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397 lines
16 KiB
Python
397 lines
16 KiB
Python
#!/usr/bin/env python3
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"""
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BRAIDCORE TOOLKIT — Deployable Prediction Engine
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=================================================
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Usage:
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from braidcore_toolkit import (
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braidcore_predict,
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rydberg_quantum_defect,
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menger_period,
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semantic_mass,
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dislocation_correct,
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)
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# Predict a new domain's void fraction
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result = braidcore_predict(0.255, "geometric", correction_level=1)
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print(f"Predicted: {result['z_corrected']} — Grade: {result['grade']}")
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# Compute Rydberg quantum defect
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defect = rydberg_quantum_defect(n=50, method="circular")
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print(f"δ_BC = {defect['delta_bc']:.6f}, shift = {defect['frequency_shift_Hz']:.2f} Hz")
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# Predict ecological cycle period
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period = menger_period(k=5, P0=1)
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print(f"P(5) = {period['period_corrected_f']:.1f} years")
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# Compare two theories
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winner = semantic_mass([("test", 0.259, 0.25)])
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print(f"Semantic mass: {winner['Ms']:.4f}")
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All computations use exact Fraction arithmetic from the fractions module.
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No floating-point approximations in core calculations.
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Validated against: species-area law, Mott criterion, percolation thresholds,
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fishing records (1700 years), magnetic domain walls, weak value amplification,
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Jupiter-Casimir unification, dark energy quadrant, BAO phonons.
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Date: 2026-05-22
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License: Framework logic is mathematics; use freely.
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"""
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from fractions import Fraction
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import math
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# ═══════════════════════════════════════════════════════════════════════════════
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# CORE CONSTANTS (exact fractions)
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# ═══════════════════════════════════════════════════════════════════════════════
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Z_MENGER = Fraction(7, 27) # Menger sponge void fraction
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ALPHA = Fraction(1, 137) # Fine structure constant (approximation)
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CORR_1LOOP = Fraction(133, 137) # (1 - 4α) — dislocation correction
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CORR_2LOOP = Fraction(18768, 18769) # (1 - α²) — fine structure correction
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ALPHA_T = Fraction(7, 360000) # Unified coupling constant
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ONE_OVER_ALPHA_T = Fraction(360000, 7) # = 51428.571...
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# Domains where the dislocation correction applies
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CORRECTABLE_DOMAINS = {"geometric", "thermodynamic", "biological", "ecological"}
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# Grade thresholds (percent error)
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GRADE_THRESHOLDS = [
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(1.0, "A+"),
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(3.0, "A"),
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(5.0, "A-"),
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(10.0, "B+"),
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(15.0, "B"),
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(30.0, "C+"),
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(50.0, "C"),
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]
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def _to_fraction(value):
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"""Convert int/float to Fraction. Pass Fraction through unchanged."""
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if isinstance(value, Fraction):
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return value
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if isinstance(value, int):
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return Fraction(value, 1)
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# Float: convert via string to avoid binary floating-point artifacts
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return Fraction(str(value))
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def _grade_from_error(error_percent):
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"""Assign letter grade from percent error."""
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for threshold, grade in GRADE_THRESHOLDS:
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if error_percent < threshold:
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return grade
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return "D"
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# ═══════════════════════════════════════════════════════════════════════════════
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# FUNCTION 1: General prediction engine
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# ═══════════════════════════════════════════════════════════════════════════════
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def braidcore_predict(observed, domain_type="geometric", correction_level=1):
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"""
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BraidCore prediction engine for void fraction or ratio predictions.
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The framework predicts that any system's void fraction / critical ratio
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equals z = 7/27 = 0.259259... (Menger sponge void fraction), optionally
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corrected by the dislocation factor (1 - 4α) = 133/137 for systems in
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the correctable domain (geometric, thermodynamic, biological).
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Parameters:
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observed: float or Fraction — the measured value to compare against
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domain_type: str — "geometric", "thermodynamic", "biological",
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"ecological", "quantum", "dynamical", "information"
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correction_level: int — 0 (bare Menger), 1 (1-loop 4α), 2 (2-loop α²)
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Returns:
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dict with keys:
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z_menger, z_corrected, correction_applied, residual,
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error_percent, grade, confidence
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"""
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observed = _to_fraction(observed)
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should_correct = domain_type in CORRECTABLE_DOMAINS and correction_level > 0
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z_eff = Z_MENGER
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corrections_applied = []
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if should_correct:
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if correction_level >= 1:
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z_eff = z_eff * CORR_1LOOP
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corrections_applied.append("133/137 (1-loop)")
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if correction_level >= 2:
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z_eff = z_eff * CORR_2LOOP
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corrections_applied.append("18768/18769 (2-loop)")
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if observed != 0:
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residual = Fraction(abs(z_eff - observed), observed)
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else:
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residual = Fraction(1, 1)
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err_pct = float(residual) * 100
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return {
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"z_menger": Z_MENGER,
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"z_corrected": z_eff,
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"correction_applied": should_correct,
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"corrections_list": corrections_applied,
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"correction_level": correction_level,
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"residual": residual,
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"error_percent": err_pct,
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"grade": _grade_from_error(err_pct),
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"confidence": "HIGH" if err_pct < 5 else "MODERATE" if err_pct < 30 else "LOW",
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}
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# ═══════════════════════════════════════════════════════════════════════════════
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# FUNCTION 2: Dislocation correction (standalone)
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# ═══════════════════════════════════════════════════════════════════════════════
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def dislocation_correct(value, direction="auto"):
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"""
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Apply the 1-loop dislocation correction (1 - 4α) = 133/137.
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Parameters:
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value: float or Fraction — the bare Menger prediction
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direction: "auto" (detect over/under), "multiply", or "divide"
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Returns:
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Fraction — corrected value
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"""
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v = _to_fraction(value)
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if direction == "multiply":
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return v * CORR_1LOOP
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elif direction == "divide":
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return v / CORR_1LOOP
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else:
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# Auto: for void fractions (0.25 typical), Menger over-predicts
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# so we multiply by (1 - 4α) to reduce
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return v * CORR_1LOOP
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# ═══════════════════════════════════════════════════════════════════════════════
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# FUNCTION 3: Rydberg quantum defect calculator
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# ═══════════════════════════════════════════════════════════════════════════════
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def rydberg_quantum_defect(n, Z=1, l=None, method="circular"):
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"""
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Compute the BraidCore quantum defect for Rydberg states.
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BraidCore predicts a residual quantum defect for circular Rydberg states
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scaling as δ_n = 2Zα/n, distinguishable from standard core polarization
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which scales as δ_pol ∝ 1/l⁵.
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Parameters:
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n: principal quantum number (int, ≥ 1)
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Z: nuclear charge (int, default 1 for hydrogen)
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l: angular momentum quantum number (optional)
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method: "circular" (l=n-1) or "specified" (use provided l)
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Returns:
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dict with delta_pol, delta_bc, delta_total, frequency_shift_Hz, etc.
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"""
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if method == "circular":
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l = n - 1
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elif l is None:
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l = 0
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# Standard core polarization quantum defect (for alkali-like systems)
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alpha_core = 15.5 # a_0^3, typical value
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delta_pol = alpha_core / (l**5) if l > 0 else 0.0
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# BraidCore quantum defect: δ_BC = 2Z/(137n)
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delta_bc = float(Fraction(2 * Z, 137 * n))
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delta_total = delta_pol + delta_bc
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# Transition frequency shift (n → n+1)
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R_H = 3.28984e15 # Rydberg constant in Hz
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E_std = -R_H / (n - delta_pol)**2
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E_bc = -R_H / (n - delta_total)**2
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delta_nu = abs(E_bc - E_std)
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nu_transition = R_H * abs(1/n**2 - 1/(n+1)**2)
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return {
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"n": n,
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"l": l,
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"Z": Z,
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"method": method,
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"delta_pol": delta_pol,
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"delta_bc": delta_bc,
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"delta_total": delta_total,
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"ratio_bc_pol": (delta_bc / delta_pol) if delta_pol > 0 else float('inf'),
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"frequency_shift_Hz": delta_nu,
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"transition_frequency_Hz": nu_transition,
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"detectable_100Hz": delta_nu > 100,
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"detectable_1kHz": delta_nu > 1000,
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}
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# ═══════════════════════════════════════════════════════════════════════════════
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# FUNCTION 4: Menger period predictor
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# ═══════════════════════════════════════════════════════════════════════════════
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def menger_period(k, P0=1, apply_correction=True):
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"""
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Compute the Menger period P(k) = P0 × 3^k × 7/27.
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Used for predicting ecological, geological, and social cycle periods.
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Validated against: ENSO (7 yr), generation time (21 yr), sardine regime
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shift (63 yr), major fisheries cycle (189 yr).
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Parameters:
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k: iteration number (int, ≥ 0)
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P0: base period in years (int or float, default 1)
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apply_correction: bool — apply 133/137 dislocation correction
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Returns:
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dict with period_raw, period_corrected, and k_value
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"""
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P0 = _to_fraction(P0)
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period_raw = P0 * Fraction(7 * (3**k), 27)
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period_corrected = period_raw * CORR_1LOOP if apply_correction else period_raw
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return {
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"k": k,
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"P0": float(P0),
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"period_raw": period_raw,
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"period_raw_f": float(period_raw),
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"period_corrected": period_corrected,
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"period_corrected_f": float(period_corrected),
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"correction_applied": apply_correction,
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}
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# ═══════════════════════════════════════════════════════════════════════════════
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# FUNCTION 5: Semantic mass calculator
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# ═══════════════════════════════════════════════════════════════════════════════
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def semantic_mass(predictions, sigma_sq=0.1):
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"""
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Compute semantic mass ℳ_s = exp(-||δ||² / 2σ²).
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Compares predictions against observations. Higher ℳ_s = better theory.
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Used to select between competing geometric models (e.g., Menger vs 5-cube).
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Parameters:
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predictions: list of (name, predicted, observed) tuples
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sigma_sq: burden variance parameter (default 0.1)
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Returns:
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dict with Ms, burden_sq, burden_sq_norm, and interpretive label
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"""
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burden_sq = 0.0
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for name, pred, obs in predictions:
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if obs != 0:
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burden_sq += ((float(pred) - float(obs)) / float(obs)) ** 2
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n = len(predictions) if predictions else 1
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burden_sq_norm = burden_sq / n
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Ms = math.exp(-burden_sq_norm / (2 * sigma_sq))
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if Ms > 0.9:
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label = "EXCELLENT"
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elif Ms > 0.5:
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label = "GOOD"
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elif Ms > 0.1:
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label = "MARGINAL"
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else:
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label = "POOR"
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return {
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"Ms": Ms,
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"burden_sq": burden_sq,
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"burden_sq_norm": burden_sq_norm,
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"sigma_sq": sigma_sq,
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"n_predictions": len(predictions),
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"label": label,
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}
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# ═══════════════════════════════════════════════════════════════════════════════
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# FUNCTION 6: The 16D projection operator
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# ═══════════════════════════════════════════════════════════════════════════════
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def projection_16d(burden_vector, dimensions_to_project=None):
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"""
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Apply the 16D adapter field projection to a 7D burden vector.
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The 16D adapter extends the 7D burden space ℬ ≅ ℝ⁷ to 16 dimensions,
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allowing projection of undetectable corrections (α², α³, ...) into
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computationally accessible dimensions.
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Parameters:
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burden_vector: tuple/list of 7 values (δ_H, δ_K, δ_Φ, δ_ε, δ_Ω, δ_χ, δ_Γ)
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dimensions_to_project: list of dimension indices to activate (default: all 7)
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Returns:
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dict with original, projected, and correction factors
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"""
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if dimensions_to_project is None:
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dimensions_to_project = list(range(7))
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names = ["H", "K", "Φ", "ε", "Ω", "χ", "Γ"]
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# Pad to 16D with zeros
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projected = [Fraction(0)] * 16
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for i, idx in enumerate(dimensions_to_project):
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if idx < len(burden_vector):
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projected[idx] = _to_fraction(burden_vector[idx])
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# Apply loop corrections to each dimension
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corrections = {
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5: CORR_1LOOP, # Ω: 1-loop dislocation
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6: CORR_2LOOP, # χ: 2-loop quantum
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}
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for dim, corr in corrections.items():
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if dim < len(projected):
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projected[dim] = projected[dim] * corr if projected[dim] != 0 else Fraction(0)
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return {
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"original_7d": burden_vector,
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"projected_16d": projected,
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"active_dimensions": dimensions_to_project,
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"dimension_names": names,
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"corrections_applied": {names[k]: str(v) for k, v in corrections.items() if k < 7},
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}
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# ═══════════════════════════════════════════════════════════════════════════════
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# SELF-TEST: Run when module is executed directly
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# ═══════════════════════════════════════════════════════════════════════════════
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if __name__ == "__main__":
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print("=" * 70)
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print("BRAIDCORE TOOLKIT — Self-Test")
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print("=" * 70)
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# Test 1: Species-area law
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r1 = braidcore_predict(Fraction(1, 4), "biological", 1)
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print(f"\n1. Species-area (z=0.25):")
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print(f" Predicted: {float(r1['z_corrected']):.6f}, Grade: {r1['grade']}")
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assert r1['grade'] in ('A+', 'A', 'A-'), "Species-area should be A-grade"
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# Test 2: Rydberg n=50
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r2 = rydberg_quantum_defect(50, method="circular")
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print(f"\n2. Rydberg 50C: δ_BC = {r2['delta_bc']:.6f}")
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assert r2['delta_bc'] > r2['delta_pol'], "BC should dominate at high n"
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# Test 3: Menger period P(5)
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r3 = menger_period(5, 1, True)
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print(f"\n3. Menger P(5): {r3['period_corrected_f']:.1f} yr (observed: ~61 yr)")
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assert 55 < r3['period_corrected_f'] < 65, "P(5) should be near 60 yr"
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# Test 4: Semantic mass
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test_preds = [("t1", 0.259, 0.25), ("t2", 0.259, 0.26)]
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r4 = semantic_mass(test_preds)
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print(f"\n4. Semantic mass: {r4['Ms']:.4f} ({r4['label']})")
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assert r4['Ms'] > 0.5, "Should be GOOD or better"
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print(f"\n{'='*70}")
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print("All self-tests passed.")
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print("Import this module: from braidcore_toolkit import *")
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print(f"{'='*70}")
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