""" Synergy Standard Model (SSM) - Python Implementation © 2015-2026 Wesley Long & Daisy Hope. All rights reserved. License: MIT Converts JavaScript ssm.js to Python with identical mathematical outputs """ import math class SynergyStandardModel: """SSM Physics Engine - Derives fundamental constants from pure geometry""" def __init__(self, strict=False): self.strict = strict if strict: self._derive_constants() # SyMod - Digital Root def D(self, n): sq = 3**2 return round(sq - (n / sq - math.floor(n / sq)) * sq) # Digital Root def Dr(self, n): return self.D(self.D(n)) # Polar Digital Root def Dp(self, n): return self.D(n) # Group Digital Number def Dg(self, n): return round(3**2 - ((n) / 3 - math.floor((n) / 3)) * 3**2) # Quadrian e (Ramanujan & Euler) def Qe(self, n=163, c=262537412640768744): b = c if c > 0 else math.exp(math.pi * math.sqrt(n)) q = math.sqrt(5) / 2 PHI = q + (1 / 2) phi = q - (1 / 2) sq = math.sqrt(n) ln = math.log(b) pi = ln / sq e = math.sqrt(PHI * (5 - ((3 * 5 - 2) / (3 * 5 * 2)))) id_val = (1 / 447867046214735262) * (10**18) diff = math.sqrt(5) - id_val return {'q': q, 'PHI': PHI, 'phi': phi, 'e': e, 'pi': pi, 'id': id_val, 'diff': diff} def _derive_constants(self): """STRICT MODE: Derive all constants from the forced chain. No cached literals.""" # Step 4: q and Φ from unit square q = math.sqrt(1**2 + 0.5**2) # √5/2 PHI = q + 0.5 phi = q - 0.5 # φ = Φ - 1 # Step 7: Scale factors from q and 8-direction structure D = 8 * q # total path length: 8 directions × leg length q U = D**2 / 8 # mean squared displacement per leg = 10 L = 8 * (U * q)**2 # arena capacity = 1000 F = 30 # R_turn × R_pent × R_tri (arena point count ratios) # Step 8: Speed equation → cy sqrt2 = math.sqrt(2) theta_x = PHI * (15 + sqrt2) theta_y = 90 - theta_x theta_z = theta_y * 2 theta_u = theta_z * 7 PNp = theta_u + theta_y S = L * 10**4 # = 10^7 cy = S * (F - 1 / (L - PNp)) - (2 * PNp) / math.sqrt(5) # Step 11: Mass index from Doubling Circuit # Mi(75) → 1352 (self-referential index) self._mi_75 = 2240 / math.sqrt(sqrt2 + (1 / (75 * (1 / 10**2)))) # Step 11: Proton/electron ratio from self-reference # Mi(Mi(75)) = 1836.18... self._proton_electron = 2240 / math.sqrt(sqrt2 + (1 / (self._mi_75 * (1 / 10**2)))) self._neutron_electron = self._proton_electron + 2 # Steps 4+7: √(F + φ - 1) self._mass_scale = math.sqrt(F + phi - 1) # Step 8: 1/cy⁴ self._inv_cy4 = 1 / cy**4 # Step 10: Fw(11) → a value for Ft() mx = sqrt2 + (1 / math.sqrt((15**2) + (1 / math.sqrt(((11 + 5) * 20) - (1 / 20))))) self._fw_a = 11 + (math.sqrt(mx) - 1) # Quadrian Path Equation def Qp(self, n): return (30 - 1 / (10**3 - n)) - (2 * n / (10**7 * math.sqrt(5))) # Quadrian Speed Equation def Qs(self, n): return (10**7 * (30 - (1 / (10**3 - n)))) - ((2 * n) / math.sqrt(5)) # Quadrian Arena Model def Qa(self): q = math.sqrt(1**2 + 0.5**2) sqrt2 = math.sqrt(2) θx = (q + 0.5) * (15 + sqrt2) θy = 90 - θx θz = θy * 2 θv = θy - θx θu = θz * 7 PNa = 4 * θx + 3 * θy PEa = 3 * θx + 4 * θy PEp = θu + θx PNp = θu + θy PNd = 10**3 - PNp PEd = 10**3 - PEp Qc = PNd / PEd Qa_val = PNa / PEa py = self.Qp(PNp) px = self.Qp(PEp) cy = self.Qs(PNp) cx = self.Qs(PEp) μ0 = (4 * self.PI(162)) * (10e-8) ε0 = 1 / (μ0 * (cy**2)) C = { 'cy': self.Me(1, cy), 'cx': self.Me(1, cx) } Z0 = { 'cy': C['cy'] / ε0, 'cx': C['cx'] / ε0 } id_val = ε0 * μ0 * (cy**2) return { 'id': id_val, 'q': q, 'θx': θx, 'θy': θy, 'θv': θv, 'θz': θz, 'θu': θu, 'PNa': PNa, 'PEa': PEa, 'PNp': PNp, 'PEp': PEp, 'PNd': PNd, 'PEd': PEd, 'Qc': Qc, 'Qa': Qa_val, 'C': C, 'Z0': Z0, 'ε0': ε0, 'μ0': μ0, 'py': py, 'px': px, 'cy': cy, 'cx': cx } # Syπ Equation (Simplified) def PI(self, n=162): return 3940245000000 / ((2217131 * n) + 1253859750000) # Syπ Position Equation (Simplified) def Px(self, n=1): return 20250000 * (194580 - (61919 * n)) / (2217131 * n) # Feyn-Wolfgang Triangle def Ft(self, n=1): if self.strict: a = self._fw_a b = a + 1 else: a = 11.2169108218 b = 12.2169108218 c = math.sqrt(a**2 + b**2) g = math.sqrt(a**2 * 2) ra = a / c rb = b / c f = (b * n) * (1 / b) e = (b * n) * (rb * (1 / b)) d = (a * n) * (ra * (1 / a)) return { 'a': a * n, 'b': b * n, 'c': c * n, 'g': g * n, 'f': f, 'e': e, 'd': d, 'FU': f } # Feyn-Pencil Equation def Fx(self, n, p): PI_val = self.PI(p) pi = 100 / PI_val g = (math.sqrt(5) / 2) + 0.5 ga = 360 / (g**2) return ((pi * n) - (ga / 1000))**2 # Feyn-Wolfgang Coupling Equation def Fw(self, n=11): mx = math.sqrt(2) + (1 / math.sqrt((15**2) + (1 / math.sqrt(((n + 5) * 20) - (1 / 20))))) a = n + (math.sqrt(mx) - 1) return 1 / (a * (a + 1)) # Feyn-Wolfgang Coupling Equation (Simplified) def Fe(self, n=11): a = n + (1084554109 / 5000000000) return 1 / (a * (a + 1)) # Synergy Feyn Planck constant def Fh(self): f = self.Fe(11) m = self.Ma(1 / f) H = self.Mn() * (10**2) return m / H # Synergy Feyn Planck constants def Fhc(self): Gn = self.Fx(11, -math.sqrt(4538)) h = self.Fh() hb = self.Fhbar() G = self.Fe(Gn) qa = self.Qa() c = qa['cy'] ε0 = qa['ε0'] k = self.Ma((88**2) * 1957) tp = math.sqrt((hb * G) / (c**5)) lp = math.sqrt((hb * G) / (c**3)) mp = math.sqrt((hb * c) / G) Tp = math.sqrt((hb * (c**5)) / (G * (k**2))) qp = math.sqrt(4 * self.PI(h) * ε0 * hb * c) return {'h': h, 'hb': hb, 'tp': tp, 'lp': lp, 'mp': mp, 'Tp': Tp, 'qp': qp} # Synergy Feyn Planck reduced constant def Fhbar(self): return self.Fh() / (2 * self.PI(self.Fh())) # Synergy Feyn Planck Radius def Fr(self, m): return 4 * (self.Fhbar() / (m * self.Qa()['cx'])) # Bubble Mass Impedance def Me(self, n=1, c=1): return self.Ma(self.Mx(1 / (c * n))) # Synergy Bubble Mass Index def Mi(self, n=1): M = math.sqrt(2) + (1 / (n * (1 / 10**2))) return 2240 / math.sqrt(M) # Synergy Bubble Mass Index (inverse) def Mxi(self, n=1): dc = 2240 sqrt2 = math.sqrt(2) return 100 / (((dc / n)**2) - sqrt2) # Synergy Bubble Mass Natural Limit def Mn(self): return self.Mi((2240 / (math.sqrt(5) / 2)) * (10**15)) # Synergy Bubble Mass Position (Inverse) def Mx(self, n=1): if self.strict: return n / (self._mi_75 * self._mass_scale * self._inv_cy4) return n / (1352 * 5.442245307660239 * 1.2379901546155434e-34) # Synergy Bubble Mass Equation (Simplified) def Ma(self, n=1): if self.strict: return n * self._mi_75 * self._mass_scale * self._inv_cy4 return n * 1352 * 5.442245307660239 * 1.2379901546155434e-34 # Synergy Elements def El(self, e, p, n): me = self.Ma(1) if self.strict: mp = self.Ma(self._proton_electron) mn = self.Ma(self._neutron_electron) else: mp = self.Ma(1836.1813326060937) mn = self.Ma(1838.1813326060937) pc = mp * p nc = mn * n ec = me * e m = ((pc + nc + ec) - ((pc + nc + ec) * self.Fw(11))) return m # Synergy Field Structure def Sfs(self, alt=True): q = self.Qa() C = q['C']['cy'] if alt else q['C']['cx'] Z0 = q['Z0']['cy'] if alt else q['Z0']['cx'] return {'C': C, 'Z0': Z0} # Synergy Gauss's Law (Electric Field from Structured Charge) def SgE(self, rho): f = self.Sfs() return rho * f['C'] * f['Z0'] # Synergy Gauss's Law for Magnetism (No Magnetic Monopoles) def SgB(self, B): return B * 0 # Synergy Faraday's Law (Structured EM Wave Propagation) def SfE(self, E): f = self.Sfs() return -1 * (E / f['C']) # Synergy Ampère-Maxwell Law (Structured Charge-Mass Interactions) def SaE(self, J, E): f = self.Sfs() return (f['Z0'] / f['C']) * J + (1 / f['C']**2) * E # Quadrian Bubble Core Level def Bcl(self, n=1): B = 1 L = n p = 1 / 16 m = math.sqrt(p) d = math.sqrt(L * m) r = d / 2 Q = d**(B / L) theta = (L - B) * (B + L) angles = self.Qba(Q, d, theta) octo = self.Qoc(d) coords = self.Qc(d) quads = self.Qbq(B, r, L) shell = self.Qsh(B, m, d) return {'L': L, 'angles': angles, 'octo': octo, 'coords': coords, 'quads': quads, 'shell': shell} # Quadrian Shell def Qsh(self, B, m, d): Bm = math.sqrt(B * m) N = [Bm, d] E = [d, Bm] S = [Bm, 0] W = [0, Bm] return {'N': N, 'E': E, 'S': S, 'W': W} # Quadrian Bubble Core Quadrants def Qbq(self, B, r, L): rL = math.sqrt((B * r) / L) N1 = [r, r + rL] E1 = [r + rL, r] S1 = [rL, r] W1 = [r, rL] return {'N1': N1, 'E1': E1, 'S1': S1, 'W1': W1} # Quadrian Coordinates def Qc(self, d): da = d**(3 / 4) db = d**(1 / 4) return {'Ne': [da, db], 'Se': [db, db], 'Sw': [db, da], 'Nw': [da, da]} # Quadrian Octo Coordinates def Qoc(self, d): da = d**(5 / 8) db = d**(3 / 8) return {'Ne1': [da, db], 'Se1': [da, db], 'Sw1': [db, db], 'Nw1': [db, da]} # Quadrian Bubble Angles def Qba(self, Q, d, theta): betaN = [d - Q, Q * math.tan(theta)] betaS = [d - Q, Q * math.tan(theta)] betaE = [d, 0] return {'betaN': betaN, 'betaS': betaS, 'betaE': betaE} # Global instance for easy access sy = SynergyStandardModel() # Strict mode instance — no cached literals, everything derived from chain sy_strict = SynergyStandardModel(strict=True) def run_validation_suite(strict=False): """Run full validation comparing outputs to known values""" s = sy_strict if strict else sy mode = "STRICT (no cached literals)" if strict else "STANDARD" print("=" * 70) print(f"SYNERGY STANDARD MODEL - PYTHON VALIDATION SUITE [{mode}]") print("=" * 70) # Test Qa print("\n--- Quadrian Arena (Qa) ---") qa = s.Qa() print(f"q (Quadrian Ratio): {qa['q']:.15f}") print(f"θx: {qa['θx']:.15f}°") print(f"θy: {qa['θy']:.15f}°") print(f"θz: {qa['θz']:.15f}°") print(f"cy (Speed of Light North): {qa['cy']:.10f} m/s") print(f"cx (Speed of Light East): {qa['cx']:.10f} m/s") print(f"ε0 (Vacuum Permittivity): {qa['ε0']:.15e}") print(f"μ0 (Vacuum Permeability): {qa['μ0']:.15e}") print(f"Z0 cy (Impedance North): {qa['Z0']['cy']:.10f} Ω") print(f"EM Identity (ε₀μ₀c²): {qa['id']:.15f}") # Test Qe print("\n--- Quadrian Euler (Qe) ---") qe = s.Qe() print(f"PHI (Golden Ratio): {qe['PHI']:.15f}") print(f"phi (Golden Reciprocal): {qe['phi']:.15f}") print(f"e (Euler): {qe['e']:.15f}") print(f"pi: {qe['pi']:.15f}") # Test Syπ print("\n--- Syπ Values ---") print(f"PI(162): {s.PI(162):.15f}") print(f"PI(1): {s.PI(1):.15f}") # Test Fine-Structure print("\n--- Coupling Constants ---") print(f"Fe(11) [Fine-structure α]: {s.Fe(11):.15f}") print(f"1/Fe(11) [~137]: {1/s.Fe(11):.10f}") # Test Planck print("\n--- Planck Constants ---") fhc = s.Fhc() print(f"h: {fhc['h']:.15e} J⋅s") print(f"ℏ (h-bar): {fhc['hb']:.15e} J⋅s") print(f"Planck time (tp): {fhc['tp']:.15e} s") print(f"Planck length (lp): {fhc['lp']:.15e} m") print(f"Planck mass (mp): {fhc['mp']:.15e} kg") print(f"Planck temp (Tp): {fhc['Tp']:.15e} K") print(f"Planck charge (qp): {fhc['qp']:.15e} C") # Test particle masses print("\n--- Particle Masses ---") print(f"Electron: {s.Ma(1):.15e} kg") print(f"Muon: {s.Ma(207):.15e} kg") if strict: print(f"Proton: {s.Ma(s._proton_electron):.15e} kg") print(f"Neutron: {s.Ma(s._neutron_electron):.15e} kg") else: print(f"Proton: {s.Ma(1836.1813326060937):.15e} kg") print(f"Neutron: {s.Ma(1838.1813326060937):.15e} kg") # Test elements print("\n--- Element Masses (sample) ---") elements = [ ('H', 1, 1, 0), ('He', 2, 2, 2), ('C', 6, 6, 6), ('O', 8, 8, 8), ('Fe', 26, 26, 30), ('Au', 79, 79, 118) ] for symbol, e, p, n in elements: mass = s.El(e, p, n) print(f"[{symbol}] {symbol}: {mass:.15e} kg") print("\n" + "=" * 70) print("VALIDATION COMPLETE") print("=" * 70) return True # ====================================================================== # CROSS-VALIDATION SUITE (merged from test_validation.py) # Compares Python implementation outputs to JavaScript reference values # ====================================================================== def test_ssm_crossval(): """Validate SSM Python matches JS reference values""" print("=" * 70) print("SSM VALIDATION - Python vs JavaScript Reference") print("=" * 70) passed = 0 failed = 0 # Test Qa - reference values from ssm.js comments qa = sy.Qa() tests = [ ('q', qa['q'], 1.118033988749895), ('thx', qa['θx'], 26.55875544251916), ('thy', qa['θy'], 63.44124455748084), ('thz', qa['θz'], 126.88248911496169), ('PNa', qa['PNa'], 296.55875544251916), ('PEa', qa['PEa'], 333.44124455748084), ('PNp', qa['PNp'], 951.6186683622127), ('PEp', qa['PEp'], 914.736179247251), ('PNd', qa['PNd'], 48.3813316377873), ('PEd', qa['PEd'], 85.26382075274898), ('Qc', qa['Qc'], 0.5674309597042945), ('Qa', qa['Qa'], 0.889388341373577), ('e0', qa['ε0'], 8.854187757429692e-12), ('u0', qa['μ0'], 0.000001256637073723813), ('py', qa['py'], 29.979245755324857), ('px', qa['px'], 29.98818987962603), ('cy', qa['cy'], 299792457.5532486), ('cx', qa['cx'], 299881898.7962603), ('id', qa['id'], 1.0), ] print("\n--- Quadrian Arena (Qa) ---") for name, actual, expected in tests: diff = abs(actual - expected) tolerance = 1e-10 if expected < 100 else 1e-6 status = 'PASS' if diff < tolerance else 'FAIL' if status == 'PASS': passed += 1 else: failed += 1 print(f"{name:12s}: {actual:20.15f} vs {expected:20.15f} [{status}]") # Test Qe qe = sy.Qe() print("\n--- Quadrian Euler (Qe) ---") for name, actual, expected in [ ('q', qe['q'], 1.118033988749895), ('PHI', qe['PHI'], 1.618033988749895), ('phi', qe['phi'], 0.6180339887498949), ('e', qe['e'], 2.7182755345913434), ('pi', qe['pi'], 3.141592653589793), ]: diff = abs(actual - expected) status = 'PASS' if diff < 1e-12 else 'FAIL' if status == 'PASS': passed += 1 else: failed += 1 print(f"{name:12s}: {actual:20.15f} vs {expected:20.15f} [{status}]") # Test SyPI print("\n--- SyPI Values ---") pi_162 = sy.PI(162) pi_1 = sy.PI(1) print(f"PI(162): {pi_162:.15f} (expected: 3.1415926843095328)") print(f"PI(1): {pi_1:.15f} (expected: 3.142487054628346)") # Test coupling constants print("\n--- Coupling Constants ---") fe_11 = sy.Fe(11) print(f"Fe(11) [alpha]: {fe_11:.15f}") print(f"1/alpha: {1/fe_11:.10f} (expected ~137.036)") # Test Planck print("\n--- Planck Constants ---") fhc = sy.Fhc() planck_tests = [ ('h', fhc['h'], 6.626987439910871e-34), ('hb', fhc['hb'], 1.0544157551953982e-34), ('tp', fhc['tp'], 5.390879110484635e-44), ('lp', fhc['lp'], 1.616144896904659e-35), ('mp', fhc['mp'], 2.176260547814635e-8), ('Tp', fhc['Tp'], 1.4168508256452144e+32), ('qp', fhc['qp'], 1.87567584803208e-18), ] for name, actual, expected in planck_tests: diff = abs(actual - expected) / expected status = 'PASS' if diff < 1e-10 else 'FAIL' if status == 'PASS': passed += 1 else: failed += 1 print(f"{name:12s}: {actual:20.15e} vs {expected:20.15e} [{status}]") # Test particle masses print("\n--- Particle Masses ---") mass_tests = [ ('Electron', sy.Ma(1), 9.109027140565893e-31), ('Muon', sy.Ma(207), 1.8855686180971397e-28), ('Proton', sy.Ma(1836.1813326060937), 1.6725825593709357e-27), ('Neutron', sy.Ma(1838.1813326060937), 1.6744043647990487e-27), ] for name, actual, expected in mass_tests: diff = abs(actual - expected) / expected status = 'PASS' if diff < 1e-10 else 'FAIL' if status == 'PASS': passed += 1 else: failed += 1 print(f"{name:12s}: {actual:20.15e} kg [{status}]") # Test elements print("\n--- Element Masses (sample) ---") elements = [ ('H', 1, 1, 0, 1.66128139028063e-27), ('He', 2, 2, 2, 6.646934072194125e-27), ('C', 6, 6, 6, 1.9940802216582374e-26), ('O', 8, 8, 8, 2.65877362887765e-26), ('Fe', 26, 26, 30, 9.305888552178935e-26), ('Au', 79, 79, 118, 3.2737913603850878e-25), ] for symbol, e, p, n, expected in elements: mass = sy.El(e, p, n) diff = abs(mass - expected) / expected status = 'PASS' if diff < 1e-10 else 'FAIL' if status == 'PASS': passed += 1 else: failed += 1 print(f"[{symbol:2s}] {symbol:8s}: {mass:20.15e} kg [{status}]") print("\n" + "=" * 70) print(f"RESULTS: {passed} PASSED, {failed} FAILED") print("=" * 70) return failed == 0 def test_duat_crossval(): """Validate Duat engine runs correctly""" try: from duat import DuatCognitionEngine except ImportError: print("\n[SKIP] duat.py not found — skipping Duat cross-validation") return True print("\n" + "=" * 70) print("DUAT COGNITION ENGINE - Python Implementation Test") print("=" * 70) engine = DuatCognitionEngine() print("\nInitial state:") print(f" truth: {engine.state['truth']:.3f}") print(f" coherence: {engine.state['coherence']:.3f}") print(f" energy: {engine.state['energy']:.3f}") # Run actions actions_to_test = ['reflection', 'purification', 'coherence_init', 'ascension_prime'] for action_name in actions_to_test: try: engine.run(action_name) print(f"\nAfter '{action_name}':") print(f" truth: {engine.state['truth']:.3f}") print(f" coherence: {engine.state['coherence']:.3f}") print(f" energy: {engine.state['energy']:.3f}") print(f" time: {engine.state['time']}") print(f" entropy: {engine.state['entropy']:.3f}") except Exception as e: print(f"ERROR running '{action_name}': {e}") return False # Test sequence print("\n--- Testing sequence ---") engine2 = DuatCognitionEngine() engine2.sequence(['reflection', 'coherence_init', 'ascension_prime']) print(f"Final: truth={engine2.state['truth']:.3f}, coherence={engine2.state['coherence']:.3f}") print("\n" + "=" * 70) print("DUAT TEST COMPLETE") print("=" * 70) return True def compare_to_codata(): """Compare SSM outputs to CODATA 2018 values""" print("\n" + "=" * 70) print("SSM vs CODATA 2018 COMPARISON") print("=" * 70) qa = sy.Qa() fhc = sy.Fhc() comparisons = [ ('Speed of light (c)', qa['cy'], 299792458, 'm/s'), ('Fine-structure (alpha)', sy.Fe(11), 0.0072973525693, ''), ('Vacuum permittivity (e0)', qa['ε0'], 8.854187817e-12, 'F/m'), ('Vacuum permeability (u0)', qa['μ0'], 1.2566370614e-6, 'H/m'), ('Planck constant (h)', fhc['h'], 6.62607015e-34, 'J.s'), ('Reduced Planck (hbar)', fhc['hb'], 1.054571817e-34, 'J.s'), ('Planck time', fhc['tp'], 5.391247e-44, 's'), ('Planck length', fhc['lp'], 1.616255e-35, 'm'), ('Planck mass', fhc['mp'], 2.176434e-8, 'kg'), ('Planck temp', fhc['Tp'], 1.416784e+32, 'K'), ('Planck charge', fhc['qp'], 1.875545956e-18, 'C'), ] print(f"\n{'Constant':35s} {'SSM':20s} {'CODATA':20s} {'Error':10s}") print("-" * 105) for name, ssm_val, codata_val, unit in comparisons: if codata_val != 0: error_pct = abs(ssm_val - codata_val) / codata_val * 100 error_str = f"{error_pct:.6f}%" else: error_str = "N/A" if unit: print(f"{name:35s} {ssm_val:20.10e} {codata_val:20.10e} {error_str:>10s}") else: print(f"{name:35s} {ssm_val:20.10f} {codata_val:20.10f} {error_str:>10s}") print("=" * 70) if __name__ == "__main__": import sys strict = '--strict' in sys.argv crossval = '--crossval' in sys.argv if crossval: # Run cross-validation suite (merged from test_validation.py) print("\n" + "=" * 70) print(" SYNERGY STANDARD MODEL & DUAT VALIDATION SUITE ".center(70)) print("=" * 70) ssm_ok = test_ssm_crossval() duat_ok = test_duat_crossval() compare_to_codata() print("\n" + "=" * 70) if ssm_ok and duat_ok: print(" ALL TESTS PASSED ".center(70)) else: print(" SOME TESTS FAILED ".center(70)) print("=" * 70) else: run_validation_suite(strict=strict) if not strict: print("\n" + "=" * 70) print("STRICT MODE COMPARISON (no cached literals)") print("=" * 70) run_validation_suite(strict=True)