# Matter Harmony Lab 1.5.0 This lab tests bounded versions of the idea that molecular arrangement predicts material properties. Release 0.3.0 also makes a five-dimensional latent-motion proposal mathematically executable. It does **not** identify physical fourth or fifth spatial dimensions from melting and boiling data. Release 0.4.0 adds **Water Harmonics**: a 64-molecule fixed-tick animation with explicit rigid H2O geometry, a density-calibrated periodic box, a tetrahedral candidate network, and two hidden coordinates per molecule. The ordinary geometry and density are reference inputs. The ordered scaffold, coupling, latent pulse, colors, tick, and displacement scale are declared constructions. It is not a simulation of liquid-water dynamics. Release 0.5.0 adds the **Water Origami Oscilloscope**. It gives every rigid water molecule explicit TIP3P-like partial charges and calibrates an ordinary single-Debye polarization baseline to the published 25 degree C primary relaxation frequency. Two deliberately different molecular orientation histories then produce the same complete polarization trace. This makes the origami analogy precise: an observation can fold a high-dimensional state into a much smaller measured signal, so the scope trace does not uniquely reveal the microscopic motion. Release 0.6.0 adds the **Sun–Water Eye Observer**. A fixed distant 5772 K spectral source illuminates a constructed moving water surface. The engine uses the IAPWS wavelength-dependent refractive index, Fresnel reflection, vector Snell refraction, and a finite CIE-standard color observer to render a moving underwater caustic at 60 fps. It transports expected spectral energy, not individual photons or optical phase, so the result is a radiance animation and not a hologram. Release 0.7.0 adds the **Water-Drop Acoustic Observer**. A declared 4.0 mm drop drives a linear capillary–gravity ripple packet and one declared entrained bubble drives a surface-coupled airborne pressure candidate. The movie synchronizes 60 fps imagery with 48 kHz audio. Bubble formation, amplitude, damping, and room response are not predicted, so this is not a one-to-one recording or a two-phase flow calculation. Release 0.8.0 adds the **Bubble Hidden-Variable Inverse**. The ideal Minnaert value remains preserved, while a separate Rayleigh--Plesset small-amplitude branch exposes vapor pressure, surface tension, and the effective polytropic exponent. A 401-state family proves that different bubble radii, thermodynamic exponents, and fractional volume amplitudes can produce the same complete modeled pressure trace. The result is an exact non-identifiability boundary, not a claim that any member is measured. Release 0.9.0 adds **Collective-Mode Phase Harmony**. An exact water counterexample proves that an isolated molecule's normal-mode vector cannot identify bulk phase: the same H2O descriptor is paired with solid, liquid, and gas controls. A separate two-component collective spectrum then exposes the physically relevant distinction between low-frequency diffusive weight and a solid-like vibrational band. Its 101-state scan is explicitly continuous, so the engine reports a dynamical coordinate rather than inventing three universal thresholds. Release 1.0.0 adds the **Five-Dimensional Harmony Observer**. Every fixed real skew-symmetric 5-by-5 generator is reduced to two rotation frequencies and one stationary direction, so its 3D projection is a constant plus at most two elliptical harmonics. The engine classifies spectral relation, coupling rank, known-generator observability, one-history Hankel rank, projected span, finite-exposure loss, hidden-basis gauges, and tick aliases. Observation is passive in this model and does not enact a physical or quantum collapse. Release 1.1.0 adds the **Hydrogen Spectroscopy Gate**. Four resolved NIST H I Balmer features confront the strict two-positive-frequency capacity of the fixed linear five-coordinate observer. The gate fails by two features. Two free modes can fit any chosen pair, but finite exposure cannot create the two missing lines. This rejects the current linear observation model as a complete Balmer generator without rejecting every nonlinear, transition-based, time-varying, interacting, or higher-dimensional alternative. Release 1.2.0 adds **Multidimensional Vector Observers**. The same declared skew-linear family now runs in dimensions 4, 5, 6, 7, 8, and 9 and exposes latent position, latent tangent velocity, projected position, and projected velocity. One 3D observer retains a `d-3` dimensional instantaneous kernel, while a simultaneous calibrated observer bank reconstructs the state exactly when its stacked matrix has rank `d`. More observers remove projection ambiguity but do not manufacture new generator frequencies. Release 1.3.0 adds the **Hydrogen Transition Holdout**. NIST H-alpha and H-beta calibrate a one-parameter Rydberg-form baseline and a two-parameter `Delta2 + Delta4` candidate. H-gamma and H-delta are then scored without refitting after the listed air wavelengths are converted to vacuum with the Peck--Reeder standard-air relation. The extra term interpolates both training features exactly but increases held-out RMSE from 6.030 to 6.949 ppm. A training-invisible correction family proves that two fitted lines cannot identify an unrestricted continuation. The failed term is preserved; it is not relabeled as a dimension or a missing string. Release 1.4.0 adds the **Hydrogen Isotope Gate**. A 2022 QED/nuclear-structure calculation, evaluated with a deuteron radius from muonic deuterium, predicts the direct H--D 1S--2S isotope shift within 0.310 combined standard deviations. The engine then evaluates an explicit finite-range central operator, `delta V/h = g exp(-r/lambda)/r`, over 61 ranges. Every range can be paired with a coupling that fits the same central residual exactly, while the pairs disagree on later transitions. The operator is therefore neither needed by this datum nor identifiable from it; it is not promoted to a dimension. Release 1.5.0 adds the **Frozen Hydrogen-Isotope Holdout**. One interaction range is fixed at the electron reduced Compton wavelength, and its coupling is set only by the earlier 1S--2S residual. Without refitting it predicts a `-201.996425 Hz` correction to the historical H--D 2S--8S isotope shift. The ordinary prediction is `-0.700628` combined sigma from the measurement; the extra interaction moves it to `-0.720112` sigma. The operator therefore earns no predictive credit, but its effect is 51.326 times smaller than the combined uncertainty, so the target cannot exclude it either. ## Preserved property tests Release 0.2.0 fits all pentane and hexane isomers, then predicts normal boiling and fusion temperature for all nine heptane isomers without refitting. A fixed carbon-count/Wiener/Zagreb model improves held-out boiling MAE from 8.554 K to 4.500 K but worsens fusion MAE from 27.574 K to 135.934 K. The unclipped 410.46 K n-heptane fusion prediction is retained as a counterexample. ## New projection engine For each carbon skeleton, classical multidimensional scaling embeds graph shortest-path distances into three declared coordinates. Centered vertex degree and graph eccentricity provide two declared hidden coordinates. These are mathematical conventions, not measured conformers or orbitals. With row states, the engine uses \[ X_5(t)=X_5(0)e^{t\Omega^T},\qquad X_3(t)=X_5(t)P^T,\qquad V_3(t)=X_5(t)\Omega^TP^T, \] where \(P=[I_3\;0]\) and \(\Omega=-\Omega^T\). The skew generator preserves every five-dimensional point norm. A declared visualization kernel, \[ K_{ij}=\cos(\phi_i-\phi_j) \exp[-\|x_i-x_j\|^2/(2\sigma^2)], \] shows constructive/destructive phase relationships. It is not a force law. The reference temperatures of all 17 C5--C7 isomers are also linearly encoded as two frequency coordinates. Exact decoding is deliberately paired with a shuffled-label control: the shuffled temperatures decode equally exactly. Therefore the encoder is a coordinate table, not a predictive explanation. ## Run ```bash python run_experiment.py python run_projection_inverse.py python -m unittest -v python independent_audit.py python independent_projection_audit.py python render_results.py python render_projection.py python run_water_harmonics.py python independent_water_audit.py python render_water_harmonics.py python run_water_oscilloscope.py python independent_oscilloscope_audit.py python render_water_oscilloscope.py python run_sun_water_eye.py python render_sun_water_eye.py python independent_sun_water_eye_audit.py python run_water_drop_acoustics.py python render_water_drop_acoustics.py python independent_water_drop_acoustics_audit.py python run_bubble_inverse.py python independent_bubble_inverse_audit.py python run_phase_harmony.py python independent_phase_harmony_audit.py python render_phase_harmony.py python run_harmony_observer.py python independent_harmony_observer_audit.py python render_harmony_observer.py python run_hydrogen_spectrum_gate.py python independent_hydrogen_spectrum_audit.py python run_multidimensional_observer.py python independent_multidimensional_observer_audit.py python run_hydrogen_transition_holdout.py python independent_hydrogen_transition_audit.py python run_hydrogen_isotope_gate.py python independent_hydrogen_isotope_audit.py python run_hydrogen_isotope_holdout.py python independent_hydrogen_isotope_holdout_audit.py ``` The principal new outputs are: - `outputs/property_rotation_coordinates.csv`: the declared frequency coordinates for all 17 reference molecules. - `outputs/latent_projection_results.json`: state, generator, projector, matrices, trajectories, and counterexample diagnostics. - `outputs/n_heptane_projection_trajectory.csv`: 65 frames of projected 3D positions and velocities. - `outputs/n_heptane_5d_projection.gif`: animated candidate projection. - `outputs/n_heptane_5d_projection_montage.png`: four fixed frames. - `outputs/phase_harmony_results.json`: the isolated-mode counterexample, collective reference features, distances, and evidence classification. - `outputs/phase_harmony_spectra.csv`: 2,401-bin normalized reference spectra. - `outputs/phase_harmony_continuum.csv`: 101 declared gas-like fractions and their recovered diagnostics. - `outputs/phase_harmony_diagnostic.png`: the collective spectra and continuous low-frequency coordinate. - `outputs/harmony_observer_results.json`: the eight-case taxonomy, 512-case validation, observer losses, gauge collision, and trajectory. - `outputs/harmony_observer_catalog.csv`: compact multi-axis class table. - `outputs/harmony_observer_validation.csv`: all frozen randomized checks. - `outputs/harmony_observer_trajectory.csv`: instantaneous and finite-exposure projections of the same five-coordinate motion. - `outputs/harmony_observer_diagnostic.png`: projected orbit, rank taxonomy, and exposure transfer functions. - `outputs/hydrogen_spectrum_gate_results.json`: the NIST Balmer reference, two-mode capacity proof, and bounded ratio calibrations. - `outputs/hydrogen_balmer_reference.csv`: the four frozen visible reference features used by the gate. - `outputs/multidimensional_observer_results.json`: dimension-capacity table, one-observer collision, observer-bank ranks, and reconstruction checks. - `outputs/multidimensional_vector_trajectory.csv`: explicit latent and projected position/velocity vectors for the frozen 4D, 5D, and 8D examples. - `outputs/hydrogen_transition_holdout_results.json`: the frozen two-line calibration, two-line holdout, Lyman-alpha extrapolation, table-rounding checks, and finite-prefix counterexample. - `outputs/hydrogen_transition_holdout_predictions.csv`: observed and predicted vacuum wavelengths and signed errors for both tested laws. - `outputs/hydrogen_isotope_gate_results.json`: the reduced-mass/modern-theory correction ladder, propagated uncertainty, finite-range operator sweep, and non-identifiability counterexample. - `outputs/hydrogen_isotope_operator_sweep.csv`: all 61 exactly fitted range/coupling pairs and their differing prospective 1S--3S corrections. - `outputs/water_harmonics_5d_projection.gif`: 64 H2O molecules with an animated synthetic latent-to-visible harmonic state. - `outputs/water_harmonics_montage.png`: four checked animation frames. - `outputs/water_harmonics_trajectory.npz`: coordinates, hidden phase and amplitude, tetrahedral links, and the calibrated box. - `outputs/water_harmonics_results.json`: assumptions, claim ceiling, and numerical checks. - `outputs/water_origami_oscilloscope.gif`: two distinct explicit-charge water microstates beside their identical observed polarization trace. - `outputs/water_origami_oscilloscope_snapshot.png`: checked dashboard frame. - `outputs/water_origami_oscilloscope.npz`: complete paired microstates, rigid-atom coordinates, field, and observed trace. - `outputs/water_origami_oscilloscope_trace.csv`: compact scope data. - `outputs/water_origami_oscilloscope_results.json`: assumptions, metrics, and claim ceiling for release 0.5.0. - `outputs/sun_water_eye_observer_60fps.mp4`: fixed-Sun, moving-water spectral caustic and finite-observer animation at 60 fps. - `outputs/sun_water_eye_preview.gif`: compact looping preview. - `outputs/sun_water_eye_snapshot.png`: checked full-resolution frame. - `outputs/sun_water_eye_observer.npz`: caustic frames, water surfaces, spectrum, dispersion, observer functions, and metamer control. - `outputs/sun_water_eye_results.json`: frozen assumptions, metrics, and claim ceiling for release 0.6.0. - `outputs/water_drop_acoustic_observer_60fps.mp4`: synchronized 60 fps ripple-and-pressure animation with 48 kHz mono audio. - `outputs/water_drop_acoustic_observer_48khz.wav`: normalized PCM playback of the constructed pressure candidate. - `outputs/water_drop_acoustic_preview.gif`: compact visual-only preview. - `outputs/water_drop_acoustic_snapshot.png`: checked full-resolution frame. - `outputs/water_drop_acoustic_observer.npz`: surface fields, pressure components, time grids, audio samples, and calculated reference values. - `outputs/water_drop_acoustic_results.json`: frozen assumptions, checks, counterexamples, and claim ceiling for release 0.7.0. - `outputs/bubble_inverse_results.json`: corrected-frequency band, exact observation-fiber endpoints, Jacobian rank, and claim ceiling. - `outputs/bubble_inverse_family.csv`: 401 radius/amplitude states sharing the same declared pitch and oscillating-volume scale. - `outputs/bubble_inverse_family.npz`: complete equivalence family, endpoint traces, and local sensitivity matrix. - `outputs/bubble_inverse_equivalence.png`: checked plot of the radius fiber and overlapping endpoint pressure traces. ## Identifiability boundary Three exact limitations are executable: 1. Any hidden-plane rotation uncoupled from the visible coordinates produces exactly the same 3D trajectory. 2. With fixed tick \(\Delta\), plane frequencies \(\omega\) and \(\omega+2\pi k/\Delta\) agree at every integer tick. 3. Any finite scalar property interval can be relabeled as a frequency interval and decoded exactly, even after independently shuffling the labels. 4. In the water network, an uncoupled hidden rotation produces exactly zero visible displacement; a visible wave requires an explicit coupling. 5. In the explicit-charge control, two different 192-coordinate molecular histories have exactly the same three-coordinate polarization trace. 6. In the spectral observer, two different nonnegative spectra produce the same three-coordinate CIE XYZ response. 7. An intensity-only renderer cannot recover absolute optical phase; changing the field phase while preserving magnitude leaves the image unchanged. 8. One observed bubble tone does not uniquely identify bubble radius and pressure: doubling radius and quadrupling pressure preserves ideal Minnaert frequency. 9. The same displayed ripple can be paired with different declared bubble radii because this release does not solve bubble entrainment. 10. A 60 fps picture stream cannot resolve the declared 2.17 ms air transit; the synchronized pressure is calculated independently at 48 kHz. 11. Even a full damped compact-source waveform does not identify bubble radius when effective thermodynamic exponent and volume amplitude are unconstrained: release 0.8.0 constructs an exact continuous family. 12. Two exactly fitted hydrogen transitions do not identify a continuation: `D(Delta2-Delta2(3))(Delta2-Delta2(4))` is invisible on H-alpha/H-beta for every `D` and changes H-gamma/H-delta. Consequently static melting and boiling values can constrain a declared forward model, but cannot uniquely reverse-engineer hidden rotations. A physical test needs a shared coupling chosen without the target property and a fresh observable, preferably a time-dependent or spectroscopic one. ## Evidence types - Measured/reference inputs: NIST phase-change values and published resistivities. - Constructed coordinates: graph MDS positions, centered degree/eccentricity hidden coordinates, and temperature-to-frequency labels. - Written mathematics: norm preservation, hidden-kernel non-identifiability, fixed-tick frequency aliases, and the relabeling argument. - Finite computation: 17 molecular states, a 65-frame n-heptane trajectory, a 150-frame spectral-caustic movie, a 180-frame/144,000-sample acoustic movie, a 401-state bubble inverse family, a four-feature hydrogen holdout, unit tests, and independent replay. - Physical hypothesis: that one such latent generator corresponds to actual molecular dynamics or hidden dimensions. - Not established: unique 4D/5D rotations, a universal fixed grid or tick, a new electromagnetic mechanism, or a theological cause. ## Hydrogen transition holdout interpretation For a transition from upper principal index `n_u` to lower index `n_l`, the frozen baseline and candidate are \[ \tilde\nu_0=R\Delta_2,\qquad \tilde\nu_1=R\Delta_2+C\Delta_4, \qquad \Delta_k=n_l^{-k}-n_u^{-k}. \] Only H-alpha and H-beta set the parameters. On the untouched H-gamma and H-delta lines, the candidate's vacuum-wavelength RMSE is 6.948567 ppm, versus 6.030008 ppm for the simpler baseline. The candidate is worse at both endpoints induced by the displayed NIST wavelength rounding. On the separate Lyman-alpha listed-intensity-weighted centroid, its signed extrapolation error is -11.248 ppm versus +7.727 ppm for the baseline. This is a bounded model rejection, not a complete precision-hydrogen calculation. The `Delta4` term is phenomenological and was not derived from an extra-coordinate Hamiltonian, field equation, coupling, gauge symmetry, or conservation law. Ordinary fine structure, recoil, QED, proton-size, hyperfine, line-shape, and external-field terms remain live mechanisms. A higher-dimensional claim must first derive a state-dependent operator and then beat the standard precision theory on fresh transitions. ## Water-harmonics interpretation The oxygen scaffold is a compact ordered tetrahedral control with the correct declared number density, not an equilibrated liquid. The generator \[ G=\begin{bmatrix}0&C\\-C^T&0\end{bmatrix} \] is skew-symmetric and therefore norm preserving. The animation renders the first three coordinates and colors each molecule by the phase of the last two. This makes the proposal inspectable while preserving the key distinction: mathematical consistency is not physical validation. Electricity, magnetism, fluid flow, and quantum dynamics are not simulated in release 0.4.0. ## Water-origami interpretation For molecular dipole directions (d_i(t)\in\mathbb R^3), the scope reports \[ P(t)=\frac{1}{N}\sum_i d_i(t)=A d(t),\qquad A=\frac1N[I_3\ I_3\ \cdots\ I_3]. \] With 64 molecules this linear map has rank three and a 189-dimensional ambient kernel. Release 0.5.0 constructs two unit-vector trajectories whose pairwise transverse components differ but cancel, giving identical (P(t)) for every stored time. The calibrated Debye response shows ordinary field/polarization phase lag; the two 3D movies show that this measured waveform is compatible with more than one microscopic motion. The construction does not identify which movie, if either, describes liquid water. ## Sun–water eye interpretation The source is fixed in direction and approximated by a nominal 5772 K Planck spectrum. The surface moves because of three declared finite-depth linear gravity-wave components. At each wavelength, the ordinary interface baseline computes \[ n_1\sin\theta_i=n_2(\lambda)\sin\theta_t, \qquad T(\lambda)=1-R_{\mathrm F}(\lambda), \] then bins transmitted ray energy on the underwater plane. The color observer integrates the resulting spectrum against three CIE color-matching functions. This is enough to render wavelength-dependent refraction and moving caustics. It is not enough to reproduce all that a particular human sees. The standard observer is a three-coordinate population surrogate, and the executable metamer pair proves that different spectra can have the same XYZ value. The engine also drops complex phase, so its output cannot reconstruct a wavefront or qualify as holography. Optical-frequency oscillations are analytically averaged; 60 fps describes only the displayed irradiance sequence. ## Water-drop acoustic interpretation For the ripple carrier, release 0.7.0 uses the ordinary finite-depth linear dispersion relation \[ \omega^2=(gk+\sigma k^3/\rho_w)\tanh(kh). \] For one declared entrained bubble it uses the ideal Minnaert relation \[ f_M=(2\pi R_b)^{-1}\sqrt{3\gamma P_b/\rho_w}. \] The airborne branch evaluates a compact-source surrogate at retarded time, \[ p(r,t)=\frac{\rho_a}{4\pi r} \frac{d^2V_{\rm eff}}{dt^2}(t-r/c_a), \] where the effective volume amplitude and damping are declared. This captures the expected pitch, delay, decay, and far-field spreading of the bounded candidate. It does not predict the nonlinear cavity that selects a bubble, or absolute sound level, multipath room response, hearing, splash droplets, or multiple-bubble acoustics. The 48 kHz audio grid and 60 fps picture grid are different observation samplers, not a universal tick of reality. ## Bubble inverse interpretation Release 0.8.0 adds the bounded small-amplitude stiffness relation \[ \omega_0^2=\frac{3\kappa(p_\infty-p_v)+2(3\kappa-1)\sigma/R}{\rho R^2}. \] It does not replace the earlier ideal carrier. It demonstrates how ordinary nuisance variables change the inverse. Keeping frequency, decay, arrival, distance, and oscillating volume fixed leaves a continuous family in radius, effective polytropic exponent, and fractional volume amplitude. Independent imaging or thermodynamic constraints are therefore required before acoustic data can be treated as a unique geometric reconstruction. ## Collective phase-harmony interpretation Release 0.9.0 distinguishes isolated normal modes from collective bulk dynamics. The same isolated H2O mode vector is deliberately held fixed across solid, liquid, and vapor thermodynamic controls, proving that a molecule-only descriptor cannot be a phase oracle. The collective branch uses \[ F(\omega)=f_gF_g(\omega)+(1-f_g)F_s(\omega), \qquad F_s(0)=0,\ F_g(0)>0. \] For the frozen bases, zero-frequency density identifies the *declared* mixture fraction exactly. This is a model identity, not a universal material law. The scan forms a continuum, and equilibrium phase still requires temperature, pressure, density, free energy, and an external phase criterion. The rendered families are constructed diagnostics rather than condensed-phase measurements or molecular-dynamics trajectories.