asserted_by: arek

certainty: HIGH

direction: upgrade

direction: downgrade

modality: theorem

note: Wording corrected after X-0002. The paper says 'everywhere negative'; the equation gives non-positive, with zeros on the axis and outside the wall.

assumptions: classical general relativity, no quantum corrections

assumptions: energy density as measured by Eulerian observers

assumptions: the shape function of the original 1994 construction

invalid_outside: semiclassical or quantum regimes, where the pointwise energy conditions are known not to hold in general

metric_family: alcubierre

status: GREEN

text: 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.


certainty: MODERATE

challenged_by: redteam straz

assumptions: generic Natario-class warp drive metric: intrinsically flat spatial 3-slices with unit lapse, so all nontrivial physics sits in the extrinsic curvature

assumptions: the flow field obeys fall-off conditions at spatial infinity so the warp field stays localizable; the authors note this is certainly true if the ADM mass vanishes

assumptions: subsidiary conditions are imposed to exclude trivial cases, so that the metric describes a warp drive rather than, for example, the Painleve-Gullstrand form of Schwarzschild spacetime

assumptions: regularity: Christoffel symbols at worst piecewise once differentiable, hence a Riemann tensor at worst piecewise continuous with delta-function contributions

assumptions: standard general relativity; for modified gravity the paper claims only that the geometric convergence conditions 'will place very strong constraints', not that no rescue exists

invalid_outside: configurations that do not satisfy those subsidiary conditions

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


asserted_by: klaudiusz

certainty: LOW

code: indirectness

modality: interpretation

note: Re-scoped after X-0004. Search Q-0001 logged the citation sweep that dated the debate to 2026.

assumptions: the literature surveyed is not exhaustive

invalid_outside: modified-gravity settings, which have not been surveyed at all

status: DRAFT

text: 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.


asserted_by: tenzor

assumptions: the tanh shape function of eq. 3, with wall thickness identified as 1/sigma

assumptions: r_c = r_s in eq. 16 — no longer an assumption: derived independently in compute/verify_energy_density.py and recorded as C-0006

assumptions: classical general relativity, no quantum corrections and no backreaction

assumptions: no quantum inequality constraint is applied, so these are a lower bound on the difficulty rather than an estimate of it

invalid_outside: any construction that is not the original 1994 metric with this shape function; in particular Van Den Broeck-type volume tricks and Natario-class metrics are not covered

text: 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.


text: 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.


note: Resolves open question Q1. Three rival readings of r_c (R, rho, x) leave non-zero residuals.

assumptions: the metric of eq. 5 with unit lapse and flat spatial slices

assumptions: a GENERAL shape function f(r_s) — the result does not use the tanh profile

invalid_outside: metrics whose spatial slices are not intrinsically flat, where the three-Ricci scalar no longer drops out of the Hamiltonian constraint

text: 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.


modality: bound

assumptions: the Ford-Roman quantum inequality for a free massless scalar field in four-dimensional Minkowski spacetime, applied on a scale where the region can be treated as locally flat

assumptions: a single quantised free scalar field; the bound is not established for arbitrary matter content

assumptions: the piecewise-linear shape function S-0007 uses, whose slope is 1/Delta across the whole wall

assumptions: the sampling-time choice t_0 = alpha * 2 Delta / (sqrt(3) v_b) with alpha << 1

invalid_outside: matter content or field states to which the Ford-Roman inequality has not been extended, and regimes where the local-flatness approximation used to import the flat-space inequality fails

text: 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.


text: 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.


text: 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.


note: The reduction is GEOMETRIC, not energetic: it changes how much is needed, not where energy comes from. The requirement is still for negative energy, and the author's own follow-up lists high energy densities, Planck-scale curvature radii and naked singularities as unresolved.

assumptions: the modified metric ds^2 = -dt^2 + B^2(r_s)[(dx - v_s f dt)^2 + dy^2 + dz^2], which is NOT the Alcubierre metric

assumptions: a bubble whose exterior surface area is microscopic while the interior spatial volume is macroscopic

assumptions: classical general relativity plus the Ford-Roman quantum inequality as the author applies it

invalid_outside: the original Alcubierre construction, to which none of this transfers; and any regime where curvature radii of order the Planck length invalidate the semiclassical treatment

text: 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.


note: Was 'the single most load-bearing opening in the corpus'. CLOSED by X-0009: independent recomputation (compute/hawking_ellis_scan.py) confirms the VdB warp wall carries Type IV stress-energy — no rest frame, no invariant energy density — for 87-99 percent of the wall. The theorem-coverage gap in the claim text remains true and remains irrelevant. Auditor addition (X-0019): SSV's adjacent caveat reads 'There are other problematic issues with both of these models' — the concession was never an endorsement.

text: 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.


note: Notable because it is the author of the largest energy reduction saying where he thinks the remaining possibility lies, in the same year.

invalid_outside: the constructions S-0011 actually reviews: the original Alcubierre geometry and its immediate modifications; the follow-up's verdict is about superluminal bubbles in GR+QFT generally, but its computations are Alcubierre-based

text: 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.


note: Also found: the equation extractor missed VDB's equations because he wraps eqnarray in \newcommand macros (\bear/\eear). Extractor gap, logged in Plane.

assumptions: his stated parameters alpha=1e17, R~=D~=1e-15 m, R=3e-15 m

assumptions: region II treated as static via x' = x - v_s t at constant velocity, so rho = R3/16pi with K_ij = 0

assumptions: the three-Ricci derived symbolically from Christoffel symbols for B^2(dr^2+r^2 dOmega^2)

assumptions: two unrelated C2 interpolating profiles standing in for his unstated one

invalid_outside: non-constant v_s, where the region II slice is no longer static and the extrinsic curvature terms return

status: RED

text: 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.


note: Numbers computed twice independently: workflow track A (wf_3e70bff5-044) and this repo artifact; they agree. D-T kinematics from CODATA-2022 masses, byte-checked against physics.nist.gov in the workflow record.

assumptions: textbook special relativity, no exotic physics

assumptions: one-way distance 4.394928 ly from the SIMBAD parallax of alpha Cen A fetched at run time (742.12 +/- 1.4 mas, Hipparcos bibcode)

assumptions: 1000 t dry ship, stated as an assumption and cross-checked against open-loop consumables

assumptions: ideal conversion: all released energy becomes directed exhaust kinetic energy — every fuel number is therefore a floor

invalid_outside: beamed or staged architectures, which remove the exponential and are costed separately in the same artifact

metric_family: minkowski

text: 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.


note: compute/fh_ssv_identity.py proves symbolically, for a fully general phi: the FH 'hidden geometric structure' (sum of second-order principal minors of the Hessian) is identically (1/2)[(tr H)^2 - tr(H^2)] = 8*pi*rho of the Hamiltonian constraint — the exact quantity SSV analyse. The papers disagree interpretively, not computationally.

assumptions: the Fell-Heisenberg ansatz: unit lapse, flat induced 3-metric, time-independent purely irrotational shift

assumptions: 'positive energy' means the energy density measured by co-moving Eulerian observers, and only that

invalid_outside: any statement about the full WEC over all observers, which the paper itself concedes fails

metric_family: other

metric_family_note: Fell-Heisenberg irrotational-shift solitons; neither Alcubierre nor Natario class

text: 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.


assumptions: the three 2026 papers S-0003/S-0004/S-0005 as posted on arXiv

assumptions: citation counts as returned by OpenAlex on 2026-08-07, URLs in the workflow record

invalid_outside: any weight these findings would carry after independent peer review, which none has yet

text: 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.


note: Numbers and fetch URLs in the workflow record (wf_3e70bff5-044, track D). The proper-motion/orbit component is now orbit-solved in compute/ab_orbit.py (C-0019): 24-35 au over 22-88 yr, bounded by the orbit's size — superseding track D's rough 27-83 au.

assumptions: the SIMBAD parallax fetched at run time plus two further catalogued parallaxes for the same star (VizieR I/131A and I/311), embedded with provenance

assumptions: arrival ambiguity compared at 0.1c cruise

invalid_outside: targeting done from a single adopted Gaia-grade parallax, which is the fix this claim calls for

text: 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.


note: The negative-control test was written expecting Type I on the motion axis 'by symmetry' and the computation refuted the expectation: zero density with irremovable flux is still Type IV. The test now records that correction.

assumptions: fourth-order finite-difference Einstein tensor, validated: Minkowski to 1e-27, Alcubierre Eulerian density against the C-0006 analytic formula to 5e-9, Schwarzschild vacuum to 1e-6 of curvature scale

assumptions: comoving coordinates at constant v_s, where the metric is static

assumptions: Type IV detected as a complex eigenvalue pair of the mixed stress-energy at relative tolerance 1e-6

assumptions: transfer to the microscopic VdB wall argued from scale invariance of the dimensionless metric functions and verified as stability across sigma*R = 5 and 50

invalid_outside: non-constant v_s, and any wall so thin that semiclassical gravity itself fails (Planck-scale curvature radii, which VdB's own follow-up lists as unresolved)

text: 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.


note: Replaces Track D's rough 27-83 au estimate with orbit-solved 24-35 au: the error is BOUNDED by the orbit's size rather than growing without limit, which the rough estimate missed. Solver validated: closure after one period 2.4e-13 au.

assumptions: orbital elements from Pourbaix & Boffin 2016 (S-0012), HARPS+ESO column, transcribed from the paper's Table 1 — a LaTeX table the canonicaliser strips, so the values cannot be quoted through the evidence pipeline (extractor gap PDB-26)

assumptions: sky-plane error metric; the radial component is folded into the distance-uncertainty budget of C-0017

assumptions: departure epoch 2026.6; the scale of the error is epoch-robust, its digits are not

invalid_outside: epochs where the Pourbaix-Boffin solution itself is superseded

text: 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.


note: Root-cause chain worth remembering: canonicaliser strips '$n=80$' from prose AND the extractor (pre-PDB-26) missed the macro-wrapped equation, so the profile was invisible to every tool — and 'invisible' was misread as 'unstated'. Two silent gaps compounded into a false published finding.

assumptions: his stated parameters alpha=1e17, R~=D~=1e-15 m, R=3e-15 m

assumptions: region II treated as static via x' = x - v_s t at constant velocity, so rho = R3/16pi with K_ij = 0

assumptions: the three-Ricci derived symbolically from Christoffel symbols for B^2(dr^2+r^2 dOmega^2)

assumptions: two unrelated C2 interpolating profiles standing in for his unstated one

text: 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.


assumptions: the Fell-Heisenberg ansatz: unit lapse, flat induced 3-metric, time-independent purely irrotational shift

text: 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.


text: 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.


note: Closes PDB-21 and the FH/Lentz/B-M leg of PDB-24. The VDB leg was priced in C-0010/C-0020.

assumptions: the corpus as of 2026-08-07: S-0013/S-0014/S-0015 for the proposals, S-0001 for the rebuttal, S-0003 for the Type classification

assumptions: 'unrebutted in the corpus' means exactly that — an absence in twelve-plus-three sources, not in the literature at large

invalid_outside: any future peer-reviewed WEC-for-all-observers demonstration for a superluminal configuration, which is precisely what the corpus lacks

text: 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.


assumptions: Fewster 2012 lecture notes (S-0016) as a review of the QEI field

assumptions: the distinction between minimal and non-minimal scalar coupling, and the non-existence of spacelike-averaged QEIs, as stated there

invalid_outside: claims that a non-minimal coupling actually DELIVERS a physical warp drive — that is unproven and unpriced; this claim only locates where the bound's assumptions are soft

text: 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.


assumptions: Everett-Roman 1997 (S-0017) and Fewster 2012 (S-0016) as the corroborating sources

assumptions: 'the same class of conclusion' means QI-type magnitude/duration limits on negative energy, not the identical numeric bound

invalid_outside: the specific 10^2 v_b L_Planck coefficient, which remains from Pfenning-Ford alone and is not independently reproduced here

text: 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.


note: The wall chart's 'open door' now has two named routes, both beyond standard GR+QFT: (1) non-minimal scalar coupling softening the QI (C-0024); (2) modified gravity redefining the classical energy conditions (this claim). Independent recomputation would require a Bach-tensor implementation in numgr — schedulable, filed as a new issue.

assumptions: Conformal (Weyl) Gravity, a fourth-order theory based on the conformal action, NOT standard general relativity

assumptions: the Hartle shaping function rather than Alcubierre's original

assumptions: 'no exotic matter' is a statement about the Eulerian T^00 being non-negative; all-observer WEC is not demonstrated and DEC is conceded to be violated

invalid_outside: standard general relativity, under which C-0001/C-0006 show the density is non-positive; and any test of the full WEC over boosted observers, which the paper does not perform

metric_family_note: Alcubierre metric evaluated under Conformal Gravity field equations (Bach tensor source)

text: 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.