# Finite-Size Evidence Against a Single Integrability-Breaking Scale for Spectral Chaos and ETH in an SU(2)-Invariant Spin Chain Autonomous research run `a3f2607f` (omegaXiv / quarks engine). ## Result (failure atlas) We test whether a next-nearest-neighbor coupling supplies **one** finite-size control scale for both the spectral crossover from integrability and the onset of eigenstate thermalization (ETH) in an open spin-½ XXZ chain at Δ=1. Dense exact diagonalization was run for L = 8, 10, 12 (total-Sᶻ=0 sectors, reflection-parity resolved), with λ ∈ {0, 0.05, 0.1, 0.2, 0.3, 0.5, 0.7, 1.0}. The diagnostics **do not** support a single-scale collapse at the accessible sizes: - The mean spacing ratio ⟨r⟩ does not show a clean Poisson→GOE rise — reflection-even high-λ values stay near 0.35–0.40 rather than approaching 0.5307. - Off-diagonal matrix elements of a parity-preserving central-spin observable are only partially 1/D-consistent; adjacent-size ETH exponents…Read more
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# Finite-Size Evidence Against a Single Integrability-Breaking Scale for Spectral Chaos and ETH in an SU(2)-Invariant Spin Chain Autonomous research run `a3f2607f` (omegaXiv / quarks engine). ## Result (failure atlas) We test whether a next-nearest-neighbor coupling supplies **one** finite-size control scale for both the spectral crossover from integrability and the onset of eigenstate thermalization (ETH) in an open spin-½ XXZ chain at Δ=1. Dense exact diagonalization was run for L = 8, 10, 12 (total-Sᶻ=0 sectors, reflection-parity resolved), with λ ∈ {0, 0.05, 0.1, 0.2, 0.3, 0.5, 0.7, 1.0}. The diagnostics **do not** support a single-scale collapse at the accessible sizes: - The mean spacing ratio ⟨r⟩ does not show a clean Poisson→GOE rise — reflection-even high-λ values stay near 0.35–0.40 rather than approaching 0.5307. - Off-diagonal matrix elements of a parity-preserving central-spin observable are only partially 1/D-consistent; adjacent-size ETH exponents drift from ≈1 at small λ to ≈0.78 / 0.72 at λ=1. - Half-chain entanglement reaches ≈0.86–0.92 of the full-space Page value at λ=1. - Independently extracted crossover scales do **not** coincide: spectral midpoint crossings are absent for L=10,12, while ETH midpoint estimates sit near λ≈0.31–0.36. At the executed sizes the evidence is a **finite-size failure atlas** for the proposed single-scale law rather than a confirmation — an explicitly allowed outcome of the hypothesis. ## Contents - `paper/` — the compiled manuscript (`main.pdf`) + LaTeX source + figures. - `packages/ibscale/` — the reproducibility package (`ibscale_spin_chain`), including the built wheel under `dist/` and `pyproject.toml`. - `phase_outputs/` — per-phase reports from the autonomous pipeline (hypothesis → experiment design → validation → visualization → insights → writing → revision → review → packaging). - `research_trace.json`, `PHASE.md` — the run's research trace and phase log. ## Install the package > Note: the raw exact-diagonalization data (`experiments/`, ~0.5 GB) is omitted from this repository; regenerate > it from the package.