Quantum-Q Archive

Quantum-Q Papers

Research archive for the Quantum Lattice Model.

This archive collects QLM papers, identity notes, and focused extensions across foundations, closure, routing, kinematics, and wave dynamics.

{ℏ, ℓP, tP} E = ℏ dθ/dτ c = ℓP/tP EP = ℏ/tP

December 4, 2025 | Updated June 14, 2026

QLM I: Reduced-Action Foundations and Planck-Unit Derivations

Canon / Foundation

The foundational QLM paper establishing the per-radian primitive triplet {ℏ, ℓP, tP}, the covariant phase-flow law, the saturated Planck tick, and the reduced-action derivation of Planck-unit quantities.

  • E = ℏ dθ/dτ
  • c = ℓP/tP
  • EP = ℏ/tP
  • mP = ℏtP/ℓP^2
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December 26, 2025 | Updated June 14, 2026

QLM II: Planck Energy Density Cap and Minimal Saturated-Core Completion

Canon-Compatible Extension

Develops the QLM local Planck energy-density cap and applies it to a minimal non-singular saturated-core completion for gravitational collapse.

  • uP = ℏ/(ℓP^3 tP)
  • ρmax = mP/ℓP^3
  • Rc(M) = (3M / 4πmP)^(1/3) ℓP
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February 23, 2026 | Updated June 14, 2026

QLM III: Invariant Transport and Lorentz Kinematics from Proper Ticks

Canon / Kinematics

Reconstructs Lorentz kinematics from invariant lattice transport, local proper-tick accumulation, radar synchronization, and QLM phase-gradient relations.

  • c = ℓP/tP
  • E/p = c
  • E^2 - (pc)^2 = (mc^2)^2
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February 25, 2026 | Updated June 14, 2026

QLM IV: Geometric Routing and Gravitational Throttling

Consistent Extension

Develops the exterior routing-admittance sector of QLM, interpreting Schwarzschild redshift and gravitational throttling as geometric suppression of radial phase-action routing.

  • Y(r) = 1 - 2(M/mP)(ℓP/r)
  • rs = 2(M/mP)ℓP
  • Zg(r) = Y(r)^-1/2
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March 8, 2026 | Updated June 14, 2026

QLM V: Quantum Phase Transport and Wave Dynamics

Canon-Compatible Dynamics

Develops the quantum dynamical layer of QLM, organizing Schrodinger, Klein-Gordon, and Dirac equations as continuum descriptions of coherent phase-action transport.

  • dS = ℏ dθ
  • E = ℏω
  • J = (ℏ/m)ρ∇θ
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March 24, 2026

The Planck Energy Identity in the Quantum Lattice Model

Standalone Identity Note

A focused standalone derivation isolating the compact QLM Planck energy identity as saturated one-tick reduced-action throughput.

  • EP = mP c^2 = ℏ/tP
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June 12, 2026

Mass as Temporal-Spatial Phase Closure

Focused Closure Extension

Develops a focused QLM interpretation of rest mass as local temporal-spatial phase-action closure and recovers E = mc^2 from the closure condition r = cτ.

  • m = ℏτ/r^2
  • r = cτ
  • mc^2 = ℏω
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