The wall chart
Which theorem blocks each route
The programme's founding question, answered as a landscape. Every superluminal route is blocked by a theorem we recomputed independently; two doors remain open but only beyond standard physics; and the slow ship is an engineering problem.
The founding construction. Recomputing the energy from the metric gives a scaling law |E| ∝ v²R²/d, and about 188 solar masses of negative energy for a 100-metre bubble at light speed with a millimetre wall. The quantum inequality then forces the wall thinner than 10⁻³³ metres, and the requirement rises to roughly 10²⁰ galaxy masses.
A geometric modification hides a macroscopic pocket behind a microscopic bubble, cutting the energy by 32 orders of magnitude — a result we independently reproduced from the paper's own stated profile. But the bubble wall's stress-energy is Hawking-Ellis Type IV: it has no rest frame, so there is no observer for whom its energy density is even defined, let alone positive. We confirmed this by direct computation.
Several proposals claim warp geometries sourced by purely positive energy. Each proves positivity only for one family of observers (the co-moving Eulerian frame); a sufficiently fast but still sub-light observer sees negative density. The rebuttal in the corpus shows this explicitly, and the Fell-Heisenberg text itself concedes the weak energy condition is violated in compact regions.
A genuinely positive-energy warp shell — but explicitly sub-light, described by its own authors as a shell of matter that 'requires propulsion'. It is a rocket in geometric dress, not a faster-than-light route.
In Conformal Gravity — a fourth-order alternative to Einstein's theory — the Alcubierre metric with a particular shape function has non-negative energy density, needing no exotic matter. Two caveats keep it open rather than solved: Conformal Gravity is a speculative theory, not accepted physics; and the positivity shown is again the single-observer density, with the dominant energy condition conceded to be violated. We verified the setup is non-degenerate (the metric is not conformally flat); reproducing the full sign needs the fourth-order Bach tensor, which is scheduled.
The quantum inequality that forbids the thick wall is derived for a free, minimally-coupled scalar field. A non-minimally-coupled field has stress-energy that can violate the null energy condition, and no such bound exists for some averaging schemes. This is a specific, named place an escape could live — but nobody in the corpus has shown it actually delivers, and it is not yet priced against the 20-order-of-magnitude gap.
No theorem blocks a slow ship. A 4-person round trip to Alpha Centauri at 0.2c takes 43.9 years; the crew ages 43.1. The obstacle is the rocket equation — carried fuel ranges from a million kilograms (ideal antimatter) to 10¹⁵ kg (fusion with only charged products usable), because two-body kinematics puts 80% of fusion's yield into a neutral neutron no nozzle can direct.