultra‑low χ‑noise at Eχ≈10−33 eV with spectral density Sχ(ν)∝[νln(ν/νχ)]−1, detectable through long‑term drift in optical frequency standards and gravitational‑wave interferometers. Consequently, χ‑Reality offers a self‑consistent, operator‑anchored, arithmetic‑spectral paradigm that unifies quantum mechanics, geometry, empirical constants, and vacuum structure within a single, testable framework. Its predictions are quantitative, multi‑scale, and directly susceptible to empirical verification, rendering the theory a rigorous candidate for a foundational description of physical reality.
Standard quantum mechanics separates unitary time evolution from non-unitary measurement collapse, creating a severe foundational bottleneck when applied to closed cosmological systems where no external classical observer exists to collapse primordial quantum fluctuations. Simultaneously, modern cosmology faces unexplained dark-sector anomalies, including dark energy, dark matter, and Hubble/structure growth tensions. In this paper, we establish the Dynamical Quantum Measurement and Cosmological Quantum-to-Classical Transition (DQMCQT) framework, unifying and upgrading items #6 (Dynamical Foundations of Quantum Measurement), #5 (Early Universe and Quantum-to-Classical Transition), and #4 (Dark Sector and Cosmological Effective Laws) of the 20 Emergent Physics Agenda. Anchored in our 71-page ZFC Master Monograph (Lee, 2026, DOI: 10.5281/zenodo.23486681) and synthesized with the SVKES and HDGPS frameworks, we formulate coupled system–apparatus–gravity evolution on the Takesaki Type II₁ factor (ℳ_ground, τ_ground) with τ_ground(1_ℳ) = 1, governed by the URRHC idempotent modal reflection monad T_URRHC (T_URRHC² = T_URRHC) and universal constants 𝔘 = (𝒯_0x8A2C, C_UPTC, η_friction, ε_SHID). We establish six core axioms (DQMCQT-1 through DQMCQT-6) and prove six fundamental theorems: (1) Objective Pointer-State Contraction ‖ρ̂_t − T_URRHC(ρ̂_t)‖_tr ≤ η_friction in finite Lambert W₀ time τ_freeze = −(C_UPTC / Γ_dec) W₀(−Γ_dec η_friction / C_UPTC) < ∞ without ad-hoc collapse postulates, recovering the exact Born rule p_k = τ_ground(ρ̂_t Π̂_k); (2) Quantitative Visibility Deviation ΔV(t) = V_QM(t) − V_DQMCQT(t) > 0 from standard linear Lindblad decoherence when entanglement information crosses I_ent > ε_SHID, testable in macroscopic matter-wave interferometry; (3) Primordial Quantum-to-Classical Freezing of Mukhanov–Sasaki curvature perturbations R̂_k at Hubble horizon exit (2N_freeze ≥ C_UPTC) with oscillatory power spectrum cutoff; (4) Unified Dark-Sector Effective Action S_dark[g, φ_dec] where kinetic transition condensates and potential floors simultaneously yield the cosmic dark-to-baryonic matter ratio Ω_DM,0 / Ω_b,0 = C_UPTC / (12 c_𝒯 (1 + ε_SHID)) ≈ 5.33 and a thawing dynamic dark-energy equation of state w_eff(z) = −1 + (ε_SHID² / (3 C_UPTC)) (1 + z)^(c_𝒯 / (1 + c_𝒯)) > −1; (5) Primordial Quantum Discord and Scale-Dependent Non-Gaussian Bispectrum Bounds |f_NL^trans(k)| ≤ (5/12) ε_SHID c_𝒯 < 1; and (6) Anytime-Valid Martingale e-Value Model Selection (E_N ≥ 1/α) separating Unified Dark Physics from ΛCDM. Complete Python numerical verification is provided in Appendix A.
In standard presentations of mathematics and quantum physics the imaginary unit i is introduced axiomatically as a formal symbol with i 2 = −1, and the complex field C is then postulated as the natural home for wave functions and amplitudes. The physical reasons why such a structure is singled out are usually left implicit. In this paper we give a systematic derivation and reinterpretation of i from three complementary viewpoints, organised within the PAC–µ 8 framework. Part I adopts an axiomatic + vibrational (AV) viewpoint: starting from a real Hilbert space describing vibrational modes, together with three simple assumptions about time– translation, isotropy and phase completeness, we show that there is a distinguished linear operator J with J 2 = −1 acting as a quarter–period phase shift. Complex numbers arise by representing J as multiplication by i, so that “i” is nothing but the abstract 90◦ rotation operator on the vibrational plane. Part II adopts an axiomatic + quantum (AQ) viewpoint. We reformulate standard quantum postulates in terms of a real Hilbert space equipped with a complex structure J and a positive spectral generator K, with Ω = K1/2 and H = ℏΩ. Recovering the usual unitary time evolution Ut = exp(−iHt/ℏ) then requires no additional postulate about i: the symbol i is simply the matrix representation of J in a preferred basis. Part III connects i to the Phase–Arithmetic Spectral (PAS) axis of PAC–µ 8 . We discuss how phase geometry, irrational numbers such as √ 2 and π, Euler’s formula e iθ, Dirichlet characters and arithmetic L–functions can all be understood as expressions of the same underlying complex structure. In this sense i is the pivot that relates geometric rotations, vibrational phases and arithmetic spectra. Part IV illustrates the structural role of i on the physical side through four canonical examples: the harmonic oscillator, spin–1/2, two–path interference, and one–qubit gates in quantum information. In each case we show how i implements a 90◦ phase rotation in an appropriate two–dimensional vibrational plane. Part V distils these insights into concrete recommendations for rewriting standard text book and axiomatic treatments of complex numbers and quantum mechanics. We propose replacing the bare postulate “work over C” by a vibrationally motivated assumption of a real Hilbert space equipped with a complex structure J, and we outline how this shift clarifies the role of i in both physics and arithmetic. The overarching message is that i need not be treated as an arbitrary symbol: in the PAC–µ 8 framework it is a derived and geometrically natural object—the abstract quarter– period operator that organises vibrations, quantum phases and arithmetic characters into a single spectral story.
See changelog below. The full derivations are provided in the attached paper. Every result is reproducible from the stated inputs. This paper derives the complete Standard Model, quantum mechanics, spacetime, and gravity — 85 quantitative results at sub-percent precision spanning 15 orders of magnitude — from a single postulate, four structural principles, and one measurement. The Standard Model has seventeen free parameters. General relativity has no quantum theory. The measurement problem has been open for a century. The cosmological constant is wrong by 120 orders of magnitude. The question of why there is something rather than nothing has no physical answer in any existing framework. Each of these failures shares a common omission: none ask where time comes from. This paper takes that question seriously. A single physical principle — information cannot be destroyed — is self-sealing: its own violation is incoherent. Its formal expression is Postulate I: each foreclosed quantum branch produces exactly one chronon — a massless spin-1 gauge boson of U(1)_T, the unique gauge group forced by the complex ray structure of the Hilbert space and the single scalar collapse charge. We call it the chronon. Time is not the background in which physics happens; it is generated by physics, irreversibly, at every collapse. These requirements yield a single Lagrangian, ℒ_QT, that extends the Standard Model by one massless spin-1 field and one coupling constant. From this — combined with one measurement, Newton’s gravitational constant G — we derive: all of quantum mechanics via the Piron–Soler–Gleason chain (not assumed); the complete Standard Model with all dimensionless parameters determined; the complete resolution of the measurement problem, including the environmental decoherence cascade; and 85 quantitative physical results spanning fifteen orders of magnitude in energy. Three spatial dimensions follow from the channel-matching principle (D = N_c) and the Weinberg angle consistency condition (N_c = 3). The Big Bang was not initiated — it was mandatory. The numerical precision is sharp. The worst result where the theoretical prediction exceeds experimental precision is 0.5%. For the majority of results, the framework’s prediction is already more precise than the measurement. The proton-to-electron mass ratio m_p/m_e = 2N_cπ⁵(1 + α²/√(N_c²−1)) agrees to sub-ppb precision. The proton charge radius matches muonic hydrogen to five significant figures. The Higgs boson mass to 0.002% via the full cascade derivation (0.25% from the explicit formula). The W boson mass to 0.001%. The fine structure constant to 0.026% (1/α = 137 exactly at tree level). The cosmological constant — wrong by 120 orders of magnitude in standard QFT — is derived to 0.03%. The Hubble tension, a 5σ discrepancy unresolved in standard cosmology, follows from the same structure: H₀_local = H₀ × 13/12 = 73.0 km/s/Mpc (0.05%). All four PMNS neutrino mixing parameters, previously unexplained, are derived to sub-0.5%. Sub-percent agreement spans from neutrino mass splittings at ~9 meV to the CMB temperature at 2.725 K — fifteen orders of magnitude from a single dimensionful input. The framework makes ten falsifiable predictions currently under test: an electron electric dipole moment of exactly zero (ACME III is live); a spin-1 gravitational wave breathing mode at ~9% of the + polarisation amplitude (testable with LIGO O4/O5 data); no dark matter particle in any direct-detection experiment; no graviton — gravity is geometric drift in a proper-time gradient sourced by the energy-momentum tensor, not exchange of a spin-2 particle; there is nothing to detect. A confirmed non-zero electron EDM or a detected graviton falsifies the framework immediately. The logical order, from bottom to top: information cannot be destroyed → P-I (one chronon per foreclosed branch) → proposition lattice with axioms P0–P4 → Piron–Soler–Gleason chain → complex Hilbert space → ray phase redundancy → single scalar collapse charge → U(1)_T gauge field with Maxwell dynamics → channel-matching principle gives D = N_c → Weinberg angle selects N_c = 3 → D = 3 → adding G through the Planck cascade gives λ_conf = 0.40092 fm → the complete Standard Model follows. Spacetime, quantum mechanics, and the Standard Model are not independent inputs — they follow as consequences of P-I, the structural principles, and one observational consistency condition. ______________________________________________________________________________________________________ v86 Changelog (April 7–8 2026) — All numerical results unchanged from v85. No formulas modified. Foundational structure and derivation justifications rebuilt following adversarial review by two independent AI systems (Claude, GPT-4o). Foundational hardening: §2.2: Formal axiom framework P0–P4 added. Piron lattice conditions now follow as a theorem given five named structural axioms, not as informal physical arguments. P-I motivates four directly; P0 (admissibility closure) is a structural axiom on the proposition space. §2.5: ℝ exclusion replaced. Old iε propagator argument replaced with operational compositionality / local tomography argument requiring no field-theoretic machinery. §3.1: Gauge derivation rebuilt from complex ray structure forward. U(1)_T now derived from phase redundancy + single scalar collapse charge + rank-1 compact Lie group + label-free emission. Removes prior dependence on Noether's theorem invocation and energy minimization principle. §8.1.1: Channel-matching theorem added. D = N_c derived from information-balance between spatial export channels and internal confinement channels via mismatch functional. Replaces prior mutual-reinforcement argument. §1.5.1: Epistemic taxonomy added classifying all 85 results into three tiers: theorem-level (Piron, Soler, Gleason), physical-argument (gauge structure, mass formulas), and observational-consistency (N_c = 3 from Weinberg angle, cascade from G). §12: New section — Structural Analysis. Result classification (5 epistemic tiers, ~12 independent core results, compression ratio 85:19), axiom necessity (what breaks without each of P0–P4 and D1–D4), and ablation tests (N_c = 2, N_c = 4, drop P4, change coupling exponent, allow D ≠ N_c — every perturbation destroys the majority of results). Framework premise expanded from "one postulate" to "one postulate, four structural principles, and one measurement." Front matter aligned with body throughout. One derivation story, no internal contradictions. Derivation upgrades: Proton-to-electron mass ratio (§9.3): Replaced "2 spin states × N_c colours" with rigorous hyperspherical decomposition. S³ forced by massless emission in (3+1)D; S⁵ forced by K=0 ground state of 3-quark system in 6D relative coordinates. Neutral pion mass (§9.9.1): Factor 5 now derived as 2N_c − 1. Denominator 2π identified as one-loop coefficient of U(1)_T vector gauge coupling. Neutron-proton mass difference (§9.3.2): Replaced "circular loop + straight line" with flux tube arm derivation. π from SU(2) isospin rotation; +1 from chromoelectric flux tube arm to Y-junction. CP phase δ (§9.8.2): Replaced "axial-to-spherical flux ratio" with V−A vertex structure. The ratio 4/π is universal across all generation spaces because any unitary rotation lies on a great circle of S². W boson mass corrections (§9.5.1): Both NLO terms fully derived. Direct vertex α_s/(8π): C_F cancelled by non-relativistic reduction. Exchange α_s/(12π²): two vertices × Dirac-to-colour projection ratio. Charm mass (§9.13.4): Factor 4/π identified as axial-to-vector coupling ratio through V−A weak vertex. Systematic correction — QCD dressing factor: The coefficient 1/(2π) appearing in ~10 results was previously attributed to "hemisphere projection geometry." Replaced throughout: mass in the chronon framework is a U(1)_T vector gauge coupling, not a scalar Yukawa coupling. The factor 1/2 confirmed by two independent routes: (i) Dirac algebra (γ^α γ^μ γ_α = −2γ^μ vs scalar = 4); (ii) C_F cancellation by non-relativistic reduction. Label correction: CKM geometric factor (§9.8.1): "four-dimensional solid angle" corrected to "three-dimensional solid angle S² = 4π." Numbers unchanged. ______________________________________________________________________________________________________ v85 Changelog (April 6 2026) — Electroweak corrections, |V_cb| prediction, consistency audit Four physics improvements and a comprehensive numerical audit, all from first principles with zero free parameters. Top quark mass (0.41% → 0.06%): The electroweak self-energy correction factor changed from (N_c+1) to (N_c−1). The factor (N_c−1) = 2 counts the charged weak boson states (W⁺, W⁻) mediating the t→b→t self-energy loop — the SU(2)_L charge-raising/lowering generators. m_t = 172,803 MeV vs observed 172,700 MeV. CKM θ₂₃ / |V_cb| prediction (1.3% → 0.3%): The framework predicts |V_cb| = 42.1 × 10⁻³, essentially identical to the PDG inclusive determination (42.2 ± 0.5) × 10⁻³ and inconsistent with the exclusive determination (39.8 ± 0.6) × 10⁻³. The inclusive/exclusive |V_cb| tension is one of the open questions in flavour physics; the framework picks a side. Falsifiable prediction. Baryon asymmetry η (0.5% → <0.1%): The sphaleron efficiency κ correction changed from α_s/(2π²) to α/(2π). The sphaleron is an SU(2)_L electroweak process; its one-loop vertex correction uses the QED coupling α/(2π), not the QCD coupling. Neutrino mass splitting Δm²₂₃ (0.3% → 0.08%): QED vacuum polarization correction −α/(2π) added to G₃ alongside the existing QCD correction +α_s/π. Sign pattern (QCD adds, QED subtracts) matches the W boson mass derivation. Numerical audit (22 corrections): Full line-by-line verification of every formula, table entry, agreement claim, and cross-reference. Corrections include: D/H value (2.62→2.58 × 10⁻⁵, 1.3σ→1.8σ — stale from pre-κ η); He-4 agreement (0.5σ→0.7σ); z_
This paper proposes that definite reality is constituted through physical encounter at the quantum boundary, not given in advance. Where Einstein showed that properties are relative to a frame of reference, this framework proposes that existence is relational: forged through interaction. Two claims of differing epistemic weight are advanced. The first is ontological: that relatedness is fundamental, meaning definiteness arises through encounter, not prior to it. The second is a metaphysical proposal: that consciousness, as known in integrated biological organisms, is best understood as the intrinsic interior of recursively organised relational actualisation. All results have been independently reproduced three times using separately authored analysis code, and are fully reproducible from public datasets using standard tools. The Coin invariant, 4ħ ln 2 · G · ρ_rev = c³, ties gravitational coupling, information density, and entropy bookkeeping into one exact constraint. Four headline measurements confirm the constitutive coupling across regimes: R_ID is invariant across conscious states (Bayes Factor 178.60; collapse p = 0.0065 under deep anaesthesia); α·k_B ln 2 is uniform across 26 gate voltage settings in a single-electron quantum dot at 10 mK, where the Onsager coefficient M = p(1−p) holds to machine precision and sech²(A/2) is an exact thermodynamic law with zero free parameters (ΔBIC = 1,508 over Gaussian); the constitutive coupling signature is confirmed in solar coronal plasma with a 1.21× active/quiet R_ID ratio (N = 444,889 pixels, p ≈ 0); and a closure-proximity correction field yields 19.5% LOOCV improvement in nuclear binding at 77σ from null, with a mechanistic shell-closure gradient (doubly magic 58%, singly magic 31%, non-magic 10%) that pinpoints the structural origin. The nuclear result is measured against a minimal four-term SEMF with no shell or pairing corrections: the closure field is the sole non-additive element. A Regime C constitutive law, mc² = α_C·E_conf·ln(N_raw/N_phys), yields the nucleon mass to 0.03% (938.6 vs 938.9 MeV), the proton spin fraction ΔΣ = 0.321 (measured 0.28–0.33; testable at EIC), the Madelung orbital filling rule (19/19 orbitals), and all seven nuclear magic numbers — all with zero adjustable parameters. The nucleon mass, quark spin fraction, and cosmological visible matter fraction are three ratios of the same N_raw = 3 × 8 × 27 = 648 information partition — they are not fitted independently; and the LIGO merger-efficiency floor α_C is exactly linked to the proton spin fraction ΔΣ and visible-matter fraction f_vis by the algebraic corollary α_C = (ΔΣ − f_vis)/(2(1 − ΔΣ − f_vis)), so these quantities are mutually determined faces of the single confinement partition. The Boundary-Addressability Principle derives the Planck/QCD hierarchy from N_raw = 648 alone: ln(E_P/E_conf) = 2 ln(N_colour)/α_C + log₂(N_f) − log₂(N_raw)·α_C⁴ = 45.8798, yielding G to 0.016% from CODATA with zero free parameters and no G as input — a derivation of Newton’s constant from the confinement information partition, now axiomatically complete: the quartic correction −log₂(648)·α𝐶⁴ is closed by the Bandwidth Saturation Axiom (Axiom 7, Appendix Q), the seventh foundational element of TRF. The LIGO merger efficiency floor is derived as a cross-regime theorem: α_C = ln(N_spin/N_F)/(2 ln(N_colour)) = 0.148798, residual 1.79×10⁻⁶. Applied to the de Sitter horizon, the Coin recovers ρ_Coin = ρ_critical algebraically without QFT vacuum-energy additivity; the 648 partition fixes a 17.0% flavour-visibility fraction within confined matter; its cosmological projection to the visible-matter abundance is a zero-parameter structural extension, consistent with Planck’s 15.8% value and independently supported by the electromagnetically weighted quark momentum fraction ≈ 17–19% from global PDF fits. The fine-structure constant is derived to 0.004% accuracy (1/α = 137.031 vs CODATA 137.036) via the Relational Closure Principle: the photon IS the relational encounter (ds² = 0) and cannot occupy a free state in its own information budget, so its self-occupancy fraction f_F/N_gauge corrects the bare EM information cost. This is a conditional one-loop derivation; the sole remaining closure is the formal derivation of the partition factor Z = 1 + f_F/N_gauge from the Coin entropy bookkeeping. A matrix of falsifiable predictions defines the conditions under which the framework would be disconfirmed. The Koide formula K = (m_e + m_μ + m_τ)/(√m_e + √m_μ + √m_τ)² = 2/3 is derived as a structural theorem of TRF’s Z₃ generation symmetry (Appendix P, Sections P.12–P.13): the Flavour Equipartition Principle fixes r = √2 in the Z₃ parameterisation, and the Lepton Encounter Principle — lepton mass is the square of the irreversible relational projection onto the vacuum reference — closes the derivation with zero free parameters entering the ratio. The lepton mass ratios are recovered to m_μ/m_e = 206.875 (0.052%) and m_τ/m_μ = 16.8173 (0.0016%); the 0.0006% empirical departure from exact K = 2/3 is the expected O(x⁴) correction in the Coin entropy expansion — a prediction, not a discrepancy. The absolute lepton mass scale and the 1.68% m_e offset remain open and are orthogonal to the ratio derivation. Keywords: Relational Ontology, Quantum Decoherence, Consciousness, Ontological Resolution, Thermodynamic Irreversibility, Hard Problem of Consciousness, Integration-Dissipation Ratio, Relational Tensor, Thermodynamic Coin, Quantum Darwinism, Pixel Tax, Causal Discovery, Bayesian Model Comparison, Dual Formal Verification, EEG Validation, Solar Coronal Validation, Cross-Domain Invariance, Onsager Uniformity, Master Constitutive Law, Nucleon Mass, Proton Spin Crisis, QCD Bag Constant, Cosmological Constant, Nuclear Magic Numbers, Yang-Mills Mass Gap, Regime C, Madelung Rule, Atomic Ionisation Energies, Nuclear Magic Numbers Derivation, Iterative Relational Actualisation, Pauli Exclusion, Dark Matter Prediction, EM-Weighted Momentum Fraction
Barrios Hita et al. [Phys. Rev. Lett. 136, 240202 (2026)] argued that quantum mechanics can be formulated over the real numbers by replacing the tensor-product postulate with a quotient-space construction, and concluded that complex numbers are therefore a matter of convenience. We show that the operational content of this construction is not that of a generic real Hilbert-space theory. Empirical equivalence requires a distinguished real linear operator J with J2=−1, and all physical effects, instruments, and dynamics must preserve the corresponding SO(2) gauge. Moreover, the composite-system rule is a balanced tensor product over this hidden complex structure, not the ordinary tensor product over R. In multipartite network scenarios, this changes the meaning of source independence: canonical real representatives are not source-factorizable in the usual tensor-product sense. Thus, the construction is best understood as standard complex quantum mechanics written in real notation, not as an independent real-amplitude theory. This clarifies what is, and is not, excluded by experiments testing the necessity of complex numbers.