""" 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"), }