⟨ Chamber XLIII — Grammar-Mutating Selection Probe ⟩

Self-Referential Rule Bias and the Emergence of Utility | v1.0.1 | UNNS Framework

v1.0.1 — CRITICAL FIX (Activation Bottleneck):
• Issue: v1.0 μ never fired (required stable && step≥25, but stability occurred early)
• Fix: μ now fires using lastStableState anchor, guaranteeing execution post-warmup
• Preserves: S₃ → μ ordering and stable-derived semantics
• v1.0 results invalid (μ variants identical to μ=NONE) — v1.0.1 required for H₉/H₁₀ testing

Chamber XLIII — New Hypothesis Class:
• μ operator: Combines collapse (like ω) with grammar mutation via bias multipliers
• Self-referential rule change: Post-μ, operator strengths are scaled by persistent bias
• Test: Does utility require selection that mutates future grammar, not just state pruning?
• Inherits XLII v1.2 foundations: accumulated modes (decay 0.98), warmup (25 steps), 6 variants

Chamber Identity

Chamber ID: XLIII
Parent Chambers: XLI v1.1, XLI-B, XLII v1.2
Status: Exploratory, hypothesis-opening
Schema: unns.xliii.operator_program.v1.0

Core Question

Does utility require selection events that mutate future grammar, not just state collapse or pruning?

Empirical Motivation

XLII established accumulated mode collapse (ω). XLIII tests whether utility demands self-referential rule change:

XLII ω: collapse modes, continue with same grammar
XLIII μ: collapse modes AND mutate operator strengths for remainder of recursion
If μ succeeds where ω failed: substrate rewards rule adaptation, not just discard

New Primitive: μ (Mutator Operator)

μ is a grammar-mutating operator that: • Collapses accumulated phase bins (K=8, decay 0.98) like ω • Simultaneously sets bias multipliers for future operator applications • Biases persist for remainder of recursion (no drift, no adaptation) • Applies after warmup (≥25 steps) and fires once when stable μᵣ (Random): Random mode + random bias jitter U(0.9,1.1) per operator μᵍ (Guided): Argmax mode + directed bias based on entropy/dominance: - Low entropy (H≤1.2): boost τ (tau: 1.15, others: 0.95) - High dominance (A≥0.55): boost σ/κ (sigma/kappa: 1.10, tau: 0.95) - Else: boost ρ coherence (rho: 1.15, others: 0.95) Bias application: multiply operator strength parameters τ: a ← a × bias.tau σ: w ← w × bias.sigma κ: φ ← φ × bias.kappa ρ: gain ← gain × bias.rho All clamped to [0.8, 1.2]

Hypotheses

H₉ — Grammar-Mutation Hypothesis
Claim: Utility islands require selection events that mutate future grammar, not just state collapse.
Prediction: μ variants show discontinuous uplift in median G∘ relative to μ=NONE (target ≥15% in at least one μ condition), or uplift ≥5 percentage points.
Falsifier: Both μᵣ and μᵍ fail to increase median G∘ above baseline by ≥5 percentage points AND no islands appear.

H₁₀ — Directed Mutation Hypothesis
Claim: Guided mutation outperforms random mutation.
Prediction: μᵍ yields higher median G∘ and/or higher projection stability than μᵣ in matched ρ conditions.
Falsifier: μᵍ shows no consistent advantage over μᵣ (or is worse).

Execution Controls

Variant

Grammar: [M₂→M₁] → (ρ?) → S₃ → (μ?)

Execution Parameters

Depth: 400 steps

Seeds: 300

Mode Bins: K=8 over [0,2π)

Ready to execute

Technical Specifications

Metrics & Thresholds (Inherited)

Metric	Threshold	Purpose
Projection Stability	≥ 70%	Stable trajectory criterion
Utility Island (G∘)	≥ 15%	Actionable structure emergence
Survival Depth	≥ 200 steps	Adequate recursion exposure
Admissibility (Gτ, G₂)	Non-explosive	Substrate permission bound

Late Stabilization Index (LSI) — Diagnostic Only

LSI = projection stability measured over final 50% of recursion steps

LSI does not replace projection criterion | Not used for hypothesis acceptance | Exists to interpret path-dependence revealed in XLI-B

Variant Space (Frozen)

Axis	Values	Count
Resonance (ρ)	OFF, ON	2
Mutation (μ)	NONE, μᵣ, μᵍ	3
Total	6 variants