RH-1 — Mechanical Construction & Wiring

Instance note (2026-08-01, family restructure). This file is the build recipe for one realized instance — RH-1. The machine topology it instantiates lives canonically in The Replicator — Architecture, and element-level physics now has canonical homes in The Phonons and The Photons; this file keeps the instance recipes — what atoms go where in RH-1. Known internal inconsistency: §9–§10 still carry desktop-era two-cap geometry that conflicts with the free-standing v0.4 spec; to be fixed when this instance doc is next revised.

The medium split. The through-air scan / levitation band is attenuation-capped at a few hundred kHz — lower datarate, universal reach. The work band operates in the melt or a coupling medium, where the MHz regime and its datarate return. The panel's screen is tuned across both. This is why "max datarate" has two answers.

FIRST-LIGHT Dayton DAEX25 voice-coil exciter for the piezo driver (broadband, glue-on, free B₀; but low power density and a ~20 kHz ceiling); plain FR4 for the screen. Its one real advantage — the magnet's free B₀ — is recovered at the optimum by a thin permanent-magnet bias layer, or taken from the bore winding.

Should the panels be wired at all? A tempting simplification is to delete the six drive runs and let the caps' EM field excite the panels directly. Three ways that could work, ranked honestly:

• Direct EM→acoustic (EMAT). A coil plus a static B field drives eddy currents in a conductive face; the Lorentz force launches sound with no contact. Established NDT art MEASURED, and we already have the static field. But it is typically tens of dB less efficient than piezo — and this is the muscle channel, the one place we specifically bought k² ≈ 0.9. It puts the highest-power channel behind the lossiest coupling, dumps the loss as heat inside a sealed chamber, and makes acoustic phase a derived quantity of the EM field rather than something commanded — losing the control authority holographic sculpting depends on. Rejected as the primary path.
• Radiation pressure. Force ≈ P/c, so a watt of EM pushes ~10⁶× weaker than a watt of sound. Not a drive mechanism.
• Wireless power, local drive — the option worth keeping. Do not convert EM to phonons in the field; convert it to electricity at the panel. The panel carries a rectenna (already in the architecture, §6) and a local single-crystal driver does the acoustic work at full k². The EM carries power and the phase reference; the panel phase-locks to it — which is exactly the coupling-lock of §7, promoted from an initialization step to a load-bearing one. Keeps: no cable runs, sealed panels with no electrical penetrations, one distribution carrier. Costs: each panel needs local rectification, phase-lock and amplification — so the panel is cordless, not passive.

Baseline for RH-1 stays wired: it is simpler, it is the efficient path, and it keeps amplitude and phase directly commanded. The cordless panel is the credible second increment, and the honest reason to want it is sealing and assembly, not performance.

Holographic synthesis — the method that generates all of the above. The spiral grating, the graded phononic screen and the q-BIC leakage map are not three unrelated tricks; they are three outputs of one design procedure. Record the interference of the reference wave the feed actually launches across the surface, Ψ_ref, against the object wave you want in the build volume, Ψ_obj, and modulate the surface impedance by it: Z(r) = X₀ + M·Re{Ψ*ref·Ψobj}. That is the optical holography recording equation written onto an aperture instead of an emulsion; running the reference wave across the modulated surface reconstructs the object wave. The consequence for this build: the plate pattern stops being a shape we choose and becomes a pattern we compute — the same status the drive already has in the Field Compiler, now extended to the passive half of the boundary. Modulation depth M is the leakage rate, i.e. the q-BIC symmetry-breaking knob above; a frequency-dependent reconstruction is rainbow trapping. Both carriers use it: EM caps after the holographic leaky-wave art (Azad et al., Sci. Rep. 15, 2025 — omnidirectional conical beam with elevation scan, the right primitive for addressing a ring at a chosen height in a cylindrical volume), and the acoustic panels after the printed acoustic hologram already carried in the spec (Melde et al. 2016). MEASURED on both sides. Two refinements the art already supplies. (i) Make the surface impedance a tensor rather than a scalar — an anisotropic hologram — and circular polarisation falls out of the pattern itself, with no parasitic elements. That is the cleanest source of the handedness knob this architecture wants: chirality by impedance, not only by mirroring geometry. (ii) The method assumes a clean reference wave, which makes the launcher a first-class part, not the "radial ring feed" hand-wave in the table above. A spoof surface-plasmon-polariton (SSPP) feed gives a slow, tightly-bound surface wave whose wavenumber is set by corrugation depth — shorter reference wavelength means finer fringes, i.e. more independent holographic pixels on a Ø300 cap — and the accompanying waveguide-stripline launcher is measured at 142% impedance bandwidth (8–20 GHz) while explicitly not corrupting the radiation pattern, which is what a multi-octave, angle-defined aperture needs from its feed (Sci. Rep. 15, 1149, 2025). MEASURED The time axis (added 2026-07-22). Everything above is space-only holography: a static Z(r), one reference tone, amplitude and phase. Letting the surface modulate in time as well — Z(r, t) — has now been demonstrated as a space-time holographic metasurface antenna — spatiotemporal, heterodyne, multifrequency — with frequency conversion and holographic beamforming in the far field and multifrequency 2D/3D holographic imaging in the near field (Sci. Adv., 2026, adx7090) MEASURED. Three consequences land directly on this build. (i) It encodes the chord alphabet natively. Space-only holography holds amplitude and phase but is single-tone; a space-time hologram carries the frequency content too — what the .pattern format has been asking an aperture to store all along. (ii) Frequency conversion happens at the aperture, so one surface can accept one carrier and emit another — relevant to a machine whose whole difficulty is that its carriers live in different bands. (iii) Time modulation breaks reciprocity, which makes the ADD and REMOVE paths genuinely separable rather than two uses of one symmetric channel. Their near-field 3D imaging demonstration is, in form, the scan mode of this machine. Bounds, so this is not oversold: the space-time result is EM-only — frequency conversion within a band, not the acoustic↔EM transduction of §2; and the time axis is not free — a modulated surface needs an active switching element in every cell, driven at the modulation frequency, spending exactly the virtue that made the passive hologram attractive: no per-element electronics. So it is a tier, not a replacement — passive Z(r) where a fixed transform suffices, active Z(r,t) where frequency agility or nonreciprocity is worth the wiring. A hologram is recorded for one reference/object pair — multi-function needs multiplexing and pays crosstalk; a printed hologram is fixed, so steering is by frequency, not at will; and leaky-wave apertures trade aperture efficiency against taper (radiate too early and the far end is starved). It is a synthesis method, not new physics — it changes how the pattern is computed, not what the machine can do.

Why not co-locate the two carriers? The spec's earlier "dual-carrier doublet" put acoustic and EM on one site through a diplexer — a channel-count economy that gave up the launcher-disc geometry. Separating them by surface lets each hit its own optimum (spiral disc for EM, large panel for acoustic) and drops the diplexer entirely. The one thing co-location bought — both carriers overlapping at a point — is recovered where it actually matters: the caps' EM and the panels' acoustic overlap in the build volume, on the workpiece, not on the plate — multi-field addressing moves from the boundary to the target.

Revision: the Ø130 bore was sized for a capability the machine doesn't need — dropped, not just corrected (operator, 2026-08-03). The first pass through this section corrected the throat (Ø110→Ø220) but left the recorded Ø130 bore unquestioned. It shouldn't have been: neither of the two things the bore is credited with — the optical stem and feed transport — needs anywhere near that diameter. Keeping a structured (flying-doughnut) pulse collimated over the 300 mm plate-to-plate span needs a clear aperture of order 2–3 mm (Gaussian-beam estimate, w₀=√(λz_R/π) at z_R=300 mm). Fine-powder or melt-droplet transport at the target build rate (~200 g object in ~10 min) is a volumetric flow of ~0.08 cm³/s — a ~1 mm channel carries that easily even at a lazy 0.2 m/s. Neither number is near Ø130.

What actually sizes Ø130: the material-class table below credits the bore winding with "in-plate induction... ingot-bay crucible" — bulk induction melting of solid ingot-scale conductive feedstock, not fine powder. Induction levitation coils typically want an ID 1.5–3× the sample diameter for workable coupling; back-solving, a ~40 mm ingot at a generous 3× ratio gives a coil bore of ~120 mm — right at Ø130. That is almost certainly the real size driver, with the optical stem and powder transport riding along on an axis that was already there for free.

Ruling (operator, 2026-08-03): drop bulk ingot-scale induction melting from the shared plate/bore axis as a baseline capability. It was never separately justified — it rode in silently, oversizing three identical plate assemblies to serve a function that, on inspection, wants its own coil sized for its own sample, not a shared Ø130 axis. The bore shrinks to Ø12 (chosen: a 2 mm largest-feed-element budget × 4 for clog-avoidance margin, rounded to a practical drilled dimension — comfortably covers the optical stem too, and the flying-doughnut pulse's on-axis null means a feed stream riding the axis doesn't even clip the ring intensity). OPEN follow-up: if the machine still wants to melt ingots in-house, that needs its own independently-sized induction station, not a shared bore — not designed here. Ripple: desktop_replicator_hardware_spec.html §3/§6.0/ §6.1/§8 and replicator_architecture.html's transport-phase ladder credited the dropped capability and are being updated to match.

The throat is now sized by PZT packing, not bore clearance. With the bore this small, bore clearance no longer constrains the throat at all. Three PZT discs (Ø25 mm assumed — a small piezo element, not measured) arranged at 120° on a common throat must not overlap: minimum pitch radius = d/(2·sin60°) ≈ 14.4 mm. Adding a small margin gives throat r = 18 mm → Ø36.

The horn profile, refitted. Same construction as before — a quarter-ellipse meridian, tangent to the axial direction at the throat (PZTs push straight in), tangent to the plate plane at the mouth (wave exits parallel to the face) — but now throat r=18, mouth r=202 (radial throw 184 mm, more than double the earlier corrected-throat case), over the same 20 mm throat-to-mouth thickness taper. Ellipse semi-axes: 184 mm (radial), 20 mm (axial) — a folded meridian arc length of ≈187 mm inside only 20 mm of axial depth, an even more dramatic fold than before.

Checked against Webster again. Area ratio (mouth:throat, linear — it's an annulus) is now 202:18 ≈ 11.2:1; at the same 35 kHz cutoff the exponential-horn minimum length is still under 2 mm. The 187 mm folded profile remains nowhere near that floor — the gyroid's length is still doing acoustic-library work (R3), not loading work; that conclusion didn't change with the bore.

Radius compression, honestly reported again. Mouth:throat = 202:18 = 11.2:1 — this time overshooting the 6.7:1 φ-class reference point in R3, from the other side. First pass undershot at 1.84:1; this pass overshoots. Landing on opposite sides of the φ-class number across two independent geometry revisions is a reasonable argument that the fit tracks the actual constraints each time, not a thumb on the scale toward or away from φ.

Cell counts, updated. At the graded 2–5 mm cell size (viscothermal floor, R3), the annulus (mean radius ~110 mm, radial throw 184 mm) holds roughly 138–346 cells around the circumference and 37–92 across the radial throw depending where in the grade a given ring sits.

4 · The active back-wall — the "transporter sheets" (plan-B upgrade; baseline ships without)

The six panels sit between seven columns (40×40 mm) that carry the structure, the dense RX strips, and — on three of them — the service bundles. Each panel is a driven reconfigurable phononic + EM metasurface, a hex lattice of addressable cells, doing three jobs at once:

1. Boundary control — sets the acoustic boundary condition on the equator, shaping the field from the sides.
2. Passive mode expansion — the lattice expands the few column feeds into many spatially-addressable field DOF.
3. State display — the cells are emissive, so a panel shows its own drive pattern as a live hex wave. The wavy lit sheet is the boundary condition made visible — the same make-the-invisible-visible contract as the compiler's field view (RSW-1). This is also where power-up is read (§7).

5 · The windings — three contrawound pairs (rev 2026-07-30, supersedes the single 44-turn winding)

Each of the three plate assemblies carries one contrawound (enantiomeric torus-knot) winding pair on its Ø290 torus — two independent feed circuits per pair, always (R5; one both-handed wire on one amplifier is racemic rank-1, forbidden). These are the only wound conductors in the machine — the spiral gratings are printed, flat, and not coils. The pair does three jobs, selected by drive:

• Sum mode — the strong field: confined poloidal flux; induction levitation of small conductive droplets in the bore column — established art at that scale. MEASURED. (Bulk ingot-scale induction melting through this same coil is dropped, 2026-08-03, §3c — the Ø12 bore no longer has room for it; an ingot-scale melt stage, if wanted, needs its own independently-sized coil.)
• Difference mode — the fast field: the poloidal parts cancel, leaving an effective single-turn ring current — low-inductance, fast: the toroidal-pulse exciter at the coax-horn throat, and (three pairs stacked = six circuits) the traveling-wave bore lift of spec §4. MEASURED art (contrawound toroidal helix antennas)
• The potential port — a wound toroid confines B inside itself and leaves a structured external vector potential A. Whether that couples usefully to matter phase (beyond the measured Aharonov–Bohm / Josephson effects) is the program's phase-sector experiment. OPEN

The four-channel mnemonic, corrected again (2026-07-30): sound and microwave both live on the plates (muscle and ears share the aperture; panels are plan B), light is the fingertip and the eyes (the bidirectional bore stem), and the windings are the strong field and the experiment — sum mode powers, difference mode excites, and the potential-sector claim they carry is the one thing here still OPEN.

6 · The energy loop — harvest to coil

The boundary that shapes the field also recovers energy from it. Four measured harvest paths return power to the drive rail, which feeds the drivers and the bore windings — an ordinary open-system loop, no thermodynamic heterodoxy required:

7 · Power-up — initialization and coupling-lock

On power-up the coupled plate–winding system (plus plan-B panels where fitted) is brought to operating state in a fixed sequence — this is the honest reading of the transporter's white-glowing bars ("energy initialization"):

1. Self-calibration. Every element pings every other; the machine measures its TX→RX identity matrix and runs the empty-cavity reference (the same reference run the compiler takes before a scan). Without this matrix the field compile is blind.
2. Coupling-lock. The three plate assemblies and their contrawound windings are tuned into resonant lock — a tune-and-match, exactly like locking an NMR probe or a laser cavity — and the facing plate pairs settle onto the open-resonator mode (the focusing term, R8). A resonant handshake, established once at start-up; plan-B panels join the lock where fitted.
3. Cavity ring-up. The high-Q coupled mode is pumped to its operating energy over many cycles — the cavity is charged before the first verb.

The columns' vertical light strips (and the panels) display this sequence: calibrating, locking, ringing-up, ready. The glowing bars are not decoration — they are the initialization state, made visible.

8 · The signal chain — element to electronics

With the carriers separated by surface, there is no diplexer: each element rides a single band on a single line. Two simple chains, one per plate type.

9 · System wiring — where the bundles run

Status note (2026-07-30): the routing below is the desktop-variant (two-plate) wiring plan; it generalizes to the free-standing stack by adding the middle assembly's bundle (routes with the lower plate's) and the storage-deck bundle (routes direct to base). "Panels" rows apply only where plan-B panels are fitted.

Bundles leave each surface as one 8-conductor shielded run (drive pair · RX pair · power · ground · shield/aux). The lower cap connects straight into the base deck; the upper cap's run, its bore-winding pair, feed riser, and crown power descend three of the seven columns. The panel drives and column RX strips run down all seven.

Interlock, unchanged: a Hall sensor at the sealed detent gates all drive power above metrology level. Front glass open → only mW-class listening is electrically possible.

10 · Build sheet — for the model and the first chassis

Modeler's note: the caps read as the amber-lit bullseye (spiral face, lit bore); the six back panels as hex-tiled sheets glowing with their live boundary state; the columns as dark bars with white light strips (the power-up indicators of §7). Two round pads on the axis, a faceted glowing back wall, a glass door — the transporter chamber, built to function.