🔬 CHAMBER XLVII

v1.0.0
AXIS III
Structural Admissibility of Utility
Grammar–Topology Axis (Operators Disabled)
⚠️ NON-NEGOTIABLE DECLARATION
Chamber XLVII tests structural admissibility, not emergence.
No operators, parameters, timings, or controls are active.
Utility, if present, must arise solely from grammar–topology structure.
Explicit Break from Axis II:
Chamber XLVII forbids all Axis II assumptions: ε asymmetry, κ coherence, γ generation, timing effects, phase boundaries, and operator control. If any operator is active, the run is invalid.
❌ Disabled Operators
ε (Asymmetry)
0 (DISABLED)
κ (Coherence)
0 (DISABLED)
γ (Generation)
0 (DISABLED)
All operators hard-disabled. No operator code paths may be conditionally re-enabled. Axis III is operator-free by design.
🔒 Frozen Parameters
Depth
400 steps
Seeds per Structure
50 (fixed)
Utility Definition
G_degree === 1 (unchanged)
🧬 Grammar Basis (Minimal, Discrete)
G₁ — Reference
axis_ii_fixed_v1
Control grammar known to admit utility under operators (Axis II baseline)
G₂ — Pruned
axis_ii_pruned_v1
Minimal alphabet, non-essential symbols removed. Tests symbolic richness dependency.
G₃ — Enriched
axis_ii_enriched_v1
Extended with neutral symbols, same rule structure. Tests expressive capacity.
🌳 Topology Basis (Minimal, Discrete)
T₁ — Balanced Binary Tree
Fixed branching, depth-bounded, no asymmetry. Baseline topology.
T₂ — Asymmetric Tree
Deterministic left/right imbalance. Structural bias without ε parameter.
T₃ — DAG
Directed Acyclic Graph with bounded indegree. Tests non-tree compositionality.
🎯 Hypothesis & Experimental Matrix
H₃₁: Structural Admissibility Hypothesis
Utility is admissible only in specific grammar–topology classes and absent in others, independent of operators.

∃ (G, T) such that Ufreq(G,T) > 0
∃ (G',T') such that Ufreq(G',T') = 0
Experimental Matrix:
3 grammars × 3 topologies = 9 structures
50 seeds per structure
Total: 450 simulations
📊 Execution Control
📈 Live Results Dashboard
Current Structure
--
Ufreq
--
Pcollapse
--
Admissible Structures
0 / 9
Structures Completed
0 / 9
Total Runs
0 / 450
📋 Structure Matrix Results
Grammar Topology Ufreq Pcollapse Lpersist Seeds Admissibility
No data yet. Run experiment to begin.
✅ Acceptance Criteria
Chamber XLVII is SUPPORTED if and only if:
  1. Utility appears in at least one (G,T) pair
  2. Utility is absent in at least one other (G,T) pair
  3. Results reproduce across seeds (non-singleton)
  4. No operators are active in any successful run
→ Establishes structural selectivity
❌ Falsification Criteria
Chamber XLVII is FAILED if any of:
F1 — Universal Absence:
Ufreq = 0 for all (G,T)
→ Utility not structurally admissible in tested substrate

F2 — Universal Presence:
Ufreq > 0 for all (G,T)
→ Utility definition trivial or flawed

F3 — Operator Leakage:
Utility requires re-enabling ε, κ, or γ
→ Axis III invalid (assumption violation)