QMU Registration of Gyroscopic Coupling in a Nonspinning Ferromagnet: Public-Trace Reproduction, a Composition Envelope, and a Material-Participation Constraint
Ahrens and Vinante recently measured gyroscopic spin-rotation coupling between two librational modes of a nonspinning, superconductively levitated hard-ferromagnet microsphere. The measured coupling provides a direct experimental relation between the magnetic moment $\mu$ and the collective intrinsic angular momentum $S$ associated with the particle magnetization. This study independently reconstructs the central experimental observable from the complete public archive. All five deposited MD5 checksums are verified, and all 315 two-channel traces are analyzed using the correlation model specified in the experimental supplement. Three of the four reconstructed Einstein--de Haas frequencies $f_I$ agree with the published central values to within $0.3%$. Dataset 1, which contains the smallest measured quadrature ratio, reconstructs $17.4%$ above the published central value but remains consistent within $1.24$ combined standard deviations. An inverse-variance fit to the four published material factors gives $g_{\mathrm{mat}}=1.16263\pm0.02578$, corresponding to $\Gamma_{\mathrm{mat}}=g_{\mathrm{mat}}/2=0.58131\pm0.01289$. The size-scaling quantity $f_I R^2/M$ is consistent with a common material factor across the four experimental configurations, with $\chi^2=0.969$ for three degrees of freedom and $p=0.809$ under the stated independence approximation. The experimental result is registered in Quantum Measurement Units using $\mathrm{angm}=h=m_e{\lambda_C}^2F_q$, $\mathrm{magm}={e_\mathrm{emax}}^2{\lambda_C}^2F_q$, $\mathrm{mchg}=m_e/{e_\mathrm{emax}}^2$, and $\mathrm{ccf}={e_\mathrm{emax}}^2/e$. These definitions produce the exact correlations $\mathrm{magm}/\mathrm{angm}=1/\mathrm{mchg}$ and $\mathrm{ccf}\,\mathrm{mchg}=m_e/e$. The resulting dimensionless QMU registration is $\Gamma_{\mathrm{QMU}}=(\mu\,\mathrm{ccf}/\mathrm{magm})/(S/\mathrm{angm})=g/2=(\mu\,\mathrm{ccf}/S)\mathrm{mchg}$. For a spherical particle, the experimental closure becomes $\Gamma_{\mathrm{QMU}}=5M\,\mathrm{ccf}\,\mathrm{mchg}/(4\pi\rho R^2f_I)=5Mm_e/(4\pi\rho R^2f_Ie)$. This expresses the measured gyroscopic coupling as a dimensionless ratio of magnetic moment and angular momentum while preserving an exact bridge to the experimentally reported quantities. Public composition reports for commercial Magnequench MQP-S-11-9-20001 powder are converted from weight percent to atomic percent and evaluated with the deliberately simplified constituent model used in the source study. The resulting composition controls give $g_{\mathrm{ctrl}}=1.3647$--$1.3952$ and $\Gamma_{\mathrm{ctrl}}=0.6823$--$0.6976$. Within this model, agreement with the measured value requires the rare-earth share of modeled angular momentum to increase from approximately $0.48$--$0.50$ to approximately $0.661$. The equivalent transition-metal participation factor is $\beta_{\mathrm{TM}}=0.468$--$0.516$. The QMU identity $\Gamma_{\mathrm{QMU}}=g/2$ is an exact registration of the measured observable rather than an independent material prediction. A predictive Aether Physics Model calculation must determine the species- and phase-resolved magnetic-moment and angular-momentum population sums before comparison with the experiment. The paper therefore defines the numerical target, identifies the principal material-participation constraint, and proposes composition, phase, temperature, particle-metrology, and blind-registration experiments capable of distinguishing competing closures. The deposit includes the complete paper, Overleaf-compatible LaTeX source, publication figures, machine-readable result summaries, composition inputs, claims ledger, figure-regeneration code, and package-validation report.
Ahrens and Vinante recently measured gyroscopic spin-rotation coupling between two librational modes of a nonspinning, superconductively levitated hard-ferromagnet microsphere. The measured coupling provides a direct experimental relation between the magnetic moment μ and the collective intrinsic angular momentum S associated with the particle magnetization. This study independently reconstructs the central experimental observable from the complete public archive. All five deposited MD5 checksums are verified, and all 315 two-channel traces are analyzed using the correlation model specified in the experimental supplement. Three of the four reconstructed Einstein--de Haas frequencies fI agree with the published central values to within 0.3. Dataset 1, which contains the smallest measured quadrature ratio, reconstructs 17.4 above the published central value but remains consistent within 1.24 combined standard deviations. An inverse-variance fit to the four published material factors gives gmat=1.16263±0.02578, corresponding to Γmat=gmat/2=0.58131±0.01289. The size-scaling quantity fIR2/M is consistent with a common material factor across the four experimental configurations, with χ2=0.969 for three degrees of freedom and p=0.809 under the stated independence approximation. The experimental result is registered in Quantum Measurement Units using angm=h=meλC2Fq, magm=eemax2λC2Fq, mchg=me/eemax2, and ccf=eemax2/e. These definitions produce the exact correlations magm/angm=1/mchg and ccfmchg=me/e. The resulting dimensionless QMU registration is ΓQMU=(μccf/magm)/(S/angm)=g/2=(μccf/S)mchg. For a spherical particle, the experimental closure becomes ΓQMU=5Mccfmchg/(4πρR2fI)=5Mme/(4πρR2fIe). This expresses the measured gyroscopic coupling as a dimensionless ratio of magnetic moment and angular momentum while preserving an exact bridge to the experimentally reported quantities. Public composition reports for commercial Magnequench MQP-S-11-9-20001 powder are converted from weight percent to atomic percent and evaluated with the deliberately simplified constituent model used in the source study. The resulting composition controls give gctrl=1.3647--1.3952 and Γctrl=0.6823--0.6976. Within this model, agreement with the measured value requires the rare-earth share of modeled angular momentum to increase from approximately 0.48--0.50 to approximately 0.661. The equivalent transition-metal participation factor is βTM=0.468--0.516. The QMU identity ΓQMU=g/2 is an exact registration of the measured observable rather than an independent material prediction. A predictive Aether Physics Model calculation must determine the species- and phase-resolved magnetic-moment and angular-momentum population sums before comparison with the experiment. The paper therefore defines the numerical target, identifies the principal material-participation constraint, and proposes composition, phase, temperature, particle-metrology, and blind-registration experiments capable of distinguishing competing closures. The deposit includes the complete paper, Overleaf-compatible LaTeX source, publication figures, machine-readable result summaries, composition inputs, claims ledger, figure-regeneration code, and package-validation report.
This paper develops the multi-receiver and first-occupation dynamics of the free one-spin phtn. The preceding papers determine the five-dimensional free-carrier geometry and the topological conditions under which one identified receiver seat can become a persistent occupied Ligamen Circulatus. The present work determines how one normalized phtn competes among many admissible receiver seats, how successive incomplete interactions compose into the first completed occupation, what portion of the complete event can be registered by four-dimensional occupied matter, and why receiver closure does not send a physical notification backward to the source. At Aether moment n, the primitive one-phtn event space is Hn(1)=HF,n⊕HLC,n⊕HR,n, where the sectors represent the surviving free carrier, the port-labeled occupied-seat alternatives, and an explicit remainder. Overlapping receiver labels are reduced through the Gram matrix Gyz=⟨LCy∣LCz⟩, so the number of independent closure alternatives is Meff=rankG. The completed-occupation projector is idempotent, Nocc2=Nocc, and therefore one normalized direct event contains either no completed occupation or one completed occupation. A coherent sum of receiver alternatives does not multiply the transported phtnx=mxλC3Fq2 or angmx=mxλC2Fq. The most general primitive linear coupling from the one-dimensional free channel into the orthogonal receiver closure space has one complex one-moment coordinate ϑy,n per admitted seat. Its anti-Hermitian generator is An=∑y(ϑy,n∣LCy⟩⟨Fn∣−ϑy,n∗∣Fn⟩⟨LCy∣). This generator reduces exactly to a two-mode rotation between the free phtn and the unique bright receiver mode ∣Bn⟩=Θn−1∑yϑy,n∣LCy⟩, where Θn2=∑y∣ϑy,n∣2. All receiver combinations orthogonal to ∣Bn⟩ are dark during that update. Beginning from the free state, the coherent free and closure weights are cos2Θn and sin2Θn. When completed records are orthogonal, absorbing, and supplied by one unique surviving free history, the one-moment weights compose into the exact first-occupation law Sn+1=Sn(1−qn) and Wn,y=Snqy,n, where qn=sin2Θn and qy,n=qn∣ϑy,n∣2/Θn2. The finite event ledger satisfies SN+1+∑n=0N∑yWn,y=1. The cumulative closure depth is DN=−lnSN, and the receiver fractions conditional on closure during moment n are W(y∣n)=∣ϑy,n∣2/∑z∣ϑz,n∣2. The intrinsic temporal lift ζh(Φ)=exp(ihΦ/2) remains 4π periodic, while occupied half-spin matter registers the quotient QT(ζh)=ζh2. A temporal deck-pair construction shows that durable material observables are invariant under ζh↦−ζh and omit both deck-odd branch information and coherence between mutually exclusive material records. The resulting four-dimensional restriction preserves the first-occupation measure but cannot, by linearity alone, select one realized extremal record. An additional Aether-internal registration principle remains necessary. Receiver attachment cancels the terminal free boundary without constructing a reverse chain to the source. If ∂ΓT(N)=vN−v0 and ∂By=ℓy−vN, then ∂(ΓT(N)+By)=ℓy−v0. The source remains the historical root of the completed event, while the terminal active free boundary is replaced locally by the occupied receiver boundary. Every receiver-local trace-preserving operation leaves the unconditioned source reduced state unchanged, ρS′=ρS. Global five-dimensional event completion is therefore compatible with local four-dimensional causality and cannot be used as a backward or faster-than-c material communication channel. The paper derives eleven coefficient-free prediction and falsifier classes, including effective receiver rank, rank-one bright coupling, coherent dark-mode extinction, geometric first-occupation statistics, additive closure depth, strict single-record occupation, local-accessibility nulls, no backward notification, and temporal quotient invariance. The strongest near-term experimental program combines receiver-response tomography, bright- and dark-mode preparation, first-occupation statistics, closure-depth additivity, and single-record anticoincidence. The most general primitive linear coupling from the one-dimensional free channel into the orthogonal receiver closure space has one complex one-moment coupling value ϑy,n for each admitted seat. These values together form the receiver coupling vector (ϑ1,n,ϑ2,n,…,ϑMn,n). The remaining constitutive problems are the QMU law that determines the magnitudes and relative phases of the receiver coupling values ϑy,n and the Aether-internal rule that realizes one material record in an individual event. The reproducibility package contains the manuscript PDF, complete Overleaf source, stage derivations, figures, claims ledger, equation inventory, prediction-falsifier ledger, validation scripts, public validation report, manifest, checksums, and license. The integrated validation suite completed 744,970 automated checks with zero failures. The maximum residual among exact identities was below 1.2×10−13. These checks establish formal and computational consistency of the stated derivations; they do not constitute independent empirical validation.
How a finite real cycle acquires a complex structure and a rule for composition Quantum theory uses a common imaginary unit when individual systems become a composite. This framework constructs that compatibility from finite real source histories. On the complete contrast sector of a three-cycle, the forward and backward comparisons give J=3P−P2,J2=−I The complex structure appears after the real comparison is specified. At a qualified unmarked boundary, opposite reference shifts select QAB=2I−JA⊗JB The range is the balanced complex tensor product. Its many-source composition is associative. A finite controlled contact supplies a nonfactorizable complex-linear operation, and exact residual bounds quantify departure from the selected sector. A source model that produces the contact A reversible controller compares operation orders on 24 proper signed frames. Its ordered, arrow-insensitive axis detector produces the retained cyclic response. The contact algebra gives [[G,G],[G,G]][G,G]≅C3. The construction prints the controller, scratch cleanup, full contrast probes, admissible operations and refusal states. A triaxial real response tensor realizes the detector and provides an explicit map between material contrasts and event-count contrasts. A record must survive the test of future operations A present tensor can hide a material marker that a later operation reveals. The framework derives independent force-gradient calibration and a delayed odd-field release. With a nonzero release field, energy and vector torque reconstruct the entire marker change: DU=−Δp⋅E,Dτ=Δp×E.Δp=∣E∣2E×Dτ−DUE The test includes shared calibration errors, stray fields, finite release pulses, marker relaxation and a complete operation inventory. It distinguishes detection of a retained record from agreement with its frozen prediction and from discrimination between physical theories. From proved structure to existing experiments The paper adds a conditional probability-correspondence theorem for the balanced composite, examines independent-source quantum-network experiments, and reproduces all eight measured rows of a public torque dataset. These supply composition benchmarks and demonstrated apparatus capabilities. Their published significances are kept attached to the hypotheses they actually test. The calibrated material release law is also a conventional electrostatic prediction; it is not presented as a QTT-exclusive signal. One material coefficient, two readouts A new archival calculation transfers a published same-particle libration calibration to a separate precession measurement. In the qualified rotor regime, the cross-readout relation is Ξ=ωlib2EpωsΩElcosϕl=alibaprec. An unchanged dipole-to-inertia coefficient gives unity. The calculation yields a slope of 2.909 from the libration calibration, compared with the published precession slope of 2.950, a central difference of 1.4135%. This shared electrostatic consistency relation eliminates the separate dipole and inertia; unequal field gains, dynamical corrections and shared uncertainty remain explicit. Reversal and long-term dipole-stability observations identify complementary laboratory capabilities. The complete matched-tensor delayed-release test remains an experimental target. When do two descriptions differ in any future experiment? The finite-reference extension follows a controlled source contact through shared references, fresh references, inverse operations, intermediate measurements and feedback. Its complete order-three response is gn=∑k=02pkζkn,ζ=e2πi/3,g3=1,g2=g1. A finite observable-span algorithm tests two fully specified models across every permitted future word. It either certifies agreement or returns the preparation, operation sequence, terminal outcome and exact probability difference. In the populated compatible-instrument benchmark, the complete quantum representation gives the same records without an additional target fit. A source-selected physical coupling or preparation remains a distinct route to predictive value. The framework includes nine vector figures, the retained source proofs and countermodels, complete reference-history benchmarks, calibration and vector-reconstruction theorems, runnable exact and numerical checks, published-input receipts, a data assessment and an experimental packet specification. The introduction defines the QTT terms needed to follow the construction without prior familiarity with the corpus. The probability-interface theorem, finite-memory bounds and covariance-weighted witness specify which further laboratory comparisons can distinguish physical models. Source anchors QTT Main Book, especially pp. 56, 248-250, 352 and 827-829; Artian's Completed-Event Four-Capacity Theorem; Frame-cycle derivation map, completed-event lexicon, and Artian's Universe and laboratory readout. Stable citation: 10.5281/zenodo.22882084.
This paper develops the realization calculus required to derive the four-fifths physical realization law in Quantum Measurement Units (QMU) without treating representation dimensions as sequential physical paths. A preceding temporal--charge analysis of the Aether unit established two distinct representation ranks. The complete exposed realization capacity has rank four, generated by electrostatic polarity crossed with the contemporaneously available left/right temporal-torque routes, while the nonconstant Aether chronogeometry has rank five. This establishes the geometric ratio 4/5, but rank counting alone does not imply the physical scaling αa4/5. To determine the required realization law, let R be a positive self-adjoint realization operator acting on a finite-dimensional QMU representation space. A scalar realization deficit is required to be continuous, invariant under orthogonal or unitary change of basis, additive under independent direct sums, additive under composition of commuting positive realizations, and antisymmetric under reciprocal inversion. These requirements select, up to normalization, the logarithmic determinant measure D(R)=−lndetR. For an isotropic rank-n realization, R=xIn, the realization measure becomes D(xIn)=−nlnx. Representation rank therefore enters as an extensive multiplicity rather than as a count of sequential trajectories. The remaining physical input is stated explicitly as the Closure-Measure Conservation Principle: when two complete representations describe redistribution of the same stationary Aether closure asymmetry, with no source or sink of closure content between them, their total logarithmic realization measure is invariant. Applying this principle to the rank-four realization RF=αaI4 and the rank-five Aether realization RA=ΞFI5 gives −4lnαa=−5lnΞF, and therefore ΞF=αa4/5, or equivalently ΞF5=αa4. The determinant equality is thus a consequence of conservation of an extensive realization measure rather than an independent constitutive assumption. Because QMU defines resonance as rson=Fq2, the corresponding resonance realization is quadratic: ΞR=ΞF2=αa8/5. The exponent 8/5 therefore does not arise from eight directed loxodromic paths or from independent channel counting. It follows from the four-to-five closure transfer followed by the quadratic QMU resonance relation. The paper audits this construction against Ledger One, Aucurl=Fq2λC2, reciprocal curl--magnetic-flux realization, the six-port Aether decomposition, invariant deformation measures, and the scalar common mode. The common mode is shown not to generate the fractional exponent. Three distinct mathematical structures are kept separate throughout the analysis: the angular closure capacity 16π2, the logarithmic realization measure −lndetR, and the later boundary-to-spatial cosmological projection. In particular, the cosmological coefficient 8π/3 is not derived from the logarithmic measure developed here. In the companion cosmology analysis it follows only conditionally from boundary-trace preservation, linearity, and spatial isotropy, while the subsequent Spatial Resonance Response Law remains a separate constitutive premise. The result isolates the new physical assumption required for the four-fifths law, derives all subsequent exponent relations algebraically, and provides the realization foundation used by the current QMU cosmology program while leaving its macroscopic response law logically independent and experimentally falsifiable.