Replication Package – Cosmology from a Three-Bit Seed

Abstract

Replication package for the pre-geometric seed cosmology (Weller 2026: Cosmology from a Three-Bit Seed, 10.5281/zenodo.22586235, which is the program's single source of truth and supersedes the prior corpus documents wherever they differ). Every quantitative claim in the papers regenerates from this package: one script, one command, one expected output per claim. Environment: Python 3.11+ with mpmath, sympy, numpy, and scipy; the spin-foam claims additionally used sl2cfoam-next at commit 052e4346 (github.com/qg-cpt-marseille/sl2cfoam-next, master, 2025-08-28), verified by file-level comparison against the upstream tree. The transfer-matrix dumps it produced are included, so all post-processing reproduces without rebuilding the library; for full from-scratch regeneration, sl2cfoam_tools/ contains the nine utilities added (a one-line Makefile change), buildable per the upstream README. The branching-ratio claims split by dependency: branching_su2.py needs numpy only (~30 s, all assertions exact); the EPRL sweep needs the library. The dark-energy elimination and quantum-partition claims require only numpy and scipy; one_species.py is the shared module (background integrator and approximate DESI-DR1 BAO scorer); BAO verdicts are clear-tier only (Δχ² ≳ 15 or several σ), and the full-likelihood confrontation awaits the survey covariances. The tensor-sector audit of §G and the pivot-layer likelihood reruns use camb and cobaya (the BK15 dataset ships with the CosmoMC repository; the BK18lf_dust baseline dataset is downloaded from bicepkeck.org; set BK15_DATASET and BK18_DATASET to their paths); the tensor-revision, early-transfer, and pivot-layer computational records otherwise need only numpy, scipy, and sympy. The package's sectors. The spectrum and the measure: the root-measure derivation with saddle silence verified at both accessible orders and the second-order block c(r) = −1/3 + (4/3)cos²r; the equator cross-check reproducing the root harmonic (root arc π, unit u = π·3^(−1/3), all assertions exact); and the exact quadrupole-suppression action cost ΔS = 3S₀/4^g. The energy sector, where the script sequence is the derivation: one power of Tr(D) = 4π (the two-power alternative is a double count), the UV-dominated degeneracy sum with saturation depth g* ≈ 3.1, the constraint cap κ = 3/(2π) exact at the time-symmetric matching surface, the collapse theorem η_B/(rA_s) = 15πWc·g_b·κ·rate/(2g*) verified symbolically with no dimensionful survivor (K = 2.1242; c·rate = 4.029 at the quark-sector convention as published, 4.54 under the first tensor revision, 4.86 under the consolidated one, 5.0 at the pivot values, where the counting target is η_B/(rA_s) = 10.5 – the scaling is 1/r, within the two registered order-unity residues), and the budget identification ω_b = f(η_B), ω_cdm = (27/5)ω_b with the route-uniqueness assertion and the logged closed-form marker at 3.4σ (disfavored). The branching-ratio sector (structure paper Section 5.2): the elementary 1 → 4 transition's channel space derived by SU(2) admissibility (eight channels; the failed-edge selection rule forced), the single-edge failure probability exact in the topological SU(2) model – 18/323, within the distribution 224/323 and 9/323, every Table-2 entry an exact rational including the e(AB,CD) selection-rule zero – and 0.10–0.12 in Lorentzian EPRL across γ = 0.1–1.2, Dl-converged, with γ = √3/9 a named adverse point; three implementations concordant everywhere they overlap, with the retirement forensics retained as records (p_scan.py, gamma_minimal_closure.py). The spin-foam sector: the composite bound state (M_T = 1.9704(11) against threshold 4.049(71), margin 2.08(7), Borromean), the spin-saturation asymptote 2.77(5), label-free level certification by correlator effective-mass plateaus (agreement to a few parts in 10³), the documented open j→∞ axis, the exchange-statistics characters (−1 baryon, +1 dark; operator identity P₁₂TP₁₂ = −T), and the vertex channel structure (curl trace 15/16, split 15/96). The dark-energy elimination and quantum partition (transition paper §12; predictions letter §5): the six sourcing channels each closed, yielding the coefficient map c_measured = 0.759 ± 0.015 with 3/4 at −0.7σ (H₀ = 67.41), the T_d representation structure (the move's added slot splitting 1/4 : 3/4 exactly), the sharpened Ω_k = −1.7 × 10⁻³ with T_ig = 0.558 T_P pinned from the anomaly corner, the depth-doubling reducing to ρ_c0·V₄/ℏ = c/Ω_Λ = 1.095, and the flow cap C ≲ 0.03 (2σ) with phantom signature w(0.3) ≈ −1.013. The tensor sector carries the audit's full history in four layers. §G regenerates the first August 2026 revision (the note Correcting Errors in the Tensor-to-Scalar Ratio Calculation): the ensemble correction, the bare-edge rule from the eight-channel space, the exact core r_core = 4/[15(3−2p)²] = 0.031067 at the anchor, the stationary edge-age law and offset kernel, the template mapping validated against the BK15 likelihood (calibration ratio 1.0593 vs 1.057 computed), the BK18 direct evaluation, and a preserved failed validation (the literal metric embedding does not reproduce the closed form); its intermediate values carry superseded-by markers pointing forward. §I regenerates the consolidated tensor revision (the note Deriving the Assertions in the Tensor-to-Scalar Ratio Calculation): the wedge-share inheritance rule derived, the deposit supports derived as exact geometry (the 60° ring partition a theorem), the inter-move channel enumerated with its canonical chart identification (own-shell cross terms vanish identically; the boundary–existence channel a constant −5.5% at the anchor), the constant-anchor sensitivity budget, the transition-stage tensor table (own-shell variances stationary over all 28 reachable age states), giving F = 0.905 ± 0.016, physical r = 0.0281 ± 0.0005, reported r = 0.0297 ± 0.0005, n_t = n_s − 1 = −0.03512, and the likelihood readoff (0.35σ from the BK15 peak; 1.3σ from BK18's best fit) – the constant-anchor package, registered as closed in the monograph; the pivot layer supersedes its numerical values, and bk_readoff_v30.txt carries a superseded-by header. §J closes the early transfer at linear order on the transition paper's own conversion dynamics: the background family, the mode-by-mode transfer analytic in k² with no k⁰ residue, and the band bounds (non-distorting to one part in 10⁵², tensor–scalar asymmetry bounded alongside). The pivot layer (v8) regenerates the adoption of the scale-local pricing premise – the tilt run down from its exact anchor value 1 − n_s = ln 2/(2π²) to n_s(k*) = 0.97268 at n* = k*R = 5393 (exact sum T(n*) = 8.1287 from n = 2), with α_s(k*) = +0.00075 and the run-down amplitude A_s(k*) = e^(−S₀)·S₀/S₀(n*) = 2.0813 × 10⁻⁹ – together with the three computations the monograph cites as archived in its anchor registration. The ancestor-line recursion (ancestor_recursion.py): an exact backward recursion over the descendant tree under the stated measure – uniform p, the classical action cost e^(−ΔS) at any one-loop offset, and the descendant-existence feedback – returning no band tilt at any offset (p_g/p₀ → 1 by g ≈ 7; local tilt below 2 × 10⁻⁵ at g = 10; the low-harmonic suppression 51/17/5/1.4/0.4% at g = 1–5), which closes the constant-anchor package by computation rather than by data. The running-trace decomposition (running_trace_decomposition.py): w_run(n) = deg(n)·g(n)/λ_n exactly, the logarithm the Hessian's after the Green's function cancels the degeneracy, with the K₅-intertwiner weight (n+1)/λ_n shown to sum linearly, so the helicity reduction is the only discretely derived ingredient of the trace ({6j} = 1/√(2(n+1)) verified for n = 1–7). The discrete Laplacian on the 1→4 complex (discrete_laplacian.py): three discrete operators on the K₅ root refined by centroid moves (literal metric, regular-in-own-chart, graph), none carrying S³ shell structure – S₅ degeneracies 1, 4, 4, 11, …; edge lengths never refine (the root chord 1.58 persists); the embedded flat volume grows ×1.7 per generation – placing the budget's spectral ingredients on the saddle. The tensor chain re-evaluated at p(k*) = 0.02732 (canonical_intermove_pivot.py, config_window_final_pivot.py): the inter-move correction −4.27%, the window factor 0.9488, F(k*) = 0.9084 ± 0.016, r_core(k*) = 0.030739, physical r = 0.0279 ± 0.0005, reported r = 0.0292 ± 0.0005, n_t(k*) = (n_s − 1) − 4p²/(3 − 2p) = −0.02833. The B-mode likelihoods rerun at the pivot values (bk15_pivot.py, bk15_chunk.py, bk18_chunk.py; cobaya 3.6.2, camb 2.0.4, seven foreground parameters profiled): BK15 framework-shape profile r_ML = 0.039, σ = 0.027, the prediction 0.4σ from the peak and preferred over the null by Δχ² = 2.5; the flat/framework calibration ratio 1.051 against the CAMB template factor 1.049 over BK bins 1–3 (bb_template_pivot.py) and the projection 1.046; BK18lf flat within Δχ² ≈ 0.3 over r = 0–0.03, the prediction Δχ² = 0.5 above the null, the 95% crossing at r ≈ 0.040 at fixed cosmology (published 0.036 with cosmology varied). Each script has its record beside it; PIVOT_RERUN_README.txt assembles the layer. The seed state: monogamy-saturation identification (W state, node-primitive) and unfrustrated Bell-bond triangle (link-primitive) with entanglement invariants and floor-entropy comparison. Scope is stated plainly: the scale-local pricing premise and the bare-saddle normalization are stated premises, not derivations – the recursion shows the running is not in the stated measure, and the decomposition shows two of its four ingredients are continuum objects – with the joint A_s–n_s line their registered falsifier; P-ROOT fixes the root harmonic n₀ = 3^(1/3) and no longer enters the amplitude, so the amplitude no longer discriminates the root measure; the j→∞ double limit is an open axis and falsifying the binding there is a standing invitation; the η_B residue is two registered order-unity items plus one Standard-Model convention; Ω_Λ =