| Moving-head clock length and locality | statement | lemma S69 | arxiv |
| Spin-local energy orthogonality | statement | proposition S73 | arxiv |
| Reference phases measure the collision weight exactly | statement | lemma S86 | arxiv |
| Discrete cosine differences inherit the logarithm | statement | proposition S58 | arxiv |
| Vanishing-error scaling | statement | corollary S54 | arxiv |
| Expansion of a traceless operator | statement | lemma S4 | arxiv |
| Admissible logarithmic patch sizes | statement | lemma S82 | arxiv |
| The continuum width-\(\delta\) mass is \(\Theta(\delta\log(1/\delta))\ | statement | corollary S57 | arxiv |
| Bad-time fraction | statement | lemma S76 | arxiv |
| Positive spectral representation and almost-sure frequency identification | statement | lemma S85 | arxiv |
| 46YF6Q3MFB | statement | proposition S9 | arxiv |
| The \(1/T\) dependence is sharp for the every-window criterion | statement | proposition S91 | arxiv |
| Fourier estimate for bounded regular energy densities | statement | lemma S87 | arxiv |
| Companion map and local staircase | statement | lemma S63 | arxiv |
| Ensemble means and probability bounds | statement | corollary S27 | arxiv |
| Scalar dephasing with no Hilbert-space or patch-count prefactor | statement | theorem S88 | arxiv |
| Prime-power local bands and time windows | statement | corollary S72 | arxiv |
| General periodic-clock anti-concentration | statement | theorem S61 | arxiv |
| Autocorrelation and every-window relaxation at rate \(b_N+1/T\ | statement | theorem S89 | arxiv |
| Static local matrix elements | statement | lemma S39 | arxiv |
| Exact infinite-time local return formula | statement | theorem S11 | arxiv |
| Counting equally spaced points in an interval | statement | lemma S41 | arxiv |
| Measurability of the every-window functionals | statement | lemma S23 | arxiv |
| Maximal-LFSR Floquet phases | statement | lemma S36 | arxiv |
| Return matrix as a local operator overlap | statement | lemma S3 | arxiv |
| Same-scale two-sided equivalence | statement | theorem S21 | arxiv |
| Same-scale separated form | statement | corollary S19 | arxiv |
| Cosine-grid difference count | statement | theorem S47 | arxiv |
| Two-sided difference-law discrepancy, with half-open intervals | statement | lemma S46 | arxiv |
| Local return matrix | definition | definition S2 | arxiv |
| Periodic-clock eigenstates | statement | proposition S35 | arxiv |
| Residual zero-frequency weight | statement | corollary S50 | arxiv |
| Transfer block of the temporal channel | statement | lemma S16 | arxiv |
| LFSR local-band concentration | statement | theorem S49 | arxiv |
| Gauss and Jacobi sums | statement | lemma S66 | arxiv |
| Trace norm versus Hilbert--Schmidt norm | statement | lemma S5 | arxiv |
| Kolmogorov discrepancy of the cosine grid | statement | lemma S42 | arxiv |
| Prime-power static local matrix elements | statement | lemma S71 | arxiv |
| Conserved energy lower-bounds the zero-frequency trace weight | statement | lemma S28 | arxiv |
| Exponentially fine microscopic energy | statement | proposition S55 | arxiv |
| Weak ETH controls exact local memory | statement | lemma S32 | arxiv |
| Arcsine density for the cosine energy | statement | lemma S40 | arxiv |
| Local spectral weights | statement | lemma S13 | arxiv |
| Positive-kernel return theorem | statement | theorem S24 | arxiv |
| Infinite-time LFSR equilibration | statement | theorem S51 | arxiv |
| Weak ETH plus finite-time mixing, without exponent loss | statement | corollary S34 | arxiv |
| Linear same-scale comparison with physical local errors | statement | theorem S25 | arxiv |
| Cesaro orthogonality | statement | lemma S10 | arxiv |
| Stationary local state | statement | corollary S52 | arxiv |
| General periodic-clock every-window relaxation | statement | corollary S62 | arxiv |
| Explicit formula for the local operator projection | statement | lemma S1 | arxiv |
| Same-time random-ensemble criterion | statement | corollary S33 | arxiv |
| Continuum difference concentration | statement | lemma S45 | arxiv |
| Deterministic extensive Hilbert--Schmidt upper bound | statement | lemma S29 | arxiv |
| Quasi-linear fixed-accuracy windows | statement | corollary S77 | arxiv |
| Local operator return controls infinite-temperature thermalisation | statement | theorem S6 | arxiv |
| Maximal-LFSR Pauli matrix elements; external | statement | theorem S37 | arxiv |
| Commutativity, bounded term incidence, and conserved operators | statement | proposition S79 | arxiv |
| Autocorrelation representation | statement | lemma S20 | arxiv |
| Tent domination | statement | lemma S12 | arxiv |
| Density of the difference | statement | lemma S44 | arxiv |
| Direct every-window LFSR bound | statement | theorem S53 | arxiv |
| Prime-power static spectrum | statement | proposition S70 | arxiv |
| Thermalisation directly from the complete local autocorrelation | statement | corollary S26 | arxiv |
| Conservation-law floor for Haar-local ensembles | statement | theorem S30 | arxiv |
| Choosing the frequency resolution | statement | corollary S15 | arxiv |
| Fej\'er local-band theorem | statement | theorem S14 | arxiv |
| One event covers every longer window and every local input | statement | corollary S92 | arxiv |
| Integration against a Kolmogorov perturbation | statement | lemma S43 | arxiv |
| Explicit polynomial rates and high probability | statement | corollary S90 | arxiv |
| Many-body local return superoperator | definition | definition S8 | arxiv |
| One-clock-particle factorisation | statement | proposition S74 | arxiv |
| Haar two-copy twirl, with its elementary commutant proof | statement | lemma S83 | arxiv |
| Reference-time design input: exact-Haar specialization | statement | theorem S81 | arxiv |
| Separated finite-window theorem | statement | theorem S18 | arxiv |
| Maximal cycle and Floquet phases | statement | lemma S64 | arxiv |
| Lower logarithmic singularity of the arcsine difference | statement | lemma S56 | arxiv |
| Weyl matrix elements from finite-field character sums | statement | theorem S67 | arxiv |
| Trace pairing and additive characters | statement | lemma S65 | arxiv |
| Scalar autocorrelation at the reference time | statement | lemma S84 | arxiv |
| Separated stationary-memory theorem | statement | theorem S17 | arxiv |
| Perturbation stability without resolving microscopic gaps | statement | theorem S94 | arxiv |
