EMWave Technical Manual Geometry Discovery Observatory

1. Purpose of the observatory

The instrument is designed to make wave superposition, state-space geometry and atlas growth visible and measurable. A signal source can be the manual CH1–CH6 generator, browser/tab audio, a local audio file or a hybrid mix. The active source stream is transformed into geometry, measured as fingerprints, and classified inside the Discovery and Atlas workflow.

• Signal synthesis: define controlled sine components by frequency, phase and amplitude.
• Signal-source routing: switch between Manual, Live Audio, Microphone, File Playback and Hybrid without changing the laboratories.
• Time-domain inspection: observe the resulting waveform and channel contributions.
• Spatial field interpretation: inspect a normalized plane-wave field model in 3D.
• Spectrum laboratory: identify dominant components, beat spacing and frequency ratios.
• Vector Phasor Laboratory: inspect active channel phasors, resultant magnitude and cancellation behavior.
• Geometry laboratories: visualize Lissajous, topology, resonance landscapes, constellations, fingerprints and atlas regions derived from the active signal model.
• Measurement inspection: evaluate RMS, Vpp, THD, crest factor, form factor, phase relations and signal classification.
• Worker foundation: prepare measurement frames off the UI thread where supported, with safe fallback behavior.
• Diagnostics: verify module availability, DOM wiring, renderer health and regression-sensitive browser behavior.
• Auditory monitoring: listen to the generator/audio source path with speaker-safe output scaling.

6. Digital Scope Laboratory · time domain

The digital scope displays all active channels and the summed result Σ. It is the primary laboratory for waveform shape, phase interaction, constructive interference, destructive interference and beat patterns.

11. Spectrum Laboratory

The Spectrum Laboratory shows analytic bins derived directly from the configured sine components. It is not a noisy sampled FFT display. When multiple active channels share the same frequency, their amplitudes are vector-summed using phase information before display.

12. Vector Phasor Laboratory

The Vector Phasor Laboratory displays each active channel as a rotating vector. The vector angle is calculated from θ = 2πft + φ, using the configured frequency, phase and amplitude of the channel. Same-frequency channels produce a conventional static phasor relationship when RUN is stopped; different-frequency channels rotate at their own angular rates during RUN mode.

13. Orbital / Lissajous Polarization Laboratory

The Lissajous laboratory is a dedicated analytical laboratory for signal-state geometry. It plots X = E(t) against a quadrature state derived from the same active channel configuration. The trace therefore originates from the real signal model rather than from decorative particles or arbitrary animation.

Integer frequency ratios such as 1:1, 2:1, 3:2, 4:3 or 5:4 form closed or slowly repeating figures. Non-harmonic ratios evolve without exact closure. The trace now uses an age-colored phosphor layer: older samples remain dimmer, newer samples become brighter, and the live marker reports the instantaneous X/Y state. The topology layer marks detected crossings and reports loops, winding, symmetry, eccentricity and path length so experimental setups can be compared as geometric structures, not only as waveforms. The Resonance Landscape view extends this idea by scanning a phase / frequency-ratio field and revealing where stable, high-area Lissajous geometries form ridges, islands and valleys.

14. Resonance Landscape Explorer

The Resonance Landscape is a geometric parameter-space map. Instead of showing only the current Lissajous figure, it scans a controlled region of CH2/CH1 frequency ratio and relative phase. Each point in the map represents a synthesized Lissajous state generated from the same signal engine.

15. Geometry Fingerprint Laboratory

The Geometry Fingerprint Laboratory gives the current signal-derived structure a compact measurable identity. Fingerprints encode closure, symmetry, crossings, winding, area and complexity so discoveries can be compared, ranked and classified automatically. It combines area, closure, crossings, loop estimate, winding number, symmetry and a combined complexity score into a short fingerprint ID.

• Fingerprint ID: stable hash-like label generated from the current geometry metrics.
• Area / Closure: compact measures of occupied orbit size and periodic return quality.
• Cross / Loops / Wind: topology indicators used for comparing geometric families.
• Sym / Complex: symmetry average and combined structural complexity score.

16. Experiment Constellation Laboratory

The Constellation Laboratory maps experiments as points in normalized geometry space. Each point is derived from area, closure, crossings, loops, winding number, symmetry and complexity, so the view compares relationships between experiments rather than only displaying one waveform.

• Atlas regions: labels such as Reference Basin, Closure Ridge, Harmonic Flower Field, Winding Island, Symmetry Plateau, Open Drift Sea and Topological Outlier summarize the active geometry neighborhood.
• Nearest neighbors: the LIVE point is connected to the closest known experiments by normalized Euclidean distance.
• Interactive loading: clicking a constellation point loads that experiment through the same control and URL-state path as the Experiment Library. Ctrl-click / Cmd-click copies a direct share URL for that experiment.
• Purpose: helps locate families, unusual cases and nearby experiments for guided exploration.

21. Showpiece Experiment Library

The Showpiece Experiment Library now acts as a guided laboratory layer, not only as a preset loader. Each entry loads a complete operating state: active channel count, frequency, phase, amplitude, time span, polarization mode and laboratory mode. The cards also describe purpose, observation targets, difficulty, demonstration value and expected laboratory response.

• Purpose: accelerate training, demonstrations and laboratory discussion without random presets.
• Reproducibility: loading an experiment updates the same URL state as manual operation, including source mode and audio quality where the preset defines them, so the resulting setup can be shared or archived.
• Analytical coupling: experiments are selected to show clear relationships across the scope, Spectrum Laboratory, Vector Phasor Laboratory, Topological Lissajous Laboratory, Resonance Landscape, Discovery Engine and 3D field view.
• Favorites: the star control stores preferred experiments locally in the browser using localStorage.
• Filters: category buttons reduce the list to fundamentals, three-phase, Lissajous, resonance landscape, special ratios, harmonics, orbital, engineering, showpieces or favorites.
• Expected response: every card indicates which laboratory should show the most important behavior before the experiment is loaded.

22. Special Ratio Geometry experiments

The Special Ratio Geometry EXP group contains reproducible two-channel experiments based on Fibonacci pairs, Lucas-related pairs, prime pairs, deliberate detuning and rational approximations of irrational constants such as √2, √3 and the golden ratio. These presets load directly into Discovery mode with orbital polarization so local geometry-space variants can be scanned immediately.

Discovery candidates support the full workflow: select a marker, use Load Discovery to apply its frequency, phase and amplitude values to the live instrument, then use Save Discovery when the candidate should become a persistent atlas / EXP entry.

• Important accuracy note: browser controls use finite numeric frequencies, so golden-ratio and square-root examples are rational approximations, not mathematically exact irrational ratios.
• Fibonacci / Lucas pairs: useful for long-cycle periodic figures that approach golden-family behavior while remaining exactly reproducible.
• Prime pairs: useful for long repeat lengths, slow beat-like structure and dense state-space fingerprints.
• Detuned harmonic cases: useful for comparing a known ratio island, such as 4:3, against a nearby drifting variant.

23. Technical assumptions and model boundary

The instrument uses a normalized analytical plane-wave representation. It is not a full electromagnetic field solver and does not model antenna geometry, boundary conditions, conductive losses, material permeability, dielectric dispersion, near-field coupling or calibrated RF power density.

• Good for: coherent wave relationships, phase studies, harmonic structure, polarization concepts and teaching demonstrations.
• Not intended for: certified RF exposure analysis, antenna design sign-off, EMC compliance, finite-element simulation or calibrated power measurement.
• Laboratory rule: validate absolute voltage, current, phase, field strength and power with calibrated measurement equipment.

22. Example experiments

23. Signal Measurement Laboratory

The Signal Measurement Laboratory adds compact electrical readouts for the summed waveform Σ. The values are calculated from the same sampled scope signal and analytic spectrum bins used by the instrument, so the panel remains synchronized with the visible time-domain and frequency-domain laboratories.

The phase table reports each active channel relative to CH1. For channels with a different frequency, the displayed angle is an initial phase offset φ0 rather than a fixed phase relationship over time.

21. Measurement Worker Foundation

The instrument now includes an optional Web Worker layer for calculation-heavy measurement preparation. The worker can build timestamped measurement frames containing waveform summary, scope metrics, spectrum bins, phasor data, Lissajous metrics and advanced signal measurements without blocking the main UI thread.

• Main thread: owns DOM interaction, Plotly rendering, WebGL scene updates, audio control and user events.
• Worker thread: owns DOM-free measurement-frame preparation using the same core and measurement modules.
• Worker bridge: initializes the worker, tracks status, exposes requestMeasurementFrame() and provides fallback-safe orchestration.
• Status: the footer Worker readout and diagnostics panel show whether the worker is ready, active or in fallback mode.

22. Developer Observatory

The instrument includes a hidden developer observatory for release checks, diagnostics, profiling and CSS architecture review. These tools are disabled by default and are controlled by the small DEV checkbox in the footer. When DEV is enabled, the DIAG, PERF, PROFILE and CSS buttons appear in the header. When DEV is disabled, all developer panels close and the normal operator interface remains clean.

23. PROFILE · runtime microscope

PROFILE extends the basic performance view with a deeper runtime microscope. It is designed to guide future optimization with measurements instead of guesswork.

• Overview: ranks the most expensive operations, counts calls, shows worst spikes and reports frame-budget distribution.
• Timeline: displays a rolling last-10-second activity history for Scope, Field, Plotly, Workers, Animation and DOM domains.
• Baseline: stores a local performance reference and compares current runtime behavior against the saved baseline.
• Worker profiler: reports worker latency, worker compute time and queue-related timing when worker tasks are active.
• Export / copy: allows profile snapshots to be copied or exported for development notes and regression comparison.

24. Built-in verification tools

The online instrument includes built-in verification paths for quick browser-side checks, diagnostics, performance inspection, profiling and stylesheet auditing. Development-only documents and standalone test pages are intentionally not shipped in the public package.

25. Symbol Observatory

Symbol Observatory maps text and number systems into the existing signal engine. The v1.4.6 Number Wheel Observatory and Math Flow Explainer adds a node-and-transition view for digital-root, Rodin-cycle and modular arithmetic paths, so operators can see the actual number walk behind the generated frequencies. The Universal Symbol Alphabet supports Latin A-Z/a-z, digits 0-9, Greek Α-Ω/α-ω, mathematical signs, punctuation and an explicit space separator. Symbols can be written directly into CH1-CH6, compressed into one channel as a sentence signature, distributed as word channels, or reduced into a compact fingerprint so the normal Scope, 3D, Spectrum, Lissajous, Fingerprint and Atlas workflows can inspect the generated geometry.

• Encoding methods: Linear Symbol Set, Prime, Fibonacci, Golden Ratio, Musical 12-TET, Pythagorean, Just-Ratio Symbol Set, Symbol Index Proportional, Binary Weight, Morse Weight, Digital Root, Rodin Cycle 1-2-4-8-7-5 (Index) and Modular Doubling 2ⁿ mod 9 (Text Order). These define how each symbol index becomes a frequency before folding into the 1 Hz–20 kHz instrument range.
• Number geometry: Digital Root, Rodin Cycle and Modular Doubling are treated as neutral modular-arithmetic pattern generators. Rodin-cycle mode is symbol-index based; modular-doubling mode is text-order based. They are useful for symbolic topology, closure, winding and visual comparison, not as physical energy claims.
• Base frequency: defines the seed carrier. Changing the base moves the whole symbolic structure while preserving the selected alphabet mathematics.
• Targets: Symbols → Channels maps visible letters directly; Sentence → One Channel compresses a whole sentence into CH1; Words → Channels assigns up to six words to CH1–CH6; Sentence Fingerprint creates a compact multi-channel signature.
• Advanced targets: Ratio Geometry Glyphs uses frequency ratios and phase offsets for Lissajous-style shape alphabets; Phase Symbol Set keeps frequency nearly fixed while phase carries the symbol; Amplitude Symbol Set emphasizes amplitude coding; Fourier DNA Channels distributes a sentence checksum and slot signatures over six harmonic channels.
• Mapping modes: First Symbols maps direct symbols; Word Superposition chooses representative symbols; Sequential Prep reserves a safe UI path for later animated streams.
• Channel output: APPLY SYMBOL MAP sets channel count, channel frequencies, phase angles and amplitudes. CLOSE returns the laboratory panel to Spectrum so Symbol Observatory does not occupy the work area when not needed.
• Publishable DNA: EXPORT WAV renders the active Symbol DNA texture into a mono 44.1 kHz WAV file for external testing, documentation or publishing. SAVE DNA stores a reproducible JSON profile with the text, encoding, base, target, mode, mapping and audio texture.
• DNA Library: saved profiles can be loaded later, renamed, duplicated, deleted after confirmation, exported as a full JSON library or imported again. The selected entry displays its text, encoding, target, mode, base frequency, creation date and audio-DNA summary.
• Clear behavior: CLEAR SYMBOL DNA disengages the special symbol texture so normal channel/audio operation is restored without closing the Observatory.

26. Version history

This manual is written for operation, not as a development diary. Detailed revision notes are kept outside the Help page so the documentation stays light, readable and timeless.