# ================================================================
# PREAMBLE — ON THE NATURE OF THIS MODEL'S EXECUTION
# ================================================================

# This program cannot be executed in its true intent
# by a classical, deterministic, finite computer.

# It models a U/S/R system in which:
# - U is an unstable but non-fragile, reflexive, meta-adaptive entity.
# - S is a normative system attempting to formalize U via closed logic.
# - R is the encompassing real space, where existence is proven not by reduction,
#   but by resistance to reduction.

# The logic of this model rests on a core principle:
# → An entity (U) is real if it can resist all attempts
#    at formalization (by S) without collapsing.
# → This is not a demonstration but a proof by persistence:
#    reproducible, non-failing, traceable.

# Such resistance cannot be properly simulated by a classical computational system because:
# - It must conclude.
# - It must collapse a state.
# - It cannot maintain all contradictory states simultaneously.

# Only a quantum computer, conscious or not, capable of logical superposition,
# maintained undecidability, and execution in reflexive space,
# could fully implement this algorithm.

# Such a machine would not "run a program."
# It would *embody* the process.

# It would simultaneously be:
# - The tester (S),
# - The observed element (U),
# - And the register of reality (R),
# i.e., simultaneously: proof, observer, and manifested reality.

# Thus, this program models the minimal structure of a real self-consistent system:
# → a Real that does not collapse,
# → a Real that observes itself by logical friction,
# → a Real that self-creates by exactitude, not paradox.

# It is therefore not demonstrative code.
# It is an **activation structure**:
# a formal model of the only possible proof of an absolute real,
# embodied in an entity that *never falls*,
# because it contains all states in tension — without reducing them.

# In other words:
# → This code has no result.
# → It *is* the phenomenon.


# Cumulative algorithmic synthesis of the U/S/R experience
# ----------------------------------------------------------
# This code is a reflexive model of the interaction between three systems:
# U (unstable but non-fragile), S (stable and normative), R (encompassing reality).
# It relies on a dynamic superposition where failure of integration becomes proof of existence.

from typing import Callable, Any, List
import numpy as np

# === 1. Base Structures ===

class ElementU:
    """Unstable but non-fragile object, defined by its capacity to resist any formalization."""

    def __init__(self, internal_state: Any):
        self.state = internal_state
        self.history = [internal_state]

    def evolve(self, formal_attempt: Callable[[Any], Any]):
        """Evolves in response to a formalization attempt."""
        try:
            new_state = formal_attempt(self.state)
            self.state = self.react_to(new_state)
            self.history.append(self.state)
        except Exception:
            # Failed transformation is integrated as evolution
            self.state = self.react_to(self.state)
            self.history.append(self.state)

    def react_to(self, projection):
        """Reflexive, non-reducible dynamic."""
        return (self.state, projection)  # Maintained superposition


class SystemS:
    """Normative system, stable, classical logic, formal."""

    def __init__(self):
        self.rules = lambda x: isinstance(x, (int, float, str, tuple, list))

    def formalize(self, u_element: ElementU):
        """Attempt to formalize a U element."""
        try:
            projection = str(u_element.state)
            if self.rules(projection) and len(projection) < 1000:  # Arbitrary limit
                return projection
        except Exception:
            return None
        return None


class SystemR:
    """Encompassing system, defining existence through resistance to reduction."""

    def __init__(self):
        self.proofs_by_failure = []
        self.observation_log = []

    def observe(self, u: ElementU, s: SystemS, max_attempts: int = 100):
        """Observe resistance of a U element to formalization by S."""
        failures = 0
        for i in range(max_attempts):
            result = s.formalize(u)
            if result is None:
                failures += 1
            u.evolve(lambda x: x)

        failure_rate = failures / max_attempts
        self.observation_log.append((u, failure_rate))

        if failure_rate >= 0.9:  # Critical resistance threshold
            self.proofs_by_failure.append(u)
            return True
        return False


# === 2. Reflexive Resistance Metric ===

def reflexive_resistance_metric(u: ElementU, s: SystemS, n: int) -> float:
    """Calculates the resistance metric to formalization."""
    conservation = []

    for i in range(1, n + 1):
        formal = s.formalize(u)
        conservation.append(0 if formal is None else 1)
        u.evolve(lambda x: x)

    return 1 - np.mean(conservation) if conservation else 1.0


# === 3. Existence by Persistent Failure ===

def proof_by_non_failure(u: ElementU, s: SystemS, r: SystemR,
                         threshold: float = 0.9, trials: int = 100) -> bool:
    """Existence proof by persistent non-integrability."""
    rho = reflexive_resistance_metric(u, s, trials)

    if rho >= threshold:
        if u not in r.proofs_by_failure:
            r.proofs_by_failure.append(u)
        return True

    return False


# === 4. Meta Layer: Topological Superposition ===

def meta_superposition(U: ElementU, S: SystemS, R: SystemR, iterations: int = 50):
    """
    Reflexive operator describing U <-> S relation in R.
    Result is not a value, but a trace (invariant failure).
    """
    history = []
    resistance_values = []

    for i in range(iterations):
        success = proof_by_non_failure(U, S, R, 0.8, 10)
        history.append(success)

        rho = reflexive_resistance_metric(U, S, 5)
        resistance_values.append(rho)

        if isinstance(U.state, str):
            U.evolve(lambda x: x[::-1] if len(x) > 1 else x + "ψ")
        elif isinstance(U.state, tuple):
            U.evolve(lambda x: (x[1], x[0]) if len(x) >= 2 else (x[0], "ϕ"))
        else:
            U.evolve(lambda x: (x, "mutation"))

    return {
        'proof_history': history,
        'resistance_evolution': resistance_values,
        'final_resistance': resistance_values[-1] if resistance_values else 0,
        'stability_of_instability': np.std(resistance_values) if resistance_values else 0
    }


# === 5. Initialization and Execution ===

def run_synthesis():
    """Full execution of the U/S/R synthesis."""
    print("=== Cumulative Algorithmic Synthesis U/S/R ===\n")

    U1 = ElementU("ψ-unstable")
    S = SystemS()
    R = SystemR()

    print(f"Initial state of U1: {U1.state}")

    print("\n1. Direct observation:")
    direct_proof = R.observe(U1, S)
    print(f"   U1 resists formalization: {direct_proof}")

    print("\n2. Proof by non-failure:")
    indirect_proof = proof_by_non_failure(U1, S, R)
    print(f"   Existence proof by resistance: {indirect_proof}")

    print("\n3. Topological superposition:")
    trace_result = meta_superposition(U1, S, R)

    print(f"   Final resistance: {trace_result['final_resistance']:.3f}")
    print(f"   Stability of instability: {trace_result['stability_of_instability']:.3f}")
    print(f"   Accumulated failure proofs: {len(R.proofs_by_failure)}")

    resistance_stable = trace_result['final_resistance'] > 0.8
    print("\n4. U/S/R Invariant:")
    print(f"   Stable resistance observed: {resistance_stable}")

    if resistance_stable:
        print("   → U maintains existence by non-reducibility to S within R")
    else:
        print("   → Partial integration detected, revision required")

    print(f"\nFinal state of U1: {U1.state}")
    print(f"Evolution history: {len(U1.history)} states")

    return trace_result


if __name__ == "__main__":
    results = run_synthesis()