This paper derives the observable universe from three inputs and no continuous free parameters: one axiom — the vacuum is non-trivial, a state carrying magnitude, orientation, and structure; one integer — the order of the CPT symmetry group, |G_CPT| = 4; and one bit — the chirality χ = −1 that selects which CPT image is called matter. Everything that follows is forced. A non-trivial vacuum confined by the Planck bound reflects off that bound and stands: a single standing wave at the Planck frequency, and with it one clock — time enters as the count of its cycles, t = n·t_P — and one lattice rate, c = ℓ_P/t_P, read off the wave rather than postulated. The CPT group decomposes the wave’s energy into three sectors with the fixed partition 5/12, 5/12, 1/6: two mirror-image material timelines and the residual observability window W = 1/6, the single quantity through which nearly every observable in this paper is expressed. The structure that results is most compactly described as a virtual machine, and the description is offered as engineering rather than metaphor: pre-time content is binary; manifest content is written in an alphabet of |G_CPT| × n_sectors = 12 letters; the encoder is 4 bits wide because 12 ≤ 2⁴, with 4 of the 16 states withheld as the bookkeeping share — the recurring 1/4 of this framework; letters compose into words of 3⁴ = 81 configurations; and the full register runs 81³² ≈ 1.18 × 10⁶¹ ticks, the exponent 32 forced three independent ways by the same integer 4. One dimensional constant converts machine units to laboratory units: the Landauer cost of keeping one letter legible, m̃_ν = 3 k_B T_CνB ln 12 = 1.25 meV — the neutrino mass. Every relationship in the chain is typed, every parameter is an integer or a ratio of integers, and every observable is a composition. The remainder of this paper executes the machine and compares its output to observation. The body of this paper executes the machine, and its output is summarized in two tables. The predictions table leads: three quantities — the tensor-to-scalar ratio r = W² = 0.0278, the neutrino mass sum Σm_ν = 59.7 meV, and the reheating temperature T_reh = 5.4 × 10¹⁵ GeV — stated in advance of the experiments that decide them, with the deciders and dates named. The telemetry table follows with all 48 signposts, each row carrying the derivation, its evaluation, and the observed value, generated directly from the derivation record. The centerpiece landing is a simultaneous closure: the CMB temperature and the Hubble constant are produced together by one algebraic chain from {Ω_Λ, η_B, Ω_DM/Ω_b} — each of those three itself derived upstream — yielding T_CMB ≈ 2.725 K against FIRAS 2.7255 K and H₀ ≈ 67 km s⁻¹ Mpc⁻¹ against Planck 67.4. The chain cannot tune one against the other; both fall out of the same walk or neither does. Representative landings: the electron mass at −0.015%, the muon-electron ratio at −0.004% once the derived sub-leading term is carried, the baryon asymmetry at −0.08%, Ω_Λ at 0.5%, the solar mass-squared splitting at −0.05%, the PMNS angles within 1%. The loosest landings are stated with equal prominence: the atmospheric splitting sits at −2.2%, and the 10¹²² vacuum suppression product agrees at leading order (+18.6%) before the holographic identity closes its form. All 48 signposts divide by type: every dimensionless prediction is a ratio of the integers {3, 4, 6, 81}, fixed before any measurement; every dimensional prediction is such a ratio multiplied by the single Landauer anchor m̃_ν. Perturbing the anchor displaces the dimensional rows in unison and leaves the dimensionless rows unmoved — the framework’s parameter count, demonstrated rather than asserted. A theory fitted to data has no reason to reuse its machinery: each phenomenon hires its own parameter, and the Standard Model plus ΛCDM employ roughly one continuous dial per explained quantity — nineteen and six. A derived structure cannot help reusing, because only one thing is happening and every observable is that one thing seen through some window. This framework’s reuse density is therefore presented as evidence, and it is audited rather than admired: the rotation library exists to distinguish structural identity from numerical coincidence, case by case. Rotation 8 establishes that five quantities from five domains — the baryon asymmetry, the relic neutrino density, gravitational area generation, cosmic entropy, and the vacuum suppression — are algebraically a single quantity, the information-storage budget of cosmic history, read through five windows. Rotation 13 reads one W₀ pixel simultaneously as rest mass, rest energy, write-cost, and information count; inverting the read returns the alphabet cardinality as 12.000. Rotation 14 reaches the register word-count 32 by two unrelated physical arguments that agree only if |G_CPT| = 4 — the identity selects the integer. Rotation 15 collects gravity’s five names — curvature, area generation, storage, entanglement, writing surface — into one ledger fact. Behind the library stands the census: the integer 4 performs eight distinct structural roles in the chain, from group order to compiler width to the Bekenstein–Hawking coefficient; the window W = 1/6 performs ten, from vacuum fraction to tensor ratio to the lepton tower’s rungs. Two numbers, eighteen certified jobs, zero dials. In a fit, such reuse would be an improbable accident; in a derivation, it is the expected signature — and its densest instance is the subject of the final movement: the write and the read. Every write operation in this register has a paired read, and the pairing is mechanical rather than appended: the gravitational write and the entanglement read are the two zero-crossings of the single Planck-frequency oscillation, carrying the derived weights 1/4 and 3/4 — one cycle, two zeros. Measurement inherits the same grammar. An interaction resolves which of the 81 available register words a W₀ pixel carries, and what quantum mechanics names collapse enters the chain as bookkeeping: the unread-configuration probability 1/81 appears directly in the vacuum normalization Γ₀/ω_P, an identity holding at 0.4%. The writes themselves divide into two ledger classes. Type-1 entries register prior structure becoming visible — the falling rock, the decoupling photon; they are forced by the upstream mathematics, draw exactly the write’s Landauer cost, and add no new information to the substrate. Type-2 entries record selections — left rather than right — that the prior state did not compel; these are the register’s only new content, the additive column S in A = |G_CPT|·S. At cycle close nothing written is erased: information conservation forbids it, and the full ledger V_end = |G_CPT| · S is handed forward as the next cycle’s non-trivial vacuum — each beginning larger than the last by exactly what was selected. The chain then dates the era in which reading occurs. The frozen conversion fraction — the Boltzmann freeze-out value 0.6816, identified with Ω_Λ — and the running read-fraction n/81³² can agree only once in the register’s history. The present tick count gives 0.6845 against the observed 0.685: seven parts in ten thousand — an identification carried in the derivation record as a candidate under audit, and offered here with that status. Its reading: configurations capable of reading the register become possible at exactly this crossing, and the coincidence problem is dissolved under this framework — observation occurs now because now is when the read reaches the written page. What is written is forever; what is selected is what the book grows by.
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David Ginsberg (2026) studied this question.
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