Part II TLPL Dashboard Documentation Version
by D Law
copyright 2026
fair use only
Component ID TLPL_OVERVIEW_001
Title TLPL Overview
Content
Purpose: Introduce TLPL as a sector‑based quantum–geometric model.
Key ideas: sectors, rapidity scalar, curvature feedback, curvature‑dependent tunneling.
Usage: simulation, visualization, conceptual experiments.
Component ID TLPL_THEORY_002
Title Theory
Content
Sector decomposition: Δxμ→Si.
Quantum state: ∣ψ⟩=∑iai∣ϕi⟩.
Scalar field: ϕ(t,x)=12ln (t+xt−x).
Curvature coupling: Rμν=κS[ϕ,ψ].
Tunneling: Tij=e−2κaij.
Component ID TLPL_EQUATIONS_003
Title Equations
Content
Normalization: ∑i∣ai∣2=1.
Barrier: aij=α∣ϕi−ϕj∣+βR‾ij+δdij.
Hamiltonian: Hij=Vi for i=j, Hij=−JTijAij for i≠j.
Dynamics: iℏa˙i=∑jHijaj.
Component ID TLPL_GRAPH_004
Title Sector Graph
Content
Graph nodes: sectors Si with attributes ϕi,Ri,Vi.
Edges: adjacency Aij with weight wij=Tij.
Visualization: node color ~ Ri; edge width ~ Tij.
ASCII Diagram (convertible)
Code
[S1]--(w12)--[S2]--(w23)--[S3]
Component ID TLPL_DYNAMICS_005
Title Dynamics
Content
Algorithm:
Initialize {ai(0)},{ϕi},{Vi}.
Compute S[ϕ,ψ] and Ri.
Compute aij and Tij.
Build H and integrate iℏa˙=Ha for Δt.
Repeat.
Notes: Use small time steps; monitor normalization.
Component ID TLPL_VISUALS_006
Title Visuals
Content
Figures: Sector lattice, rapidity contours, feedback loop, probability flow.
Render hints: convert ASCII diagrams to SVG; map edge widths to Tij on a log scale.
Component ID TLPL_IMPLEMENT_007
Title Implementation Notes
Content
Data model: sectors table with fields id, x, t, phi, R, V, a.
APIs: compute_phi(sector), compute_S(state), compute_R(S), compute_T(i,j).
Integration hooks: component IDs map to dashboard panels; diagrams are SVG assets generated from ASCII templates.
Component ID TLPL_EXAMPLES_008
Title Example Scenarios
Content
3‑node linear example: parameters and expected plots.
Parameter sweep: vary κ and η to observe localization transition.
Part III Figures Conversion Notes
ASCII to SVG: use node positions from sector coordinates; draw edges with stroke width proportional to log(1+Tij).
Probability plots: time series of Pi(t) with legend.
Rapidity contours: compute ϕ(t,x) on grid and contour plot.
Integration Hooks and Component Mapping
Place TLPL_OVERVIEW_001 on dashboard home.
Place TLPL_THEORY_002 in Theory section.
Place TLPL_EQUATIONS_003 in Equations panel with LaTeX rendering.
Place TLPL_GRAPH_004 in Visuals panel; link to interactive graph renderer.
Place TLPL_DYNAMICS_005 in Simulation panel with run controls.
Place TLPL_VISUALS_006 in Media panel.
Place TLPL_IMPLEMENT_007 in Developer docs.
Place TLPL_EXAMPLES_008 in Examples panel.
Each component includes a short ID for programmatic import.
