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Glossary
775 terms defined in Binary Pulse Theory, read from the text itself. 632 carry a definition from the lexicon.
A
Acceleration Equation
The Acceleration Equation is the second Friedmann equation: how what fills a universe speeds up or slows its expansion, with pressure gravitating as well as density. Matter, with no pressure, slows the expansion. The Null Vacuum, with p⦵ = −ρ⦵c², gives ρ + 3p/c² = −2ρ⦵ and turns the pull into a push, ä / a = +8πGρ⦵ / 3: Vacuum Pressure, the reason a universe's expansion accelerates late in its life. Formally, ä / a = −(4 · π · G / 3) · (ρ + 3 · p / c²), where ä [𝕋⁻²] is the acceleration of the scale factor, a [∅] the scale factor, G [𝕄⁻¹·𝕃³·𝕋⁻²] the universe's gravitational constant, ρ [𝕄·𝕃⁻³] the density and p [𝕄·𝕃⁻¹·𝕋⁻²] the pressure of what fills it, and c [𝕃·𝕋⁻¹] light speed: [𝕋⁻²] = [𝕋⁻²]. It connects to Vacuum Pressure, Friedmann Equation, Gravity of a Universe and Null Vacuum.
ä / a = −(4 · π · G / 3) · (ρ + 3 · p / c²)
Defined in The Dark Sector: Data Matter, the Null Vacuum, and Vacuum Pressure Lexicon entry 8/10
Accretion Luminosity
Accretion Luminosity is the light a feeding well gives off: about a tenth of the rest energy of what falls in, ten times more efficient than fusion, so a quasar swallowing a few Suns a year outshines a trillion stars. Formally, L = η · M′ · c², where L [𝕄·𝕃²·𝕋⁻³] is the light, η [∅] ≈ 0.1 the share radiated, M′ [𝕄·𝕋⁻¹] the mass falling in each unit of time and c [𝕃·𝕋⁻¹] light speed: [𝕄·𝕃²·𝕋⁻³] = [𝕄·𝕃²·𝕋⁻³]. It connects to Eddington Luminosity, Quasar, Well–Bulge Relation and Galaxy (BPT).
L = η · M′ · c²
Also in 5.12
Defined in Galaxies: the Wells and the Stars Around Them Lexicon entry 8/10
Alpha Fundamental Frequency Eq
The Alpha Fundamental Frequency is the first and lowest mode of the Alpha String, the reciprocal of the Pulse Tempo, one full back-and-forth pulse: the seed cycle of the universe, which its first nova, the Null Nova, sounds as the torus. Before its first nova the universe exists in this mode as a circle, a sealed loop of pure recursion, the Pulsecore, and the book calls it the indivisible cycle of recursion, the Fundamental Frequency of the Universe and the primordial 'Alpha note' of reality, the cosmic heartbeat before expansion. The Null Nova, Harmonic 1 of Data Harmonics, folds the circle into a torus with dual radii (R, r), in which recursion exceeds circular containment and Local Recursion and Global Containment become Harmonic Partners. Every later harmonic is built on it. The second harmonic, f₂ = 2/①⥂⧗ = 2f₁, the octave, is the Data Nova, Harmonic 2: the Pulsecore's data pours out onto the torus, lays its lattice over the space the Null Nova made and gives it its axes, and the universe learns to breathe. Higher harmonics continue the ladder. The book writes f₁ = 1/①⥂⧗, where f₁ is the fundamental frequency [𝕋⁻¹] and ①⥂⧗ the Pulse Tempo, one full back-and-forth pulse along the Alpha String length PD, carried as [𝕋]. The check reads [𝕋⁻¹] = 1/[𝕋] = [𝕋⁻¹]. For our universe the Pulse Tempo is the Planck time, so f₁ ≈ 1.855 × 10⁴³ Hz. The Alpha Fundamental Frequency connects to Pulse Tempo Definition, Pulse Diameter, Our Alpha Strings Fundamental Frequency, 2. Alpha Harmonic Overtones, Alpha Wavelength of Harmonics, Toroidal Genesis and Data Nova.
f₁ = 1 / ①⥂⧗ [𝕋⁻¹]
Defined in The Alpha String Harmonic Ladder Calculator Lexicon entry 8/10
Amplification Factor Eq
The Amplification Factor A(n) is the ratio of total data capacity after one completed pulse to that after the previous one, A(n) = ℜ(n)/ℜ(n−1), which under the Recursive Growth Law is exactly two. It is one of the UniSphereal Recursive Growth Relations, alongside the Binary Increment Law. Because each pulse re-contains everything every earlier pulse held and adds as much again, the ratio between successive levels is two at every depth (n ≥ 1) and never tapers. The first count itself is not an amplification but a genesis: the Zinf's one whole completion, ℜ(0) = 1, from which every doubling follows. Growth is bounded by the substrate rather than by any decline in this factor. The tapering ratio (n + 1)²/n², 4 at the first step and tending to 1, belongs to the square, quadratic structural capacity developed in Quantum Pulse Theory. Formally, A(n) = ℜ(n)/ℜ(n−1) = 2 for n ≥ 1, where A(n) is the amplification factor between successive pulses, the doubling ratio; ℜ(n) the total data capacity after n completed pulses; ℜ(n−1) that after the previous pulse; and n the count of completed pulses. All are [∅]. It connects to Amplification Factor Properties, UniSphereal Recursive Growth Relations, Recursive Growth Law, Substrate Capacity Limit Properties and Quadratic Amplification.
A(n) = ℜ(n) / ℜ(n−1) = 2
Also in 2.8 , 3.3 , 4.1 , 8.6 , 9.9
Defined in The Foundational Equation and Structural Growth Calculator Lexicon entry 8/10
Arc Length Calculation Eq
The Arc Length Calculation is the integral that gives the length of the Emergence Arc and finds it equal to π times the Pulse Domain Radius, the book's grounds for calling π the intrinsic geometric constant of binary transition. Integrating the speed along the semicircle the binary transition traces in the complex plane, z(θ) = L × exp(iθ), whose height is the Emergence Arc, the book obtains a total path of π × L; read instead as a graph of height over a straight base of πL, the curve would be about 3.820 L long. From this it concludes that π emerges from the first binary distinction as a fundamental property of emergent geometry, governing the minimal-energy trajectory, and it compares the role of this geometry with that of extra dimensions in Zwiebach's string theory. The calculation leads into the Variational Principle for Binary Transitions, which picks the optimal path. s = ∫₀^π |dz/dθ| dθ = π × L where s [𝕃] is the arc length of the Emergence Arc traced in the complex plane, θ [∅] the phase parameter running from 0 to π (θ = π t/τ⥂), dθ [∅] its differential, |dz/dθ| [𝕃] the speed along the arc, |i·L·exp(iθ)| = L, z [𝕃] the Complex Arc Trajectory z(θ) = L × exp(iθ), whose imaginary part L sin θ is EA(t), and L [𝕃] the characteristic Pulse Domain Radius. The result is [𝕃], which the book verifies. It connects to Emergence Arc Function, Intrinsic Geometric Constant, Variational Principle for Binary Transitions, Semicircular Arc and Pulse Domain Radius.
s = ∫₀^π |dz/dθ| dθ = π × L [𝕃]
Defined in π as the Geometric Heart of Binary Computation Calculator Lexicon entry 8/10
Arm Number
Amplification is strongest at a wavelength twice the disk's critical one, λ_crit = 4π²G·S_d/κ_ep² (Toomre, 1981); fitting that wavelength round the circumference gives the count (Carlberg & Freedman, 1985; D'Onghia et al., 2013). A heavy, self-gravitating disk grows two or three grand arms; a light disk in a heavy halo grows many short ones, flocculent.
m_a = κ_ep² · R / (4 · π · G · S_d)
Also in Galaxies and the Cosmic Web , 6.1 , 6.4
Defined in Galaxies: the Wells and the Stars Around Them not in the lexicon yet
Arm Pitch Angle
Michikoshi & Kokubo (2014), from swing amplification and N-body disks: about 22° for a flat rotation curve, about 11° round a dominant central mass, wider in a disk that turns nearly as one. Observed spirals run from about 5° to 40°, and a bigger central well goes with tighter arms (Seigar et al., 2008), as a steeper fall in Ω, a larger Γ, requires.
i_p = arctan((2 / 7) · √(4 − 2 · Γ) / Γ)
Also in Galaxies and the Cosmic Web , 6.1 , 6.4
Defined in Galaxies: the Wells and the Stars Around Them not in the lexicon yet
Ascend Phase Eq
The Ascend Phase is the 0 → 1 half of the pulse cycle, the upward phase in which information increases and new states are created, expanded and propagated. Every universe's pulse is a complete cycle of two asymmetric directional phases: the Ascend Phase (0 → 1), encoding emergence and expansion, and the Collapse Phase (1 → 0), encoding resolution and consolidation. The ascend phase drives the outward flow of information, creating new states and propagating complexity; computationally it performs constructive operations such as branching, information creation and extension of the system state. The book grounds the arrow of time in this asymmetry between the two phases, and it presents the ascend-then-collapse alternation as the rhythm of construction and contraction under all recursive computation. Formally, ∆ↁⓘ (↥) > 0 (information increase) and ∆ↁS (↥) ≥ 0 (entropy production allowed), where ∆ↁⓘ is the change in data information [1ᵇ], ∆ↁS is the change in data entropy [∅], and ↥ marks the 0 → 1 transition [∅]. The book's check reads [1ᵇ] > [∅] and [∅] ≥ [∅]. It connects to the Collapse Phase, Phase-Dependent State Evolution, Binary Pulse Oscillation and the Pulse Diameter.
∆ↁⓘ (↥) > 0
Defined in Pulse Phase Temporal Genesis and Directional Operations Calculator Lexicon entry 8/10
Ascendant Ceiling
From the book's laws the universe's matter is about 3,500 · (m_P/m_p)⁴ proton masses, its stars holding 6 % of it (Part 2.10), and its Data Matter 27/5 times that (Part 3.13), so M_U ≈ 2.23 × 10⁴ · (m_P/m_p)⁴ · m_p; the Ascendant Mass is √(ln 2 / 4π) · 2^(L + 2) · m_P ≈ 2.75 × 10³ · (m_P/m_p)⁴ · m_p. Their ratio is 8.1 at every level: at most eight Ascendant Wells, and eight only if the whole universe ended in eight equal wells. Counting the matter alone, without its Data Matter, it is 1.3: at most one. At ours M_U ≈ 4.6 × 10²³ Suns, the measured matter of the observable universe.
N≡ ≤ M_U / M≡
Also in The Universe from Its Level , 1.13 , 3.14
Defined in Galaxies: the Wells and the Stars Around Them not in the lexicon yet
Ascendant Mass
In the universe's own Suns, 0.54·m_P·(m_P/m_p)² each with m_P/m_p = 2^(L/3)/14.3 (Parts 2.10 and 6.10), M≡ ≈ 356 × 2^(L/3) Suns: about 356 Suns for every well its universe forms, so always about an eighth of the universe's whole mass, Data Matter with it, at every level. At ours, about 6 × 10²² Suns, some 14 % of the matter of the observable universe.
M≡ = √(ln(2) / (4 · π)) · 2^(L + 2) · m_P
Also in 1.13 , 3.1 , 3.10 , 3.14 , 8.10
Defined in Galaxies: the Wells and the Stars Around Them not in the lexicon yet
The full PulseCore lexicon — every term across the book, the simulation and the calculator.