Tensorial RR-NS Bound String Visualizer

𝔅₃ / obstacle transport space Drag to rotate · Scroll to zoom · Release event deposits charge at ∂𝔒 Bound · Wound · J(T)=1.000

RR window 𝔒∂𝔒

Effective Coupling κeff

0.000

κeff = κbase + δκ

Admissibility J(T)

1.000

J:Tstr⊗Tobs⊗Tenv → [0,1]

Release Ratio R/Ebind

0.000

release when R > Ebind

Holonomy / Winding

Wound

Hol(∇)=e^iα → ℤ₂

Elastic Energy Emin(ρ)

0.000

κEρ² exp(-βρ⁻¹ᐟ³)

Localized Inflow δκ

0.000

release ⇒ κeff = κbase + δκ

RR--NS Tensorial Sim

single-file HTML · Canvas 2D projection

RR--NS Measurement Layer

Window angle width θwindow

Width90°

Narrower windows concentrate fixed RR content, increasing κbase in this visualization.

Total RR content QRR

QRR4.0

NS fluctuation field B(2)

NS5.0

The NS field drives endpoint shaking and contributes to release pressure.

Tensorial Elasticity Layer

String density ρ(φ)

ρ1.40

Critical density ρcrit(o)

ρcrit1.20

Critical-density rupture
If enabled, low admissibility J(T)<Jcrit is treated as a one-time constraint-fracture event that sends inflow pulses to ∂𝔒.

Obstacle binding strength Ebind

Ebind3.50

Elastic material scale κE

κE1.10

Elastic exponential β

β1.00

Transport / View

Camera zoom

Zoom1.5×

Simulation speed

Speed1.00×

Model Map

State: T = Tstr ⊗ Tobs ⊗ Tenv. The string contributes density, endpoint, and holonomy; the obstacle contributes binding and critical density; the environment contributes RR and NS fields.

Release: the app now supports two interpretations. In elastic mode, elastic energy and NS drive compete against binding and RR stabilization. In rupture mode, low admissibility J(T)<Jcrit can itself trigger a one-time constraint-fracture event, interpreted as winding charge expulsion to the two boundary orbits ∂𝔒 = 𝔬₁ ∪ 𝔬₂. When either event fires, the wound sector projects to unwound and a localized δκ pulse is added to κeff.

RR window

boundary orbits

bound endpoint

release pulse

Computational Appendix

These are the equations the browser is actually running. The file is a finite-dimensional toy realization, not a full string-theory solver.

RRκbase = QRR · π / (θwindow + ε)

NSBvis = 0.3 · NSslider

TensorT = Tstr ⊗ Tobs ⊗ Tenv = (ρ, endpoint, Hol) ⊗ (Ebind, ρcrit) ⊗ (κ, B)

J(T)J = sigmoid(6(ρ-ρcrit)) · windingTerm · contactTerm

ElasticEmin(ρ) = κE ρ² exp(-β ρ^(-1/3))

ReleaseR = 1.24Emin + 0.82Bvis; threshold = Ebind(0.74+0.50(1-J))+0.28κbase

Ruptureif ruptureMode and J < Jcrit: wound → unwound, event = constraint-fracture

Inflowif event: δκ += 0.85ρ + 0.15Bvis + 0.35·max(ρcrit-ρ,0)

Varianceσ² = 15Bvis / (κbase + δκ + ε)