E ≠ ∅

N(e) = { e′ | e′ ∼ e }

e ≺ e′ ⇒ τ(e) < τ(e′)

D_QEC = { X>0, ρ≥θ_c, S_τ≤θ_s }

Γ : e_k ≺ e_{k+1}

∇_μ ( X ∇^μ τ ) = 0

ρ = ||∇Ψ_c||²

X = −∇τ·∇τ

B_n = Σ_{e∈E_n} R_Φ(e)

𝓑(τ) = ∫_{Σ_τ∩D_QEC} ρ d³x

O^μ O_μ = −1

TRQC

Timeline-Relative Quantum Collapse

Reference · 32 Items

Canonical Stacks

A compact reference for the structural foundations stack and the Lorentzian Regime I stack. Click any item to expand its definition.

Project Hub ↗

Structural Foundations Stack

M1 – M16

M1Event SetStack▾

E is a nonempty set of events. Events are ontic; no background geometry is assumed.

E ≠ ∅

M2Structural Time FieldStack▾

τ maps events to a totally ordered set. Only the order is physical; any strictly increasing relabeling is gauge.

τ : E → T

M3Influence Partial OrderStack▾

≺ is a strict partial order compatible with τ: if e ≺ e′ then τ(e) < τ(e′).

e ≺ e′ ⇒ τ(e) < τ(e′)

M4Adjacency and NeighborhoodsStack▾

∼ is symmetric adjacency. Neighborhoods N(e) are finite, defining primitive locality without distances.

N(e) = { e′ | e′ ∼ e }

M5Collapse FieldStack▾

Φ assigns each event a real collapse value; variations across neighborhoods define collapse terrain.

Φ : E → R

M6Structural Time Validity IndicatorStack▾

X_struct(e)=1 when all neighbors lie strictly above or strictly below in τ; otherwise time is locally ambiguous.

X_struct(e) ∈ {0,1}

M7Collapse Roughness FunctionalStack▾

R_Φ(e) sums squared collapse differences across N(e); large values indicate sharply structured collapse terrain.

R_Φ(e) = Σ(Φ(e′)−Φ(e))²

M8Structural Time Shear FunctionalStack▾

S_τ(e) measures irregularity of τ-steps across N(e); small values indicate well-laminated stacks.

S_τ(e) = Σ(τ(e′)−τ(e)−Δτ_avg)²

M9Structural ThresholdsStack▾

θ_c and θ_s set the minimum roughness and maximum shear required for robust classical structure.

θ_c (min roughness), θ_s (max shear)

M10Projection / Classicality DomainStack▾

D_QEC is the set of events with time valid, roughness high enough, and shear low enough.

D_QEC = { X_struct=1, R_Φ≥θ_c, S_τ≤θ_s }

M11Observer ChainsStack▾

Observers are influence-forward, time-increasing chains through the event network.

observer = influence-forward chain

M12Structural Angle-of-Attack per StepStack▾

Δ_Γ(k)=τ(e_{k+1})−τ(e_k) defines stack ascent per link.

Δ_Γ(k) = τ(e_{k+1}) − τ(e_k)

M13Structural AgingStack▾

Total aging is the sum of Δ_Γ(k) along a chain segment; an experienced version sums only within D_QEC.

Δτ[Γ] = Σ(τ_{k+1} − τ_k)

M14Layered Collapse BrightnessStack▾

Brightness B_n is the total roughness in a τ-layer; it measures collapse activity per layer.

B_n = Σ_{e∈E_n} R_Φ(e)

M15Arrow-of-Time PostulateStack▾

Brightness does not increase as τ advances: B_{n+1} ≤ B_n in the regime of interest.

B_{n+1} ≤ B_n

M16Projection Weight SketchStack▾

A noncanonical sketch for weighting classical regions; included as a possible direction, not a foundation axiom.

Continuum Regime

Lorentzian Regime I Stack

L1 – L16

L1Collapse FieldStack▾

Ψ_c is a real scalar field on an effective Lorentzian manifold; it encodes collapse terrain in the continuum regime.

Ψ_c : M → R

L2Observer FieldStack▾

O^μ is a unit timelike vector field; its integral curves represent continuum observers.

O^μ O_μ = −1

L3Structural Time FieldStack▾

τ is a dynamical scalar field; it is interpretable as time only in collapse-active regions.

τ : M → R (dynamical)

L4Time–Gradient InvariantStack▾

X is defined from the structural-time gradient and diagnoses whether τ behaves timelike.

X = −∇τ · ∇τ

L5Collapse-Active DomainStack▾

The collapse-active region is defined by X > 0.

X > 0 (collapse-active)

L6τ-Sector LagrangianStack▾

A quartic-gradient effective Lagrangian yields stable second-order dynamics for τ.

L7Structural Time Field EquationStack▾

The canonical τ-PDE where X > 0.

∇_μ ( X ∇^μ τ ) = 0

L8Angle of AttackStack▾

dτ/ds = O^μ ∇_μ τ gives the rate of structural time along observer proper time.

dτ/ds = O^μ ∇_μ τ

L9Admissible ObserversStack▾

Admissible observers satisfy dτ/ds > 0, preventing closed-time behavior for physical chains.

dτ/ds > 0 (admissibility)

L10Collapse PotentialStack▾

A representative double-well potential with a structural source term provides concrete collapse dynamics.

L11Collapse Equation of MotionStack▾

A covariant PDE governs Ψ_c evolution with coupling to the observer congruence.

L12Collapse IntensityStack▾

ρ is a positive-definite collapse intensity built from gradients of Ψ_c tangent to τ-slices.

ρ = ||∇Ψ_c||²

L13Structural Shear of τStack▾

A shear norm measures local bending of τ-layers; bounded shear supports coherent projection.

S_τ(x) (τ-shear)

L14Projection / Classicality DomainStack▾

D_QEC in the Lorentzian regime requires X>0, sufficient intensity, and bounded shear.

D_QEC: X>0, ρ≥θ_collapse, shear≤θ_shear

L15Observer Termination SurfaceStack▾

Projection-supporting observer evolution terminates when gradients vanish or shear exceeds threshold.

Σ_τ(O): ||∇Ψ_c||→0 or shear>θ_shear

L16Collapse Brightness per LayerStack▾

Layer-wise brightness integrates ρ over the τ-slice within D_QEC; used for the arrow-of-time postulate.

𝓑(τ) = ∫_{Σ_τ∩D_QEC} ρ d³x

No matching stacks found.

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