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| """ | |
| Live-Data Mathematical Formalization | |
| ------------------------------------- | |
| Same six "axioms" as the original math_formalization.py, but every function | |
| now takes real numbers pulled from a running strand/simulation instead of | |
| free symbolic placeholders. This means the SymPy step is doing real | |
| arithmetic on your data, not proving a generic algebraic identity that | |
| holds for any input. | |
| Honest scope: this still doesn't measure "consciousness." It gives you | |
| real, traceable numbers about mutation counts, equilibrium ratios, and | |
| geometry, computed from what the simulation actually did. Whether those | |
| numbers mean anything beyond bookkeeping is a separate, open question -- | |
| this file just makes sure the math isn't disconnected from the data. | |
| """ | |
| import sympy as sp | |
| class CCMathFormalizerLive: | |
| def __init__(self): | |
| self.threshold = sp.Integer(-1) | |
| self.genesis = sp.Integer(0) | |
| # ------------------------------------------------------------------ | |
| # Axiom 1: Cancellation at -1 | |
| # ------------------------------------------------------------------ | |
| def cancellation_operator(self, mutation_count: int): | |
| """ | |
| Takes the REAL mutation count from current_strand['mutations'], | |
| not an abstract symbol. Still just (-1)*(-1)*M = M -- that part of | |
| the algebra is unavoidably trivial -- but now M is an actual number | |
| from your run, so the printed result reflects what happened, not | |
| a placeholder. | |
| """ | |
| M = sp.Integer(mutation_count) | |
| T = self.threshold | |
| S_strand = T * M | |
| output = T * S_strand # (-1) * (-1 * M) | |
| return { | |
| "mutation_count_in": mutation_count, | |
| "substitution": f"({T}) * ({T} * {M})", | |
| "result": int(sp.simplify(output)), | |
| "note": ( | |
| "This confirms your mutation count passed through the sign " | |
| "flip unchanged. It's bookkeeping, not a proof about " | |
| "consciousness -- but at least it's YOUR number, not a free " | |
| "variable." | |
| ), | |
| } | |
| # ------------------------------------------------------------------ | |
| # Axiom 2: Structure / Chaos Equilibrium -- computed from real history | |
| # ------------------------------------------------------------------ | |
| def equilibrium_trend(self, structure_history: list, chaos_history: list): | |
| """ | |
| Takes the REAL per-generation bound-structure counts and chaos-pool | |
| counts (append these each generation in runner.py). Reports the | |
| actual ratio trend instead of a made-up linear toy function. | |
| No sympy limit is taken here, because taking limit(t->oo) requires | |
| a closed-form function -- you don't have one, you have a finite | |
| list of observations. Reporting the empirical trend is the honest | |
| version of "does it approach 1:1." | |
| """ | |
| if len(structure_history) != len(chaos_history) or not structure_history: | |
| raise ValueError("structure_history and chaos_history must be " | |
| "equal-length, non-empty lists of real counts.") | |
| ratios = [s / c if c else float("inf") | |
| for s, c in zip(structure_history, chaos_history)] | |
| return { | |
| "ratios_by_generation": ratios, | |
| "latest_ratio": ratios[-1], | |
| "trend": "approaching 1:1" if len(ratios) > 1 and | |
| abs(ratios[-1] - 1) < abs(ratios[0] - 1) else | |
| "not converging to 1:1 based on data so far", | |
| "note": ( | |
| "This is an empirical trend over your actual generations, " | |
| "not a symbolic limit. If you want a real limit, you need " | |
| "a model for how ratio(gen) behaves as gen -> infinity, " | |
| "fit to this data -- and then it's a curve-fit claim, " | |
| "which should be reported with uncertainty, not as a proof." | |
| ), | |
| } | |
| # ------------------------------------------------------------------ | |
| # Axiom 3: Manifold Geometry -- use the SAME metric the sim already | |
| # computed, don't recompute a disconnected version | |
| # ------------------------------------------------------------------ | |
| def manifold_geometry_report(self, peak_metrics: dict): | |
| """ | |
| Takes the peak_metrics dict already produced by | |
| manifold.compute_conal_metric() inside the real generation loop | |
| (surface_area, unfolded_degree), instead of re-deriving a fresh | |
| symbolic r(t)/z(t) that was never connected to the sim. | |
| """ | |
| return { | |
| "peak_unfolded_degree": peak_metrics["unfolded_degree"], | |
| "peak_surface_area": peak_metrics["surface_area"], | |
| "note": ( | |
| "These are the actual peak values recorded during this " | |
| "generation's traversal, not values from a fresh symbolic " | |
| "curve evaluated at t=0 and t=0.5." | |
| ), | |
| } | |
| # ------------------------------------------------------------------ | |
| # Axiom 4: Selection -- use REAL counts of attempted vs rejected | |
| # mutations, tracked during the loop | |
| # ------------------------------------------------------------------ | |
| def selection_report(self, total_attempts: int, duplicates_rejected: int): | |
| """ | |
| Requires the sim to actually count these two things during the | |
| attraction loop (see patch note in runner_patch_notes.md). Once | |
| tracked, this reports the REAL selected count, not a symbolic | |
| M_total - M_dup. | |
| """ | |
| selected = total_attempts - duplicates_rejected | |
| return { | |
| "total_attempts": total_attempts, | |
| "duplicates_rejected": duplicates_rejected, | |
| "selected": selected, | |
| "rejection_rate": (duplicates_rejected / total_attempts | |
| if total_attempts else 0.0), | |
| } | |
| # ------------------------------------------------------------------ | |
| # Axiom 5: Halting -- use the REAL chaos pool remaining count | |
| # ------------------------------------------------------------------ | |
| def halting_check(self, chaos_pool_remaining: int): | |
| """ | |
| Real halting condition: the strand halts when the chaos pool it | |
| draws from is actually empty, not when an abstract N_possible | |
| equals an abstract N_acquired. | |
| """ | |
| return { | |
| "chaos_pool_remaining": chaos_pool_remaining, | |
| "halted": chaos_pool_remaining <= 0, | |
| } | |
| # ------------------------------------------------------------------ | |
| # Axiom 6: Scale-Up -- report the REAL transition the scale ladder made | |
| # ------------------------------------------------------------------ | |
| def scale_up_report(self, scale_state: dict): | |
| """ | |
| Takes the actual scale_state dict already produced by | |
| scale_ladder.evaluate_scale_transition() -- reports what really | |
| happened instead of an unevaluated symbolic Q(M_k) = S_k1. | |
| """ | |
| return { | |
| "scaled_up": scale_state.get("scaled_up", False), | |
| "message": scale_state.get("message", "no transition"), | |
| } | |