Three histories meet one shared field. The field recurs; their cumulative state does not. This instrument stops at a common observation coordinate while the modeled process continues.
The three members below are model responses, not physical devices. They share an input, respond differently, and leave three visible traces.
A shared input is generated from selected harmonic components. It is a constructed signal, not a measured environment.
Fixed seed + selected harmonics
→ generate fixed coefficients {Aₖ, φₖ}
→ cosine superposition
→ u(θ)The replay reads the frozen coefficients and values; it does not generate a new signal on each visit. The exact definitions and frozen records are linked below.
Each member responds to the same input through its own fixed response parameter. The current model uses periodic responses, rather than an arbitrary starting state.
(u, λᵢ, periodic condition) → member-specific response → mᵢ(θ)
The periodic condition selects the response used here; this is not a simulation started from an arbitrary initial value.
Differences from the shared reference accumulate along the model coordinate. Each accumulated value retains magnitude, not the full sequence or direction of earlier differences.
{mⱼ(θ)} for the three members
→ mean across members → m̄(θ)
(mᵢ(θ), m̄(θ))
→ absolute difference → dᵢ(θ)
→ trapezoidal accumulation
starting from zero, without reset
→ Hᵢ(θ)With the same input for all three members, the absolute difference from the mean response is the same quantity as the mean-centred error residual in the definitions below.
The baseline, response and accumulated difference contribute to the radius. Centre displacement, angular offset and rendering then shape the visible trace.
(Rᵢ, mᵢ(θ), Hᵢ(θ)) → weighted combination using fixed αᵢ, β → rᵢ(θ) (rᵢ, cᵢ, θ, δᵢ) → position projection → pᵢ(θ) → observation window and rendering → visible mark
The endpoint taper belongs to rendering. It does not describe a physical disappearance.
Follow what enters, how it is transformed, and what remains visible.
Here, θ is a model angular coordinate, not physical time. These relationships describe the mark's deterministic construction, not an empirically validated model of a physical system.
The receipt is a deterministic mathematical construct, not battery telemetry, a measurement of a natural process, or proof that physical memory behaves this way.
u(θ) = Σₖ Aₖ cos(kθ + φₖ) dmᵢ/dθ = λᵢ(u − mᵢ) eᵢ = u − mᵢ dᵢ = |eᵢ − meanⱼ(eⱼ)| Hᵢ(θ) = ∫₀ᶿ dᵢ(s) ds rᵢ = Rᵢ + αᵢmᵢ + βHᵢ pᵢ = cᵢ + rᵢ[cos(θ+δᵢ), sin(θ+δᵢ)]
The field contains four seeded low-frequency harmonics. Three exact periodic responses use different λᵢ. Their mean-centred error residual is integrated without reset and enters radius through β. Centre drift and latency displacement are frozen parts of the existing kernel.
Interpretation: one environment, unequal response histories, and cumulative non-return. After 2π the same field phase is encountered again while Hᵢ retains the previous passage.
Boundary: the interpretation belongs to this declared model. No empirical dataset was fitted or measured here. “Same field again, different state” is exact inside this kernel and must not be upgraded into a physical claim.
Observation: all three histories are recorded at θ=2.50π. The taper renders the end of the visible record; it is not a disappearance event.
These open the frozen artifacts themselves — raw bytes, not documentation. The replay above is the native trace, rendered.
spec (text, 3 KB) · native trace (JSON, 752 KB) · manifest (JSON, 4 KB) · verification (JSON, 4 KB) · canonical state (SVG, 125 KB)
