The Sign Correction

The first draft of this paper contained a critical sign error. It is corrected here for the record.

8.1 — What was wrong

The first draft wrote the rotation velocity as v²(r) = GM(r)/r + Λc²r²/3. The Λ term was positive, adding to v². This is wrong. Λ > 0 is repulsive. The correct equation, as derived from AP08, is v²(r) = GM(r)/r − Λc²r²/3. Λ subtracts from v². It makes rotation curves decline faster, not slower. This error was identified by external review. You hold the correction. Λ is still present in the field equations; it is simply not the mechanism for flattening rotation curves. The mechanism is the tension field of ε.

8.2 — What changed

The mechanism changed entirely. The first draft attributed flat rotation curves to the Λ term in the Einstein equations; this paper attributes them to the tension field of ε between 0 and 1. Λ is a constant, repulsive, the same everywhere. The tension field is the substrate’s coherence, attractive, topology-dependent. The two are different things.

8.3 — What survived

The conceptual architecture survived intact: gravity = condition of 0, c = condition of 1, the galaxy as the eye, the pipe and the room, the central black hole as topological anchor, the transition scale a₀ = cH₀/(2π), Tully-Fisher v⁴ ∝ M, the claim that dark matter is not needed. What changed was the physical mechanism — not Λ (a repulsive constant), but the tension field of ε (attractive topology).