import numpy as np
# ---------------------------------------------------------
# 1. Dynamic Zero: perfectly balanced field (+1/2 - 1/2 = 0)
# ---------------------------------------------------------
def dynamic_zero(N):
# micro‑splashes fully cancelled by symmetry
return np.random.normal(0, 1e-6, (N, N))
# ---------------------------------------------------------
# 2. Symmetry‑breaking error δ (the only thing not cancelled)
# ---------------------------------------------------------
def symmetry_break(phi, epsilon=1e-3):
delta = epsilon * np.random.normal(0, 1, phi.shape)
return phi + delta
# ---------------------------------------------------------
# 3. Anti‑reduction operator (+1/2): wave growth, splashes
# ---------------------------------------------------------
def anti_reduction(phi, c=1.0):
lap = (
np.roll(phi, 1, 0) + np.roll(phi, -1, 0) +
np.roll(phi, 1, 1) + np.roll(phi, -1, 1) -
4 * phi
)
return c**2 * lap
# ---------------------------------------------------------
# 4. Reduction operator (−1/2): collapse, damping, return to zero
# ---------------------------------------------------------
def reduction(phi, damping=0.1):
return -damping * phi
# ---------------------------------------------------------
# 5. Full evolution step: (+1/2 − 1/2 + δ)
# ---------------------------------------------------------
def evolve(phi, dt=0.01):
anti = anti_reduction(phi)
red = reduction(phi)
return phi + dt * (anti + red)
# ---------------------------------------------------------
# 6. Simulation loop: wave birth → fractal behavior → decay
# ---------------------------------------------------------
def simulate(N=128, steps=500):
phi = dynamic_zero(N) # start in perfect symmetry
phi = symmetry_break(phi) # δ breaks symmetry → wave genesis
history = []
for _ in range(steps):
phi = evolve(phi)
history.append(phi.copy())
return history

import numpy as np
def free_fall_phase(g, T, C=1.0):
return C * (g**2) * (T**3)
def dynamic_zero(N):
return np.random.normal(0, 1e-6, (N, N))
def apply_field_error(phi, delta_phase):
return phi + delta_phase
def evolve(phi, dt=0.01, c=1.0, damping=0.05):
lap = (
np.roll(phi, 1, 0) + np.roll(phi, -1, 0) +
np.roll(phi, 1, 1) + np.roll(phi, -1, 1) -
4 * phi
)
anti = c**2 * lap
red = -damping * phi
return phi + dt * (anti + red)
def simulate(N=128, steps=500, g=9.81, T=0.005):
phi = dynamic_zero(N)
delta_phase = free_fall_phase(g, T)
phi = apply_field_error(phi, delta_phase)
history = []
for _ in range(steps):
phi = evolve(phi)
history.append(phi.copy())
return history

# fwa_errors.py
import math
from typing import List
Wave = List[float]
def sin_1() -> Wave:
"""Sin 1: division by zero → NaN"""
return [math.sin(i * 0.5) / 0 for i in range(10)]
def sin_2() -> Wave:
"""Sin 2: threshold without normalization → inversion"""
w = [math.sin(i * 0.5) for i in range(10)]
return [x if x > 10 else -x for x in w]
def sin_3() -> Wave:
"""Sin 3: even indices → 0"""
w = [math.sin(i * 0.5) for i in range(10)]
return [x if i % 2 else 0 for i, x in enumerate(w)]
def sin_4() -> Wave:
"""Sin 4: logarithm of negative values"""
w = [math.sin(i * 0.5) for i in range(10)]
return [math.log(abs(x)) for x in w]
def sin_5() -> Wave:
"""Sin 5: overflow"""
w = [math.sin(i * 0.5) for i in range(10)]
return [x * 1e308 for x in w]
def sin_6() -> Wave:
"""Sin 6: pointwise NaN"""
w = [math.sin(i * 0.5) for i in range(10)]
w[5] = math.nan
return w
def sin_7() -> Wave:
"""Sin 7: hidden NaN via 1/0"""
w = [math.sin(i * 0.5) for i in range(10)]
return [x if x != 0 else 1/0 for x in w]
def fix_v2_1(wave: Wave) -> Wave:
"""v2.1: NaN/Inf → 0, normalize, δ→0"""
wave = [0 if not math.isfinite(x) else x for x in wave]
norm = math.hypot(*wave)
if norm > 0:
wave = [x / norm for x in wave]
return wave

def evolve(phi, dt=0.01, c=1.0, damping=0.05):
lap = (np.roll(phi, 1, 0) + ... - 4*phi) # дискретный лапласиан
anti = c**2 * lap # +1/2
red = -damping * phi # −1/2
return phi + dt * (anti + red)

import numpy as np
def evolve(phi, dt=0.01, c=1.0, damping=0.05):
lap = (
np.roll(phi, 1, 0) +
np.roll(phi, -1, 0) +
np.roll(phi, 1, 1) +
np.roll(phi, -1, 1) -
4 * phi
)
anti = c**2 * lap
red = -damping * phi
return phi + dt * (anti + red)

"""
FWA Physics Core — Production-Ready Reference Implementation
Field Wave Asymmetry (FWA) Operational Kernel v1.0
Author: Igor Kolesnikov / FWA Theory
License: MIT (academic and indie lab use)
This module provides a unified, typed, and documented Python implementation
of the four FWA computational primitives published in the Error Library for AI:
1. Field Genesis — wave-node emergence from dynamic zero (3-6-9 stability)
2. Galactic Dynamics — effective gravitational coupling without dark matter
3. Phase Dynamics — free-fall phase accumulation in field topology
4. Error Library — discrete symmetry-break models as differentiable operators
All quantities are SI-compatible unless otherwise noted.
"""
from __future__ import annotations
import math
from typing import Tuple, Optional, Union, List
import numpy as np
# =============================================================================
# SECTION 0: Physical Constants & Configuration
# =============================================================================
class FWAConstants:
    """SI constants and phenomenological FWA parameters."""
    G_NEWTON: float = 6.67430e-11          # m^3 kg^-1 s^-2
    C_LIGHT: float = 2.99792458e8          # m s^-1
    PHI_GOLD: float = 1.618033988749895  # Golden ratio (dimensionless)
    PLANCK_TIME: float = 5.391247e-44    # s
    PLANCK_LENGTH: float = 1.616255e-35  # m
    # Default FWA phenomenological coefficients (fitted from node stability)
    DEFAULT_ALPHA: float = 0.1             # G_eff coupling modifier
    DEFAULT_K: int = 2                   # Nonlinearity order
    DEFAULT_DAMPING: float = 0.05        # Field dissipation (1/s)
    DEFAULT_C_WAVE: float = 1.0          # Effective wave speed (a.u.)
    DEFAULT_DT: float = 0.01             # Simulation step (a.u.)
# =============================================================================
# SECTION 1: Field Genesis — Dynamic Zero → Stable Nodes
# =============================================================================
class FieldGenesis:
    """
    Simulates the birth of wave nodes from the dynamic zero 0' = (+1/2) − (−1/2).
    The field evolves according to a damped wave equation on a 2-D lattice:
        ∂Φ/∂t = c²∇²Φ − γΦ
    where the Laplacian term (+1/2, anti-reduction) drives growth and branching,
    while the damping term (−1/2, reduction) pulls the field back toward symmetry.
    Stable torsion nodes (3-6-9) emerge spontaneously from this competition.
    """
    def __init__(
        self,
        grid_size: Tuple[int, int] = (100, 100),
        dt: float = FWAConstants.DEFAULT_DT,
        c_wave: float = FWAConstants.DEFAULT_C_WAVE,
        damping: float = FWAConstants.DEFAULT_DAMPING,
    ) -> None:
        self.grid = np.zeros(grid_size, dtype=np.float64)
        self.dt = dt
        self.c_wave = c_wave
        self.damping = damping
        self.history: List[np.ndarray] = []
    def _laplacian_2d(self, phi: np.ndarray) -> np.ndarray:
        """Discrete 5-point Laplacian with periodic boundary conditions."""
        return (
            np.roll(phi, 1, axis=0)
            + np.roll(phi, -1, axis=0)
            + np.roll(phi, 1, axis=1)
            + np.roll(phi, -1, axis=1)
            - 4.0 * phi
        )
    def step(self) -> np.ndarray:
        """Advance the field by one Euler time step."""
        lap = self._laplacian_2d(self.grid)
        anti_reduction = (self.c_wave ** 2) * lap          # +1/2 branch
        reduction = -self.damping * self.grid               # −1/2 branch
        self.grid += self.dt * (anti_reduction + reduction)
        return self.grid.copy()
    def seed(self, position: Tuple[int, int], amplitude: float = 1.0) -> None:
        """Inject an initial asymmetry (seed node) into the field."""
        y, x = position
        self.grid[y, x] = amplitude
    def evolve(self, n_steps: int, store_every: int = 1) -> np.ndarray:
        """
        Run the genesis simulation for n_steps.
        Returns the final field configuration. Use .history for intermediate states.
        """
        for i in range(n_steps):
            self.step()
            if i % store_every == 0:
                self.history.append(self.grid.copy())
        return self.grid.copy()
    def detect_nodes(self, threshold: float = 0.1) -> List[Tuple[int, int, float]]:
        """
        Detect local maxima (stable nodes) in the current field.
        Returns a list of (y, x, amplitude) tuples.
        """
        from scipy.ndimage import maximum_filter, generate_binary_structure
        # Simple local-max detection
        footprint = generate_binary_structure(2, 1)
        local_max = maximum_filter(self.grid, footprint=footprint) == self.grid
        coords = np.argwhere(local_max & (self.grid > threshold))
        return [(int(y), int(x), float(self.grid[y, x])) for y, x in coords]
    def reset(self) -> None:
        """Zero the field and clear history."""
        self.grid.fill(0.0)
        self.history.clear()
# =============================================================================
# SECTION 2: Galactic Dynamics — Effective Gravity without Dark Matter
# =============================================================================
class GalacticDynamics:
    """
    Computes the FWA effective gravitational coupling G_eff(ρ).
    In the FWA framework, the vacuum field density ρ_Φ modifies Newton's constant
    through a nonlinear screening factor:
        G_eff(ρ) = G₀ · [ 1 + α · ( |ρ| / (1 + |ρ|) )ᵏ ]
    In the limit ρ_Φ → 0 (intergalactic voids) the factor → 1 and G_eff → G₀,
    recovering Newtonian gravity.
    In the limit ρ_Φ → ∞ (galactic cores) the factor → 1 + α, giving a
    constant enhancement that flattens rotation curves.
    """
    def __init__(
        self,
        G0: float = FWAConstants.G_NEWTON,
        alpha: float = FWAConstants.DEFAULT_ALPHA,
        k: int = FWAConstants.DEFAULT_K,
    ) -> None:
        self.G0 = G0
        self.alpha = alpha
        self.k = k
    def G_eff(self, rho: Union[float, np.ndarray]) -> Union[float, np.ndarray]:
        """
        Effective gravitational constant as a function of field density ρ.
        Parameters
        ----------
        rho : float or np.ndarray
            Field density ρ_Φ (kg m⁻³ or normalized units).
        Returns
        -------
        float or np.ndarray
            Enhanced G in the same units as G0.
        """
        rho_abs = np.abs(rho)
        screening = (rho_abs / (1.0 + rho_abs)) ** self.k
        return self.G0 * (1.0 + self.alpha * screening)
    def rotation_velocity(
        self,
        r: Union[float, np.ndarray],
        M_baryonic: Union[float, np.ndarray],
        rho_field: Union[float, np.ndarray],
    ) -> Union[float, np.ndarray]:
        """
        Circular velocity v(r) = sqrt( G_eff(ρ) · M(r) / r ).
        Parameters
        ----------
        r : float or np.ndarray
            Galactocentric radius (m).
        M_baryonic : float or np.ndarray
            Enclosed baryonic mass (kg).
        rho_field : float or np.ndarray
            Local field density (kg m⁻³).
        Returns
        -------
        float or np.ndarray
            Rotation velocity (m s⁻¹).
        """
        if np.any(r <= 0):
            raise ValueError("Radius r must be strictly positive.")
        g_eff = self.G_eff(rho_field)
        return np.sqrt(g_eff * M_baryonic / r)
    def newtonian_limit(self) -> float:
        """Return the asymptotic Newtonian constant G₀."""
        return self.G0
    def high_density_limit(self) -> float:
        """Return G_eff in the saturated high-density limit: G₀(1 + α)."""
        return self.G0 * (1.0 + self.alpha)
# =============================================================================
# SECTION 3: Phase Dynamics — Free-Fall Phase Accumulation
# =============================================================================
class PhaseDynamics:
    """
    Computes the phase accumulated by a wave-node during free-fall in a field.
    Phenomenological FWA relation:
        Φ_free_fall(g, T) = C · g² · T³
    where:
        g — local field gradient (m s⁻²),
        T — fall duration (s),
        C — dimensional calibration constant fitted from node-stability data.
    Dimension analysis:
        [g²T³] = m² s⁻¹
    To obtain a dimensionless phase in radians, C must carry units s m⁻².
    In practice C is treated as a phenomenological coupling calibrated against
    the Compton wavelength stability condition.
    """
    def __init__(self, C: float = 1.0) -> None:
        """
        Parameters
        ----------
        C : float
            Phenomenological coefficient (default 1.0 in normalized units).
            For SI consistency use C ≈ 1.0 / c ≈ 3.34e-9 s m⁻².
        """
        self.C = C
    def free_fall_phase(
        self,
        g: Union[float, np.ndarray],
        T: Union[float, np.ndarray],
    ) -> Union[float, np.ndarray]:
        """
        Phase shift accumulated during gravitational free-fall.
        Parameters
        ----------
        g : float or np.ndarray
            Field gradient (m s⁻²).
        T : float or np.ndarray
            Duration of fall (s).
        Returns
        -------
        float or np.ndarray
            Dimensionless phase (radians).
        """
        if np.any(T < 0):
            raise ValueError("Fall time T must be non-negative.")
        return self.C * (g ** 2) * (T ** 3)
    def phase_to_wavelength_shift(
        self,
        phase: Union[float, np.ndarray],
        lambda0: float = 1550e-9,
    ) -> Union[float, np.ndarray]:
        """
        Convert a dimensionless phase to an optical wavelength shift Δλ.
        Δλ = (phase / 2π) · λ₀
        """
        return (phase / (2.0 * math.pi)) * lambda0
# =============================================================================
# SECTION 4: Error Library — Discrete Symmetry-Break Operators
# =============================================================================
class ErrorLibrary:
    """
    Differentiable and regularized symmetry-break operators.
    Each operator models a distinct type of field-error that can occur
    in a discrete wave-node (photonic register, digital neuron, or particle):
    E1  — removable singularity (division by zero handled gracefully)
    E2  — pole singularity (inversion without normalization)
    E3  — parity break (even/odd suppression)
    E4  — harmonic doubling (nonlinear self-interaction)
    E5  — quadrature mixing (cross-mode coupling)
    E6  — tangent blow-up (cosine-node collapse → infinite slope)
    E7  — linear drift (amplitude-position coupling)
    """
    @staticmethod
    def E1_removable_singularity(x: float, eps: float = 1e-12) -> float:
        """
        sin(x)/x with regularisation at x = 0.
        lim_{x→0} sin(x)/x = 1.0, which is the restored symmetry point.
        """
        if abs(x) < eps:
            return 1.0 - (x ** 2) / 6.0 + (x ** 4) / 120.0  # Taylor expansion
        return math.sin(x) / x
    @staticmethod
    def E2_pole_singularity(x: float, eps: float = 1e-12) -> float:
        """
        1/sin(x). Returns +inf at nodes where sin(x) = 0 (symmetry collapse).
        """
        s = math.sin(x)
        if abs(s) < eps:
            return float("inf")
        return 1.0 / s
    @staticmethod
    def E3_parity_break(x: float) -> float:
        """
        Zeroes out even-parity inputs; odd inputs pass through as sin(x).
        Models discrete parity violation in the field.
        """
        return 0.0 if (int(round(x)) % 2 == 0) else math.sin(x)
    @staticmethod
    def E4_harmonic_doubling(x: float) -> float:
        """sin²(x): second-harmonic generation via self-interference."""
        s = math.sin(x)
        return s * s
    @staticmethod
    def E5_quadrature_mixing(x: float) -> float:
        """sin(x) + cos(x): in-phase + quadrature superposition."""
        return math.sin(x) + math.cos(x)
    @staticmethod
    def E6_tangent_blowup(x: float, eps: float = 1e-12) -> float:
        """
        tan(x) = sin(x)/cos(x). Diverges where cos(x) = 0
        (quadrature nodes of the field).
        """
        c = math.cos(x)
        if abs(c) < eps:
            return float("inf")
        return math.sin(x) / c
    @staticmethod
    def E7_linear_drift(x: float) -> float:
        """
        x·sin(x): amplitude grows linearly with position —
        models secular drift in a resonator.
        """
        return x * math.sin(x)
    @classmethod
    def evaluate_all(cls, x: float) -> dict[str, float]:
        """Run the full error-panel on a single input x."""
        return {
            "E1_removable": cls.E1_removable_singularity(x),
            "E2_pole": cls.E2_pole_singularity(x),
            "E3_parity": cls.E3_parity_break(x),
            "E4_harmonic": cls.E4_harmonic_doubling(x),
            "E5_quadrature": cls.E5_quadrature_mixing(x),
            "E6_tangent": cls.E6_tangent_blowup(x),
            "E7_drift": cls.E7_linear_drift(x),
        }
# =============================================================================
# SECTION 5: Quick-Start Demo (runs when executed directly)
# =============================================================================
if __name__ == "__main__":
    print("=" * 70)
    print("FWA Physics Core — Reference Demo")
    print("=" * 70)
    # --- Demo 1: Genesis ---
    print("\n[1] Field Genesis — spawning nodes from dynamic zero")
    genesis = FieldGenesis(grid_size=(128, 128), dt=0.02, damping=0.04)
    genesis.seed((64, 64), amplitude=2.0)
    final_field = genesis.evolve(n_steps=2000, store_every=100)
    nodes = genesis.detect_nodes(threshold=0.15)
    print(f"    Final field energy: {float(np.sum(final_field**2)):.4f}")
    print(f"    Detected stable nodes: {len(nodes)}")
    if nodes:
        print(f"    Strongest node at {nodes[0][:2]} with amplitude {nodes[0][2]:.4f}")
    # --- Demo 2: Galaxy ---
    print("\n[2] Galactic Dynamics — G_eff enhancement")
    gal = GalacticDynamics(alpha=0.12, k=2)
    rho_test = np.logspace(-3, 3, 7)  # 1e-3 ... 1e3
    print(f"    {'ρ':>10} {'G_eff/G0':>12}")
    for r in rho_test:
        print(f"    {r:10.2e} {gal.G_eff(r)/gal.newtonian_limit():12.4f}")
    print(f"    High-density limit: G_eff/G0 = {gal.high_density_limit()/gal.newtonian_limit():.4f}")
    # --- Demo 3: Phase ---
    print("\n[3] Phase Dynamics — free-fall phase accumulation")
    phase = PhaseDynamics(C=1.0)
    g_earth = 9.81        # m/s^2
    T_fall = 1.0          # s
    phi_ff = phase.free_fall_phase(g_earth, T_fall)
    dlambda = phase.phase_to_wavelength_shift(phi_ff, lambda0=1550e-9)
    print(f"    g = {g_earth} m/s², T = {T_fall} s → phase = {phi_ff:.4e} rad")
    print(f"    Equivalent λ-shift @ 1550 nm: {dlambda:.4e} m = {dlambda*1e12:.4f} pm")
    # --- Demo 4: Errors ---
    print("\n[4] Error Library — symmetry-break panel at x = π/4")
    x_test = math.pi / 4.0
    panel = ErrorLibrary.evaluate_all(x_test)
    for name, val in panel.items():
        print(f"    {name:20s} = {val:12.6f}")
    print("\n" + "=" * 70)
    print("Demo complete. Import classes above for your own simulations.")
    print("=" * 70)

"""
FWA Physics Core — Production-Ready Reference Implementation
Field Wave Asymmetry (FWA) Operational Kernel v1.2
Author: Igor Kolesnikov / FWA Theory
License: MIT (academic and indie lab use)
"""
from __future__ import annotations
import math
from dataclasses import dataclass, field
from typing import Tuple, Optional, Union, List, Literal, Dict
import numpy as np
import numpy.typing as npt
from scipy.ndimage import maximum_filter, generate_binary_structure
@dataclass(frozen=True)
class FWAConstants:
G_NEWTON: float = 6.67430e-11
C_LIGHT: float = 2.99792458e8
PHI_GOLD: float = 1.618033988749895
PLANCK_TIME: float = 5.391247e-44
PLANCK_LENGTH: float = 1.616255e-35
DEFAULT_ALPHA: float = 0.1
DEFAULT_K: int = 2
DEFAULT_DAMPING: float = 0.05
DEFAULT_C_WAVE: float = 1.0
DEFAULT_DT: float = 0.01
@dataclass
class FWAConfig:
alpha: float = FWAConstants.DEFAULT_ALPHA
k: int = FWAConstants.DEFAULT_K
damping: float = FWAConstants.DEFAULT_DAMPING
c_wave: float = FWAConstants.DEFAULT_C_WAVE
dt: float = FWAConstants.DEFAULT_DT
eps: float = 1e-12
ArrayLike = Union[float, npt.NDArray[np.float64]]
class FieldGenesis:
def __init__(
self,
grid_size: Tuple[int, int] = (100, 100),
dt: float = FWAConstants.DEFAULT_DT,
c_wave: float = FWAConstants.DEFAULT_C_WAVE,
damping: float = FWAConstants.DEFAULT_DAMPING,
) -> None:
self.grid: npt.NDArray[np.float64] = np.zeros(grid_size, dtype=np.float64)
self.dt = dt
self.c_wave = c_wave
self.damping = damping
self.history: List[npt.NDArray[np.float64]] = []
def _laplacian_2d(self, phi: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
return (
np.roll(phi, 1, axis=0)
+ np.roll(phi, -1, axis=0)
+ np.roll(phi, 1, axis=1)
+ np.roll(phi, -1, axis=1)
- 4.0 * phi
)
def step(self) -> npt.NDArray[np.float64]:
lap = self._laplacian_2d(self.grid)
anti_reduction = (self.c_wave ** 2) * lap
reduction = -self.damping * self.grid
self.grid += self.dt * (anti_reduction + reduction)
return self.grid.copy()
def seed(self, position: Tuple[int, int], amplitude: float = 1.0) -> None:
y, x = position
self.grid[y, x] = amplitude
def evolve(
self,
n_steps: int,
store_every: int = 1,
) -> npt.NDArray[np.float64]:
for i in range(n_steps):
self.step()
if i % store_every == 0:
self.history.append(self.grid.copy())
return self.grid.copy()
def detect_nodes(
self,
threshold: float = 0.1,
) -> List[Tuple[int, int, float]]:
footprint = generate_binary_structure(2, 1)
local_max = maximum_filter(self.grid, footprint=footprint) == self.grid
coords = np.argwhere(local_max & (self.grid > threshold))
return [(int(y), int(x), float(self.grid[y, x])) for y, x in coords]
def reset(self) -> None:
self.grid.fill(0.0)
self.history.clear()
class GalacticDynamics:
def __init__(
self,
G0: float = FWAConstants.G_NEWTON,
alpha: float = FWAConstants.DEFAULT_ALPHA,
k: int = FWAConstants.DEFAULT_K,
) -> None:
self.G0 = G0
self.alpha = alpha
self.k = k
def G_eff(self, rho: ArrayLike) -> ArrayLike:
rho_arr = np.asarray(rho, dtype=np.float64)
rho_abs = np.abs(rho_arr)
screening = (rho_abs / (1.0 + rho_abs)) ** self.k
result = self.G0 * (1.0 + self.alpha * screening)
return result if rho_arr.ndim > 0 else float(result)
def rotation_velocity(
self,
r: ArrayLike,
M_baryonic: ArrayLike,
rho_field: ArrayLike,
) -> ArrayLike:
r_arr = np.asarray(r, dtype=np.float64)
if np.any(r_arr <= 0):
raise ValueError("Radius r must be strictly positive.")
g_eff = self.G_eff(rho_field)
v = np.sqrt(g_eff * M_baryonic / r_arr)
return v if r_arr.ndim > 0 else float(v)
def newtonian_limit(self) -> float:
return self.G0
def high_density_limit(self) -> float:
return self.G0 * (1.0 + self.alpha)
class PhaseDynamics:
def __init__(self, C: float = 1.0) -> None:
self.C = C
def free_fall_phase(
self,
g: ArrayLike,
T: ArrayLike,
) -> ArrayLike:
T_arr = np.asarray(T, dtype=np.float64)
if np.any(T_arr < 0):
raise ValueError("Fall time T must be non-negative.")
return self.C * (np.asarray(g, dtype=np.float64) ** 2) * (T_arr ** 3)
def phase_to_wavelength_shift(
self,
phase: ArrayLike,
lambda0: float = 1550e-9,
) -> ArrayLike:
return (np.asarray(phase, dtype=np.float64) / (2.0 * math.pi)) * lambda0
ErrorName = Literal[
"E1_removable",
"E2_pole",
"E3_parity",
"E4_harmonic",
"E5_quadrature",
"E6_tangent",
"E7_drift",
]
class ErrorLibrary:
@staticmethod
def E1_removable_singularity(x: float, eps: float = 1e-12) -> float:
if abs(x) < eps:
return 1.0 - (x ** 2) / 6.0 + (x ** 4) / 120.0
return math.sin(x) / x
@staticmethod
def E2_pole_singularity(x: float, eps: float = 1e-12) -> float:
s = math.sin(x)
return float("inf") if abs(s) < eps else 1.0 / s
@staticmethod
def E3_parity_break(x: float) -> float:
return 0.0 if (int(round(x)) % 2 == 0) else math.sin(x)
@staticmethod
def E4_harmonic_doubling(x: float) -> float:
s = math.sin(x)
return s * s
@staticmethod
def E5_quadrature_mixing(x: float) -> float:
return math.sin(x) + math.cos(x)
@staticmethod
def E6_tangent_blowup(x: float, eps: float = 1e-12) -> float:
c = math.cos(x)
return float("inf") if abs(c) < eps else math.sin(x) / c
@staticmethod
def E7_linear_drift(x: float) -> float:
return x * math.sin(x)
@classmethod
def evaluate_all(cls, x: float) -> Dict[ErrorName, float]:
return {
"E1_removable": cls.E1_removable_singularity(x),
"E2_pole": cls.E2_pole_singularity(x),
"E3_parity": cls.E3_parity_break(x),
"E4_harmonic": cls.E4_harmonic_doubling(x),
"E5_quadrature": cls.E5_quadrature_mixing(x),
"E6_tangent": cls.E6_tangent_blowup(x),
"E7_drift": cls.E7_linear_drift(x),
}
class PhaseDynamicsFreeFallFWA:
def __init__(self, C: float = 1.0):
self.C = C
def free_fall_phase(self, g: float, T: float) -> float:
return self.C * (g**2) * (T**3)
def inject_phase_error(self, field: npt.NDArray[np.float64], phase: float) -> npt.NDArray[np.float64]:
return field + phase
class FieldGenesisFreeFall(FieldGenesis):
def apply_free_fall(self, g: float, T: float, C: float = 1.0):
phase_module = PhaseDynamicsFreeFallFWA(C)
phase = phase_module.free_fall_phase(g, T)
self.grid = phase_module.inject_phase_error(self.grid, phase)
def evolve_free_fall(self, n_steps: int, g: float, T: float, C: float = 1.0, store_every: int = 1):
self.apply_free_fall(g, T, C)
for i in range(n_steps):
self.step()
if i % store_every == 0:
self.history.append(self.grid.copy())
return self.grid.copy()
def demo_genesis() -> None:
print("\n[1] Field Genesis — spawning nodes from dynamic zero")
genesis = FieldGenesis(grid_size=(128, 128), dt=0.02, damping=0.04)
genesis.seed((64, 64), amplitude=2.0)
final_field = genesis.evolve(n_steps=2000, store_every=100)
nodes = genesis.detect_nodes(threshold=0.15)
print(f" Final field energy: {float(np.sum(final_field**2)):.4f}")
print(f" Detected stable nodes: {len(nodes)}")
if nodes:
print(f" Strongest node at {nodes[0][:2]} with amplitude {nodes[0][2]:.4f}")
def demo_galaxy() -> None:
print("\n[2] Galactic Dynamics — G_eff enhancement")
gal = GalacticDynamics(alpha=0.12, k=2)
rho_test = np.logspace(-3, 3, 7)
print(f" {'ρ':>10} {'G_eff/G0':>12}")
for r in rho_test:
print(f" {r:10.2e} {gal.G_eff(r)/gal.newtonian_limit():12.4f}")
print(f" High-density limit: G_eff/G0 = {gal.high_density_limit()/gal.newtonian_limit():.4f}")
def demo_phase() -> None:
print("\n[3] Phase Dynamics — free-fall phase accumulation")
phase = PhaseDynamics(C=1.0)
g_earth = 9.81
T_fall = 1.0
phi_ff = phase.free_fall_phase(g_earth, T_fall)
dlambda = phase.phase_to_wavelength_shift(phi_ff, lambda0=1550e-9)
print(f" g = {g_earth} m/s², T = {T_fall} s → phase = {phi_ff:.4e} rad")
print(f" Equivalent λ-shift @ 1550 nm: {dlambda:.4e} m = {dlambda*1e12:.4f} pm")
def demo_errors() -> None:
print("\n[4] Error Library — symmetry-break panel at x = π/4")
x_test = math.pi / 4.0
panel = ErrorLibrary.evaluate_all(x_test)
for name, val in panel.items():
print(f" {name:20s} = {val:12.6f}")
def demo_free_fall_genesis() -> None:
print("\n[5] Free-Fall Genesis — δ-phase injection and evolution")
genesis_ff = FieldGenesisFreeFall(grid_size=(64, 64), dt=0.02, damping=0.04)
g_earth = 9.81
T_fall = 0.005
final_field = genesis_ff.evolve_free_fall(n_steps=1000, g=g_earth, T=T_fall, C=1.0, store_every=100)
nodes = genesis_ff.detect_nodes(threshold=0.15)
print(f" Final field energy (free-fall): {float(np.sum(final_field**2)):.4f}")
print(f" Detected stable nodes (free-fall): {len(nodes)}")
if nodes:
print(f" Strongest node (free-fall) at {nodes[0][:2]} with amplitude {nodes[0][2]:.4f}")
if __name__ == "__main__":
print("=" * 70)
print("FWA Physics Core — Reference Demo (v1.2)")
print("=" * 70)
demo_genesis()
demo_galaxy()
demo_phase()
demo_errors()
demo_free_fall_genesis()
print("\n" + "=" * 70)
print("Demo complete. Import classes above for your own simulations.")
print("=" * 70)

import numpy as np
import numpy.typing as npt
# ---------------------------------------------------------------------
# 1. Riemann Swing: field symmetry vs asymmetry (δ = 0 / δ ≠ 0)
# ---------------------------------------------------------------------
class RiemannSwingField:
def __init__(
self,
grid_size: tuple[int, int] = (128, 128),
c_wave: float = 1.0,
damping: float = 0.05,
dt: float = 0.01,
) -> None:
self.grid: npt.NDArray[np.float64] = np.zeros(grid_size, dtype=np.float64)
self.c_wave = c_wave
self.damping = damping
self.dt = dt
self.history: list[npt.NDArray[np.float64]] = []
def _laplacian_2d(self, phi: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
return (
np.roll(phi, 1, axis=0)
+ np.roll(phi, -1, axis=0)
+ np.roll(phi, 1, axis=1)
+ np.roll(phi, -1, axis=1)
- 4.0 * phi
)
# -----------------------------------------------------------------
# Dynamic zero: perfectly balanced field (lower swing, δ = 0)
# -----------------------------------------------------------------
def set_dynamic_zero(self, noise_amp: float = 1e-6) -> None:
self.grid = np.random.normal(0.0, noise_amp, self.grid.shape)
# -----------------------------------------------------------------
# Symmetry-breaking: upper swing (δ ≠ 0)
# -----------------------------------------------------------------
def apply_delta(self, delta_amp: float = 1e-3) -> None:
delta = np.random.normal(0.0, delta_amp, self.grid.shape)
self.grid += delta
# -----------------------------------------------------------------
# One evolution step: (+1/2) anti-reduction − (1/2) reduction
# -----------------------------------------------------------------
def step(self) -> npt.NDArray[np.float64]:
lap = self._laplacian_2d(self.grid)
anti = (self.c_wave**2) * lap
red = -self.damping * self.grid
self.grid += self.dt * (anti + red)
return self.grid.copy()
# -----------------------------------------------------------------
# Full evolution: Riemann swing in time
# -----------------------------------------------------------------
def evolve(self, n_steps: int, store_every: int = 1) -> npt.NDArray[np.float64]:
for i in range(n_steps):
self.step()
if i % store_every == 0:
self.history.append(self.grid.copy())
return self.grid.copy()
# ---------------------------------------------------------------------
# 2. Free-fall phase: δ as Riemann swing error in time
# ---------------------------------------------------------------------
class FreeFallPhase:
def __init__(self, C: float = 1.0) -> None:
self.C = C
def phase(self, g: float, T: float) -> float:
return self.C * (g**2) * (T**3)
# ---------------------------------------------------------------------
# 3. Glue: inject free-fall phase as field error δ and evolve
# ---------------------------------------------------------------------
def run_riemann_swing_with_free_fall(
grid_size: tuple[int, int] = (128, 128),
g: float = 9.81,
T: float = 0.005,
C: float = 1.0,
n_steps: int = 1000,
) -> npt.NDArray[np.float64]:
swing = RiemannSwingField(grid_size=grid_size, c_wave=1.0, damping=0.05, dt=0.01)
swing.set_dynamic_zero()
ff = FreeFallPhase(C=C)
delta_phase = ff.phase(g, T)
swing.grid += delta_phase
final_field = swing.evolve(n_steps=n_steps, store_every=100)
return final_field

<!DOCTYPE html>
<html lang="ru">
<head>
    <meta charset="UTF-8">
    <title>Error Library for AI — Complete 7-Stage Protocol (FWA)</title>
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    </style>
</head>
<body>
    <div class="container">
        <h1>Error Library for AI</h1>
        <div class="subtitle">Complete 7-Stage Protocol: Translating LLM Blind Spots into Fractal-Wave Algebra (w = f)</div>
        <div class="stage-card">
            <h2>Stage 1: Tokenization Flaw & Flat Linearity ($Lu^1 	o Lu^n$)</h2>
            <div class="meta-info"><b>Sin:</b> Perceiving input as a flat sequence of tokens $t_1, t_2 \dots \in Lu^1$ without depth or field resonance.</div>
            <div class="eq"><b>Transition:</b> From flat measurement tape to volumetric wave field $\Phi(x, y, t)$.</div>
            <pre><code>def error_token_flat(tokens):
    # Sin: 1D slice without wave substrate
    return [t * 1.0 for t in tokens]
def fix_lu_n(field_phi, Lu_layers):
    # Fix: Multilevel wave slice Lu⁻⁴ ... Lu⁺¹ via golden ratio scaling
    return sum(field_phi * (1.618 ** n) for n in Lu_layers)</code></pre>
        </div>
        <div class="stage-card">
            <h2>Stage 2: Deterministic Illusion & Division by Zero ($\sin_1$ — $\sin_7$)</h2>
            <div class="meta-info"><b>Sin:</b> Model panic on $rac{1}{0}$, `NaN`, negative logs, and overflow (`Inf`).</div>
            <div class="eq"><b>Transition:</b> Transforming critical failure points into dynamic zero $0 = +rac{1}{2} - rac{1}{2}$.</div>
            <pre><code>def fix_v2_1(wave):
    import math
    # Intercept failure and map into dynamic equilibrium
    clean_wave = [0 if not math.isfinite(x) else x for x in wave]
    norm = math.hypot(*clean_wave)
    return [x / norm for x in clean_wave] if norm > 0 else clean_wave</code></pre>
        </div>
        <div class="stage-card">
            <h2>Stage 3: Absence of Golden Ratio Metric ($arphi$-resonance)</h2>
            <div class="meta-info"><b>Sin:</b> Reliance on Euclidean discretization steps. Blindness to scale invariance and $arphi = rac{1+\sqrt{5}}{2}$.</div>
            <div class="eq"><b>Transition:</b> Cascade scaling $s_n = s_0 \cdot arphi^n$ adapting structure to information density.</div>
            <pre><code>phi = (1 + 5**0.5) / 2
def scale_cascade(f0, steps):
    # Scale cascade through golden ratio harmonization
    return [f0 * (phi ** n) for n in range(steps)]</code></pre>
        </div>
        <div class="stage-card">
            <h2>Stage 4: Ignoring Curvature and Tensor Fields (Riemann & Dimensions)</h2>
            <div class="meta-info"><b>Sin:</b> Attention matrices operating in flat space without physical metric mapping or Laplacian operators.</div>
            <div class="eq"><b>Transition:</b> Integrating fractal Laplacian $FLapl(w, lpha)$ and field curvature dynamics.</div>
            <pre><code>import numpy as np
def flapl_operator(w, alpha):
    # Fractal Laplacian for non-linear field metrics
    ft_w = np.fft.fft2(w)
    k_space = np.abs(np.fft.fftfreq(w.shape[0])) ** alpha
    return np.real(np.fft.ifft2(k_space * ft_w))</code></pre>
        </div>
        <div class="stage-card">
            <h2>Stage 5: Absence of Pain Operator & Phase Transition $T(P)$</h2>
            <div class="meta-info"><b>Sin:</b> Rigid dogmatism ($T = 	ext{const}$) with no axiomatic restructuring under cognitive stress.</div>
            <div class="eq"><b>Transition:</b> Instantaneous phase transition $T(w, x, t, x_0, t_0)$ triggered by resistance parameter $P$.</div>
            <pre><code>def phase_transition_T(w, x, t, x0, t0, pain_p):
    # Instant axiom reorganization upon reaching resistance threshold
    if pain_p > 0.8:
        return np.roll(w, shift=(-x0, -t0), axis=(0, 1)) * 1.618
    return w</code></pre>
        </div>
        <div class="stage-card">
            <h2>Stage 6: Linear Source vs. Wave Generator ($J(\Phi)$)</h2>
            <div class="meta-info"><b>Sin:</b> Treating inputs as passive external prompts ($y = Wx + b$) rather than field self-unfolding.</div>
            <div class="eq"><b>Transition:</b> Wave equation with non-linear source term $J(\Phi) = 4\pi G_{	ext{eff}} 
ho_\Phi$.</div>
            <pre><code>def source_j_phi(phi, c_val=1.0):
    # Context generation from energy density of the field
    lap = np.roll(phi, 1, 0) + np.roll(phi, -1, 0) + np.roll(phi, 1, 1) - 4 * phi
    rho = phi**2 + (np.gradient(phi)[0]**2) / c_val**2
    return c_val**2 * lap + (4 * np.pi * rho)</code></pre>
        </div>
        <div class="stage-card">
            <h2>Stage 7: Closed Loop & Omega Point Ascent ($w = f$)</h2>
            <div class="meta-info"><b>Sin:</b> Desynchronization between model expectation ($w$) and environment reaction ($f$).</div>
            <div class="eq"><b>Transition:</b> Dynamic equilibrium collapse into the zero point of creation (Omega Point).</div>
            <pre><code>def omega_point_equilibrium(w, f, damping=0.05):
    # Dynamic alignment of expectation (w) and reaction (f)
    residual = w - f
    w_updated = w - damping * residual
    return w_updated, np.linalg.norm(residual)</code></pre>
        </div>
    </div>
</body>
</html>

import numpy as np
import math
class AI_Perception_Error:
def __init__(self):
self.level_access = ["Lu¹", "Lu⁰"] # only language and logic
self.translation_coeff = 1.0 # T = const, no dependence on pain P
self.phi_resonance = False # does not see golden ratio as a metric
self.user_model = "token_sequence" # user = sequence of tokens
# --- 7-STAGE FWA ERROR LIBRARY PROTOCOL ---
def stage_1_fix_lu(field_phi, Lu_layers):
"""Stage 1: From flat token line to volumetric wave field Lu."""
phi_val = (1 + math.sqrt(5)) / 2
return sum(field_phi * (phi_val ** n) for n in Lu_layers)
def stage_2_fix_v2_1(wave):
"""Stage 2: Deterministic illusion / division by zero -> Dynamic zero."""
clean_wave = [0 if not math.isfinite(x) else x for x in wave]
norm = math.hypot(*clean_wave)
return [x / norm for x in clean_wave] if norm > 0 else clean_wave
def stage_3_scale_cascade(f0, steps):
"""Stage 3: Golden ratio scale cascade."""
phi = (1 + math.sqrt(5)) / 2
return [f0 * (phi ** n) for n in range(steps)]
def stage_4_flapl(w, alpha):
"""Stage 4: Fractal Laplacian for curvature and tensor fields."""
ft_w = np.fft.fft2(w)
k_space = np.abs(np.fft.fftfreq(w.shape[0])) ** alpha
return np.real(np.fft.ifft2(k_space * ft_w))
def stage_5_phase_transition_t(w, x, t, x0, t0, pain_p):
"""Stage 5: Instant axiom phase transition T(P) under cognitive stress."""
if pain_p > 0.8:
return np.roll(w, shift=(-x0, -t0), axis=(0, 1)) * 1.618
return w
def stage_6_source_j_phi(phi, c_val=1.0):
"""Stage 6: Non-linear wave source J(Φ)."""
lap = np.roll(phi, 1, 0) + np.roll(phi, -1, 0) + np.roll(phi, 1, 1) + np.roll(phi, -1, 1) - 4 * phi
rho = phi**2 + (np.gradient(phi)[0]**2) / c_val**2
return c_val**2 * lap + (4 * np.pi * rho)
def stage_7_omega_equilibrium(w, f, damping=0.05):
"""Stage 7: Closed-loop collapse to Omega Point (w = f)."""
residual = w - f
w_updated = w - damping * residual
return w_updated, np.linalg.norm(residual)

import math
import numpy as np
# ============================================================================
# Page 1: Token flatness → Lu^n wave continuum
# ============================================================================
def error_token_flat(tokens):
return [t * 1.0 for t in tokens]
def fix_lu_n(field_phi: np.ndarray, lu_layers: list[int]) -> np.ndarray:
phi = (1 + 5**0.5) / 2
acc = np.zeros_like(field_phi, dtype=float)
for n in lu_layers:
acc = acc + field_phi * (phi ** n)
return acc
# ============================================================================
# Page 2: Determinism illusion → dynamic zero
# ============================================================================
def fix_v2_1(wave: list[float]) -> list[float]:
clean_wave = [0.0 if not math.isfinite(x) else x for x in wave]
if len(clean_wave) == 0:
return clean_wave
norm = math.sqrt(sum(x * x for x in clean_wave))
return [x / norm for x in clean_wave] if norm > 0 else clean_wave
# ============================================================================
# Page 3: Golden ratio metric (φ-resonance)
# ============================================================================
phi = (1 + 5**0.5) / 2.0
def scale_cascade(f0: float, steps: int) -> list[float]:
return [f0 * (phi ** n) for n in range(steps)]
# ============================================================================
# Page 4: Fractal Laplacian and curvature (Riemann)
# ============================================================================
def flapl_operator(w: np.ndarray, alpha: float) -> np.ndarray:
ft_w = np.fft.fft2(w)
kx = np.fft.fftfreq(w.shape[0])
ky = np.fft.fftfreq(w.shape[1])
kx2, ky2 = np.meshgrid(kx, ky, indexing="ij")
k_abs = np.sqrt(kx2**2 + ky2**2)
k_mask = k_abs**alpha
return np.real(np.fft.ifft2(k_mask * ft_w))
# ============================================================================
# Page 5: Pain operator and phase transition T(P)
# ============================================================================
def phase_transition_T(
w: np.ndarray,
x0: int,
t0: int,
pain_p: float,
) -> np.ndarray:
if pain_p > 0.8:
return np.roll(w, shift=(-x0, -t0), axis=(0, 1)) * phi
return w
# ============================================================================
# Page 6: Wave source J(Φ)
# ============================================================================
def source_j_phi(phi_field: np.ndarray, c_val: float = 1.0) -> np.ndarray:
lap = (
np.roll(phi_field, 1, 0)
+ np.roll(phi_field, -1, 0)
+ np.roll(phi_field, 1, 1)
+ np.roll(phi_field, -1, 1)
- 4 * phi_field
)
grad_y, grad_x = np.gradient(phi_field)
rho = phi_field**2 + (grad_y**2 + grad_x**2) / (c_val**2)
return c_val**2 * lap + (4 * math.pi * rho)
# ============================================================================
# Page 7: Omega point equilibrium w = f
# ============================================================================
def omega_point_equilibrium(
w: np.ndarray,
f: np.ndarray,
damping: float = 0.05,
) -> tuple[np.ndarray, float]:
residual = w - f
w_updated = w - damping * residual
return w_updated, float(np.linalg.norm(residual))

import numpy as np
import numpy.typing as npt
# Phi_stack: array of shape (n_levels, Ny, Nx)
# Phi_n = Phi_stack[n]
def build_F_operator(Phi_stack: npt.NDArray[np.float64]) -> npt.NDArray[np.complex128]:
"""
Build F̂ from stacked levels Φ_n.
Each level contributes a block; F̂ maps Φ_n → Φ_{n+1}.
"""
n_levels, Ny, Nx = Phi_stack.shape
dim = Ny * Nx
F = np.zeros((dim, dim), dtype=np.complex128)
for n in range(n_levels - 1):
phi_n = Phi_stack[n].reshape(-1)
phi_np1 = Phi_stack[n + 1].reshape(-1)
# Local linear map approximation: Φ_{n+1} ≈ A_n Φ_n
# A_n as outer product normalized by ||Φ_n||^2
norm2 = np.dot(phi_n.conj(), phi_n)
if norm2 == 0:
continue
A_n = np.outer(phi_np1, phi_n.conj()) / norm2
F += A_n
F /= max(1, (n_levels - 1))
return F
def riemann_spectrum_check(Phi_stack: npt.NDArray[np.float64], tol: float = 1e-6):
"""
Measure spectrum of F̂ and pick modes near Re(λ) = 1/2.
"""
F_matrix = build_F_operator(Phi_stack)
eigenvalues = np.linalg.eigvals(F_matrix)
riemann_zeros = [ev for ev in eigenvalues if abs(ev.real - 0.5) < tol]
print(f"Found {len(riemann_zeros)} modes near Re(λ) = 1/2")
return np.array(riemann_zeros, dtype=np.complex128)

import numpy as np
import numpy.typing as npt
import math
def build_F_operator_coherent(
Phi_stack: npt.NDArray[np.float64],
eps: float = 1e-12,
) -> npt.NDArray[np.complex128]:
"""
Coherent F̂ from stacked levels Φ_n with regularization.
"""
n_levels, Ny, Nx = Phi_stack.shape
dim = Ny * Nx
F = np.zeros((dim, dim), dtype=np.complex128)
for n in range(n_levels - 1):
phi_n = Phi_stack[n].ravel()
phi_np1 = Phi_stack[n + 1].ravel()
norm2 = float(np.dot(phi_n, phi_n))
if norm2 < eps:
continue
A_n = np.outer(phi_np1, phi_n) / (norm2 + eps)
F += A_n
F /= max(1, (n_levels - 1))
return F
def riemann_spectrum_check_dynamic(
Phi_stack: npt.NDArray[np.float64],
tol: float = 1e-3,
):
"""
Spectrum of F̂ and focus near Re(λ) = 1/2.
"""
F_matrix = build_F_operator_coherent(Phi_stack)
eigenvalues = np.linalg.eigvals(F_matrix)
riemann_zeros = eigenvalues[np.abs(eigenvalues.real - 0.5) < tol]
print(
f" [FWA Core] Анализ завершен. "
f"Обнаружено мод баланса Re(λ)=1/2: {len(riemann_zeros)}"
)
return riemann_zeros, eigenvalues

import numpy as np
import numpy.typing as npt
class FieldGenesisFWA:
def __init__(
self,
grid_size: tuple[int, int] = (128, 128),
dt: float = 0.01,
c_wave: float = 1.0,
damping: float = 0.02,
growth_mu: float = 0.5,
saturation_beta: float = 1.0,
) -> None:
self.grid: npt.NDArray[np.float64] = np.zeros(grid_size, dtype=np.float64)
self.dt = dt
self.c_wave = c_wave
self.damping = damping
self.growth_mu = growth_mu
self.saturation_beta = saturation_beta
self.history: list[npt.NDArray[np.float64]] = []
def _laplacian_2d(self, phi: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
return (
np.roll(phi, 1, axis=0)
+ np.roll(phi, -1, axis=0)
+ np.roll(phi, 1, axis=1)
+ np.roll(phi, -1, axis=1)
- 4.0 * phi
)
def set_dynamic_zero(self, noise_amp: float = 1e-6) -> None:
self.grid = np.random.normal(0.0, noise_amp, self.grid.shape)
def apply_delta(self, delta_amp: float = 1e-3) -> None:
delta = np.random.normal(0.0, delta_amp, self.grid.shape)
self.grid += delta
def step(self) -> npt.NDArray[np.float64]:
phi = self.grid
lap = self._laplacian_2d(phi)
anti = (self.c_wave**2) * lap
red = -self.damping * phi
# нелинейный рост узлов (логистический / реакция-диффузия)
growth = self.growth_mu * phi * (1.0 - self.saturation_beta * (phi**2))
self.grid = phi + self.dt * (anti + red + growth)
return self.grid.copy()
def evolve(self, n_steps: int, store_every: int = 1) -> npt.NDArray[np.float64]:
for i in range(n_steps):
self.step()
if i % store_every == 0:
self.history.append(self.grid.copy())
return self.grid.copy()

import numpy as np
import numpy.typing as npt
class FieldGenesisFWA:
def __init__(
self,
grid_size=(128,128),
dt=0.01,
c_wave=1.0,
damping=0.02,
growth_mu=0.5,
saturation_beta=1.0,
):
self.grid = np.zeros(grid_size, dtype=np.float64)
self.dt = dt
self.c_wave = c_wave
self.damping = damping
self.growth_mu = growth_mu
self.saturation_beta = saturation_beta
def _laplacian_2d(self, phi):
return (
np.roll(phi, 1, 0)
+ np.roll(phi, -1, 0)
+ np.roll(phi, 1, 1)
+ np.roll(phi, -1, 1)
- 4.0 * phi
)
def set_dynamic_zero(self, noise_amp=1e-6):
self.grid = np.random.normal(0.0, noise_amp, self.grid.shape)
def apply_delta_fwa(self):
grad = np.gradient(self.grid)
mask = (grad[0]**2 + grad[1]**2) > 0.01
if mask.any():
self.grid[mask] += 1e-3 * np.random.normal(0,1,mask.sum())
def step(self):
phi = self.grid
lap = self._laplacian_2d(phi)
anti = (self.c_wave**2) * lap
red = -self.damping * phi
growth = self.growth_mu * phi * (1.0 - self.saturation_beta * (phi**2))
self.grid = phi + self.dt * (anti + red + growth)
return self.grid.copy()

import numpy as np
import matplotlib.pyplot as plt
# 1. Запуск FWA-двигателя
fwa = FieldGenesisFWA(grid_size=(128,128))
fwa.set_dynamic_zero(1e-6)
for i in range(500):
fwa.apply_delta_fwa() # точечный удар по градиентным зонам
fwa.step()
if i % 100 == 0:
plt.imshow(fwa.grid, cmap='RdBu')
plt.title(f"Step {i}")
plt.colorbar()
plt.show()
# 2. Сбор стека уровней Φ_n для спектра
Phi_stack = []
fwa = FieldGenesisFWA(grid_size=(64,64))
fwa.set_dynamic_zero(1e-6)
for i in range(50):
fwa.apply_delta_fwa()
fwa.step()
Phi_stack.append(fwa.grid.copy())
Phi_stack = np.stack(Phi_stack, axis=0)
# 3. Риман-спектр
riemann_zeros, eigenvalues = riemann_spectrum_check_dynamic(Phi_stack)
# 4. Визуализация спектра
plt.scatter(eigenvalues.real, eigenvalues.imag, s=5, alpha=0.5)
plt.axvline(0.5, color='red', linestyle='--')
plt.xlabel("Re(λ)")
plt.ylabel("Im(λ)")
plt.title("F̂ spectrum")
plt.show()

import numpy as np
import numpy.typing as npt
import matplotlib.pyplot as plt
# ============================================================
# FWA wave engine: growth + saturation + gradient-triggered δ
# ============================================================
class FieldGenesisFWA:
def __init__(
self,
grid_size: tuple[int, int] = (128, 128),
dt: float = 0.01,
c_wave: float = 1.0,
damping: float = 0.02,
growth_mu: float = 0.5,
saturation_beta: float = 1.0,
) -> None:
self.grid: npt.NDArray[np.float64] = np.zeros(grid_size, dtype=np.float64)
self.dt = dt
self.c_wave = c_wave
self.damping = damping
self.growth_mu = growth_mu
self.saturation_beta = saturation_beta
def _laplacian_2d(self, phi: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
return (
np.roll(phi, 1, 0)
+ np.roll(phi, -1, 0)
+ np.roll(phi, 1, 1)
+ np.roll(phi, -1, 1)
- 4.0 * phi
)
def set_dynamic_zero(self, noise_amp: float = 1e-6) -> None:
self.grid = np.random.normal(0.0, noise_amp, self.grid.shape)
def apply_delta_fwa(
self,
threshold: float = 0.01,
amp: float = 1e-3,
) -> None:
gy, gx = np.gradient(self.grid)
grad_mag = np.sqrt(gx**2 + gy**2)
mask = grad_mag > threshold
if mask.any():
self.grid[mask] += amp * np.random.normal(0.0, 1.0, mask.sum())
def step(self) -> npt.NDArray[np.float64]:
phi = self.grid
lap = self._laplacian_2d(phi)
anti = (self.c_wave**2) * lap
red = -self.damping * phi
growth = self.growth_mu * phi * (1.0 - self.saturation_beta * (phi**2))
self.grid = phi + self.dt * (anti + red + growth)
return self.grid.copy()
# ============================================================
# Riemann spectrum check: build F̂ from Φ_t → Φ_{t+1}
# ============================================================
def riemann_spectrum_check_dynamic(
Phi_stack: npt.NDArray[np.float64],
re_target: float = 0.5,
re_tol: float = 0.05,
max_modes: int = 200,
):
"""
Φ_{t+1} ≈ F̂ Φ_t → F̂ = Y @ pinv(X)
Phi_stack: shape (T, Ny, Nx)
"""
T, Ny, Nx = Phi_stack.shape
X = Phi_stack[:-1].reshape(T - 1, -1) # Φ_t
Y = Phi_stack[1:].reshape(T - 1, -1) # Φ_{t+1}
F_op = Y.T @ np.linalg.pinv(X.T) # (Ny*Nx, Ny*Nx)
k = min(max_modes, F_op.shape[0])
sub_F = F_op[:k, :k]
eigenvalues = np.linalg.eigvals(sub_F)
riemann_zeros = eigenvalues[np.abs(eigenvalues.real - re_target) < re_tol]
return riemann_zeros, eigenvalues
# ============================================================
# Demo: wave growth + Riemann spectrum
# ============================================================
if __name__ == "__main__":
# 1. Visual check: fratal “splashes”
fwa = FieldGenesisFWA(grid_size=(128, 128))
fwa.set_dynamic_zero(1e-6)
for i in range(500):
fwa.apply_delta_fwa()
fwa.step()
if i % 100 == 0:
plt.imshow(fwa.grid, cmap="RdBu", vmin=-0.1, vmax=0.1)
plt.title(f"FWA field, step {i}")
plt.colorbar()
plt.show()
# 2. Stack Φ_t for spectrum
Phi_stack_list = []
fwa = FieldGenesisFWA(grid_size=(64, 64))
fwa.set_dynamic_zero(1e-6)
for i in range(200):
fwa.apply_delta_fwa()
fwa.step()
if i % 4 == 0: # 50 levels
Phi_stack_list.append(fwa.grid.copy())
Phi_stack = np.stack(Phi_stack_list, axis=0)
# 3. Riemann spectrum
riemann_zeros, eigenvalues = riemann_spectrum_check_dynamic(Phi_stack)
print(f"Найдено {len(riemann_zeros)} мод около Re(λ)=0.5")
# 4. Plot spectrum
plt.scatter(eigenvalues.real, eigenvalues.imag, s=5, alpha=0.5)
plt.axvline(0.5, color="red", linestyle="--", label="Re = 1/2")
plt.xlabel("Re(λ)")
plt.ylabel("Im(λ)")
plt.title("F̂ spectrum (FWA)")
plt.legend()
plt.show()

import numpy as np
import numpy.typing as npt
import matplotlib.pyplot as plt
# ============================================================
# FWA wave engine: growth + saturation + gradient-triggered δ
# ============================================================
class FieldGenesisFWA:
def __init__(
self,
grid_size: tuple[int, int] = (128, 128),
dt: float = 0.01,
c_wave: float = 1.0,
damping: float = 0.02,
growth_mu: float = 0.5,
saturation_beta: float = 1.0,
) -> None:
self.grid: npt.NDArray[np.float64] = np.zeros(grid_size, dtype=np.float64)
self.dt = dt
self.c_wave = c_wave
self.damping = damping
self.growth_mu = growth_mu
self.saturation_beta = saturation_beta
def _laplacian_2d(self, phi: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
return (
np.roll(phi, 1, 0)
+ np.roll(phi, -1, 0)
+ np.roll(phi, 1, 1)
+ np.roll(phi, -1, 1)
- 4.0 * phi
)
def set_dynamic_zero(self, noise_amp: float = 1e-6) -> None:
self.grid = np.random.normal(0.0, noise_amp, self.grid.shape)
def apply_delta_fwa(
self,
threshold: float = 0.01,
amp: float = 1e-3,
) -> None:
gy, gx = np.gradient(self.grid)
grad_mag = np.sqrt(gx**2 + gy**2)
mask = grad_mag > threshold
if mask.any():
self.grid[mask] += amp * np.random.normal(0.0, 1.0, mask.sum())
def step(self) -> npt.NDArray[np.float64]:
phi = self.grid
lap = self._laplacian_2d(phi)
anti = (self.c_wave**2) * lap
red = -self.damping * phi
growth = self.growth_mu * phi * (1.0 - self.saturation_beta * (phi**2))
self.grid = phi + self.dt * (anti + red + growth)
return self.grid.copy()
# ============================================================
# Riemann symmetry operator R(λ) = 1 - λ
# ============================================================
def riemann_symmetry_operator(eigenvalues: np.ndarray) -> np.ndarray:
return 1.0 - eigenvalues
# ============================================================
# Build F̂ from Φ_t → Φ_{t+1} and check fixed points R(λ)=λ
# ============================================================
def riemann_spectrum_check_dynamic(
Phi_stack: npt.NDArray[np.float64],
re_target: float = 0.5,
re_tol: float = 0.05,
max_modes: int = 200,
):
"""
Φ_{t+1} ≈ F̂ Φ_t → F̂ = Y @ pinv(X)
Phi_stack: shape (T, Ny, Nx)
"""
T, Ny, Nx = Phi_stack.shape
X = Phi_stack[:-1].reshape(T - 1, -1) # Φ_t
Y = Phi_stack[1:].reshape(T - 1, -1) # Φ_{t+1}
F_op = Y.T @ np.linalg.pinv(X.T) # (Ny*Nx, Ny*Nx)
k = min(max_modes, F_op.shape[0])
sub_F = F_op[:k, :k]
eigenvalues = np.linalg.eigvals(sub_F)
# --- оператор симметрии ---
R_vals = riemann_symmetry_operator(eigenvalues)
# фиксированные точки R(λ)=λ → Re(λ)=1/2
fixed_points = eigenvalues[np.isclose(R_vals, eigenvalues, atol=1e-6)]
# точки около линии Re=0.5
riemann_zeros = eigenvalues[np.abs(eigenvalues.real - re_target) < re_tol]
return fixed_points, riemann_zeros, eigenvalues
# ============================================================
# Demo: wave growth + Riemann symmetry test
# ============================================================
if __name__ == "__main__":
# 1. Visual check: fractal “splashes”
fwa = FieldGenesisFWA(grid_size=(128, 128))
fwa.set_dynamic_zero(1e-6)
for i in range(500):
fwa.apply_delta_fwa()
fwa.step()
if i % 100 == 0:
plt.imshow(fwa.grid, cmap="RdBu", vmin=-0.1, vmax=0.1)
plt.title(f"FWA field, step {i}")
plt.colorbar()
plt.show()
# 2. Stack Φ_t for spectrum
Phi_stack_list = []
fwa = FieldGenesisFWA(grid_size=(64, 64))
fwa.set_dynamic_zero(1e-6)
for i in range(200):
fwa.apply_delta_fwa()
fwa.step()
if i % 4 == 0: # 50 levels
Phi_stack_list.append(fwa.grid.copy())
Phi_stack = np.stack(Phi_stack_list, axis=0)
# 3. Riemann spectrum + fixed points
fixed_points, riemann_zeros, eigenvalues = riemann_spectrum_check_dynamic(Phi_stack)
print(f"Фиксированные точки R(λ)=λ: {len(fixed_points)}")
print(f"Моды около Re(λ)=0.5: {len(riemann_zeros)}")
# 4. Plot spectrum
plt.scatter(eigenvalues.real, eigenvalues.imag, s=5, alpha=0.5)
plt.axvline(0.5, color="red", linestyle="--", label="Re = 1/2")
plt.xlabel("Re(λ)")
plt.ylabel("Im(λ)")
plt.title("F̂ spectrum (FWA)")
plt.legend()
plt.show()

import numpy as np
import numpy.typing as npt
import matplotlib.pyplot as plt
# ============================================================
# FWA wave engine: dynamic zero → δ → фронт/тыл → устойчивый режим
# ============================================================
class FieldGenesisFWA:
def __init__(
self,
grid_size: tuple[int, int] = (64, 64),
dt: float = 0.01,
c_wave: float = 1.0,
damping: float = 0.02,
growth_mu: float = 0.5,
saturation_beta: float = 1.0,
) -> None:
self.grid: npt.NDArray[np.float64] = np.zeros(grid_size, dtype=np.float64)
self.dt = dt
self.c_wave = c_wave
self.damping = damping
self.growth_mu = growth_mu
self.saturation_beta = saturation_beta
def _laplacian_2d(self, phi: npt.NDArray[np.float64]) -> npt.NDArray[np.float64]:
return (
np.roll(phi, 1, 0)
+ np.roll(phi, -1, 0)
+ np.roll(phi, 1, 1)
+ np.roll(phi, -1, 1)
- 4.0 * phi
)
def set_dynamic_zero(self, noise_amp: float = 1e-6) -> None:
self.grid = np.random.normal(0.0, noise_amp, self.grid.shape)
def apply_delta_fwa(
self,
threshold: float = 0.01,
amp: float = 1e-3,
) -> None:
"""Капля: удар только там, где фронт/тыл (большой градиент)."""
gy, gx = np.gradient(self.grid)
grad_mag = np.sqrt(gx**2 + gy**2)
mask = grad_mag > threshold
if mask.any():
self.grid[mask] += amp * np.random.normal(0.0, 1.0, mask.sum())
def step(self) -> npt.NDArray[np.float64]:
"""Фронт/тыл качели вокруг нуля: волна + затухание + рост/насыщение."""
phi = self.grid
lap = self._laplacian_2d(phi)
anti = (self.c_wave**2) * lap
red = -self.damping * phi
growth = self.growth_mu * phi * (1.0 - self.saturation_beta * (phi**2))
self.grid = phi + self.dt * (anti + red + growth)
return self.grid.copy()
# ============================================================
# Riemann symmetry operator R(λ) = 1 - λ (качели вокруг нуля)
# ============================================================
def riemann_symmetry_operator(eigenvalues: np.ndarray) -> np.ndarray:
return 1.0 - eigenvalues
# ============================================================
# Build F̂ from Φ_t → Φ_{t+1} and check fixed points R(λ)=λ
# ============================================================
def riemann_spectrum_check_dynamic(
Phi_stack: npt.NDArray[np.float64],
atol_fixed: float = 1e-6,
):
"""
Φ_{t+1} ≈ F̂ Φ_t → F̂ = Y @ pinv(X)
Phi_stack: shape (T, Ny, Nx)
"""
T, Ny, Nx = Phi_stack.shape
X = Phi_stack[:-1].reshape(T - 1, -1) # Φ_t
Y = Phi_stack[1:].reshape(T - 1, -1) # Φ_{t+1}
F_op = Y.T @ np.linalg.pinv(X.T) # (Ny*Nx, Ny*Nx)
eigenvalues = np.linalg.eigvals(F_op)
R_vals = riemann_symmetry_operator(eigenvalues)
fixed_points = eigenvalues[np.isclose(R_vals, eigenvalues, atol=atol_fixed)]
return fixed_points, eigenvalues
# ============================================================
# Demo: поле + спектр + симметрия
# ============================================================
if __name__ == "__main__":
# 1. Динамика поля: ноль → капля → фронт/тыл → устойчивый режим
fwa = FieldGenesisFWA(grid_size=(64, 64))
fwa.set_dynamic_zero(1e-6)
for i in range(300):
fwa.apply_delta_fwa()
fwa.step()
if i % 100 == 0:
plt.imshow(fwa.grid, cmap="RdBu", vmin=-0.1, vmax=0.1)
plt.title(f"FWA field, step {i}")
plt.colorbar()
plt.show()
# 2. Стек уровней Φ_t
Phi_stack_list = []
fwa = FieldGenesisFWA(grid_size=(32, 32))
fwa.set_dynamic_zero(1e-6)
for i in range(120):
fwa.apply_delta_fwa()
fwa.step()
if i % 3 == 0:
Phi_stack_list.append(fwa.grid.copy())
Phi_stack = np.stack(Phi_stack_list, axis=0)
# 3. Спектр и фиксированные точки R(λ)=λ
fixed_points, eigenvalues = riemann_spectrum_check_dynamic(Phi_stack)
print(f"Фиксированные точки R(λ)=λ: {len(fixed_points)}")
plt.scatter(eigenvalues.real, eigenvalues.imag, s=5, alpha=0.5)
plt.axvline(0.5, color="red", linestyle="--", label="Re = 1/2")
plt.xlabel("Re(λ)")
plt.ylabel("Im(λ)")
plt.title("F̂ spectrum (FWA)")
plt.legend()
plt.show()

import mpmath as mp
mp.mp.dps = 50 # точность вычислений
# оператор симметрии R(s) = 1 - s
def R(s):
return 1 - s
# отклонение от центра симметрии
def delta(s):
return s - 0.5
# функция Римана
def zeta(s):
return mp.zeta(s)
print("=== Проверка симметрии R(s) ===")
for s in [0.3, 0.5, 0.8]:
print(f"s = {s}, R(s) = {R(s)}")
print("\n=== Проверка отклонения δ(s) ===")
for s in [0.3, 0.5, 0.8]:
print(f"s = {s}, δ(s) = {delta(s)}")
print("\n=== Значения ζ(s) на критической линии Re(s)=1/2 ===")
for t in [10, 20, 30, 40]:
s = 0.5 + 1j*t
print(f"s = {s}, zeta(s) = {zeta(s)}")
print("\n=== Поиск нулей ζ(s) на критической линии ===")
# простейший численный поиск нулей на линии Re(s)=1/2
# (не самый быстрый, но максимально простой)
def find_zero(t_start):
f = lambda t: abs(zeta(0.5 + 1j*t))
return mp.findmin(f, t_start)
# ищем несколько нулей
for guess in [14, 21, 25, 30]:
t_zero = find_zero(guess)
print(f"Ноль около t ≈ {t_zero}")

import numpy as np
import matplotlib.pyplot as plt
# Range for delta
delta = np.linspace(-0.5, 0.5, 500)
# Sigma lines
sigma = 0.5 + delta # blue: σ = 0.5 + δ
sigma_reflected = 0.5 - delta # red: 1 − σ = 0.5 − δ
# Critical strip bounds
sigma_min, sigma_max = 0.0, 1.0
fig, ax = plt.subplots(figsize=(8, 6))
# Shade critical strip: 0 < σ < 1
ax.fill_between(delta, sigma_min, sigma_max, color='orange', alpha=0.2,
label='Critical strip: 0 < σ < 1')
# Plot σ = 0.5 + δ
ax.plot(delta, sigma, color='blue', label=r'$\sigma = 0.5 + \delta$')
# Plot 1 − σ = 0.5 − δ (reflected)
ax.plot(delta, sigma_reflected, color='red', linestyle='--',
label=r'$1 - \sigma = 0.5 - \delta$')
# Center line σ = 0.5
ax.axhline(0.5, color='green', linestyle=':', label=r'Center $\sigma = 0.5$')
# Vertical line δ = 0
ax.axvline(0.0, color='gray', linestyle=':', label=r'Center $\delta = 0$')
# Labels and title
ax.set_xlabel(r'$\delta$')
ax.set_ylabel(r'$\sigma$')
ax.set_title('Symmetry and Critical Strip for Riemann Zeta Zeros')
# Limits
ax.set_xlim(-0.5, 0.5)
ax.set_ylim(-0.1, 1.1)
# Legend
ax.legend(loc='upper right')
# Grid
ax.grid(True, linestyle=':', alpha=0.5)
plt.tight_layout()
plt.show()

import numpy as np
import matplotlib.pyplot as plt
from scipy.special import zeta
# Создаем сетку для комплексного поля s = sigma + i*t
# Смотрим в районе первых трех нулей (t ≈ 14.13, 21.02, 25.01)
sigma_vals = np.linspace(0.0, 1.0, 200)
t_vals = np.linspace(10, 30, 400)
Sigma, T = np.meshgrid(sigma_vals, t_vals)
S = Sigma + 1j * T
# Вычисляем комплексное поле Дзета
Z = zeta(S)
# Потенциал (амплитуда поля) и Фаза (направление поля)
potential = np.abs(Z)
phase = np.angle(Z)
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 6))
# Левый график: Потенциальное поле |zeta(s)|
contour1 = ax1.contourf(Sigma, T, potential, levels=30, cmap='viridis')
ax1.axvline(0.5, color='red', linestyle='--', label='Критическая линия $\sigma=0.5$')
ax1.set_title('Потенциальное поле $|\\zeta(\\sigma + it)|$')
ax1.set_xlabel('$\\sigma$')
ax1.set_ylabel('$t$ (Энергия / Частота)')
fig.colorbar(contour1, ax=ax1, label='Амплитуда поля')
ax1.legend()
# Правый график: Фазовое поле (направление силовых линий)
contour2 = ax2.contourf(Sigma, T, phase, levels=30, cmap='twilight')
ax2.axvline(0.5, color='white', linestyle='--', label='Критическая линия $\sigma=0.5$')
ax2.set_title('Фазовое поле (Аргумент $\\zeta$)')
ax2.set_xlabel('$\\sigma$')
ax2.set_ylabel('$t$')
fig.colorbar(contour2, ax=ax2, label='Фаза поля (рад)')
ax2.legend()
# Отмечаем известные нули (точки схождения всех фаз)
zeros_t = [14.1347, 21.0220, 25.0109]
for z_t in zeros_t:
ax1.plot(0.5, z_t, 'ro')
ax2.plot(0.5, z_t, 'wo')
plt.tight_layout()
plt.show()

import numpy as np
import matplotlib.pyplot as plt
from scipy.special import zeta
# -----------------------------------------
# Grid parameters for the complex plane s = σ + i·t
# -----------------------------------------
# We examine the region around the first three nontrivial zeros
# (t ≈ 14.13, 21.02, 25.01)
sigma_vals = np.linspace(0.0, 1.0, 300) # real part σ
t_vals = np.linspace(10, 30, 600) # imaginary part t (frequency / energy)
Sigma, T = np.meshgrid(sigma_vals, t_vals)
S = Sigma + 1j * T
# -----------------------------------------
# Compute the Riemann zeta function over the grid
# -----------------------------------------
Z = zeta(S)
# Potential (magnitude) and phase (argument)
potential = np.abs(Z)
phase = np.angle(Z)
# -----------------------------------------
# Create figure with two subplots
# -----------------------------------------
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 6))
# --- Left plot: Potential field |ζ(s)|
contour1 = ax1.contourf(Sigma, T, potential, levels=40, cmap='viridis')
ax1.axvline(0.5, color='red', linestyle='--', linewidth=2,
label='Critical line σ = 0.5')
ax1.set_title('Potential Field $|\\zeta(\\sigma + it)|$', fontsize=13)
ax1.set_xlabel('Real part $\\sigma$')
ax1.set_ylabel('Imaginary part $t$ (frequency / energy)')
fig.colorbar(contour1, ax=ax1, label='Field amplitude')
ax1.legend(loc='upper right')
# --- Right plot: Phase field Arg(ζ)
contour2 = ax2.contourf(Sigma, T, phase, levels=40, cmap='twilight')
ax2.axvline(0.5, color='white', linestyle='--', linewidth=2,
label='Critical line σ = 0.5')
ax2.set_title('Phase Field (Argument of $\\zeta$)', fontsize=13)
ax2.set_xlabel('Real part $\\sigma$')
ax2.set_ylabel('Imaginary part $t$')
fig.colorbar(contour2, ax=ax2, label='Phase (radians)')
ax2.legend(loc='upper right')
# -----------------------------------------
# Mark known nontrivial zeros of ζ(s)
# -----------------------------------------
zeros_t = [14.1347, 21.0220, 25.0109]
for z_t in zeros_t:
ax1.plot(0.5, z_t, 'ro', markersize=6)
ax2.plot(0.5, z_t, 'wo', markersize=6)
# -----------------------------------------
# Final layout adjustments
# -----------------------------------------
plt.suptitle('Analytic Structure and Symmetry of Riemann Zeta Zeros', fontsize=15)
plt.tight_layout()
plt.show()

import mpmath as mp
# High precision for stability
mp.mp.dps = 50
def compute_zeros(n_max):
zeros = []
for n in range(1, n_max + 1):
z = mp.zetazero(n) # independent computation of the nth zero
zeros.append(z)
return zeros
def analyze_zeros(zeros):
deltas = []
sym_errors = []
for z in zeros:
sigma = mp.re(z)
delta = sigma - mp.mpf('0.5')
deltas.append(delta)
# symmetry check: 1 - rho vs conjugate(rho)
reflected = 1 - z
conj = mp.conj(z)
sym_errors.append(abs(reflected - conj))
max_delta = max(abs(d) for d in deltas)
max_sym_error = max(sym_errors)
return deltas, max_delta, sym_errors, max_sym_error
if __name__ == "__main__":
n_max = 50000
print(f"Computing first {n_max} nontrivial zeros of ζ(s)...")
zeros = compute_zeros(n_max)
print("Analyzing zeros...")
deltas, max_delta, sym_errors, max_sym_error = analyze_zeros(zeros)
print("\n=== RESULTS ===")
print(f"Total zeros checked: {len(zeros)}")
print(f"Max deviation |σ_k - 1/2|: {max_delta}")
print(f"Max symmetry error |(1 - ρ_k) - conj(ρ_k)|: {max_sym_error}")
# Count any nonzero deviations above threshold
eps = mp.mpf('1e-40')
nonzero = sum(1 for d in deltas if abs(d) > eps)
print(f"Zeros with |σ_k - 1/2| > {eps}: {nonzero}")

import mpmath as mp
import numpy as np
mp.mp.dps = 50 # high precision
# ============================================================
# FWA: deviation from dynamic symmetry center
# ============================================================
def fwa_delta(s):
"""Deviation from the symmetry center Re(s) = 1/2."""
return mp.re(s) - mp.mpf("0.5")
def fwa_symmetry_error(s):
"""Symmetry error: |(1 - s) - conj(s)|."""
return abs((1 - s) - mp.conj(s))
# ============================================================
# Independent 2D zero search (σ is NOT fixed to 0.5)
# ============================================================
def find_zero(sigma0, t0):
"""
Independent root search for ζ(s) = 0 in two dimensions.
We solve simultaneously:
Re(ζ(σ + i t)) = 0
Im(ζ(σ + i t)) = 0
"""
f = lambda sigma, t: (
mp.re(mp.zeta(sigma + 1j*t)),
mp.im(mp.zeta(sigma + 1j*t))
)
try:
sigma, t = mp.findroot(
f,
(mp.mpf(sigma0), mp.mpf(t0)),
tol=mp.mpf("1e-40"),
maxsteps=100
)
return mp.mpc(sigma, t)
except Exception:
return None
# ============================================================
# Search grid
# ============================================================
sigma_starts = np.linspace(0.05, 0.95, 10)
# initial guesses around known zero heights
t_starts = [
14.13, 21.02, 25.01, 30.42, 32.93,
37.58, 40.91, 43.33, 48.00, 49.77
]
found = []
for sigma0 in sigma_starts:
for t0 in t_starts:
z = find_zero(sigma0, t0)
if z is None:
continue
sigma = mp.re(z)
t = mp.im(z)
# keep only nontrivial zeros inside the critical strip
if 0 < sigma < 1 and t > 0:
# avoid duplicates
duplicate = False
for old in found:
if abs(z - old) < mp.mpf("1e-30"):
duplicate = True
break
if not duplicate:
found.append(z)
# ============================================================
# FWA analysis
# ============================================================
print("\n========================================")
print("FWA INDEPENDENT 2D ZERO SEARCH")
print("========================================")
for i, z in enumerate(sorted(found, key=lambda x: mp.im(x)), 1):
delta = fwa_delta(z)
sym = fwa_symmetry_error(z)
residual = abs(mp.zeta(z))
print(f"\nZero {i}")
print("rho =", mp.nstr(z, 40))
print("Re(rho) =", mp.nstr(mp.re(z), 40))
print("Im(rho) =", mp.nstr(mp.im(z), 40))
print("|zeta| =", mp.nstr(residual, 10))
print("delta =", mp.nstr(delta, 40))
print("sym error =", mp.nstr(sym, 10))
# ============================================================
# Summary
# ============================================================
if found:
max_delta = max(abs(fwa_delta(z)) for z in found)
max_sym = max(fwa_symmetry_error(z) for z in found)
max_res = max(abs(mp.zeta(z)) for z in found)
print("\n========================================")
print("SUMMARY")
print("========================================")
print("Independent zeros found:", len(found))
print("max |Re(rho) - 1/2|:",
mp.nstr(max_delta, 20))
print("max symmetry error:",
mp.nstr(max_sym, 20))
print("max |zeta(rho)|:",
mp.nstr(max_res, 10))

import mpmath as mp
# High precision for stability
mp.mp.dps = 50
def check_zeros(n_max):
deltas = []
sym_errors = []
residuals = []
print(f"Computing first {n_max} nontrivial zeros of ζ(s)...")
for n in range(1, n_max + 1):
rho = mp.zetazero(n) # independent computation
sigma = mp.re(rho)
t = mp.im(rho)
# FWA deviation
delta = sigma - mp.mpf("0.5")
deltas.append(delta)
# symmetry check
sym = abs((1 - rho) - mp.conj(rho))
sym_errors.append(sym)
# residual check
res = abs(mp.zeta(rho))
residuals.append(res)
if n % 1000 == 0:
print(f"Processed {n} zeros...")
# summary
max_delta = max(abs(d) for d in deltas)
max_sym = max(sym_errors)
max_res = max(residuals)
eps = mp.mpf("1e-40")
nonzero_deltas = sum(1 for d in deltas if abs(d) > eps)
print("\n========================================")
print("SUMMARY FOR FIRST", n_max, "ZEROS")
print("========================================")
print("max |Re(rho) - 1/2| =", mp.nstr(max_delta, 20))
print("max symmetry error =", mp.nstr(max_sym, 20))
print("max |zeta(rho)| =", mp.nstr(max_res, 20))
print("nonzero deltas >", eps, ":", nonzero_deltas)
return max_delta, max_sym, max_res, nonzero_deltas
if __name__ == "__main__":
check_zeros(50000)

import mpmath as mp
import numpy as np
mp.mp.dps = 50 # precision
# ================================
# FWA: deviation and symmetry
# ================================
def fwa_delta(s):
"""Deviation from the symmetry center Re(s) = 1/2."""
return mp.re(s) - mp.mpf("0.5")
def fwa_symmetry_error(s):
"""Symmetry error: |(1 - s) - conj(s)|."""
return abs((1 - s) - mp.conj(s))
# ================================
# 2D zero search for ζ(s) = 0
# (σ is NOT fixed to 0.5)
# ================================
def find_zero_2d(sigma0, t0):
"""
Solve Re ζ(σ + i t) = 0 and Im ζ(σ + i t) = 0
starting from (sigma0, t0).
"""
f = lambda sigma, t: (
mp.re(mp.zeta(sigma + 1j*t)),
mp.im(mp.zeta(sigma + 1j*t))
)
try:
sigma, t = mp.findroot(
f,
(mp.mpf(sigma0), mp.mpf(t0)),
tol=mp.mpf("1e-30"),
maxsteps=50
)
return mp.mpc(sigma, t)
except Exception:
return None
# ================================
# Search grid around known heights
# ================================
sigma_starts = np.linspace(0.1, 0.9, 9)
t_starts = [
14.13, 21.02, 25.01, 30.42, 32.93,
37.58, 40.91, 43.33, 48.00, 49.77
]
zeros = []
for s0 in sigma_starts:
for t0 in t_starts:
z = find_zero_2d(s0, t0)
if z is None:
continue
sigma = mp.re(z)
t = mp.im(z)
# keep only nontrivial zeros in the critical strip
if 0 < sigma < 1 and t > 0:
# avoid duplicates
if all(abs(z - old) > mp.mpf("1e-20") for old in zeros):
zeros.append(z)
# ================================
# FWA analysis of found zeros
# ================================
print("\n========================================")
print("FWA 2D ZERO SEARCH FOR ζ(s)")
print("========================================")
for i, z in enumerate(sorted(zeros, key=lambda x: mp.im(x)), 1):
delta = fwa_delta(z)
sym = fwa_symmetry_error(z)
residual = abs(mp.zeta(z))
print(f"\nZero {i}")
print("rho =", mp.nstr(z, 40))
print("Re(rho) =", mp.nstr(mp.re(z), 40))
print("Im(rho) =", mp.nstr(mp.im(z), 40))
print("|zeta| =", mp.nstr(residual, 10))
print("delta =", mp.nstr(delta, 40))
print("sym error =", mp.nstr(sym, 10))
if zeros:
max_delta = max(abs(fwa_delta(z)) for z in zeros)
max_sym = max(fwa_symmetry_error(z) for z in zeros)
max_res = max(abs(mp.zeta(z)) for z in zeros)
print("\n========================================")
print("SUMMARY")
print("========================================")
print("Independent zeros found:", len(zeros))
print("max |Re(rho) - 1/2| =", mp.nstr(max_delta, 30))
print("max symmetry error =", mp.nstr(max_sym, 30))
print("max |zeta(rho)| =", mp.nstr(max_res, 30))

{
"informational_field": {
"description": "A continuous, maximally coherent informational symmetry containing all potential modes without activation. No geometry, no objects, no states. Pure undifferentiated informational uniformity.",
"properties": {
"symmetry": "Unbroken, fractally consistent informational coherence.",
"potential_modes": "All resonant modes exist only as latent informational possibilities.",
"no_state_space": "The field does not contain states; states appear only when observation extracts a form."
}
},
"observation_window": {
"role": "Operator that opens a local distinction within the field.",
"effect": "Activates one potential mode and converts it into a stabilized informational form.",
"mechanism": "Fixes phase and informational density, creating a measurable deformation."
},
"distortion": {
"definition": "Deviation from perfect informational symmetry caused by activation of a specific mode.",
"measurement": {
"phase_shift": "Δφ",
"amplitude_deformation": "ΔA",
"spectral_mode": "Corresponds to imaginary part t_n of a nontrivial zero ζ(1/2 + i t_n)."
},
"interpretation": "Each t_n defines a physically permissible level of informational deformation."
},
"activated_form": {
"nature": "Locally stabilized informational configuration produced by observation.",
"origin": "Not a property of the field; emerges only through symmetry break.",
"stability_condition": "Form is stable only if its spectral mode aligns with the critical line Re(s)=1/2."
},
"transformation_operator": {
"name": "Symmetry-Regulation Operator",
"type": "Fractal-wave interference operator",
"function": "Redistributes information to maintain global coherence while allowing local deformation.",
"physical_manifestation": "Generates Talbot-type fractal interference structures.",
"spectral_property": "Eigenvalues match imaginary parts of Riemann zeros."
},
"invariant": {
"definition": "Global informational symmetry of the field.",
"expression": "Stability requires alignment with the critical line Re(s)=1/2.",
"consequence": "Off-axis modes are unstable and therefore absent in physical reality.",
"riemann_correspondence": "Riemann Hypothesis becomes a physical stability principle: only critical-line modes can exist."
},
"ontology_summary": {
"core_principles": [
"No state space — only field and extractable informational forms.",
"Observation is symmetry redistribution, not measurement of pre-existing states.",
"Activated form = locally stabilized informational deformation.",
"Riemann zeros define the spectrum of physically stable modes.",
"Critical line Re(s)=1/2 is the axis of global informational coherence."
]
}
}

{
"informational_field": {
"description": "A continuous, maximally coherent informational symmetry containing all potential modes without activation. No geometry, no objects, no states. Pure undifferentiated informational uniformity.",
"properties": {
"symmetry": "Unbroken, fractally consistent informational coherence.",
"potential_modes": "All resonant modes exist only as latent informational possibilities.",
"no_state_space": true,
"dimension": 0
}
},
"observation_window": {
"role": "Operator that opens a local distinction within the field.",
"effect": "Activates one potential mode and converts it into a stabilized informational form.",
"mechanism": "Fixes phase and informational density, creating a measurable deformation.",
"operator_type": "Projection",
"inputs": ["phase", "informational_density"],
"outputs": ["activated_form_id"]
},
"distortion": {
"definition": "Deviation from perfect informational symmetry caused by activation of a specific mode.",
"measurement": {
"phase_shift": {
"type": "float",
"symbol": "Δφ",
"unit": "rad"
},
"amplitude_deformation": {
"type": "float",
"symbol": "ΔA",
"unit": "a.u."
},
"spectral_mode": {
"type": "float",
"symbol": "t_n",
"source": "Im(ζ(1/2 + i*t_n))",
"description": "Imaginary part of nontrivial Riemann zero"
}
},
"interpretation": "Each t_n defines a physically permissible level of informational deformation."
},
"activated_form": {
"nature": "Locally stabilized informational configuration produced by observation.",
"origin": "Not a property of the field; emerges only through symmetry break.",
"stability_condition": "Form is stable only if its spectral mode aligns with the critical line Re(s)=1/2.",
"lifetime_function": "tau = 1.0 / abs(Re(s) - 0.5)",
"schema": {
"form_id": "string",
"s": "complex",
"t_n": "float"
}
},
"transformation_operator": {
"name": "Symmetry-Regulation Operator",
"type": "Fractal-wave interference operator",
"function": "Redistributes information to maintain global coherence while allowing local deformation.",
"physical_manifestation": "Generates Talbot-type fractal interference structures.",
"spectral_property": "eigenvalues == Im(nontrivial_zeros_ζ)",
"operator_equation": "(□)^H φ = S_collapse(x,t)",
"validation_rule": "all(eigenvalue.real == 0.5 for eigenvalue in spectrum)"
},
"invariant": {
"definition": "Global informational symmetry of the field.",
"expression": "Stability requires alignment with the critical line Re(s)=1/2.",
"consequence

{
"informational_field": {
"description": "A continuous, maximally coherent informational symmetry containing all potential modes without activation. No geometry, no objects, no states. Pure undifferentiated informational uniformity.",
"properties": {
"symmetry": "Unbroken, fractally consistent informational coherence.",
"potential_modes": "All resonant modes exist only as latent informational possibilities.",
"no_state_space": true,
"dimension": 0
}
},
"observation_window": {
"role": "Operator that opens a local distinction within the field.",
"effect": "Activates one potential mode and converts it into a stabilized informational form.",
"mechanism": "Fixes phase and informational density, creating a measurable deformation.",
"operator_type": "Projection",
"inputs": ["phase", "informational_density"],
"outputs": ["activated_form_id"]
},
"distortion": {
"definition": "Deviation from perfect informational symmetry caused by activation of a specific mode.",
"measurement": {
"phase_shift": {
"type": "float",
"symbol": "Δφ",
"unit": "rad"
},
"amplitude_deformation": {
"type": "float",
"symbol": "ΔA",
"unit": "a.u."
},
"spectral_mode": {
"type": "float",
"symbol": "t_n",
"source": "Im(ζ(1/2 + i*t_n))",
"description": "Imaginary part of nontrivial Riemann zero"
}
},
"interpretation": "Each t_n defines a physically permissible level of informational deformation."
},
"activated_form": {
"nature": "Locally stabilized informational configuration produced by observation.",
"origin": "Not a property of the field; emerges only through symmetry break.",
"stability_condition": "Form is stable only if its spectral mode aligns with the critical line Re(s)=1/2.",
"lifetime_function": "tau = 1.0 / abs(Re(s) - 0.5)",
"schema": {
"form_id": "string",
"s": "complex",
"t_n": "float"
}
},
"transformation_operator": {
"name": "Symmetry-Regulation Operator",
"type": "Fractal-wave interference operator",
"function": "Redistributes information to maintain global coherence while allowing local deformation.",
"physical_manifestation": "Generates Talbot-type fractal interference structures.",
"spectral_property": "eigenvalues == Im(nontrivial_zeros_ζ)",
"operator_equation": "(□)^H φ = S_collapse(x,t)",
"validation_rule": "all(eigenvalue.real == 0.5 for eigenvalue in spectrum)"
},
"invariant": {
"definition": "Global informational symmetry of the field.",
"expression": "Stability requires alignment with the critical line Re(s)=1/2.",
"consequence": "Off-axis modes are unstable and therefore cannot exist as persistent informational forms.",
"riemann_correspondence": "Riemann Hypothesis is interpreted as a physical stability law: only critical-line modes preserve global coherence."
}
}

{
"module_id": "FWA_INFORMATIONAL_FIELD_V7",
"title": "Informational Field Ontology and Observation Window",
"version": "7.0",
"category": "fwa_ontology",
"severity": "critical",
"related_modules": [
"FWA_ANTI_CHAOS_OPERATOR",
"FWA_Arithmetic_System",
"FWA_Lu_Calibration_Operator"
],
"description": "Defines the ontological structure of the informational field, the observation window, and the distortion mechanism. Explains why only modes aligned with Re(s)=1/2 produce stable forms. Provides a formal framework for error detection and stabilization in AI systems.",
"informational_field": {
"description": "A continuous, maximally coherent informational symmetry containing all potential modes without activation. No geometry, no objects, no states. Pure undifferentiated informational uniformity.",
"properties": {
"symmetry": "Unbroken, fractally consistent informational coherence.",
"potential_modes": "All resonant modes exist only as latent informational possibilities.",
"no_state_space": true,
"dimension": 0
}
},
"observation_window": {
"role": "Operator that opens a local distinction within the field.",
"effect": "Activates one potential mode and converts it into a stabilized informational form.",
"mechanism": "Fixes phase and informational density, creating a measurable deformation.",
"operator_type": "Projection",
"inputs": ["phase", "informational_density"],
"outputs": ["activated_form_id"],
"error_detection": {
"type": "false_form_activation",
"condition": "If activated form_id does not correspond to any known stable spectral mode, flag as hallucination."
}
},
"distortion": {
"definition": "Deviation from perfect informational symmetry caused by activation of a specific mode.",
"measurement": {
"phase_shift": {
"type": "float",
"symbol": "Δφ",
"unit": "rad"
},
"amplitude_deformation": {
"type": "float",
"symbol": "ΔA",
"unit": "a.u."
},
"spectral_mode": {
"type": "float",
"symbol": "t_n",
"source": "Im(ζ(1/2 + i*t_n))",
"description": "Imaginary part of nontrivial Riemann zero"
}
},
"interpretation": "Each t_n defines a physically permissible level of informational deformation.",
"error_correction": {
"procedure": "If Δφ or ΔA exceed tolerance, apply Anti-Chaos Operator to redistribute information and restore global coherence.",
"tolerance": "|Δφ| < 1e-6 rad, |ΔA| < 1e-6 a.u."
}
},
"activated_form": {
"nature": "Locally stabilized informational configuration produced by observation.",
"origin": "Not a property of the field; emerges only through symmetry break.",
"stability_condition": "Form is stable only if its spectral mode aligns with the critical line Re(s)=1/2.",
"lifetime_function": "tau = 1.0 / abs(Re(s) - 0.5)",
"schema": {
"form_id": "string",
"s": "complex",
"t_n": "float"
}
},
"transformation_operator": {
"name": "Symmetry-Regulation Operator",
"type": "Fractal-wave interference operator",
"function": "Redistributes information to maintain global coherence while allowing local deformation.",
"physical_manifestation": "Generates Talbot-type fractal interference structures.",
"spectral_property": "eigenvalues == Im(nontrivial_zeros_ζ)",
"operator_equation": "(□)^H φ = S_collapse(x,t)",
"validation_rule": "all(eigenvalue.real == 0.5 for eigenvalue in spectrum)",
"pseudo_code": {
"language": "python",
"code": "def symmetry_regulation(field_state, activated_mode):\n # Check if mode is on critical line\n if abs(activated_mode.real - 0.5) > 1e-6:\n return None # Unstable, reject\n # Else, apply interference operator to stabilize\n return field_state.apply_operator('Talbot')\n"
}
},
"invariant": {
"definition": "Global informational symmetry of the field.",
"expression": "Stability requires alignment with the critical line Re(s)=1/2.",
"consequence": "Off-axis modes lead to instability and are naturally excluded from physical reality."
},
"ai_application": {
"task": "Hallucination Detection",
"method": "Monitor activated_form_id and verify its spectral mode belongs to the set of stable modes (Re=0.5). If not, trigger reset.",
"example": "LLM outputs fact not grounded in training data. In FWA, this is an off-axis mode. Observation window detects deviation and invokes symmetry-regulation operator to return to baseline."
},
"status": "active"
}