Continuous spectrum
View article: Spatio-temporal Resolution Emission Spectra of Continuous Propagating Positive Leader Channels in Long Spark Discharges
Spatio-temporal Resolution Emission Spectra of Continuous Propagating Positive Leader Channels in Long Spark Discharges Open
The data supports the manuscript entitled "Spatio-temporal Resolution Emission Spectra of Continuous Propagating Positive Leader Channels in Long Spark Discharges". The files contain all data used therein and can be decompressed and opened…
View article: Harmonic Hamiltonian relaxation: a variational framework for high-dimensional lattice invariants
Harmonic Hamiltonian relaxation: a variational framework for high-dimensional lattice invariants Open
We introduce harmonic Hamiltonian relaxation (HHR), a variational spectral framework for locating ground states of operators defined on high-dimensional discrete lattices. The method embeds the discrete configuration space into a continuou…
View article: Harmonic Hamiltonian relaxation: a variational framework for high-dimensional lattice invariants
Harmonic Hamiltonian relaxation: a variational framework for high-dimensional lattice invariants Open
We introduce harmonic Hamiltonian relaxation (HHR), a variational spectral framework for locating ground states of operators defined on high-dimensional discrete lattices. The method embeds the discrete configuration space into a continuou…
View article: Functional Analytic Stability of the ˆHHSRF Operator: Resolvent Compactness, ϵ-Regularization, and the Hilbert-Schmidt Defense
Functional Analytic Stability of the ˆHHSRF Operator: Resolvent Compactness, ϵ-Regularization, and the Hilbert-Schmidt Defense Open
This paper provides a rigorous standalone defense of the operator-theoretic stability ofthe ˆHHSRF Hamiltonian. We address critical functional analytic traps, specifically the nonsummabilityof prime-weighted singular potentials and the pot…
View article: Stark many-body localization in one-dimensional Bose gas under the continuous limit
Stark many-body localization in one-dimensional Bose gas under the continuous limit Open
The experimental data of the article "Stark many-body localization in one-dimensional Bose gas under the continuous limit".
View article: Probing the dynamics of stringy flux tubes with large $R$-charge
Probing the dynamics of stringy flux tubes with large $R$-charge Open
We study the generalized cusp anomalous dimension, or quark-antiquark potential on the three-sphere, in the presence of a large $R$-charge $L$ and at strong coupling. Considering the insertion of a local scalar operator of charge $L$ on a …
View article: Functional Analytic Stability of the ˆHHSRF Operator: Resolvent Compactness, ϵ-Regularization, and the Hilbert-Schmidt Defense
Functional Analytic Stability of the ˆHHSRF Operator: Resolvent Compactness, ϵ-Regularization, and the Hilbert-Schmidt Defense Open
This paper provides a rigorous standalone defense of the operator-theoretic stability ofthe ˆHHSRF Hamiltonian. We address critical functional analytic traps, specifically the nonsummabilityof prime-weighted singular potentials and the pot…
View article: Stark many-body localization in one-dimensional Bose gas under the continuous limit
Stark many-body localization in one-dimensional Bose gas under the continuous limit Open
The experimental data of the article "Stark many-body localization in one-dimensional Bose gas under the continuous limit".
View article: Functional Analytic Stability of the ˆHHSRF Operator: Resolvent Compactness, ϵ-Regularization, and the Hilbert-Schmidt Defense
Functional Analytic Stability of the ˆHHSRF Operator: Resolvent Compactness, ϵ-Regularization, and the Hilbert-Schmidt Defense Open
This paper provides a rigorous standalone defense of the operator-theoretic stability ofthe ˆHHSRF Hamiltonian. We address critical functional analytic traps, specifically the nonsummabilityof prime-weighted singular potentials and the pot…
View article: Probing the dynamics of stringy flux tubes with large $R$-charge
Probing the dynamics of stringy flux tubes with large $R$-charge Open
We study the generalized cusp anomalous dimension, or quark-antiquark potential on the three-sphere, in the presence of a large $R$-charge $L$ and at strong coupling. Considering the insertion of a local scalar operator of charge $L$ on a …
View article: Final Season F2 — Dynamical spectrum: from a static vertical-line backbone to a living spectrum
Final Season F2 — Dynamical spectrum: from a static vertical-line backbone to a living spectrum Open
This record contains the main manuscript and Supplementary Information. Season 2 and Final Season Paper F1 of the QCRM Unified Theory introduced a depth-corrected resonance operator and a Bahamut-style Hilbert–Pólya candidate H_B, together…
View article: Final Season F2 — Dynamical spectrum: from a static vertical-line backbone to a living spectrum
Final Season F2 — Dynamical spectrum: from a static vertical-line backbone to a living spectrum Open
This record contains the main manuscript and Supplementary Information. Season 2 and Final Season Paper F1 of the QCRM Unified Theory introduced a depth-corrected resonance operator and a Bahamut-style Hilbert–Pólya candidate H_B, together…
View article: Emitted spectrum of the PUV system at different discharge voltages, showing strong output in the UVC region (Adapted from the manufacturer’s manual).
Emitted spectrum of the PUV system at different discharge voltages, showing strong output in the UVC region (Adapted from the manufacturer’s manual). Open
Emitted spectrum of the PUV system at different discharge voltages, showing strong output in the UVC region (Adapted from the manufacturer’s manual).
View article: Continuous Time and Discrete Energy: The Tension-Geometric Origin of Wave–Particle Duality
Continuous Time and Discrete Energy: The Tension-Geometric Origin of Wave–Particle Duality Open
Wave–particle duality exposes the deep paradox between the discrete emission of energy quanta and the continuous flow of time. Conventional quantum theory represents this duality through probabilistic wave functions but does not explain ho…
View article: Final Season F2 — Dynamical spectrum: from a static vertical-line backbone to a living spectrum
Final Season F2 — Dynamical spectrum: from a static vertical-line backbone to a living spectrum Open
This record contains the main manuscript and Supplementary Information. Season 2 and Final Season Paper F1 of the QCRM Unified Theory introduced a depth-corrected resonance operator and a Bahamut-style Hilbert–Pólya candidate H_B, together…
View article: A Prime Curvature Hamiltonian on the Logarithmic Axis with 0.657% Agreement to the Riemann Spectrum
A Prime Curvature Hamiltonian on the Logarithmic Axis with 0.657% Agreement to the Riemann Spectrum Open
View article: Spectral Stability and Continuum Limit of the Sobolev-Ozok Lattice (SOL) Model
Spectral Stability and Continuum Limit of the Sobolev-Ozok Lattice (SOL) Model Open
This work investigates the mathematical well-posedness of the Sobolev–Ozok Lattice (SOL) framework by analyzing the spectral properties of a discrete third-order Sobolev curvature operator defined on a Planck-scale lattice. The primary obj…
View article: Continuous Time and Discrete Energy: The Tension-Geometric Origin of Wave–Particle Duality
Continuous Time and Discrete Energy: The Tension-Geometric Origin of Wave–Particle Duality Open
Wave–particle duality exposes the deep paradox between the discrete emission of energy quanta and the continuous flow of time. Conventional quantum theory represents this duality through probabilistic wave functions but does not explain ho…
View article: Spectral Stability and Continuum Limit of the Sobolev-Ozok Lattice (SOL) Model
Spectral Stability and Continuum Limit of the Sobolev-Ozok Lattice (SOL) Model Open
This work investigates the mathematical well-posedness of the Sobolev–Ozok Lattice (SOL) framework by analyzing the spectral properties of a discrete third-order Sobolev curvature operator defined on a Planck-scale lattice. The primary obj…
View article: A Discrete Z60 Hamiltonian with Three Band Spectrum and Modular Internal Structure
A Discrete Z60 Hamiltonian with Three Band Spectrum and Modular Internal Structure Open
View article: A Discrete Z60 Hamiltonian with Three Band Spectrum and Modular Internal Structure
A Discrete Z60 Hamiltonian with Three Band Spectrum and Modular Internal Structure Open
View article: Multi-agent interference and pair-correlation dynamics in Riemann-type spectra in QCRM (Season 2 – S5)
Multi-agent interference and pair-correlation dynamics in Riemann-type spectra in QCRM (Season 2 – S5) Open
This paper extends the QCRM Unified Theory (Quantum Conscious Resonance Model) by introducing a multi-agent depth-interference framework for Riemann-type spectra. In earlier chapters (S2–S4), a depth-corrected resonance operator L = -(1/z0…
View article: Multi-agent interference and pair-correlation dynamics in Riemann-type spectra in QCRM (Season 2 – S5)
Multi-agent interference and pair-correlation dynamics in Riemann-type spectra in QCRM (Season 2 – S5) Open
This paper extends the QCRM Unified Theory (Quantum Conscious Resonance Model) by introducing a multi-agent depth-interference framework for Riemann-type spectra. In earlier chapters (S2–S4), a depth-corrected resonance operator L = -(1/z0…
View article: Informational Condensation in the Rank-1 Limit: Emergence of Causal Order from a Pre-Geometric Substrate
Informational Condensation in the Rank-1 Limit: Emergence of Causal Order from a Pre-Geometric Substrate Open
This work originated from a simple, free-form exploration. Science, while fundamentally built upon method, is first and foremost curiosity taking shape. Although it may initially appear excessively technical, science is merely curiosity di…
View article: Informational Condensation in the Rank-1 Limit: Emergence of Causal Order from a Pre-Geometric Substrate
Informational Condensation in the Rank-1 Limit: Emergence of Causal Order from a Pre-Geometric Substrate Open
This work originated from a simple, free-form exploration. Science, while fundamentally built upon method, is first and foremost curiosity taking shape. Although it may initially appear excessively technical, science is merely curiosity di…
View article: Limit absorption and Green function estimates for matrix-valued periodic operators
Limit absorption and Green function estimates for matrix-valued periodic operators Open
The boundary value of the resolvent of a generic periodic tight-binding Hamiltonian with matrix symbols is shown to satisfy a limit absorption principle which is continuous in energy in dimensions $d=3$, and in dimension $d=2$ away from cr…
View article: Limit absorption and Green function estimates for matrix-valued periodic operators
Limit absorption and Green function estimates for matrix-valued periodic operators Open
The boundary value of the resolvent of a generic periodic tight-binding Hamiltonian with matrix symbols is shown to satisfy a limit absorption principle which is continuous in energy in dimensions $d=3$, and in dimension $d=2$ away from cr…
View article: Continuous Topology and Discrete Arithmetic
Continuous Topology and Discrete Arithmetic Open
The tension between the discrete cardinality of prime numbers and the continuous geometry of the complex plane is reconciled by treating primes as spectral residues governed by the explicit formulae of the Riemann zeta function.
View article: Emission spectrum obtained in 0.1M NH<sub>4</sub>ReO<sub>4</sub> – 0.2M H<sub>2</sub>SO<sub>4</sub> solution.
Emission spectrum obtained in 0.1M NH<sub>4</sub>ReO<sub>4</sub> – 0.2M H<sub>2</sub>SO<sub>4</sub> solution. Open
Emission spectrum obtained in 0.1M NH4ReO4 – 0.2M H2SO4 solution.
View article: EP241217a: a likely Type II GRB with an achromatic bump at z = 4.59
EP241217a: a likely Type II GRB with an achromatic bump at z = 4.59 Open
EP241217a is an X-ray transient detected by the Einstein Probe (EP) lasting for about 100 seconds and without accompanying $γ$-ray detection. The optical spectroscopy reveals the redshift of EP241217a is 4.59. By combining the $γ$-ray uppe…