508 lines
19 KiB
Python
508 lines
19 KiB
Python
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#!/usr/bin/env python3
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"""
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hertzian_extrapolation.py
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=========================
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Project per-element lattice frequencies onto the electromagnetic spectrum
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as PAIRS of constructively-interfering frequencies at a configurable ratio.
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Background
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----------
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The Resonance Engine fractal echo (papers/fractal-echo-analysis.txt §2.3)
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exposes a measured harmonic comb in lattice time units:
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f0 = 0.6031 Hz_lattice (fundamental, from modulation.log)
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harmonics: 0.6031, 1.2076, 1.8094, 2.4125, 3.0157 (5 integer harmonics)
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That comb is the BEAT of the two driving waves:
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Khra wavelength = 128 cells (the carrier)
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Gixx wavelength = 8 cells (the fine wave)
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native ratio = 128 / 8 = 16
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A single Hz number per element discards the physics. Every element gets a
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PAIR (f_low, f_high) at a configurable ratio, and the beat
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|f_high - f_low| is what was actually measured.
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Lattice -> physical bridge (papers/harmonic-duality-em-spectrum.md §3):
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f_phys = (f_lattice * c_s) / dx
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with c_s = 1/sqrt(3) and dx the cell size, absorbed into a scale factor
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kappa that is calibrated against one anchor.
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Mappings (--mapping)
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--------------------
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period : f_lat(Z) = f0 * Period(Z) (period as harmonic number)
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mode : f_lat(Z) = f0 * HarmonicMode(Z) (mode count from the CSV)
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phi : f_lat(Z) = f0 * phi^((A-A0)/scale) (asymmetry as phi ladder)
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Ratios (--ratio)
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----------------
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khra-gixx : 16 (the lattice's native Khra/Gixx ratio - default)
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phi : 1.618 (golden ratio; matches Spooky2 404.5/654.5 kHz)
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octave : 2
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fifth : 1.5 (perfect fifth)
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fourth : 4/3 (perfect fourth)
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major3 : 5/4
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minor3 : 6/5
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<number> : custom positive ratio > 1
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Pair modes (--pair-mode)
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------------------------
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What does the anchor / scaled f_lattice represent?
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beat : the beat frequency |f_high - f_low| (default; matches the
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fractal-echo measurement directly)
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low : the low / carrier frequency f_low
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high : the high frequency f_high
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Whichever is chosen, the script derives the other two from the ratio
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and emits all three columns per element.
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Usage
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-----
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# Paired Lyman-alpha mapping at native lattice ratio (default)
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python scripts/hertzian_extrapolation.py --anchor h-lyman-alpha
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# Cu K-alpha anchored, per-Z spread, native ratio
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python scripts/hertzian_extrapolation.py --anchor cu-kalpha --mapping mode
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# Golden-ratio pair anchored to Spooky2 healing protocol
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python scripts/hertzian_extrapolation.py --anchor custom \
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--custom-z 1 --custom-freq 404500 \
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--ratio phi --pair-mode low
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No external dependencies; stdlib only.
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"""
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from __future__ import annotations
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import argparse
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import csv
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import math
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import sys
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from pathlib import Path
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# ---------------------------------------------------------------------------
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# Physical constants and measured lattice values
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# ---------------------------------------------------------------------------
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C_LIGHT = 2.99792458e8
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C_S_LATTICE = 1.0 / math.sqrt(3)
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H_PLANCK = 6.62607015e-34
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E_CHARGE = 1.602176634e-19
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EV_TO_HZ = E_CHARGE / H_PLANCK
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PHI = (1.0 + math.sqrt(5.0)) / 2.0
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# Fractal echo measurement (papers/fractal-echo-analysis.txt §2.3)
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F0_LATTICE = 0.6031
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HARMONIC_COMB = [F0_LATTICE * n for n in (1, 2, 3, 4, 5)]
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# Native lattice wave geometry
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LATTICE_KHRA = 128
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LATTICE_GIXX = 8
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NATIVE_RATIO = LATTICE_KHRA / LATTICE_GIXX # 16.0
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# ---------------------------------------------------------------------------
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# Ratio aliases
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# ---------------------------------------------------------------------------
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RATIOS = {
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"khra-gixx": NATIVE_RATIO, # 16.0
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"phi": PHI, # 1.6180339887...
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"octave": 2.0,
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"fifth": 1.5,
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"fourth": 4.0 / 3.0,
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"major3": 5.0 / 4.0,
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"minor3": 6.0 / 5.0,
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}
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def parse_ratio(value: str) -> tuple[float, str]:
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"""Return (ratio, name)."""
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if value in RATIOS:
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return RATIOS[value], value
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try:
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r = float(value)
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except ValueError:
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raise SystemExit(f"Unknown ratio '{value}'. Aliases: "
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f"{', '.join(sorted(RATIOS))} or numeric > 1.")
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if r <= 1.0:
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raise SystemExit(f"Ratio must be > 1.0; got {r}")
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return r, f"r={r:g}"
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# ---------------------------------------------------------------------------
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# Anchor catalog (Z, friendly name, frequency in Hz)
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# ---------------------------------------------------------------------------
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ANCHORS = {
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"h-21cm": (1, "H 21-cm hyperfine line", 1.420405751768e9),
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"h-lyman-alpha": (1, "H Lyman-alpha (n=2 -> n=1)", 2.4660718e15),
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"h-balmer-alpha": (1, "H Balmer-alpha (n=3 -> n=2)", 4.5680000e14),
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"h-rydberg": (1, "H Rydberg / ionization", 3.2898419603e15),
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"cmb-peak": (1, "CMB blackbody peak (160 GHz)",1.60e11),
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"cu-kalpha": (29, "Cu K-alpha", 1.9395e18),
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"mo-kalpha": (42, "Mo K-alpha", 4.2305e18),
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"ag-kalpha": (47, "Ag K-alpha", 5.4256e18),
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"au-kalpha": (79, "Au K-alpha", 1.6857e19),
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"fe-kalpha": (26, "Fe K-alpha", 1.5414e18),
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"spooky2-low": (1, "Spooky2 healing protocol low (404.5 kHz)",
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404500.0),
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}
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# ---------------------------------------------------------------------------
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# Catalog of known atomic / EM lines for residual scoring
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# ---------------------------------------------------------------------------
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KNOWN_LINES = [
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# Spooky2 / frequency-medicine reference points
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("Spooky2 healing low (404.5 kHz)", 404500.0, None),
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("Spooky2 healing high (654.5 kHz)", 654500.0, None),
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# Hydrogen
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("H 21-cm hyperfine", 1.420405751768e9, 1),
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("H Balmer-alpha", 4.5680e14, 1),
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("H Balmer-beta", 6.1655e14, 1),
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("H Lyman-alpha", 2.4661e15, 1),
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("H Lyman-beta", 2.9226e15, 1),
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("H Lyman-gamma", 3.0826e15, 1),
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("H Rydberg ionization", 3.2898e15, 1),
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# CMB
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("CMB blackbody peak", 1.60e11, None),
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# Semiconductor band gaps
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("Ge band gap (0.67 eV)", 0.67 * EV_TO_HZ, 32),
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("Si band gap (1.12 eV)", 1.12 * EV_TO_HZ, 14),
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("GaAs band gap (1.42 eV)", 1.42 * EV_TO_HZ, 31),
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("Diamond band gap (5.47 eV)", 5.47 * EV_TO_HZ, 6),
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# Visible
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("Green light (550 nm)", C_LIGHT / 550e-9, None),
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# K-alpha X-ray
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("Al K-alpha", 1.4867e3 * EV_TO_HZ, 13),
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("Fe K-alpha", 1.5414e18, 26),
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("Cu K-alpha", 1.9395e18, 29),
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("Mo K-alpha", 4.2305e18, 42),
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("Ag K-alpha", 5.4256e18, 47),
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("W K-alpha", 1.6717e19, 74),
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("Au K-alpha", 1.6857e19, 79),
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("U K-alpha", 2.5160e19, 92),
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# Particle rest masses (E = mc^2 in Hz)
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("Electron rest mass", 0.511e6 * EV_TO_HZ, None),
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("Pion rest mass", 135e6 * EV_TO_HZ, None),
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("Proton rest mass", 938.3e6 * EV_TO_HZ, None),
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]
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def em_band(freq_hz: float) -> str:
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if freq_hz <= 0:
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return "invalid"
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if freq_hz < 3e3: return "ELF/SLF/ULF"
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if freq_hz < 3e9: return "radio"
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if freq_hz < 3e11: return "microwave"
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if freq_hz < 4.3e14: return "infrared"
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if freq_hz < 7.5e14: return "visible"
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if freq_hz < 3e16: return "ultraviolet"
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if freq_hz < 3e19: return "X-ray"
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return "gamma"
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def nearest_known_line(freq_hz: float, z_hint: int | None = None):
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if freq_hz <= 0:
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return ("invalid", 0.0, float("inf"))
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log_f = math.log10(freq_hz)
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best = None
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best_score = float("inf")
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for name, f, z in KNOWN_LINES:
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if f <= 0:
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continue
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dist = abs(math.log10(f) - log_f)
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if z_hint is not None and z is not None and z == z_hint:
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dist *= 0.5
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if dist < best_score:
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best_score = dist
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best = (name, f)
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if best is None:
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return ("none", 0.0, float("inf"))
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name, f = best
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residual_pct = 100.0 * (freq_hz - f) / f
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return (name, f, residual_pct)
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# ---------------------------------------------------------------------------
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# Mapping functions
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# ---------------------------------------------------------------------------
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def f_lattice_period(row: dict) -> float:
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return F0_LATTICE * int(row["Period"])
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def f_lattice_mode(row: dict) -> float:
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return F0_LATTICE * int(row["HarmonicMode"])
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def f_lattice_phi(row: dict, a0: float = 13.2, scale: float = 0.3) -> float:
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a = float(row["AsymmetryValue"])
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k = (a - a0) / scale
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return F0_LATTICE * (PHI ** k)
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MAPPINGS = {
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"period": f_lattice_period,
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"mode": f_lattice_mode,
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"phi": f_lattice_phi,
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}
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# ---------------------------------------------------------------------------
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# Pair derivation
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# ---------------------------------------------------------------------------
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def derive_pair(f_phys: float, ratio: float, pair_mode: str) -> tuple[float, float, float]:
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"""Given f_phys and what it represents, return (f_low, f_high, f_beat).
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ratio = f_high / f_low > 1."""
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if pair_mode == "beat":
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# f_phys = beat = f_low * (ratio - 1)
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f_low = f_phys / (ratio - 1.0)
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f_high = f_low * ratio
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f_beat = f_phys
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elif pair_mode == "low":
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f_low = f_phys
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f_high = f_low * ratio
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f_beat = f_high - f_low
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elif pair_mode == "high":
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f_high = f_phys
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f_low = f_high / ratio
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f_beat = f_high - f_low
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else:
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raise SystemExit(f"Unknown --pair-mode '{pair_mode}'")
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return f_low, f_high, f_beat
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# ---------------------------------------------------------------------------
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# Main pipeline
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# ---------------------------------------------------------------------------
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def load_table(path: Path) -> list[dict]:
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with path.open(newline="", encoding="utf-8") as fh:
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rows = list(csv.DictReader(fh))
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if not rows:
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raise SystemExit(f"No rows read from {path}")
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return rows
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def compute(rows: list[dict], mapping: str, anchor_key: str,
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custom_z: int | None, custom_freq: float | None,
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ratio: float, ratio_name: str, pair_mode: str,
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include_sqrt3: bool) -> tuple[list[dict], dict]:
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mapper = MAPPINGS[mapping]
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lat = {int(r["AtomicNumber"]): mapper(r) for r in rows}
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if anchor_key == "custom":
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if custom_z is None or custom_freq is None:
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raise SystemExit("--anchor custom requires --custom-z and --custom-freq")
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a_z, a_name, a_freq = custom_z, f"custom (Z={custom_z})", float(custom_freq)
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else:
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if anchor_key not in ANCHORS:
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raise SystemExit(f"Unknown anchor '{anchor_key}'. Options: "
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f"{', '.join(sorted(ANCHORS))} or 'custom'.")
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a_z, a_name, a_freq = ANCHORS[anchor_key]
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if a_z not in lat:
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raise SystemExit(f"Anchor Z={a_z} not in periodic table CSV.")
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f_lat_anchor = lat[a_z]
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if f_lat_anchor <= 0:
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raise SystemExit(f"Anchor lattice frequency non-positive: {f_lat_anchor}")
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kappa = a_freq / f_lat_anchor
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implied_dx = (C_LIGHT * (C_S_LATTICE if include_sqrt3 else 1.0)) / kappa
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out = []
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for r in rows:
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z = int(r["AtomicNumber"])
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f_lat = lat[z]
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f_phys = kappa * f_lat
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f_low, f_high, f_beat = derive_pair(f_phys, ratio, pair_mode)
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lo_name, lo_f, lo_res = nearest_known_line(f_low, z_hint=z)
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hi_name, hi_f, hi_res = nearest_known_line(f_high, z_hint=z)
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out.append({
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"AtomicNumber": z,
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"Symbol": r["Symbol"],
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"Element": r["Element"],
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"Period": int(r["Period"]),
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"AsymmetryValue": float(r["AsymmetryValue"]),
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"HarmonicMode": int(r["HarmonicMode"]),
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"f_lattice_Hz": f_lat,
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"ratio": ratio,
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"f_low_Hz": f_low,
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"f_high_Hz": f_high,
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"f_beat_Hz": f_beat,
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"lambda_low_m": C_LIGHT / f_low if f_low > 0 else float("inf"),
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"lambda_high_m": C_LIGHT / f_high if f_high > 0 else float("inf"),
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"em_band_low": em_band(f_low),
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"em_band_high": em_band(f_high),
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"nearest_line_low": lo_name,
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|
"nearest_line_low_Hz": lo_f,
|
||
|
|
"residual_low_pct": lo_res,
|
||
|
|
"nearest_line_high": hi_name,
|
||
|
|
"nearest_line_high_Hz": hi_f,
|
||
|
|
"residual_high_pct": hi_res,
|
||
|
|
"Stability": r["Stability"],
|
||
|
|
})
|
||
|
|
|
||
|
|
calib = {
|
||
|
|
"mapping": mapping,
|
||
|
|
"anchor_key": anchor_key,
|
||
|
|
"anchor_name": a_name,
|
||
|
|
"anchor_Z": a_z,
|
||
|
|
"anchor_freq_Hz": a_freq,
|
||
|
|
"ratio": ratio,
|
||
|
|
"ratio_name": ratio_name,
|
||
|
|
"pair_mode": pair_mode,
|
||
|
|
"f_lattice_at_anchor": f_lat_anchor,
|
||
|
|
"kappa": kappa,
|
||
|
|
"implied_dx_m": implied_dx,
|
||
|
|
"include_sqrt3": include_sqrt3,
|
||
|
|
}
|
||
|
|
return out, calib
|
||
|
|
|
||
|
|
|
||
|
|
def write_output_csv(rows: list[dict], path: Path) -> None:
|
||
|
|
cols = ["AtomicNumber", "Symbol", "Element", "Period", "AsymmetryValue",
|
||
|
|
"HarmonicMode", "f_lattice_Hz", "ratio",
|
||
|
|
"f_low_Hz", "f_high_Hz", "f_beat_Hz",
|
||
|
|
"lambda_low_m", "lambda_high_m",
|
||
|
|
"em_band_low", "em_band_high",
|
||
|
|
"nearest_line_low", "nearest_line_low_Hz", "residual_low_pct",
|
||
|
|
"nearest_line_high", "nearest_line_high_Hz", "residual_high_pct",
|
||
|
|
"Stability"]
|
||
|
|
with path.open("w", newline="", encoding="utf-8") as fh:
|
||
|
|
w = csv.DictWriter(fh, fieldnames=cols)
|
||
|
|
w.writeheader()
|
||
|
|
for r in rows:
|
||
|
|
w.writerow(r)
|
||
|
|
|
||
|
|
|
||
|
|
def print_summary(rows: list[dict], calib: dict, n_show: int = 12) -> None:
|
||
|
|
print()
|
||
|
|
print("=" * 92)
|
||
|
|
print("HERTZIAN EXTRAPOLATION SUMMARY (paired)")
|
||
|
|
print("=" * 92)
|
||
|
|
print(f" Mapping : {calib['mapping']}")
|
||
|
|
print(f" Anchor : {calib['anchor_key']} ({calib['anchor_name']})")
|
||
|
|
print(f" Anchor Z : {calib['anchor_Z']}")
|
||
|
|
print(f" Anchor f_phys : {calib['anchor_freq_Hz']:.6e} Hz "
|
||
|
|
f"(interpreted as: {calib['pair_mode']})")
|
||
|
|
print(f" Ratio : {calib['ratio']:.6f} ({calib['ratio_name']})")
|
||
|
|
print(f" f_lat at anchor : {calib['f_lattice_at_anchor']:.6f} Hz_lat")
|
||
|
|
print(f" kappa : {calib['kappa']:.6e} Hz_phys / Hz_lat")
|
||
|
|
print(f" implied dx : {calib['implied_dx_m']:.6e} m"
|
||
|
|
f" (sqrt(3) {'on' if calib['include_sqrt3'] else 'off'})")
|
||
|
|
print()
|
||
|
|
|
||
|
|
band_counts_low: dict[str, int] = {}
|
||
|
|
band_counts_high: dict[str, int] = {}
|
||
|
|
for r in rows:
|
||
|
|
band_counts_low[r["em_band_low"]] = band_counts_low.get(r["em_band_low"], 0) + 1
|
||
|
|
band_counts_high[r["em_band_high"]] = band_counts_high.get(r["em_band_high"], 0) + 1
|
||
|
|
band_order = ["ELF/SLF/ULF", "radio", "microwave", "infrared",
|
||
|
|
"visible", "ultraviolet", "X-ray", "gamma"]
|
||
|
|
print(" EM band distribution (low / high):")
|
||
|
|
for b in band_order:
|
||
|
|
lo = band_counts_low.get(b, 0)
|
||
|
|
hi = band_counts_high.get(b, 0)
|
||
|
|
if lo or hi:
|
||
|
|
print(f" {b:<14s} low={lo:>4d} high={hi:>4d}")
|
||
|
|
print()
|
||
|
|
|
||
|
|
rows_by_z = {r["AtomicNumber"]: r for r in rows}
|
||
|
|
z_anchor = calib["anchor_Z"]
|
||
|
|
sample_zs = sorted(set([1, 2, 6, 14, 26, 29, 47, 74, 79, 82, 92, 118,
|
||
|
|
z_anchor, z_anchor - 1, z_anchor + 1]))
|
||
|
|
sample_zs = [z for z in sample_zs if z in rows_by_z][:n_show]
|
||
|
|
|
||
|
|
print(f" Sample of {len(sample_zs)} elements (anchor row marked '*'):")
|
||
|
|
print(f" {'Z':>3s} {'Sym':<3s} "
|
||
|
|
f"{'f_low (Hz)':>12s} {'f_high (Hz)':>12s} "
|
||
|
|
f"{'band_low':<11s} {'band_high':<11s}")
|
||
|
|
for z in sample_zs:
|
||
|
|
r = rows_by_z[z]
|
||
|
|
mark = "*" if z == z_anchor else " "
|
||
|
|
print(f" {mark} {r['AtomicNumber']:>3d} {r['Symbol']:<3s} "
|
||
|
|
f"{r['f_low_Hz']:>12.4e} {r['f_high_Hz']:>12.4e} "
|
||
|
|
f"{r['em_band_low']:<11s} {r['em_band_high']:<11s}")
|
||
|
|
print()
|
||
|
|
print(" Nearest known lines (anchor and a few neighbours):")
|
||
|
|
for z in sample_zs[:6]:
|
||
|
|
r = rows_by_z[z]
|
||
|
|
mark = "*" if z == z_anchor else " "
|
||
|
|
print(f" {mark} Z={r['AtomicNumber']:>3d} {r['Symbol']:<3s} "
|
||
|
|
f"low -> {r['nearest_line_low']:<35s} ({r['residual_low_pct']:+7.1f}%)")
|
||
|
|
print(f" {' '*7} high -> {r['nearest_line_high']:<35s} "
|
||
|
|
f"({r['residual_high_pct']:+7.1f}%)")
|
||
|
|
print("=" * 92)
|
||
|
|
|
||
|
|
|
||
|
|
def parse_args() -> argparse.Namespace:
|
||
|
|
p = argparse.ArgumentParser(
|
||
|
|
description="Per-element Hz pair extrapolation from the lattice fractal echo.",
|
||
|
|
formatter_class=argparse.RawDescriptionHelpFormatter,
|
||
|
|
epilog=__doc__)
|
||
|
|
p.add_argument("--csv-in",
|
||
|
|
default=str(Path(__file__).resolve().parent.parent
|
||
|
|
/ "data" / "lattice-periodic-table.csv"),
|
||
|
|
help="Path to lattice-periodic-table.csv")
|
||
|
|
p.add_argument("--out", "--csv-out", default=None,
|
||
|
|
help="Output CSV path (default: data/hertzian-pairs-"
|
||
|
|
"<mapping>-<anchor>-<ratio>-<pairmode>.csv)")
|
||
|
|
p.add_argument("--mapping", choices=list(MAPPINGS), default="period",
|
||
|
|
help="Lattice frequency mapping (default: period)")
|
||
|
|
p.add_argument("--anchor", default="h-lyman-alpha",
|
||
|
|
help=f"Calibration anchor. Options: "
|
||
|
|
f"{', '.join(sorted(ANCHORS))}, or 'custom'.")
|
||
|
|
p.add_argument("--custom-z", type=int, default=None,
|
||
|
|
help="Atomic number for custom anchor")
|
||
|
|
p.add_argument("--custom-freq", type=float, default=None,
|
||
|
|
help="Frequency in Hz for custom anchor")
|
||
|
|
p.add_argument("--ratio", default="khra-gixx",
|
||
|
|
help=f"Pair ratio. Aliases: {', '.join(sorted(RATIOS))}, "
|
||
|
|
f"or numeric > 1. Default: khra-gixx (16).")
|
||
|
|
p.add_argument("--pair-mode", choices=["beat", "low", "high"],
|
||
|
|
default="beat",
|
||
|
|
help="What the anchor frequency represents. Default: beat "
|
||
|
|
"(matches the fractal-echo measurement).")
|
||
|
|
p.add_argument("--include-sqrt3", action="store_true",
|
||
|
|
help="Honour c_s = 1/sqrt(3) when computing implied dx")
|
||
|
|
p.add_argument("--quiet", action="store_true",
|
||
|
|
help="Suppress the stdout summary table")
|
||
|
|
return p.parse_args()
|
||
|
|
|
||
|
|
|
||
|
|
def main() -> int:
|
||
|
|
args = parse_args()
|
||
|
|
csv_in = Path(args.csv_in)
|
||
|
|
if not csv_in.exists():
|
||
|
|
print(f"ERROR: input CSV not found: {csv_in}", file=sys.stderr)
|
||
|
|
return 2
|
||
|
|
|
||
|
|
ratio, ratio_name = parse_ratio(args.ratio)
|
||
|
|
rows = load_table(csv_in)
|
||
|
|
out_rows, calib = compute(rows, args.mapping, args.anchor,
|
||
|
|
args.custom_z, args.custom_freq,
|
||
|
|
ratio, ratio_name, args.pair_mode,
|
||
|
|
args.include_sqrt3)
|
||
|
|
|
||
|
|
if args.out is None:
|
||
|
|
rn = ratio_name.replace("=", "").replace(".", "p")
|
||
|
|
out_path = csv_in.parent / (
|
||
|
|
f"hertzian-pairs-{args.mapping}-{args.anchor}"
|
||
|
|
f"-{rn}-{args.pair_mode}.csv")
|
||
|
|
else:
|
||
|
|
out_path = Path(args.out)
|
||
|
|
out_path.parent.mkdir(parents=True, exist_ok=True)
|
||
|
|
write_output_csv(out_rows, out_path)
|
||
|
|
|
||
|
|
if not args.quiet:
|
||
|
|
print_summary(out_rows, calib)
|
||
|
|
print(f" Wrote: {out_path}")
|
||
|
|
|
||
|
|
return 0
|
||
|
|
|
||
|
|
|
||
|
|
if __name__ == "__main__":
|
||
|
|
sys.exit(main())
|