Findings

For the Alcubierre metric, the energy density seen by Eulerian observers is non-positive everywhere and strictly negative wherever the shape function varies off-axis, so the weak and dominant energy conditions are violated.

Generic warp drives violate the null energy condition under plausible subsidiary conditions.

For the original Alcubierre metric with the tanh shape function, the total negative energy scales as |E| ~ v_s^2 R^2 / d, where R is the bubble radius and d the wall thickness. There is no wall thickness that makes the requirement small.

A 100 m Alcubierre bubble travelling at v_s = c with a 1 mm wall requires about 3.74e32 kg of negative mass-equivalent, that is roughly 188 solar masses. The requirement is astrophysical in scale, not engineering.

The symbol r_c in Alcubierre's energy-density equation denotes the spherical radius r_s. Recomputing the density from the metric via the Hamiltonian constraint reproduces the published equation exactly, and only, under that reading.

The quantum inequality constrains the Alcubierre bubble wall to at most about 10^2 v_b Planck lengths, roughly 1.6e-33 m at light speed — about 10^-18 of a proton radius.

Under that constraint a 100 m warp bubble at light speed requires of order 10^20 galaxy masses of negative energy. Recomputing it independently from the paper's own eq. 22 and eq. 26 gives 3.47e20 galaxy masses against the 3e20 the paper states.

No energy source addresses the warp-drive requirement, because the requirement is for negative energy density and every source of energy produces positive energy. Even with the quantum inequality set aside entirely and a full 1-metre wall allowed, a 100 m bubble at light speed still needs of order a solar mass of NEGATIVE energy.

Van Den Broeck's modification reduces the total negative mass for a macroscopic warp bubble from of order 1e62 kg to of order a few solar masses (~1e30 kg) — about 32 orders of magnitude — by keeping the bubble's exterior surface microscopically small while expanding the spatial volume inside it. The author states it satisfies the Ford-Roman quantum inequality.

The strongest recent no-go result for warp drives does not cover the Van Den Broeck construction. Santiago, Schuster and Visser (2022) state that the van den Broeck spacetime 'cannot simply be dismissed out of hand' and must be addressed with different techniques, because it lies outside the Natario class their theorem treats.

Van Den Broeck's own follow-up concludes that superluminal warp bubbles are unlikely within general relativity plus quantum field theory, while stating that SUBLUMINAL bubbles remain an open possibility and that microscopic ones might even occur naturally.

For a 4-person Sol to alpha Centauri round trip, special relativity is not the obstacle — the rocket equation is. Round-trip coordinate time is 175.8/87.9/43.9 years at 0.05c/0.1c/0.2c, with crew time shorter by only 0.13/0.50/2.02 percent. At 0.2c a 1000 t ship needs, as floors, 1.25e6 kg of annihilation fuel, 1.17e10 kg of D-T at the full mass defect, or 1.08e15 kg of D-T if only charged products are steerable — the spread is driven by two-body kinematics putting 79.76 percent of the Q-value into the neutral neutron. Stopping at the target multiplies the flyby fuel by 11.4, not 2, because rapidity adds and mass ratios multiply. At 0.05c open-loop consumables alone exceed the dry mass.

Navigation to alpha Centauri A is dominated by catalogue disagreement, not by relativity: three published parallaxes for the same star imply distances spanning 4673 au, which at 0.1c is 270 days of arrival-time ambiguity — 1.7 times the 161-day relativistic clock divergence accumulated over the entire 88-year round trip. The image aimed at is also 4.4 years old on arrival. A jump-targeting computation therefore needs, in order: one adopted Gaia-grade parallax, an AB-barycentre orbit solution, and only then relativistic corrections.

Independent recomputation confirms the Type IV certification of warp-bubble walls: at v_s = 0.5 the Alcubierre wall's stress-energy carries a complex-conjugate eigenvalue pair — no rest frame, no observer-invariant energy density — over 90.6 to 99.7 percent of the wall across two sigma*R scales, bracketing S-0003's stated 87-99 percent. On the motion axis the density vanishes but an irremovable flux keeps the point Type IV. The classification is scale-stable and the Van Den Broeck f-wall is metric-identical to the Alcubierre wall, so it transfers; the VdB B-transition is Type I, as a static region must be. The energy-condition escape recorded in C-0011 is therefore closed in practice: the construction the 2022 theorem missed fails the same physical requirement by direct computation.

Targeting alpha Centauri A with the catalogue state vector extrapolated linearly misses by 24 to 35 au over coasts of 22 to 88 years from a 2026.6 departure — a planetary system's width, from geometry alone — because component A orbits the AB barycentre with a 79.91-year period and eccentricity 0.524. The full Kepler solution that removes the error costs one Newton iteration per epoch.

Whether warp-drive configurations necessarily violate the energy conditions is an open and actively contested question in the peer-reviewed literature, disputed continuously from 2021 through 2026; it is not settled in either direction.

Independent recomputation confirms the Van Den Broeck construction IN FULL, correcting C-0013: region IV reproduces to 1% with our closed form, and — under the profile the paper does state (B = alpha(-(n-1)w^n + n w^(n-1)) + 1 with n = 80, E-0032) — the region II sign split also reproduces to 1%: -1.380e30 vs the printed -1.4e30 and +4.865e30 vs +4.9e30 kg, sign boundary w = 0.9815 vs the printed 0.981. C-0013's 'profile-dependence' finding rested on a false premise (the profile was invisible because the canonicaliser strips inline math and, at the time, the extractor missed macro-wrapped equations) and on a C^1 counterexample outside the paper's stated twice-differentiable class. Residual anomaly, unresolved: VDB's printed POINTWISE peak values appear inconsistent with his own stated profile under recomputation, even though his integrated totals reproduce.

The Fell-Heisenberg positive-energy result is narrower than its abstract: positivity is proven for the Eulerian energy density only, within a restricted ansatz. On the full WEC their text states both halves in consecutive sentences, and both must be carried together: 'No amount of modification to the configuration could get rid of these WEC-violating regions' — immediately followed by — 'it may still be possible to satisfy the WEC in the presented configurations too, given sufficient modifications', conditional on another cited configuration's claimed WEC compliance. The paper concedes present WEC violation while leaving a conditional door open; it does not lift the negative-energy requirement for a superluminal jump today, and it does not close it forever.

The three 2026 warp papers are one correlated source: same single author, arXiv preprints without journal DOIs, zero citations each on OpenAlex (reproduced live with a positive control: S-0001 shows 45). Within that caveat, S-0003 certifies the Van Den Broeck walls as Hawking-Ellis Type IV — no rest frame — ABOVE a Type-I to Type-IV transition at v_s ~ 0.36 (the value lives in a source macro; the canonical text loses it), with Alcubierre and Natario walls Type-IV dominated at all speeds; and S-0005's 'no exotic matter' drive is, in its own words, causal, subluminal, and steeply but positively costly.

The positive-energy warp programme, priced on its own terms: Lentz (2020) asserts superluminal solitons from purely positive energy densities; Santiago-Schuster-Visser (2022) rebut Lentz, Bobrick-Martire and Fell-Heisenberg collectively — each 'merely asserts the existence of one sub-class of timelike observers for which the energy density is positive', which does not establish the WEC — and exhibit boosted observers who see negative density. What survives unrebutted in the corpus is explicitly SUBLUMINAL: Bobrick-Martire's positive-energy class ('any warp drive requires propulsion') and the 2024 constant-velocity solution, which satisfies the energy conditions by adding a positive-ADM matter shell. Consistently, the 2026 certifier finds the irrotational Lentz/Fell-Heisenberg-class geometry globally Type I while vortical walls are Type IV. The surviving programme is subluminal shells with shift — rockets in geometric dress — and superluminal positive energy remains asserted, contested, and unpriced.

The quantum-inequality wall bound rests on assumptions a real configuration could target, and the corpus names them: the Ford-Roman inequality is derived for a free, minimally-coupled, massless scalar field on a locally-flat patch. Fewster's lectures show the bound is not universal — a NON-minimally coupled scalar has stress-energy whose extra terms are 'not of the sum of squares form', so 'even NEC can be violated', and no quantum energy inequality exists at all for smearings over spacelike surfaces. So the honest statement is not 'the QI forbids warp drive' but 'the QI as applied by Pfenning-Ford forbids it for a minimally-coupled scalar sampled along a timelike worldline'; a non-minimal coupling or a genuinely different field content is the specific, named place an escape would have to live.

The quantum-inequality obstruction to warp drive has independent corroboration in the corpus beyond the single Pfenning-Ford paper. Everett & Roman (1997), analysing the Krasnikov tube — a different superluminal geometry — apply the same Ford-Roman inequalities and reach the same class of conclusion, explicitly noting the parallel Pfenning-Ford warp result; and Fewster's lectures derive quantum energy inequalities from first principles as 'remnants of the classical energy conditions' that quantum field theory does satisfy. The wall bound C-0007 therefore no longer rests on one paper: the inequality it uses is a reviewed, independently-applied result, which lifts the single-source downgrade even as the specific 10^2 coefficient remains Pfenning-Ford's.

A concrete escape from the negative-energy requirement exists in the corpus, but only by leaving standard general relativity. Varieschi & Burstein (2012) recompute the Alcubierre metric in Conformal Gravity — a fourth-order theory whose field equations replace Einstein's — and find that with the Hartle shaping function the Eulerian energy density T^00 is non-negative, so no exotic matter is needed. The result is stated by its authors as strictly conditional: 'if CG is the correct extension of GR'. Two limitations the corpus makes visible: conformal gravity is a speculative alternative to GR, not the accepted theory; and the positivity demonstrated is of the Eulerian T^00, the same one-observer quantity Santiago-Schuster-Visser showed is necessary but not sufficient for the full weak energy condition, while the paper itself concedes the dominant energy condition is violated.

Independent recomputation confirms the headline of the Van Den Broeck reduction: region IV reproduces to 1% with our existing closed form, the total requirement at his parameters is solar-mass scale (~1e30 kg), and the reduction versus the unmodified 100 m bubble is ~32 orders of magnitude. His +/- sign split within region II does NOT reproduce: it depends on the unstated interpolating profile, and a half-cosine profile yields no negative transition energy at all. The profile-independent negative energy is region IV's -6.2e29 kg, which no choice of B removes.

The Fell-Heisenberg positive-energy warp result is narrower than its abstract: positivity is proven for the Eulerian energy density only, within a restricted ansatz, and the published text itself concedes that the full weak energy condition is violated in compact regions and that no modification of the configuration removes those regions. It therefore does not lift the negative-energy requirement for a superluminal jump.

The three 2026 warp papers in the corpus are one correlated source, not three: the same single author, all arXiv preprints without journal DOIs, each with zero citations on OpenAlex as of 2026-08-07. Within that caveat, S-0003 certifies the Van Den Broeck walls as Hawking-Ellis Type IV — no rest frame, no invariant energy density — and energy-condition violating for all observers; and S-0005's 'warp without exotic matter' is, in its own words, a causal SUBLUMINAL reaction drive with steep but positive cost.