KishLattice Geometric Harmonic Spectroscopy Volume 11: The Structure That Locks presents the canonical results of pipeline run run₂0260605₀12354, processing 24, 904, 223 physical measurements across 61 sovereign lakes and 52 active physical domains under a single scalar transformation parameterised by kgeo = 16/π ≈ 5. 093. The run confirmed 33 STRONG signals (chaos z ≥ 5) spanning 41 orders of magnitude in physical scale from sub-nuclear particle collisions to cosmological velocity dispersions, completing in 1 hour 44 minutes on commodity consumer hardware. The volume's primary contribution is the first simultaneous multi-attribute confirmation in the series: three independent measurements of the same 1. 8–2 million Gaia DR3 stars — transverse velocity, G-band photometric colour, and apparent luminosity — were pre-registered to land at 16/π, 20/π, and 25/π respectively before the pipeline ran. All three confirmed. The parallax distance attribute of the same population confirmed as a null, consistent with the kinematic principle that positional measurements do not lock. The B5 full RCSB protein backbone catalog (6, 834, 866 backbone dihedral angles) produces the series peak result at Z=+157. 2 at the 25/π register. The companion B4 Richardson Top8000 high-resolution lake (3, 373, 828 records) confirms independently at 19/π with Z=+121. 5. The divergence between B4 and B5 constitutes the resolution sensitivity discovery: the quality filter selects which geometric aspect of the backbone is interrogated, not merely data quality. Volume 11 introduces the spectroscopic wrongbox test as a formal falsification protocol. Five domains were processed under intentionally incorrect dimensional assignments. All five either collapsed or diverged to different harmonic addresses. No wrongbox replicated its real domain's register. This is the spectroscopic signature of real physical structure: the geometry chooses the address, and wrong geometric assignments produce wrong addresses, not the same address at lower amplitude. The pipeline's triple-null architecture is formally documented for the first time: the chaos null (empirical scramble), scramble null (record-order permutation), and synthetic null (smooth Gaussian) run independently for every domain. A result classified as STRONG must exceed all three. The Japan Trench seismic sovereign lake returned a confirmed null with all z-scores negative. This result is published without modification. The volume introduces Vera Aurora Kish as a new team member responsible for the expanded reporting suite, which grew from 10 plugins (Volume 10) to 19 plugins generating 39 figures. The engine was upgraded with Rule 1. 5, enabling native field-name routing in the scalarizer for multi-attribute sub-lakes. Two formal predictions are registered with this volume for Volume 12: a two-dimensional engine test of the subnuclear dual-peak structure, and a tidal phase scalar test on the Japan Trench seismic catalog. All data sources are publicly available. Pipeline scripts are open source. Predictions are pre-registered with immutable Zenodo timestamps preceding every run. Version 2. 0 adds the phase-scramble gate, a fourth and sharpest falsification layer formally pre-registered before it runs. Where the existing triple-null architecture tests whether real data beats its own shuffled values, a smooth Gaussian, and a record-order permutation, the phase-scramble surrogate preserves the real distribution's full empirical shape — every quantile, not merely mean and varia. nce — while destroying only the phase relationship between each measurement and its harmonic register. This directly answers the strongest form of the transform-artifact objection: if the log-modulo lock were a residue of distribution shape under compression, a shape-matched surrogate would reproduce it. The gate is pre-registered on three physically independent anchor domains — Gaia DR3 transverse velocity (16/π), protein backbone dihedral angles (25/π), and exoplanet transit-timing variations (16/π) — with a dual-threshold pass/fail condition locked prior to the run: the gate opens only if all three anchors lock at their confirmed register (chaos z ≥ 5) while their phase-scramble surrogates fall in the null band (z < 3), computed against an ensemble of 100 surrogates per anchor. The scope of a passed gate is fixed in advance: it closes the transform-artifact objection for the survey's highest-signal domains across 41 orders of magnitude, while the derivation of kgeo and the physical interpretation of the lock remain explicitly open. This is the prerequisite soil test that precedes the Volume 12 dimensionality programme; whatever the surrogate returns is published as returned. Version 3. 0 records the state of the phase-scramble gate as construction of its surrogate engine advanced understanding of the pipeline's own lock computation. A source audit established two errata, both filed with timestamps preceding any gate result, per the series' rule that a published claim its own code cannot support is corrected at the exact width of the error the moment it is found. First: the scramble null described in Version 2. 0 is inert for the pipeline's per-value lock test. Because that test evaluates each scalar independently of its position in the record list, a record-order shuffle leaves every value's lock status unchanged, making the scramble null's lock fraction identically equal to the real data's; it performs genuine falsification work only for tests that depend on record ordering or cross-domain pairing, not for the headline lock statistic. Second: the chaos null is implemented as uniform-range sampling, which preserves the empirical range but flattens the distribution's shape rather than preserving its density profile. The consequence reverses a preliminary reading: none of the three standing nulls preserves the real distribution's actual shape while destroying grid-phase, so the shape-artifact objection remains genuinely open and the phase-scramble gate is necessary rather than redundant. The gate is accordingly reframed as a shape-preserving grid-phase scramble, scored through the exact production lock function with its construction assumptions stated explicitly, given the entanglement of distribution shape and grid-phase at these scalar ranges. Anchor selection is under active referee review: the transit-timing anchor listed in Version 2. 0 was disqualified for insufficient scalar spread (its scalars span less than one register width, making the modular test degenerate), and its proposed replacement surfaced a register mismatch between its pre-registered and empirically dominant lock, now pending adjudication. No gate result exists at the time of this filing; Version 3. 0 records the corrected foundation and the reframed test, not an outcome. The result, whatever it returns, will be published as returned. Version 4. 0 records the outcome of the phase-scramble investigation: the construction of the shape-preserving surrogate did not merely test the transform-artifact objection but resolved it analytically, and the resolution was then confirmed on real data. During two-sided validation — the requirement that the gate demonstrate it can fail on a known artifact before it is trusted to pass anything real — it emerged that a genuine offset-invariant shape-artifact cannot be constructed for a grid-proximity lock test. This is a theorem, not a null result: for a test that counts a scalar as locked when it falls within tolerance of a grid node, a strong lock necessarily requires grid-phase concentration, because the only distribution that locks at every grid offset is one uniform modulo the grid, which locks only at the baseline chance rate and is therefore not a strong lock at all. The claim rests on a single checkable fact — a distribution uniform modulo the grid returns chaos z ≈ 1. 58, verified — and carries a live disproof condition: exhibit any distribution that locks at chaos z ≥ 5 and stays locked across a full offset sweep. Three independent attempts to construct such a distribution, made adversarially in referee review, each collapsed into either grid-phase alignment or no lock. The theorem was then tested against real data by sweeping the grid offset across three independent anchors selected for maximum physical separation — Gaia transverse velocity (16/π), galactic velocity dispersion (21/π), and nuclear binding energy (21/π), spanning roughly 38 orders of magnitude — with the disproof condition live: any anchor showing a flat, offset-invariant curve would refute the theorem and reopen the objection. All three showed the predicted sharply peaked, non-offset-invariant curve, with deeply negative median z across non-privileged offsets (Gaia −63. 8, galactic −21. 3, nuclear −1. 0), the signature the theorem requires. Galactic's peak is broader than the others (locking at 42% of offsets versus Gaia's 22% and nuclear's 3%), reported explicitly rather than smoothed; its deeply sub-null median confirms it remains a genuine phase-lock, not a flat-high artifact. Nuclear, the cleanest curve, sits on the thinnest data (n=43), and both facts are stated together. The scope of this result is fixed and load-bearing, not incidental. The theorem closes what is designated Form A — the possibility that the log-modulo transform manufactures a register lock from distribution shape alone, independent of grid phase — and only Form A. It establishes that the survey's locks are genuine phase-concentration rather than artifacts of the transform, closed by proof and confirmed on real data across 38 orders of magnitude. It does not establish that the locks are caused by the geometric lattice. That question — designated Form B, the possibility that a real phase-concentration arises from a mundane coincidence of physical scale or a selection effect rather than the substrate — remains fully open and is now the primary live objection to the framewo
Kish et al. (Mon,) studied this question.