This document contains the Python simulation code for the M²FA model as described in NCT VII.XI (Vibrating Strings — The Oscillation Between Inverted States). The code validates the five predictions P43-P47 of the theoretical note. The simulation runs 10,000 Monte Carlo iterations and confirms:• P43 — String detection: 99.6% detection rate (CONFIRMED)• P44 — Harmonic modes: 83.1% harmonic detection (CONFIRMED)• P45 — Memory modulation: 100.0% modulation rate (CONFIRMED)• P46 — Human action: 100.0% action effect (CONFIRMED)• P47 — Vibratory residues: 70.6% residue detection (CONFIRMED)The simulation reveals that vibrating strings are the dynamic interval between inverted states. They are detectable, produce harmonic modes, are modulated by memory, respond to human action, and leave vibratory residues that constitute materiality. Keywords: M²FA, NCT VII.XI, vibrating strings, oscillation, dynamic interval,tension, potential, memory, interferences, residues, vibratory modes. Related publications:• NCT VII.XI: 10.5281/zenodo.22133220• NCT VII.X: 10.5281/zenodo.22116378• NCT VII.IX: 10.5281/zenodo.22096362• NCT VII.VIII: 10.5281/zenodo.22085607This document contains the Python simulation code for the M²FA model as described in NCT VII.XI (Vibrating Strings — The Oscillation Between Inverted States). The code validates the five predictions P43-P47 of the theoretical note. The simulation runs 10,000 Monte Carlo iterations and confirms:• P43 — String detection: 99.6% detection rate (CONFIRMED)• P44 — Harmonic modes: 83.1% harmonic detection (CONFIRMED)• P45 — Memory modulation: 100.0% modulation rate (CONFIRMED)• P46 — Human action: 100.0% action effect (CONFIRMED)• P47 — Vibratory residues: 70.6% residue detection (CONFIRMED)The simulation reveals that vibrating strings are the dynamic interval between inverted states. They are detectable, produce harmonic modes, are modulated by memory, respond to human action, and leave vibratory residues that constitute materiality. Keywords: M²FA, NCT VII.XI, vibrating strings, oscillation, dynamic interval,tension, potential, memory, interferences, residues, vibratory modes. Related publications:• NCT VII.XI: 10.5281/zenodo.22133220• NCT VII.X: 10.5281/zenodo.22116378• NCT VII.IX: 10.5281/zenodo.22096362• NCT VII.VIII: 10.5281/zenodo.22085607

Aug 27, 20260 citations

Quantum detection theory

Masao Osaki

Proceedings of the IEICE General ConferenceMar 6, 19970 citations

M²FA Model Simulation Code – NCT VII.XIII The Mosaic of the Code Plural Universes and Parallel Worlds

Marc Fidèle ASSAH

This document contains the Python simulation code for the M²FA model as describedin NCT VII.XIII (The Mosaic of the Code — Plural Universes and Parallel Worlds). Thecode validates the five predictions P53-P57 of the theoretical note.The simulation runs 10,000 Monte Carlo iterations and confirms:• P53 — Mosaic detection: 100.0% detection rate (CONFIRMED)• P54 — Codal Cluster identification: 100.0% identification rate (CONFIRMED)• P55 — Shield-Cocoon measurement: 100.0% measurement rate(CONFIRMED)• P56 — Terminal phase observation: 99.8% observation rate (CONFIRMED)• P57 — Own realities: mean mosaic diversity 0.7112 (CONFIRMED)The simulation reveals that ETCO is a mosaic of multiple worlds. Each world hasits own code and space-time. The Codal Cluster is identifiable as the common law of allcodes. The Shield-Cocoon is measurable. The terminal phase is observable. Each worldhas its own realities. Keywords: M²FA, NCT VII.XIII, mosaic of the Code, plural universes, parallelworlds, Codal Cluster, Shield-Cocoon, terminal phase, projection lens. Related publications:• NCT VII.XIII: 10.5281/zenodo.22165189• NCT VII.XII: 10.5281/zenodo.22148807• NCT VII.XI: 10.5281/zenodo.22133220• NCT VII.X: 10.5281/zenodo.22116378This document contains the Python simulation code for the M²FA model as describedin NCT VII.XIII (The Mosaic of the Code — Plural Universes and Parallel Worlds). Thecode validates the five predictions P53-P57 of the theoretical note.The simulation runs 10,000 Monte Carlo iterations and confirms:• P53 — Mosaic detection: 100.0% detection rate (CONFIRMED)• P54 — Codal Cluster identification: 100.0% identification rate (CONFIRMED)• P55 — Shield-Cocoon measurement: 100.0% measurement rate(CONFIRMED)• P56 — Terminal phase observation: 99.8% observation rate (CONFIRMED)• P57 — Own realities: mean mosaic diversity 0.7112 (CONFIRMED)The simulation reveals that ETCO is a mosaic of multiple worlds. Each world hasits own code and space-time. The Codal Cluster is identifiable as the common law of allcodes. The Shield-Cocoon is measurable. The terminal phase is observable. Each worldhas its own realities. Keywords: M²FA, NCT VII.XIII, mosaic of the Code, plural universes, parallelworlds, Codal Cluster, Shield-Cocoon, terminal phase, projection lens. Related publications:• NCT VII.XIII: 10.5281/zenodo.22165189• NCT VII.XII: 10.5281/zenodo.22148807• NCT VII.XI: 10.5281/zenodo.22133220• NCT VII.X: 10.5281/zenodo.22116378

Aug 29, 20260 citations

Detection theory and quantum mechanics (II)

Carl W. Helstrom

Information and ControlAug 1, 1968138 citations

Statistical mechanics of stationary states. VII. Quantum-mechanical theory with applications to ferromagnets

Isaac Goldhirsch, Itamar Procaccia

A quantum-statistical-mechanical theory of nonequilibrium stationary states (NESS) is presented. The average of an arbitrary dynamical operator is calculated. The theory is applied to correlation functions in a heat-conducting NESS of the Heisenberg ferromagnet. Significant changes (as compared with equilibrium) are found. Correlation functions that vanish in equilibrium due to symmetry are allowed and are very important for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ vectors in the hydrodynamic regime. In the absence of magnetic field, the change with respect to equilibrium is pronounced. A static correlation that depends on $k$ as $\frac{1}{{k}^{7}}$ is found. Such correlations are expected to be seen experimentally when magnon-phonon interactions can be neglected (i.e., $k>{10}^{6}$ ${\mathrm{cm}}^{\ensuremath{-}1}$). The influence on time correlation functions is examined and found to be well within experimental detectability.A quantum-statistical-mechanical theory of nonequilibrium stationary states (NESS) is presented. The average of an arbitrary dynamical operator is calculated. The theory is applied to correlation functions in a heat-conducting NESS of the Heisenberg ferromagnet. Significant changes (as compared with equilibrium) are found. Correlation functions that vanish in equilibrium due to symmetry are allowed and are very important for $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ vectors in the hydrodynamic regime. In the absence of magnetic field, the change with respect to equilibrium is pronounced. A static correlation that depends on $k$ as $\frac{1}{{k}^{7}}$ is found. Such correlations are expected to be seen experimentally when magnon-phonon interactions can be neglected (i.e., $k>{10}^{6}$ ${\mathrm{cm}}^{\ensuremath{-}1}$). The influence on time correlation functions is examined and found to be well within experimental detectability.

Physical Review AOct 1, 19802 citations

Detection theory and quantum mechanics

Carl W. Helstrom

Information and ControlMar 1, 1967217 citations

k

\frac{1}{{k}^{7}}

is found. Such correlations are expected to be seen experimentally when magnon-phonon interactions can be neglected (i.e.,

k>{10}^{6}

${\mathrm{cm}}^{\ensuremath{-}1}$). The influence on time correlation functions is examined and found to be well within experimental detectability.