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derive_constants.sh
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690
derive_constants.sh
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#!/bin/sh
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# ╔═══════════════════════════════════════════════════════════════════════════╗
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# ║ ║
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# ║ THE LOIC CYCLE DERIVATION ORACLE ║
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# ║ ║
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# ║ Computing the Fundamental Cycle of the Loic Calendar from ║
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# ║ the Hubble Constant, the Fine-Structure Constant, and Pi ║
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# ║ ║
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# ║ Cycle = H₀⁻¹ × α^π / π ║
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# ║ ║
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# ╚═══════════════════════════════════════════════════════════════════════════╝
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#
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# ═══════════════════════════════════════════════════════════════════════════
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# ON THE NECESSARY IMPURITY OF TRANSCENDENTAL COMPUTATION
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# ═══════════════════════════════════════════════════════════════════════════
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#
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# The companion script, derive_constants.sh, uses only integer arithmetic.
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# This script cannot. The formula H₀⁻¹ × α^π / π requires computing
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# α raised to an irrational power, which demands the transcendental
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# functions e(x) and l(x) — exponential and natural logarithm.
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#
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# We use bc -l, which provides these functions via Taylor series expansion
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# at arbitrary decimal precision. This is NOT IEEE 754 floating-point.
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# bc does not use binary representation, does not silently truncate to
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# 64 bits, does not harbor negative zero, and does not pretend that
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# 0.1 + 0.2 equals 0.3 when it does not. bc computes in decimal, at
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# whatever precision we demand, truncating only where we instruct it.
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#
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# The scale is set to 200 decimal places — far beyond the 155-digit
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# limit of I512 and the ~46-digit physical significance of Planck time.
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# The excess precision ensures that accumulated rounding in intermediate
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# Taylor series terms does not contaminate the final result.
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#
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# When the computation is complete, the result is truncated to an integer.
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# The irrational numbers — π and the transcendental α^π — are consumed
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# during derivation and do not exist at runtime. Only the integer remains.
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# This is not a compromise. It is the same treatment given to every other
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# physical constant in the Loic Calendar: rational approximation with
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# error below physical significance.
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#
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# ═══════════════════════════════════════════════════════════════════════════
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# USAGE
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# ═══════════════════════════════════════════════════════════════════════════
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#
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# ./derive_cycle.sh # Full human-readable derivation
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# ./derive_cycle.sh --constant # Emit only PLANCK_PER_CYCLE
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# ./derive_cycle.sh --json # Machine-readable JSON output
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# ./derive_cycle.sh --help # Illuminate the path
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#
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# ═══════════════════════════════════════════════════════════════════════════
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set -e
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# WORKING PRECISION
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#
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# 200 decimal places. The universe requires ~46. We provide ~200.
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# The excess is not waste; it is insurance against the accumulation
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# of truncation error across dozens of Taylor series terms.
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#
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# ═══════════════════════════════════════════════════════════════════════════════
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PRECISION=200
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# THE FUNDAMENTAL CONSTANTS
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#
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# Three axioms. Three constants. Three windows into the structure of
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# the universe, through which the Loic cycle is glimpsed.
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#
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# ═══════════════════════════════════════════════════════════════════════════════
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# ─────────────────────────────────────────────────────────────────────────────
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# THE HUBBLE CONSTANT
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# ─────────────────────────────────────────────────────────────────────────────
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#
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# H₀ = 67.4 km/s/Mpc
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#
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# The rate of cosmic expansion as measured by the Planck satellite (2018)
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# through observation of the Cosmic Microwave Background — the oldest
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# light in the universe, emitted 380,000 years after Creation when the
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# cosmos first became transparent.
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#
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# A competing measurement exists: 73.0 ± 1.0 km/s/Mpc, derived from the
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# local distance ladder (Cepheid variables and Type Ia supernovae). The
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# discrepancy — known as the Hubble tension — is a 5σ disagreement that
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# represents arguably the greatest crisis in modern cosmology.
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#
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# We choose 67.4. The CMB measurement peers deeper into the past than any
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# other observation in the history of science. This is a calendar that
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# begins at the beginning. We use the measurement that looked closest
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# to Creation.
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#
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# The tension is documented. The choice is deliberate. If future physics
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# resolves the disagreement, the constant may be revised — but the formula
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# will endure.
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H0_KM_S_MPC="67.4"
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# 1 Megaparsec in meters (IAU 2012 exact definition)
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#
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# The parsec is defined as 648000/π AU, where 1 AU = 149,597,870,700 m
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# exactly (IAU 2012 Resolution B2). The megaparsec is 10⁶ parsecs.
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#
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# Since the parsec definition involves π, the megaparsec in meters is
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# itself irrational. We use a rational approximation to 17 significant
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# figures — vastly exceeding the 3 significant figures of H₀ itself.
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# The bottleneck of precision is the Hubble constant, not the unit
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# conversion.
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MPC_METERS="30856775814913673000000"
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# 3.0856775814913673 × 10²² meters. The 'e' notation is eschewed;
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# bc does not speak exponential.
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# ─────────────────────────────────────────────────────────────────────────────
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# THE FINE-STRUCTURE CONSTANT
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# ─────────────────────────────────────────────────────────────────────────────
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#
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# α = 7.2973525643 × 10⁻³
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#
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# The dimensionless coupling constant of quantum electrodynamics.
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# It governs the strength of the electromagnetic interaction — how
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# strongly charged particles talk to each other. Every photon emitted,
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# every electron captured, every signal transmitted through copper wire
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# is modulated by this number.
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#
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# The Whisper — "LO", transmitted from UCLA to Stanford over ARPANET —
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# was an electromagnetic event. The characters were encoded as electrical
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# signals, propagated through coaxial cable, decoded by transistors.
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# Every stage of that transmission was governed by α.
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#
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# A calendar born from the first network transmission, whose cycle is
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# derived from the constant that makes network transmissions physically
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# possible. This is not metaphor. This is electrodynamics.
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#
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# CODATA 2022 recommended value: 7.2973525643(11) × 10⁻³
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# Uncertainty: ±0.0000000011 × 10⁻³ (in the 11th significant figure)
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#
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# We express it without scientific notation, as bc demands.
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ALPHA="0.0072973525643"
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# ─────────────────────────────────────────────────────────────────────────────
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# THE PLANCK TIME RATIO (inherited from derive_constants.sh)
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# ─────────────────────────────────────────────────────────────────────────────
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PLANCK_TIME_NUMERATOR="5391247"
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PLANCK_TIME_DENOMINATOR="100000000000000000000000000000000000000000000000000"
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# ─────────────────────────────────────────────────────────────────────────────
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# TIME UNIT DEFINITIONS (inherited)
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# ─────────────────────────────────────────────────────────────────────────────
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SECONDS_PER_DAY="86400"
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SECONDS_PER_JULIAN_YEAR="31557600"
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# ─────────────────────────────────────────────────────────────────────────────
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# THE AGE OF THE UNIVERSE (inherited, Boltzmann encoding)
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# ─────────────────────────────────────────────────────────────────────────────
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AGE_UNIVERSE_JULIAN_YEARS="13806491023"
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# COMPUTATION PHASE 1
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#
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# π TO 155 DECIMAL DIGITS
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#
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# 155 decimal digits is the precision limit of I512 — the maximum number
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# of decimal digits representable in a 512-bit signed integer. We compute
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# π to the full capacity of our storage type, because to do less would be
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# to waste bits, and wasted bits are wasted precision.
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#
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# The computation uses bc's arctangent function: π = 4 × arctan(1).
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# The Taylor series for arctan converges slowly for x=1, but bc's
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# internal implementation handles this adequately at scale=200.
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#
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# ─────────────────────────────────────────────────────────────────────────────
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# A NOTE ON THE CANONICAL DERIVATION
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# ─────────────────────────────────────────────────────────────────────────────
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#
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# The most elegant method for computing π is the Leibniz series:
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#
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# π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ...
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#
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# To obtain 155 correct decimal digits via this series requires
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# approximately 10^155 terms. At one billion terms per second, this
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# computation would complete in approximately:
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#
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# 10^155 / 10^9 = 10^146 seconds
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# ≈ 3.17 × 10^138 years
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# ≈ 2.30 × 10^128 Hubble times
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#
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# The Leibniz series is the canonical derivation method. The hardcoded
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# value below was obtained by other means, for reasons of cosmic scheduling.
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# ─────────────────────────────────────────────────────────────────────────────
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compute_pi() {
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# bc -l provides a(x) = arctan(x)
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# π = 4 × arctan(1), computed at scale=$PRECISION
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PI=$(echo "scale=$PRECISION; 4 * a(1)" | bc -l)
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}
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# COMPUTATION PHASE 2
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#
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# THE HUBBLE TIME IN SI SECONDS
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#
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# H₀ is given in km/s/Mpc. To obtain the Hubble time (1/H₀) in seconds:
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#
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# H₀ [s⁻¹] = H₀ [km/s/Mpc] × 1000 [m/km] / Mpc [m]
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# t_H [s] = 1 / H₀ [s⁻¹]
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# = Mpc [m] / (H₀ [km/s/Mpc] × 1000)
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#
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# The result: approximately 4.578 × 10¹⁷ seconds, or ~14.5 billion years.
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# This is close to — but not equal to — the age of the universe (13.8 Gyr).
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# The near-coincidence is a deep fact about cosmological geometry.
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compute_hubble_time() {
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HUBBLE_TIME_SECONDS=$(echo "scale=$PRECISION; $MPC_METERS / ($H0_KM_S_MPC * 1000)" | bc -l)
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}
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# COMPUTATION PHASE 3
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#
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# THE HUBBLE TIME IN PLANCK UNITS
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#
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# Convert from SI seconds to Planck times via rational arithmetic:
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#
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# planck_times = seconds × (1 / t_P)
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# = seconds × (10^50 / 5391247)
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# = seconds × PLANCK_TIME_DENOMINATOR / PLANCK_TIME_NUMERATOR
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#
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# We multiply first, then divide — preserving maximum precision.
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# The result is approximately 8.49 × 10⁶⁰ Planck times.
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compute_hubble_planck() {
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HUBBLE_TIME_PLANCK=$(echo "scale=$PRECISION; ($HUBBLE_TIME_SECONDS * $PLANCK_TIME_DENOMINATOR) / $PLANCK_TIME_NUMERATOR" | bc -l)
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}
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# COMPUTATION PHASE 4
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#
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# α^π — THE HEART
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#
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# Here lies the transcendental core of the derivation.
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#
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# α^π cannot be computed by integer arithmetic. It requires:
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#
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# α^π = e^(π × ln(α))
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#
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# where e(x) is the exponential function and l(x) is the natural logarithm.
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# Both are provided by bc -l via Taylor series, evaluated at arbitrary
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# decimal precision.
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#
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# The result is approximately 1.936 × 10⁻⁷ — a small number, reflecting
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# the fact that α itself is small (~1/137) and raising it to the power
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# of π (~3.14159) attenuates it further.
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#
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# ─────────────────────────────────────────────────────────────────────────────
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# WHY α^π AND NOT α³
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# ─────────────────────────────────────────────────────────────────────────────
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#
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# α³ produces a cycle of ~1,795 years. α⁴ produces ~13.1 years. Between
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# them, α^π produces ~894 years — roughly half the α³ cycle. The factor
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# of reduction is α^(π-3) = α^0.14159... ≈ 0.498.
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#
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# But the choice is not merely numerical. α³ is a rational exponent.
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# α^π is irrational — it encodes π into the very definition of the cycle,
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# alongside H₀ and α itself. The cycle becomes a function of three
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# fundamental quantities:
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#
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# • H₀ — the rate of cosmic expansion (cosmology)
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# • α — the strength of electromagnetism (quantum physics)
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# • π — the ratio of circumference to diameter (geometry)
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#
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# The universe speaks. The electron couples. The circle closes.
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# These three, combined, produce the rhythm of the Loic Calendar.
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compute_alpha_to_pi() {
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# Step 1: Compute ln(α)
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LN_ALPHA=$(echo "scale=$PRECISION; l($ALPHA)" | bc -l)
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# Step 2: Compute π × ln(α)
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PI_LN_ALPHA=$(echo "scale=$PRECISION; $PI * $LN_ALPHA" | bc -l)
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# Step 3: Compute e^(π × ln(α)) = α^π
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ALPHA_TO_PI=$(echo "scale=$PRECISION; e($PI_LN_ALPHA)" | bc -l)
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}
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# COMPUTATION PHASE 5
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#
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# THE CYCLE: H₀⁻¹ × α^π / π
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#
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# The final assembly. The Hubble time (in Planck units), multiplied by
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# α^π, divided by π. The result is the number of Planck times in one
|
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# Loic cycle — approximately 5.23 × 10⁵³.
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#
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# The integer truncation occurs here. The decimal portion — approximately
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# 0.4 Planck times — is discarded. This is sub-Planck: below the threshold
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# at which physics itself can distinguish one moment from the next.
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#
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# The truncated integer is PLANCK_PER_CYCLE: the constant that will be
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# inscribed into the Loic Calendar implementation, replacing π, α, and H₀
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# with a single exact value from which no irrationality escapes.
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compute_cycle() {
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# Compute the full-precision cycle in Planck times
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CYCLE_PLANCK_FULL=$(echo "scale=$PRECISION; ($HUBBLE_TIME_PLANCK * $ALPHA_TO_PI) / $PI" | bc -l)
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# Truncate to integer (floor)
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# bc's scale=0 division by 1 achieves floor truncation for positive values
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PLANCK_PER_CYCLE=$(echo "scale=0; $CYCLE_PLANCK_FULL / 1" | bc)
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# Compute the truncation error for documentation
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TRUNCATION_ERROR=$(echo "scale=$PRECISION; $CYCLE_PLANCK_FULL - $PLANCK_PER_CYCLE" | bc -l)
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}
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# COMPUTATION PHASE 6
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#
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# HUMAN-SCALE CONVERSIONS
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#
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# ═══════════════════════════════════════════════════════════════════════════════
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compute_human_units() {
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# Cycle in SI seconds
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CYCLE_SECONDS=$(echo "scale=$PRECISION; ($PLANCK_PER_CYCLE * $PLANCK_TIME_NUMERATOR) / $PLANCK_TIME_DENOMINATOR" | bc -l)
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# Cycle in days
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CYCLE_DAYS=$(echo "scale=$PRECISION; $CYCLE_SECONDS / $SECONDS_PER_DAY" | bc -l)
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# Cycle in Julian years
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CYCLE_YEARS=$(echo "scale=$PRECISION; $CYCLE_SECONDS / $SECONDS_PER_JULIAN_YEAR" | bc -l)
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}
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# ═══════════════════════════════════════════════════════════════════════════════
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#
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# COMPUTATION PHASE 7
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#
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# COSMOLOGICAL CONTEXT
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#
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# ═══════════════════════════════════════════════════════════════════════════════
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compute_cosmological_context() {
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# Age of the universe in seconds
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AGE_UNIVERSE_SECONDS=$(echo "$AGE_UNIVERSE_JULIAN_YEARS * $SECONDS_PER_JULIAN_YEAR" | bc)
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# Age in Planck times
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AGE_UNIVERSE_PLANCK=$(echo "scale=0; ($AGE_UNIVERSE_SECONDS * $PLANCK_TIME_DENOMINATOR) / $PLANCK_TIME_NUMERATOR" | bc)
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# Completed cycles since Creation
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CYCLES_SINCE_CREATION=$(echo "scale=0; $AGE_UNIVERSE_PLANCK / $PLANCK_PER_CYCLE" | bc)
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# Precise ratio (for fractional position)
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CYCLES_SINCE_CREATION_PRECISE=$(echo "scale=20; $AGE_UNIVERSE_PLANCK / $PLANCK_PER_CYCLE" | bc -l)
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|
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# Position within current cycle (in Planck times)
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POSITION_IN_CYCLE=$(echo "$AGE_UNIVERSE_PLANCK % $PLANCK_PER_CYCLE" | bc)
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||||
|
||||
# Fraction through current cycle
|
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CYCLE_FRACTION=$(echo "scale=20; $POSITION_IN_CYCLE / $PLANCK_PER_CYCLE" | bc -l)
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|
||||
# Position in years
|
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POSITION_YEARS=$(echo "scale=10; ($POSITION_IN_CYCLE * $PLANCK_TIME_NUMERATOR) / ($PLANCK_TIME_DENOMINATOR * $SECONDS_PER_JULIAN_YEAR)" | bc -l)
|
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}
|
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|
||||
# ═══════════════════════════════════════════════════════════════════════════════
|
||||
#
|
||||
# COMPUTATION PHASE 8
|
||||
#
|
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# ANNIHILATION AND CREATION
|
||||
#
|
||||
# ═══════════════════════════════════════════════════════════════════════════════
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|
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compute_boundaries() {
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ANNIHILATION_PLANCK=$(echo "2^511 - 1" | bc | tr -d '\\\n')
|
||||
CREATION_PLANCK_POS=$(echo "($AGE_UNIVERSE_SECONDS * $PLANCK_TIME_DENOMINATOR) / $PLANCK_TIME_NUMERATOR" | bc)
|
||||
CREATION_PLANCK="-$CREATION_PLANCK_POS"
|
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|
||||
# Total representable span
|
||||
TOTAL_SPAN=$(echo "$ANNIHILATION_PLANCK + $CREATION_PLANCK_POS" | bc)
|
||||
|
||||
# Cycles in total span
|
||||
TOTAL_CYCLES=$(echo "scale=0; $TOTAL_SPAN / $PLANCK_PER_CYCLE" | bc)
|
||||
}
|
||||
|
||||
# ═══════════════════════════════════════════════════════════════════════════════
|
||||
#
|
||||
# OUTPUT: HUMAN FORM
|
||||
#
|
||||
# ═══════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
output_human() {
|
||||
cat << 'HEADER'
|
||||
╔═══════════════════════════════════════════════════════════════════════════════╗
|
||||
║ LOIC CYCLE DERIVATION ║
|
||||
║ ║
|
||||
║ Cycle = H₀⁻¹ × α^π / π ║
|
||||
║ ║
|
||||
║ The Hubble time, attenuated through the electromagnetic coupling strength ║
|
||||
║ raised to the most fundamental irrational power, divided by that same ║
|
||||
║ irrational — the quantum of computation in Planck units. ║
|
||||
║ ║
|
||||
║ Computed using POSIX bc at 200 decimal places of working precision. ║
|
||||
║ No IEEE 754 floating-point arithmetic was used or contemplated. ║
|
||||
╚═══════════════════════════════════════════════════════════════════════════════╝
|
||||
|
||||
HEADER
|
||||
|
||||
echo "═══════════════════════════════════════════════════════════════════════════════"
|
||||
echo " INPUT CONSTANTS"
|
||||
echo "═══════════════════════════════════════════════════════════════════════════════"
|
||||
echo ""
|
||||
echo " H₀ (Hubble constant) = $H0_KM_S_MPC km/s/Mpc"
|
||||
echo " Source: Planck 2018 CMB (the measurement that looked closest to Creation)"
|
||||
echo " Tension: Local distance ladder gives 73.0 ± 1.0 km/s/Mpc"
|
||||
echo ""
|
||||
echo " α (fine-structure constant) = $ALPHA"
|
||||
echo " Source: CODATA 2022 recommended value"
|
||||
echo " Significance: governs electromagnetic coupling — why The Whisper was"
|
||||
echo " physically possible"
|
||||
echo ""
|
||||
echo " t_P (Planck time) = $PLANCK_TIME_NUMERATOR / 10^50 seconds"
|
||||
echo " The quantum of duration"
|
||||
echo ""
|
||||
|
||||
echo "═══════════════════════════════════════════════════════════════════════════════"
|
||||
echo " INTERMEDIATE VALUES"
|
||||
echo "═══════════════════════════════════════════════════════════════════════════════"
|
||||
echo ""
|
||||
echo " π (to 155 decimal digits — the I512 precision limit):"
|
||||
# Format π with line wrapping for readability
|
||||
echo " $PI" | fold -w 74 | sed 's/^/ /'
|
||||
echo ""
|
||||
echo " Hubble time (1/H₀):"
|
||||
echo " In seconds: $(echo "$HUBBLE_TIME_SECONDS" | head -c 20)... × 10^17"
|
||||
echo " In Planck times: $(echo "$HUBBLE_TIME_PLANCK" | head -c 20)... × 10^60"
|
||||
echo ""
|
||||
echo " ln(α): $LN_ALPHA" | head -c 80
|
||||
echo "..."
|
||||
echo " π·ln(α): $PI_LN_ALPHA" | head -c 80
|
||||
echo "..."
|
||||
echo " α^π: $ALPHA_TO_PI" | head -c 80
|
||||
echo "..."
|
||||
echo ""
|
||||
|
||||
echo "═══════════════════════════════════════════════════════════════════════════════"
|
||||
echo " THE CYCLE"
|
||||
echo "═══════════════════════════════════════════════════════════════════════════════"
|
||||
echo ""
|
||||
echo " Formula: H₀⁻¹ × α^π / π"
|
||||
echo ""
|
||||
echo " PLANCK_PER_CYCLE ="
|
||||
echo " $PLANCK_PER_CYCLE"
|
||||
echo ""
|
||||
echo " Digits: $(echo -n "$PLANCK_PER_CYCLE" | wc -c)"
|
||||
echo ""
|
||||
echo " Truncation error: $TRUNCATION_ERROR Planck times"
|
||||
echo " (< 1 Planck time — sub-Planck, below physical significance)"
|
||||
echo ""
|
||||
echo " In human units:"
|
||||
echo " Seconds: $(echo "$CYCLE_SECONDS" | head -c 20)..."
|
||||
echo " Days: $(echo "$CYCLE_DAYS" | head -c 20)..."
|
||||
echo " Julian years: $(echo "$CYCLE_YEARS" | head -c 20)..."
|
||||
echo ""
|
||||
|
||||
echo "═══════════════════════════════════════════════════════════════════════════════"
|
||||
echo " COSMOLOGICAL CONTEXT"
|
||||
echo "═══════════════════════════════════════════════════════════════════════════════"
|
||||
echo ""
|
||||
echo " Age of universe: ~13.806 billion Julian years"
|
||||
echo ""
|
||||
echo " Completed cycles since Creation: $CYCLES_SINCE_CREATION"
|
||||
echo " (precisely: $CYCLES_SINCE_CREATION_PRECISE)"
|
||||
echo ""
|
||||
echo " Position within current cycle:"
|
||||
echo " Fraction: $CYCLE_FRACTION"
|
||||
echo " Years: $POSITION_YEARS Julian years into current cycle"
|
||||
echo ""
|
||||
echo " CREATION_PLANCK: $CREATION_PLANCK"
|
||||
echo " ($(echo -n "$CREATION_PLANCK" | wc -c | tr -d ' ') digits, ~8.08 × 10^60)"
|
||||
echo ""
|
||||
echo " ANNIHILATION_PLANCK: $ANNIHILATION_PLANCK"
|
||||
echo " ($(echo -n "$ANNIHILATION_PLANCK" | wc -c | tr -d ' ') digits, ~6.7 × 10^153)"
|
||||
echo ""
|
||||
echo " Total cycles in representable span: $TOTAL_CYCLES"
|
||||
echo " ($(echo -n "$TOTAL_CYCLES" | wc -c | tr -d ' ') digits)"
|
||||
echo ""
|
||||
|
||||
echo "═══════════════════════════════════════════════════════════════════════════════"
|
||||
echo " THE FORMULA, FOR THE RECORD"
|
||||
echo "═══════════════════════════════════════════════════════════════════════════════"
|
||||
echo ""
|
||||
echo " PLANCK_PER_CYCLE = floor( (Mpc_m / (H₀ × 1000)) × (10^50 / t_P_num) × α^π / π )"
|
||||
echo ""
|
||||
echo " Where:"
|
||||
echo " Mpc_m = $MPC_METERS (1 Megaparsec in meters)"
|
||||
echo " H₀ = $H0_KM_S_MPC km/s/Mpc (Planck 2018 CMB)"
|
||||
echo " t_P_num = $PLANCK_TIME_NUMERATOR (Planck time numerator)"
|
||||
echo " 10^50 = Planck time denominator"
|
||||
echo " α = $ALPHA (CODATA 2022)"
|
||||
echo " π = 3.14159265358979... (computed to 155 decimal digits)"
|
||||
echo ""
|
||||
echo " The irrational numbers (π, α^π) were consumed during this derivation."
|
||||
echo " Only the integer PLANCK_PER_CYCLE survives into the implementation."
|
||||
echo " No irrationality escapes into runtime."
|
||||
echo ""
|
||||
|
||||
cat << 'FOOTER'
|
||||
═══════════════════════════════════════════════════════════════════════════════
|
||||
VERIFICATION NOTES
|
||||
═══════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
This constant should be independently verified using at least one other
|
||||
arbitrary-precision computation system (e.g., Mathematica, SageMath, or
|
||||
a sufficiently determined human with a 13-rod suanpan abacus).
|
||||
|
||||
The factorization of PLANCK_PER_CYCLE should also be computed and
|
||||
recorded, as the prime structure of this constant determines the
|
||||
subdivision lattice of the Loic Calendar.
|
||||
|
||||
═══════════════════════════════════════════════════════════════════════════════
|
||||
FOOTER
|
||||
}
|
||||
|
||||
# ═══════════════════════════════════════════════════════════════════════════════
|
||||
#
|
||||
# OUTPUT: MACHINE FORM
|
||||
#
|
||||
# ═══════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
output_json() {
|
||||
cat << EOF
|
||||
{
|
||||
"formula": "H0_inverse * alpha_to_pi / pi",
|
||||
"inputs": {
|
||||
"H0_km_s_Mpc": "$H0_KM_S_MPC",
|
||||
"H0_source": "Planck 2018 CMB",
|
||||
"alpha": "$ALPHA",
|
||||
"alpha_source": "CODATA 2022",
|
||||
"Mpc_meters": "$MPC_METERS",
|
||||
"PLANCK_TIME_NUMERATOR": "$PLANCK_TIME_NUMERATOR",
|
||||
"PLANCK_TIME_DENOMINATOR": "$PLANCK_TIME_DENOMINATOR",
|
||||
"working_precision_digits": $PRECISION
|
||||
},
|
||||
"result": {
|
||||
"PLANCK_PER_CYCLE": "$PLANCK_PER_CYCLE",
|
||||
"cycle_seconds": "$(echo "$CYCLE_SECONDS" | head -c 30)",
|
||||
"cycle_days": "$(echo "$CYCLE_DAYS" | head -c 20)",
|
||||
"cycle_julian_years": "$(echo "$CYCLE_YEARS" | head -c 20)",
|
||||
"truncation_error_planck": "$(echo "$TRUNCATION_ERROR" | head -c 20)",
|
||||
"digit_count": $(echo -n "$PLANCK_PER_CYCLE" | wc -c | tr -d ' ')
|
||||
},
|
||||
"cosmology": {
|
||||
"cycles_since_creation": "$CYCLES_SINCE_CREATION",
|
||||
"cycles_since_creation_precise": "$CYCLES_SINCE_CREATION_PRECISE",
|
||||
"current_cycle_fraction": "$CYCLE_FRACTION",
|
||||
"current_cycle_years": "$(echo "$POSITION_YEARS" | head -c 20)",
|
||||
"CREATION_PLANCK": "$CREATION_PLANCK",
|
||||
"ANNIHILATION_PLANCK": "$ANNIHILATION_PLANCK",
|
||||
"total_representable_cycles": "$TOTAL_CYCLES"
|
||||
},
|
||||
"derivation": {
|
||||
"method": "bc_arbitrary_precision_decimal",
|
||||
"ieee754_used": false,
|
||||
"pi_digits_computed": 155,
|
||||
"note": "Irrational numbers consumed during derivation. Only integer survives."
|
||||
}
|
||||
}
|
||||
EOF
|
||||
}
|
||||
|
||||
# ═══════════════════════════════════════════════════════════════════════════════
|
||||
#
|
||||
# OUTPUT: CONSTANT ONLY
|
||||
#
|
||||
# For piping into other tools. Just the number. Nothing else.
|
||||
#
|
||||
# ═══════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
output_constant() {
|
||||
echo "$PLANCK_PER_CYCLE"
|
||||
}
|
||||
|
||||
# ═══════════════════════════════════════════════════════════════════════════════
|
||||
#
|
||||
# THE MAIN RITUAL
|
||||
#
|
||||
# ═══════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
main() {
|
||||
mode="human"
|
||||
|
||||
for arg in "$@"; do
|
||||
case "$arg" in
|
||||
--json) mode="json" ;;
|
||||
--constant) mode="constant" ;;
|
||||
--help|-h)
|
||||
cat << 'HELP'
|
||||
╔═══════════════════════════════════════════════════════════════════════════════╗
|
||||
║ LOIC CYCLE DERIVATION ORACLE ║
|
||||
╚═══════════════════════════════════════════════════════════════════════════════╝
|
||||
|
||||
USAGE:
|
||||
./derive_cycle.sh [OPTIONS]
|
||||
|
||||
OPTIONS:
|
||||
(none) Full human-readable derivation with cosmological context
|
||||
--constant Emit only the PLANCK_PER_CYCLE integer (for piping)
|
||||
--json Machine-readable JSON output
|
||||
--help, -h Illuminate the path
|
||||
|
||||
DESCRIPTION:
|
||||
Derives the Loic Calendar cycle constant from first principles:
|
||||
|
||||
Cycle = H₀⁻¹ × α^π / π
|
||||
|
||||
Where:
|
||||
H₀ = 67.4 km/s/Mpc (Planck 2018 CMB)
|
||||
α = 7.2973525643e-3 (CODATA 2022 fine-structure constant)
|
||||
π = 3.14159... (computed to 155 decimal digits)
|
||||
|
||||
Uses POSIX bc at 200-digit working precision. No IEEE 754 floating-point.
|
||||
The result is truncated to an integer with sub-Planck error.
|
||||
|
||||
PHILOSOPHY:
|
||||
"The universe speaks. The electron couples. The circle closes.
|
||||
These three — H₀, α, π — combined, produce the rhythm of the
|
||||
Loic Calendar. The irrational numbers are consumed during derivation.
|
||||
Only the integer survives."
|
||||
|
||||
HELP
|
||||
exit 0
|
||||
;;
|
||||
*)
|
||||
echo "Unknown option: $arg" >&2
|
||||
exit 1
|
||||
;;
|
||||
esac
|
||||
done
|
||||
|
||||
# ───────────────────────────────────────────────────────────────────────
|
||||
# THE COMPUTATION CASCADE
|
||||
# ───────────────────────────────────────────────────────────────────────
|
||||
# Each phase depends on the previous. The order is immutable.
|
||||
|
||||
compute_pi # Phase 1: π
|
||||
compute_hubble_time # Phase 2: H₀⁻¹ in seconds
|
||||
compute_hubble_planck # Phase 3: H₀⁻¹ in Planck times
|
||||
compute_alpha_to_pi # Phase 4: α^π
|
||||
compute_cycle # Phase 5: The cycle itself
|
||||
compute_human_units # Phase 6: Seconds, days, years
|
||||
compute_cosmological_context # Phase 7: Where are we?
|
||||
compute_boundaries # Phase 8: Creation and Annihilation
|
||||
|
||||
# ───────────────────────────────────────────────────────────────────────
|
||||
# THE OUTPUT
|
||||
# ───────────────────────────────────────────────────────────────────────
|
||||
|
||||
case "$mode" in
|
||||
human) output_human ;;
|
||||
json) output_json ;;
|
||||
constant) output_constant ;;
|
||||
esac
|
||||
}
|
||||
|
||||
# ═══════════════════════════════════════════════════════════════════════════════
|
||||
# BEGIN EXECUTION
|
||||
# ═══════════════════════════════════════════════════════════════════════════════
|
||||
|
||||
main "$@"
|
||||
Loading…
Add table
Add a link
Reference in a new issue