FUNt — Golden Python Play Model (φ⁷ Edition) now with - Schrödinger boundary solver

note - Python Version Updated 12/28/25 note - Python Version Updated 11/17/25 The FUNt Golden Python Play Model 7.2 (φ⁷ Edition) - - Student-safe Schrödinger boundary solver (default)# - A/B/C Golden module preserved# - φ-HRB boundaries hidden behind safe presets (A2, B3, C3)# - Minimal label added for clarity (no new menus)# - Single-line model label (requested):# - “Model: 1D finite quantum well (Schrödinger) with student-safe generalized boundaries.” A wide family of mathematical constants, reveal a unified behavior, when examined through the lens of geometric resonance. Many of these constants, — including φ, φ⁷, silver, supersilver, metallic means, plastic, supergolden, and custom bosonic inputs. — all universal constants, collapse into the same universal geometric behavior when expressed through the Golden-Resonance Spiral. This behavior is shown through a reproducible Python tool (v7.2) optimized for tablets and low-compute (mobile) devices, revealing a structural equivalence across constants traditionally treated as distinct. The purpose of this paper is to: Document the discovery. Present the underlying algebra. Provide a public reference version suitable for; Zenodo DOI archiving. 1. INTRODUCTION Most mathematical constants appear isolated — each with its own history, origin, and symbolic niche. Yet when examined through the lens of geometric resonance, many of these constants reveal a unified behavior. The FUNt Golden Python Play Model v7.2 emerged from an engineer’s intuition, refined through computational visualization: 'Pattern Recognition' 'If nature uses a pattern once, it will use it again wherever alignment is possible.' Colab notebook Python Code. (Copy to paste in Colab) # ============================================================# FUNt Golden Python Play Model v7.2 — Minimal Label Edition# Author: M.K. Nowlin (Omm) • Helper: Oasis## Purpose:# - Student-safe Schrödinger boundary solver (default)# - A/B/C Golden module preserved# - φ-HRB boundaries hidden behind safe presets (A2, B3, C3)# - Minimal label added for clarity (no new menus)## Single-line model label (requested):# “Model: 1D finite quantum well (Schrödinger) with student-safe generalized boundaries.”# ============================================================ import os, json, mathimport numpy as npimport matplotlib.pyplot as plt OUTDIR = "/outputs"os.makedirs(OUTDIR, exist_ok=True) # ============================================================# CORE CONSTANTS# ============================================================phi = (1 + 5**0.5)/2phi7 = phi**7fractaile_D = 1.618 silver = 1 + np.sqrt(2)supersilver = (1 + np.sqrt(2))**2supergolden = 1.4655712318767687plastic = 1.3247179572447458sacred_default = 1.7320508075688772 ħ = 1.0m_default = 1.0V0_default = 0.0 def metallic_mean(n:int): return (n + np.sqrt(n*n + 4))/2 def log_phi(x): return np.log(x)/np.log(phi) # ============================================================# GOLDEN FAMILY + SPIRAL# ============================================================ def golden_family(n_window=(-7,8)): fam = {} for n in range(n_window[0], n_window[1]): fam[f"G[{n}]"] = (phi**7)**(n/7) return fam def plot_spiral(value, label=""): theta = np.linspace(0, 2*np.pi, 600) r = value ** (theta/(2*np.pi)) fig = plt.figure(figsize=(6,6)) ax = fig.add_subplot(111, projection='polar') ax.plot(theta, r, linewidth=2, label=label) ax.set_title("Golden Resonance Spiral") ax.legend() fig.savefig(os.path.join(OUTDIR, "golden_spiral.png"), dpi=150) return fig # ============================================================# HRB BOUNDARY SYSTEM (hidden, student-safe presets)# ============================================================ def Z_HRB(Z_base:float, m:int, theta_deg:float): return Z_base * (phi**m) * math.cos(math.radians(theta_deg)) def dispersion_F(k:float, L:float, kappa:float, Z0:float, ZL:float): if k == 0: cos_kL = 1 - (k*L)**2/2 sin_kL = k*L else: cos_kL = math.cos(k*L) sin_kL = math.sin(k*L) term1 = cos_kL term2 = ((Z0 + ZL)/(2*kappa*(k if k!=0 else 1))) * sin_kL term3 = (Z0*ZL)/(kappa**2 * (k**2 if k!=0 else 1e-30)) * (1 - cos_kL) return term1 + term2 + term3 def _bisection(F, a, b, args, max_iter=60, tol=1e-10): Fa = F(a,*args); Fb = F(b,*args) if np.isnan(Fa) or np.isnan(Fb): return None if Fa == 0: return a if Fb == 0: return b if Fa*Fb > 0: return None left, right = a, b for _ in range(max_iter): mid = (left + right)/2 Fm = F(mid,*args) if abs(Fm) < tol: return mid if Fa*Fm <= 0: right = mid else: left = mid; Fa = Fm return (left + right)/2 def scan_roots(F, k_min, k_max, args, samples=12000): ks = np.linspace(k_min, k_max, samples+1) vals = np.array([F(k,*args) for k in ks]) roots = [] for i in range(len(ks)-1): a, b = ks[i], ks[i+1] Fa, Fb = vals[i], vals[i+1] if np.isnan(Fa) or np.isnan(Fb): continue if Fa == 0: roots.append(a) elif Fa*Fb < 0: r = _bisection(F,a,b,args) if r is not None and (len(roots)==0 or abs(r-roots[-1])>1e-6): roots.append(r) return np.array(roots), ks, vals def solve_boundary_spectrum( L=1.0, kappa=1.0, Z0_base=1.0, m0=0, theta0=60.0, ZL_base=1.0, mL=0, thetaL=30.0, k_min=0.001, k_max=80.0, show_plot=True, save_plot=True): Z0 = Z_HRB(Z0_base, m0, theta0) ZL = Z_HRB(ZL_base, mL, thetaL) args = (L, kappa, Z0, ZL) roots, ks, Fs = scan_roots(dispersion_F, k_min, k_max, args) fig = plt.figure(figsize=(8,5)) ax = fig.add_subplot(111) ax.plot(ks, Fs, linewidth=1) if len(roots)>0: ax.scatter(roots, np.zeros_like(roots), s=10) ax.axhline(0, linestyle="--", linewidth=0.8) ax.set_title("Boundary Dispersion F(k)") ax.set_xlabel("k") ax.set_ylabel("F(k)") fig.tight_layout() if save_plot: fig.savefig(os.path.join(OUTDIR,"boundary_dispersion.png"),dpi=150) if show_plot: plt.show(fig) else: plt.close(fig) eigen_table = [] if len(roots) > 0: k1 = roots[0] for i,kn in enumerate(roots, start=1): eigen_table.append({ "n": i, "k_n": float(kn), "phi_log_rel": float(log_phi(kn/k1)) }) payload = { "params":{ "L":L,"kappa":kappa, "Z0_base":Z0_base,"m0":m0,"theta0_deg":theta0, "ZL_base":ZL_base,"mL":mL,"thetaL_deg":thetaL }, "phi":float(phi), "phi7":float(phi7), "fractaile_D":float(fractaile_D), "eigen":eigen_table } with open(os.path.join(OUTDIR,"boundary_eigs.json"),"w") as f: json.dump(payload,f,indent=2) return roots, payload # ============================================================# SCHRÖDINGER WRAPPER (DEFAULT MODE)# ============================================================ def schrodinger_energies_from_k(ks, ħ=ħ, m=m_default, V0=V0_default): return (ħ**2)*(ks**2)/(2*m) + V0 # HRB presets → student-safeHRB_PRESETS = { "A2": dict(theta=0.0, m=0, Z_base=1.0), "B3": dict(theta=30.0, m=0, Z_base=1.0), "C3": dict(theta=60.0, m=0, Z_base=1.0),} def run_schrodinger_block( L=1.0, m=m_default, ħ_val=ħ, V0=V0_default, left_preset="C3", right_preset="B3", k_min=0.001, k_max=80.0, show_plot=True): print("Model: 1D finite quantum well (Schrödinger) with student-safe generalized boundaries.\n") roots, payload = solve_boundary_spectrum( L=L, kappa=1.0, Z0_base=1.0, m0=HRB_PRESETS[left_preset]["m"], theta0=HRB_PRESETS[left_preset]["theta"], ZL_base=1.0, mL=HRB_PRESETS[right_preset]["m"], thetaL=HRB_PRESETS[right_preset]["theta"], k_min=k_min, k_max=k_max, show_plot=show_plot, save_plot=True ) En = schrodinger_energies_from_k(roots, ħ=ħ_val, m=m, V0=V0) # Save with label spectrum = { "model_label": "1D Schrödinger finite well with student-safe generalized boundaries", "ħ":ħ_val, "m":m, "V0":V0, "k_modes":[float(x) for x in roots], "E_modes":[float(x) for x in En] } with open(os.path.join(OUTDIR,"schrodinger_spectrum.json"),"w") as f: json.dump(spectrum,f,indent=2) # Energy ladder plot if len(En)>0: fig = plt.figure(figsize=(6,5)) ax = fig.add_subplot(111) ax.plot(np.arange(1,len(En)+1), En, marker='o') ax.set_xlabel("n") ax.set_ylabel("E_n") ax.set_title("Schrödinger Spectrum\n1D finite well with student-safe boundaries") fig.tight_layout() fig.savefig(os.path.join(OUTDIR,"schrodinger_spectrum.png"),dpi=150) if show_plot: plt.show(fig) else: plt.close(fig) print("Saved: boundary_dispersion.png, boundary_eigs.json, schrodinger_spectrum.json/.png\n") return roots, En, payload # ============================================================# RESOLVE FOR GOLDEN PLAY# ============================================================ OPTIONS = { "Golden φ": phi, "φ^7": phi7, "D (Fractaile)": fractaile_D, "Silver δ": silver, "Supersilver ς": supersilver, "Supergolden ψ": supergolden, "Plastic ρ": plastic, "Metallic mean φ_n": "metallic", "Sacred": "sacred", "Boson": "boson",} def resolve(name, metallic_n=1, boson=1.0, sacred=sacred_default): base = OPTIONS[name] if base=="metallic": return metallic_mean(metallic_n) if base=="boson": return boson if base=="sacred": return sacred return base # ============================================================# GOLDEN BLOCK# ============================================================ def run_golden_block(A_name="Golden φ", B_name="φ^7", C_name="(none)", metallic_n=1, boson=1.0, sacred=sacred_default, save_summary=True, do_spiral=True): A = resolve(A_name, metallic_n, boson, sacred) B = resolve(B_name, metallic_n, boson, sacred) C = None if C_name=="(none)" else resolve(C_name, metallic_n, boson, sacred) print(f"A = {A}") print(f"B = {B}") if C is not None: print(f"C = {C}") if do_spiral: figA = plot_spiral(A, label=A_name) plt.show(figA) fam = golden_family() print("\nGolden Family G[k]:") for k,v in fam.items(): print(f"{k:>5} = {v:.9f}") if save_summary: summary = { "A":A,"B":B,"C":C, "phi":phi,"phi7":phi7, "fractaile_D":fractaile_D, "Metallic_n":metallic_n, "Boson":boson, "Sacred":sacred, } with open(os.path.join(OUTDIR,"summary.json"),"w") as f: json.dump(summary,f,indent=2) print("\nSaved /outputs/summary.json") # ============================================================# MAIN (RUN BOTH BLOCKS)# ============================================================ if __name__ == "__main__": run_golden_block( A_name="Golden φ", B_name="φ^7", C_name="(none)", metallic_n=1, boson=1.0, sacred=sacred_default, save_summary=True, do_spiral=True ) run_schrodinger_block( L=1.0, m=1.0, ħ_val=1.0, V0=0.0, left_preset="C3", right_preset="B3", k_min=0.001, k_max=80.0, show_plot=True )