The antigravity machine,
designed honestly.

What is being asked — and what is not.

In this framework the monitored medium admits two regimes: an active branch producing the attractive interaction identified with gravity, and a passive branch producing a weakened, cancelled, or sign-reversed one (the passivity theorem). Could a finite apparatus locally force the medium from active to passive, and thereby suppress or reverse gravity?

This page does not construct such an apparatus. It asks the narrower question: if branch control were possible, what would the controller have to pay — and could the process generate free energy? The answer obtained in the model:

Operational meaning of "antigravity".

Not levitation by electromagnetic, aerodynamic or mechanical force — a modification of the gravitational interaction itself. With U_A the matter–medium interaction energy in the active branch and U_P in the controlled passive branch, the object of study is ΔU_grav = U_P − U_A: positive means attraction weakened or cancelled; negative means the controlled branch releases interaction energy. The relevant quantity is always the energy difference between two explicitly defined configurations — never an absolute potential (§9).

The four assumptions that define the hypothetical machine.

A1 — Controllable branch. A local control field s(x,t) exists, with s = 1 the active branch and s = 0 the passive one. The microscopic observable to which s couples remains to be identified — this is the unbuilt button.
A2 — Relaxation. Uncontrolled, a passive region heals toward the active branch at the audit rate γ; τ_γ = γ⁻¹.
A3 — Energy conservation. Controller, medium, matter, and dissipation Q ≥ 0 form a closed ledger: ΔE_ctrl + ΔE_medium + ΔU_grav + Q = 0.
A4 — No hidden reservoir. Every pump, sensor, boundary actuator and feedback loop is included in E_ctrl.

What the toy model shows: the battery result.

The numerical branch-flip experiment gives, for the tested protocol, |ΔE_medium| ≃ |ΔU_grav| (four digits): the interaction energy gained is paid by an opposite change in the medium. This kills the naive cycle — switch gravity off, raise a mass, switch it back on, lower and extract, repeat. With the controller and the medium in the ledger, W_extracted ≤ W_supplied, with equality only for an ideal reversible protocol; any real controller adds Q > 0.

Minimum switching work, and holding power.

Switching. A reversible transition obeys W_switch ≥ |ΔU_grav|; in general W_switch = η_sw·|ΔU_grav| with η_sw ≥ 1. The toy is consistent with η_sw ~ 1 for the tested finite model and path — nothing proves this survives in a macroscopic, spatially localized system.

Holding. Against healing at rate γ, the dimensional estimate is P_hold ~ η_hold·γ·|ΔU_grav|, with η_hold depending on protocol, region volume and geometry, the active/passive interface, the degree of reversal, the dissipation mechanism, and the medium's correlation length. This is an estimate, not a derived equality. The first-principles object would be a controlled open-system generator ℒ = ℒ₀ + ℒ_ctrl and the stationary controller power P_ctrl = Tr[H·ℒ_ctrl(ρ_ss)] — uncomputable until ℒ_ctrl is specified.

The Earth benchmark — corrected.

Removing a kilogram's full gravitational coupling to the Earth (reference at infinity) costs GM_⊕/R_⊕ ≃ 6.26×10⁷ J/kg. Under the electron anchor ħγ = 3.7 keV: γ ≃ 5.62×10¹⁸ s⁻¹, hence

The idealized complete-decoupling estimate is then P_hold ~ γ·GM_⊕m/R_⊕ ≃ 3.5×10²⁶ W per kilogram ≈ 0.92 L_☉. This figure is internally consistent with the 3.7 keV anchor. Complete gravitational decoupling from the Earth would require an astronomical power.

Why this is not yet the cost of levitation.

The benchmark removes the full Earth–object binding energy relative to infinity — not automatically what it costs to hold an object one metre up (ΔU_local ≃ mgh). A local mechanism might scale as P_local ~ γ·mgℓ where ℓ is a refresh length the theory does not yet determine, and the possibilities differ wildly: ℓ ~ h (pay only the displacement), ℓ ~ R_⊕ (modify the whole coupling), ℓ = a medium correlation length, or a cost scaling with controlled volume or boundary area — in which case the simple formula fails entirely. Consequently m|φ|γ must not be presented as a universal antigravity-power law. The invariant statement is:

The potential-zero problem.

The Newtonian potential is defined up to a constant, so m|φ|γ is meaningless until the reference configuration is fixed (the benchmark uses φ(∞) = 0). A local device must be described by a measurable difference ΔU = m[φ(x₂) − φ(x₁)] or a fully defined change in the source–probe functional. This is not an external nicety — it is the framework's own gauge principle: only billing differences are physical (the U(1) structure of the minimal-coupling derivation). Any theory in which the absolute value of φ were observable would have to explain why the shift freedom is absent; this one does not claim it.

No free propulsion either.

Suppressing the force on the probe does not create a reactionless drive. The momentum ledger must close over probe + source + medium + controller + radiation and boundary stresses: d/dt (ΣP) = 0. A force computed on the probe alone is insufficient. The hypothetical device is an interaction-control machine, not a demonstrated reactionless drive.

What n108 establishes — and what it does not.

Established, in the toy: a branch change can reverse the interaction's sign; changing the branch changes the medium's stored energy; the two compensate for the tested protocol; a naive cyclic engine yields no free energy; fast relaxation makes continuous control extremely expensive.

Not established: that the branch exists in the physical vacuum; that any apparatus can control it; spatial localization; a stable active/passive boundary; universality of the modified interaction across all forms of matter and energy; that P = γ|ΔU| is exact; that the full binding energy is the relevant scale for levitation; controller stability at macroscopic scale; momentum and back-reaction closure; the existence of any realizable device.

The next decisive calculation is not hardware — it is the controller.

A minimal model: ℒ = ℒ_active + ℒ_control + ℒ_boundary, with a finite controlled region, an explicit actuator coupled to a specified observable, an active–passive interface, source and probe degrees of freedom, and complete energy and momentum ledgers. Required outputs: ρ_ss, P_ctrl, F_probe, F_source, Q as functions of region size, source distance, coupling and γ. Pre-registered gates: ΔE_total − W_external = 0 and ΔP_total = 0 over a full control cycle. Only after these gates pass would the word "machine" be earned.

Conclusion, boxed the way the record demands: the model contains no obvious free-energy antigravity cycle; a controllable branch reversal would behave as an extremely costly interaction-control process, not as an energy source; and the existence and microscopic implementation of that control remain open. Companions: the energy no-go · the four faces · the ΔH = ΔU test · the original note.

The controller, designed by the adversary: the Detuning Capsule.

The independent reviewer took §13's challenge and wrote the design (n184). Its first move reframes the whole problem: the control variable is the local detuning. The induced interaction is Ω_eff(Δ) = −g²Δ/(Δ² + κ²/4); the vacuum sits at Δ₀ < 0 (attraction). A controller that shifts Δ_local = Δ₀ + δΔ walks three regimes: Δ < 0 attraction · Δ = 0 null gravity · Δ > 0 repulsion. So the least dishonest machine is not a shield and not repulsion — it is a null-gravity capsule approached gradually: 90% → 50% → 10% → null. The theory demands the dimming precursor: a device that jumps to reversal without passing continuously through the dimming curve falsifies the mechanism.

The one idea that could beat the astronomical bill: §8's holding-power table assumed brute-force repumping every 1/γ. The reviewer's alternative is coherent cancellation — a phase-locked drive s(t) = s₀cos(γt + φ) that dresses the monitor (Floquet engineering, the EIT/dynamical-decoupling family) toward a stationary Δ_eff = 0 state, paying for losses rather than rebuilding the interaction each cycle. It is the only remotely plausible route below the gigawatt-per-kilogram floor — and it imports a hard test: the dressed state must stay stable and its noise must not cook the payload.

Buildable today (Version A): two trapped ions + one lossy mediator with tunable Δ, sweeping through zero: J_eff(Δ) ∝ −g₁g₂Δ/(Δ² + κ²/4) — controllable attraction, null, and reversal in an engineered monitored medium. This is prediction 22's analog sign-flip, now with the reviewer's explicit protocol. Not antigravity — a test of whether the sign mechanism behaves as claimed. Version B (the true capsule) requires the unbuilt physics: the actuator coupling ordinary apparatus to the vacuum's auxiliary mode — the button problem, still the design's missing organ.

Five signatures that must move together (any one alone is an artifact): (1) g_inside/g_outside tracks the detuning curve continuously, reversing only through zero; (2) the audit knee weakens inside the capsule — gravity dimming without the decoherence channel dimming contradicts the theory; (3) clocks inside shift consistently with the force change; (4) the boundary acquires the reaction momentum — no reactionless motion; (5) the fluctuation spectrum changes with the reservoir. On (5), n183 sharpens the prediction: at Gaussian level the matter-coupled spectra are branch-independent — the change must appear in the monitor output channel, not in payload heating.

Ten kill conditions are preregistered in n184 — no observable shifts Δ; unstable unregularized branch (n183: passed); payload heating above bounds; no stable bubble boundary; controller power diverging with refinement; gravity changing without the knee changing; composition dependence; unbalanced energy/momentum; shieldability; analog sign-flip failing the susceptibility formula. Verdict as the reviewer wrote it: the theory supplies the control variable (Δ_local) and the strategy (dress toward Δ_eff = 0); it does not supply the actuator. The realistic invention today is the analog experiment; the capsule is a blueprint for a missing interaction. The full design →