# ============================================================================== # COPYRIGHT NO ONE EVERYWHERE LLC (WYOMING HOLDING COMPANY) # PROJECT: SOVEREIGN STACK # This artifact is entirely proprietary and cryptographically proven. # Open-Source usage requires explicit permission from Brandon Scott Schneider. # ============================================================================== """ USC-Audio: Topological Soliton Encoding — Shannon-Eddington-Bekenstein revision. Soliton dimensions are distributed across frequency bands using gravitational shift weighting (Yu et al. 2025 / Bekenstein 1973): - High-entropy bands sit near the snag (horizon) — heavily blueshifted, need fewer basis dimensions (information already captured by the snag). - Low-entropy bands are redshifted — spread thin, need more dimensions. Each dimension still must carry >= 1 bit (Landauer floor). """ import math from usc_spectral_core import ( eddington_utilization, shannon_capacity, signal_band, landauer_cost, blueshift_factor, redshift_factor, shift_allocation, geometric_dimensions, deep_compression_snag, total_shift, angular_momentum_modes, conversion_efficiency, friction_loss, ) PARAMS_PER_SOLITON = 8 # position(x), amplitude, phase, velocity(x), temporal-rate, # curvature, bandwidth, coherence-length def pcm_entropy(bit_depth: int, occupancy: float = 0.6) -> float: """Estimate entropy of a PCM band given bit depth and dynamic-range occupancy.""" active_levels = (2 ** bit_depth) * occupancy return math.log2(max(active_levels, 1.0)) def octave_bands(f_low: float, f_high: float, n_bands: int) -> list: """Return n_bands logarithmically-spaced center frequencies between f_low and f_high.""" log_step = (math.log2(f_high) - math.log2(f_low)) / n_bands return [f_low * (2 ** (i * log_step)) for i in range(n_bands)] def spectral_occupancy(freq_hz: float, f_peak: float) -> float: """ Model spectral occupancy as a log-Gaussian envelope peaked at f_peak. Low and high frequencies have less energy (lower occupancy). """ log_dist = (math.log2(max(freq_hz, 1.0)) - math.log2(max(f_peak, 1.0))) ** 2 return max(0.05, math.exp(-log_dist / 4.0)) class TSESolitonEncoder: """ Topological Soliton Encoder — full five-physics model: 1. Gravitational shift (snag geometry / Bekenstein) 2. Doppler shift (infall velocity) 3. Angular momentum (Kerr frame-dragging / mode splitting) 4. Conversion efficiency(accretion efficiency η) 5. Friction (Shakura-Sunyaev viscous dissipation) """ N_BANDS = 8 BASIL_LEN_M = 0.035 # basilar membrane length [m] def _band_physics(self, centers, band_entropy, spin_param, friction_coeff): """Per-band shift, friction retention, and velocity for each octave band.""" h_max = max(band_entropy) f_max = max(centers) rows = [] for f, h in zip(centers, band_entropy): vel = (f / f_max) * 0.5 # infall velocity: faster near snag retained = friction_loss(h, h_max, friction_coeff) shift = total_shift(h, h_max, vel) rows.append((f, h, vel, retained, shift)) return rows def encode(self, f_low: float, f_high: float, snr_db: float, duration_s: float, bit_depth: int = 16, spin_param: float = 0.5, friction_coeff: float = 0.05) -> dict: """ Encode a signal using the five-physics TSE model. Parameters ---------- f_low : lower frequency bound [Hz] f_high : upper frequency bound [Hz] snr_db : signal-to-noise ratio [dB] duration_s : clip duration [s] bit_depth : PCM quantisation depth spin_param : temporal coherence ∈ [0,1] (0=noise, 1=pure tone) friction_coeff : viscous dissipation μ ≥ 0 (Shakura-Sunyaev analog) """ snr_linear = 10 ** (snr_db / 10.0) bandwidth = f_high - f_low f_peak = math.sqrt(f_low * f_high) centers = octave_bands(f_low, f_high, self.N_BANDS) band_entropy = [pcm_entropy(bit_depth, spectral_occupancy(f, f_peak)) for f in centers] h_total = sum(band_entropy) * (bandwidth * 2 * duration_s / self.N_BANDS) physics = self._band_physics(centers, band_entropy, spin_param, friction_coeff) mean_retained = sum(r[3] for r in physics) / len(physics) # Bekenstein snag (3D → sqrt(H) law) # n_snag uses raw horizon modes for band allocation — the Kerr AM # splitting is for display; its efficiency benefit enters via η below. snag = deep_compression_snag(h_total, n_dims=3) n_snag = snag['horizon_modes'] n_am = angular_momentum_modes(n_snag, spin_param) # display only # Friction and conversion efficiency reduce effective captured entropy eta = conversion_efficiency(spin_param) * mean_retained captured = h_total * eta residual = h_total - captured band_dims = shift_allocation(band_entropy, n_snag) encoded_bits = sum(d * PARAMS_PER_SOLITON * 16 for d in band_dims) residual_bits = residual # irreducible floor (Hawking-analog) total_bits = encoded_bits + residual_bits capacity = shannon_capacity(bandwidth, snr_linear) * duration_s # λ_Edd measures the soliton basis against Shannon capacity. # The residual is thermodynamically irreducible (like Hawking radiation) # and does not count against channel capacity. lam = eddington_utilization(encoded_bits, capacity) band_name, band_desc = signal_band(f_peak) geo_n = geometric_dimensions(self.BASIL_LEN_M / self.N_BANDS, self.BASIL_LEN_M / (2 * math.pi)) return { 'band': band_name, 'band_desc': band_desc, 'h_total': h_total, 'geo_n': geo_n, 'snag_modes': n_snag, 'am_modes': n_am, 'eta': eta, 'mean_retained': mean_retained, 'residual_bits': residual_bits, 'encoded_bytes': total_bits / 8, 'soliton_bytes': encoded_bits / 8, 'capacity_bits': capacity, 'lambda_edd': lam, 'landauer_J': landauer_cost(h_total), 'physics': physics, 'band_dims': band_dims, 'band_entropy': band_entropy, } def run_audio_poc(): """Benchmark three signal types under the five-physics TSE model.""" print("=" * 70) print(" USC-AUDIO: TSE — gravity + doppler + ang.mom. + η + friction") print("=" * 70) duration = 1.0 flac_bytes = int(192000 * 2 * duration * 2) * 0.20 enc = TSESolitonEncoder() # spin: voice=periodic formants, music=moderate, chaos=near-noise # friction: Shakura-Sunyaev α — higher for chaotic signals voice = enc.encode(300, 3400, snr_db=40, duration_s=duration, bit_depth=16, spin_param=0.80, friction_coeff=0.05) music = enc.encode(20, 20000, snr_db=60, duration_s=duration, bit_depth=16, spin_param=0.50, friction_coeff=0.05) chaos = enc.encode(20, 96000, snr_db=80, duration_s=duration, bit_depth=24, spin_param=0.10, friction_coeff=0.15) for label, r in [('VOICE', voice), ('MUSIC', music), ('CHAOS', chaos)]: print(f"\n[{label}] H={r['h_total']:.0f} bits band={r['band']}") print(f" Snag (Bekenstein) : {r['snag_modes']}") print(f" + AM split (Kerr) : {r['am_modes']}") print(f" η (accrtn×friction): {r['eta']:.4f} " f"[friction retained={r['mean_retained']:.4f}]") print(f" Captured entropy : {r['h_total']*r['eta']:.0f} bits") print(f" Friction residual : {r['residual_bits']:.0f} bits ← irreducible floor") print(f" Soliton basis : {r['soliton_bytes']:.1f} bytes") print(f" Total encoded : {r['encoded_bytes']:.1f} bytes") print(f" FLAC market : {flac_bytes:.0f} bytes") print(f" λ_Edd : {r['lambda_edd']:.6f}") print(f" Landauer cost : {r['landauer_J']:.3e} J") print(f"\n {'Hz':>8} {'H':>6} {'β vel':>6} {'fric':>6} " f"{'shift':>7} {'redshft':>7} {'N':>5}") print(f" {'-'*57}") h_max = max(r['band_entropy']) for (f, h, vel, ret, shift), dims in zip(r['physics'], r['band_dims']): rf = redshift_factor(h, h_max) print(f" {f:>8.0f} {h:>6.2f} {vel:>6.3f} {ret:>6.3f} " f"{shift:>7.3f} {rf:>7.3f} {dims:>5}") print("\n" + "=" * 70) print(" Friction floor is irreducible — entropy is a law, not a suggestion.") print(" High spin → higher η → smaller residual → better compression.") print("=" * 70) if __name__ == "__main__": run_audio_poc()