Y Engine Implementation Laboratory

Related simulations (kept here so none get lost in separate pages)

This lab runs one fixed candidate oscillator (below). The exploratory mechanisms that led here are built as separate, focused simulations -- linked from this main page rather than left to be found only by guessing a URL:

The Geometry of Mind -- deep sequential edition -- the complete geometry-first Teacher, including the matrix bridge, manifested delay, recursive depth, distributed observer, observer aperture, possible continuation, reflexive self-awareness, inheritance, toroidal return, and Mind within Mind.

The Matrix of Mind -- deep sequential edition -- the source-traced computational Teacher, from exact polarity and declared probability through relational coordinates, recursive fields, retained flow, seven-depth return, observer formation, and Mind within Mind.

The Embodied Observer -- reciprocal body bridge -- a source-bounded sequence from typed many-to-many bodily relations through ascent, retained comparison, descent, waking and dream apertures, the DNA boundary, and conditional toroidal phase space.

Understand -- beat-by-beat narrative walkthrough of every equation this lab uses.

Part Twenty -- Ten simulations, redrawn with one shared pipeline -- the Fibonacci identity-birth tree, sequential identity birth, the recursive MindNode tree, triad-of-a-triad (seed picture and independent-oscillator view), a declared ring-torus projection of two recurrent phases, three rotating triads shown through nested phase-space embeddings, the recursive phase-address lattice, identities of identities, and a children/parents/ grandparent coverage cascade -- each now reusing this lab's own render.js primitives and mind-node-engine.js's createMindNode instead of a bespoke copy per page.

Nested ring-torus projections (full MindDynamics diagnostic) -- two live phase coordinates per identity projected through a declared embedding, with the live G5/G6/G7 vertical-runtime report behind Part Twenty's simplified "identities of identities" beat.

Nested Cascade (full coverage diagnostic) -- the live 6→2→1 cadence/coverage-grid report behind Part Twenty's simplified "children, parents, grandparent" beat.

Mind Simulation -- Emergent Observer Mode -- recursively nested observer-capable fields displayed on declared ring-torus scaffolds (Three.js); each node has one live main-loop phase and a fixed display-only tube lane. Click a drillable node to descend a scale, toggle g_return (the decisive control) live, and watch ρ/p_W/p_D/|M|/|C|/|Ω| for whichever level you are viewing.

Observer Aperture -- executable phase-two candidate -- derives a dominant right-singular participation mode from a declared relation operator, projects the complete local state into observed and presently unintegrated components, and preserves the remainder without claiming that aperture alone is an observer, truth, or phenomenal experience.

Geometry-first Teacher -- three-pass audit -- records the sequence, visual-correlation, mathematical, source-boundary, and responsive-layout checks for the 456-moment working edition.

Recursive scaling diagnostic -- one inherited A/ω ratio across the seven derived depth addresses.

Possibility oscillator diagnostic -- one total period divided among N addressable possibilities.

Triad relation diagnostic -- the changing relation between two independent cycles, without claiming causal return.

Candidate oscillator controls

Preset Whole-Cycle Radius A Tube/Hole Radius Ratio a/A Coupling Ratio κ↓/ω_base (whole → depth 1) Coupling Ratio κ/ω_base (depth → depth) Coupling Ratio κ↑/ω_base (depth 7 → whole) Lag Ratio τ↓×ω_base Lag Ratio τ×ω_base per depth Lag Ratio τ↑×ω_base Residue Decay Ratio γ/ω_base Residue Gain Ratio η/ω_base² Depth Base Frequency ω_base Depth Frequency Spread Golden-angle frequency ordering (injected comparison preset) Whole Frequency Ratio ω_H/ω_base Depth Weight Bias Ratio (0.5 = neutral)

The normalized charts X_L(θ) and X_H(φ) parameterize the declared S¹×S¹ coordinate surface. The live path is a candidate delayed oscillator projected onto that already supplied surface. Camera recentering changes the displayed reference frame; it is not the retained comparison-and-return operation required for observerhood.

Live Triadic Values

Local Inside I_L

0.000

Local Outside O_L

0.000

Local Relation R_L

0.000

Whole Inside I_H

0.000

Whole Outside O_H

0.000

Whole Relation R_H

0.000

Collective Local Phase Θ

0.000

Phasor Alignment C

0.000

Measured Frequency Ratio ν

0.000

||ν| − φ| (golden distance)

0.000

Retained delay history

warming

ν is an EMA-based estimate from the running candidate dynamics. The Golden Reference preset deliberately injects φ into the natural whole/base-frequency ratio; nonlinear coupling can make measured ν differ, and coincidence elsewhere would not establish golden emergence.

Coordinate conformance

Press "Run Coordinate Checks" to verify the normalized triad identity, torus map, implicit torus equation, decode round-trip, and Clifford S³ identity. These checks do not validate recursive Mind formation.

Directed relation probes

These probes monitor selected coordinate pairs after the oscillator update. They do not feed consequence back into the engine and therefore are not yet the causal relations of a wider identity. A→B and B→A retain separate sampled histories; ε is an unaligned vector-sum diagnostic.

Lag ratio A→B (τ×ω_base) Lag ratio B→A (τ×ω_base)

Partner	δ (rad)	Compat.	Weight A→B / B→A	Residue A→B / B→A	ε
Center on a body (dropdown or click) to inspect its selected coordinate-pair probes.

Reference-frame projection

Point of Reference Manual θ_ref (used when Manual) Manual φ_ref (used when Manual) Projection Dimension Rotate X Rotate Y SO(4) Rotation A (rad, Clifford) SO(4) Rotation B (rad, Clifford)

Y Engine Implementation Laboratory

Candidate oscillator controls

Live Triadic Values

Coordinate conformance

Directed relation probes

Declared normalized torus chart

Candidate delayed trajectory

Reference-frame projection