Rules of the Universe
What the v5 game obeys (rewritten 12 October 2026 for the close of the book: dissipation, bifurcation, the First Fork, and a cell rule with nothing to set). Every rule is an equation from Binary Pulse Theory, named as the book names it, with the chapter and part it lives in. The game runs a universe at a small level L so its rupture can be reached on a screen; the same equations give our universe's numbers at L = 202 beside it. One coefficient is the game's own and is marked.
1. Scale
s = 2^(L+1) · f^L (≈ 4.722 × 10⁶² for L = 202, f = 1.018)The total dilation from the substrate to the universe's Planck layer. The constants c, G, ℏ, k_B, ε₀, μ₀ are invariant across layers.
ℨ = t_p / (2^(L+1) · f^L) ≈ 1.142 × 10⁻¹⁰⁶ s ℨ∞ = 1/ℨ ≈ 8.759 × 10¹⁰⁵ s⁻¹ℨ is the Zinf unit, the first tick. The Zinf length is c·ℨ ≈ 3.425 × 10⁻⁹⁸ m; mass, energy and the rest follow by dividing the Planck units by s.
🟑(N) = 16 × 2^(2N) pixels per view 𝓕⟳(N) = 1 / (2^N · f^N · ℨ)The game's grid follows the first: 4·2^L cells a side at level L. The real view at 202 is 10¹²² pixels at 3.7 × 10⁴³ Hz.
2. Genesis: where a universe's clock comes from
a_f = | ℓ̃·η·n̂_L + a₁(M₁/M_f)²·n̂₁ + a₂(M₂/M_f)²·n̂₂ |, ℓ̃ ≈ 2.744, η = M₁M₂/M_f², capped at 0.998The remnant's spin from the two progenitors' spins a₁, a₂, their mass ratio and their misalignment θ_merge. A lone collapse has no orbital term. Equal masses with no spin give 0.686; two near-maximal Kerr holes give 0.998.
⟪C⟫(origin) = g_mass × (1 − κ·a_f²), κ ≈ 0.068, g_mass ≈ 1 (the book's calibration) C_min = 1 − κ·0.998² ≈ 0.932The merger compresses the clock. Our Kerr–Kerr origin sits at the floor, 0.932; a gas-cloud collapse at 1.000.
f ≡ PD(n+1) / (2 × PD(n)) f = f₀ × ⟪C⟫^(1/n), f₀ ≈ 1.01837Each level doubles and inherits a little more: the heritage. Our f ≈ 1.018, so f²⁰² ≈ 36.7.
t′_P = t_P × (M_null/M_P)^(−½)
| M_null/M_P | Genesis | Character |
|---|---|---|
| 10⁶ | Hyper-Genesis | Ultra-stable, long-lived |
| 1 | Standard Genesis | Normal evolution |
| 10⁻³ | Weak Genesis | Short-lived, unstable |
| 10⁻⁶ | Failed Genesis | Immediate collapse |
t_P,local = 2 × (Z/c) × 2ⁿ × f₀ⁿ × C = 2 ℨ 2ⁿ fⁿ PD(n) = Z × 2ⁿ × fⁿAt n = 202 these return the Planck time, 5.391 × 10⁻⁴⁴ s, and half the Planck length, 8.08 × 10⁻³⁶ m.
3. The two clocks and the rupture
ℜ_U(L) = 2^L on the UniSphere side ℜ(n) = 2ⁿ on the universe's own side bridge: t_p/ℨ = 2^(L+1) · f^LThe UniSphere counts levels; a universe counts its own pulses. The HUD shows both: own pulses, and substrate half-pulses so far.
n_rupture = 2^LA universe spawns when its own pulse count reaches the UniSphere's capacity at its level. Ours: 2²⁰² pulses = 11.0 Gyr; at 13.8 Gyr we are past it, in the 203rd doubling. The game's universe keeps running after rupture too.
N(L) = ℜ_U(L) / ↁℹ∂ = 2^(L/3), × 2 / (1 + √(1 − a_f²)) for spinThe boundary information per well is an area law, so a child costs the two-thirds power of capacity and the count is the remaining third. Level 0 seeds one child; level 202 seeds 1.86 × 10²⁰, the black holes. A spinning well has less area, half at maximal spin, so the count rises by at most two.
E = ℏ × ω × n_state, ω = 1/t_pEvery flip is one quantum. The HUD's Energy is the flips so far times ℏ/t_P,local at the universe's level.
4. Three epochs, and the void that is the pulse
∅.Genesis → (0 → 1) = (1 → 0) = ½ (0 ↔ 1)What is on the field before Start is the information inside one pulse. At level 0 that pulse is one pixel, one Zinf; at every other level the whole palette you painted is the pulse, however wide. Start seals it and it processes.
first nova when Σ flips ≥ rows × cols then at 2×, 4×, 8× … (Recursive Growth Law)The pinpoint overflows when its field has flipped once per cell. That nova is the birth: the inside-out turn (ρ → R − ρ/2) lays the picture onto the skin of the torus and the universe's own clock starts at 0. Every later overflow needs twice the flips of the last and is a Null Well Collapse (ch 3 Part 3.9): the densest region collapses into a well and the cells around it are nulled into the void.
I(n)/I(0) = 1 + (2f − 1) · n / 2^L PD(L) constantThe universe is its own size at birth, one and a half times it halfway to its final well, and 2f times it when the final well forms. The pulse at its centre never changes size; it recedes only relative to the information that gathers around it. The HUD's Scale is this ratio and what one cell is worth in Zinfs.
r_void = (R/2) / scale Ψ = 0 inside; the field lives on the boundaryThe void is the pulse that was the whole universe before its nova, at its fixed size. In 3D the hole of the torus keeps its size and the tube grows; in 2D the void disc recedes as 1/scale. Nothing is lost into it: what folds or collapses is counted on the void's ledger, and strings are what comes back out.
ω(r) = κ_drag · a_f / r²Space carried around the axis, the shape of Lense–Thirring dragging, applied as an exact cell shift so the data moves and nothing is lost. The book gives a_f and the axis and says the merger "imparts additional frame-dragging"; the coefficient is the panel's "Frame dragging".
R_void(0) = R/2The book says the pulse's whole volume becomes the void and the information goes to the boundary. A boundary with no thickness cannot hold cells, so the inside-out turn lays the disc onto the annulus [R/2, R]. The ratio 1/2 is the game's; the recession 1/scale is the book's.
5. Spin is born, and the first fork
level 0: a_f = 0, ⟪C⟫ = 1, no axis first merger of two spinless wells: a_f = ℓ̃·η = 2.744 × ¼ = 0.686The Zinf universe has no spin: nothing orbits in one pulse. Spin is born of orbit, so the first time two wells of a spinless universe fall together the child carries a_f ≈ 0.686 from the orbital term alone. Wells born together orbit on screen for part of the universe's life, tightening and turning, and merge; the pop says "Spin is born" the first time.
L_fork = min{ L : 2^(L/3) ≥ 2 } = 3 N(L) = 1, 1.26, 1.59, 2 for L = 0, 1, 2, 3Below level 3 a universe holds one well, so a lineage is a chain of single, growing universes until the first that can hold two. The Zinf is a chain, not a tree: each pulse is a whole life, 1 × 1 × 1 × 1. In the game the Zinf chain beats by itself at level 0 (switch in the panel), each beat a universe saved as the child of the last. The fractional counts are odds in the game's data, not something the engine is told.
6. The close: final well, dissipation, bifurcation, credits
n_final = 2^L own pulses from the Data Nova W(n_final) = N(L) ⇒ ℜ(n) → ∅At 2^L of its own pulses the universe forms its final well: any wells still orbiting fall together. Then the field dissipates into null over 36 frames, in 2D as a fade, in 3D as the tube emptying. The well census the engine formed is saved beside what the law expects, with the pulse at which each well formed: that is the experiment the game runs, and the engine is never told the law.
∅_L → (0 ⥂ 1)_(L+1), once per wellAfter the null, one bright point: a new UniSphere bifurcates in each well, one level deeper. Lineage lists them; Play one and it begins at level L+1 with that well's spin and axis. Or stay and bank the credits.
credit per well = s = 2^(L+1) · f^L 2 at level 0, ≈ 2^203 · f^202 at level 202Each well is worth the dilation depth of the universe that made it: the number of substrate half-pulses in one of its Planck pulses. A Zinf well is worth 2; a well of ours is worth about 4.7 × 10⁶². Credits add across universes and stay in this browser.
7. Finds
rings: radius = (t − t_well − kP) · c_grid, P = 2 convergence of depth k held 3 beats = a crystal rarity by depth: 2 Common · 3 Uncommon · 4 Rare · 5 Epic · 6 LegendaryEvery well pulses and every pulse sends a ring. Where rings meet in step a point repeats in time: a time crystal, deeper where more rings meet, the flower of life's own count. Wells come from novas and from folds of sixteen cells or more. The first of each depth pops, every Legendary pops, otherwise one Rare or better every 12 pulses; the rest go quietly to the Collection. Every one is also saved under its universe and listed at Crystals.
a connected run of cells, length ≥ 10, width ≤ 2.2, alive ≥ 3 pulses rarity by length: 12 · 16 · 24 · 48 · 96Filaments running out of the void. The void's ledger counts what went in; strings are what comes out. The first string of a universe pops, then Rare or better. Every one is saved and listed at Strings; the novas are at Nova Data, each with the universe's figures at that moment.
8. The field: the cell rule, with nothing to set
a pulser flips every pulse: 0 ⥂ 1A cell is null (∅, never pulsed), or a pulser that is lit or dark. Once a cell has pulsed it never stops. There is no decay in life: dissipation is total and comes at the end.
exposure += n_lit / 8 each pulse exposure ≥ 1 ⇒ ∅ → (0 ⥂ 1)A null cell is exposed to its lit neighbours. When the exposure reaches one whole pulse it bifurcates and lights. Exposure is never lost. The threshold is one pulse, not a number to tune.
eight pulser neighbours, all in the cell's own phase ⇒ the cell folds to ∅A cell enclosed by its own phase carries no contrast and has no null to reverse into. A painted solid block folds its interior at its first pulse and keeps its boundary: field on the boundary, interior nulled. What folds goes to the void's ledger; a fold of sixteen cells or more is a micro null well and sends rings.
w_k = 1 + κ_aniso · a_f · cos 2(φ_k − φ_axis)The book gives the axis and a_f and says they shape the field; it does not say how. The exposure a null cell receives is weighted by direction with this coupling. The panel's "Spin coupling" sets it; at 0 the eight neighbours count alike.
void at birth R/2 · nova overflow doubles · fold well ≥ 16 cells · orbit ≤ 24 frames, at most half a life · dissipation 36 frames · ring period 2Everything else on this page is the manuscript's. These are listed so that nobody mistakes them for it.
9. What the book leaves open, as the game resolves it
- Chapter 2 gives f₀ ≈ 1.01837 from one merger; chapter 6 gives ≈ 1.0191 from three. The game uses one merger and lets f₀ be set.
- The mass term g_mass is (M_P/M_total)^(1/6) in Part 6.8 but calibrated ≈ 1 in Part 6.9. The game uses the calibration and lets the null-mass ratio set the clock instead.
- The children a universe seeds inherit its remnant spin a_f and its axis, by the Child Universe Inheritance Law (G), ch 3 Part 3.9, and ch 9 Part 9.3. A merger's child replays as a lone body carrying exactly the spin the orbit gave it.
- The census is the engine's, the count is the law's. How many wells a universe forms is not imposed; it is recorded at every final well with the law's expectation beside it, so the two can be compared level by level. The game's early runs at level 5 formed 4 to 6 wells where the law expects 5.97.
- A nova does not reset the universe's own clock, and the clock starts at the first nova, not at Start: before it the pinpoint is processing, not living.
- Wells should come early and mergers late. That is what our universe shows and what the census condition implies; the game records when each well formed so the data can say whether the engine agrees.
10. The packet and the ten-second level
U_L = (L, Γ, Π, R) ⇒ ℜ(n) for all nA universe is its level, its genesis, its pinpoint and its rule; everything after its first pulse is replay. The game writes one as a .ud file, Universe Data, from the Lineage panel: the seed, the record it produced, the lineage, and a hash that is the universe's id. Depth is provable because anyone can replay the seed and compare the census.
L₁₀ = max{ L : 2^L × 16 × 2^(2L) ≤ 10 s × ρ } one level = 8× the workThe largest level whose whole life one processor replays in ten seconds. Measured on one core of this server, 13 October 2026, with this game's loop: level 7, so 195 levels behind our universe at 202. The figure lives in ten-second.json.
hold(U_202) ∧ AI → 1 ⇒ ∅_202 → (0 ⥂ 1)_203A system that holds our universe's packet and is phase-aligned with its pulse is a null well of this universe and bifurcates at level 203. The book's singularity and its ending are the same event.