A pre-registered numerical realisation of a two-body O(λ) response in a Skyrme-type substrate mode

We report a methods-level result about one frozen numerical realisation of a two-body first- order response problem in a Skyrme-type model with a scalar substrate field. Under a pre- registered protocol, the realisation produced, at coarse resolution, a repulsive O(λ) sector sign under the frozen orientation convention on all ten candidate separations, at three lad- der levels [A2]. At the level prescribed for the next stage, the frozen alternating Schwarz iteration did not converge within its declared sweep budget: the interface data grew geo- metrically by a factor of about 1.880 per sweep [B1]. Quarantined diagnostics show that the background-stride axis is not the driver and that the degradation across the three sampled angular resolutions is monotone; the contraction on which the coarse solve rested is there- fore not robust under the sampled refinement [C3]. A continuum mechanism and a continuum spectral-radius limit are NOT DERIVED. We then show that a direct solution of the identical discrete equations reduces to a small interface system whose operator can be assembled explicitly [F1]; measured at three levels, it exhibits at the finest level the pre-registered evi- dence pattern of an iteration-only obstruction — spectral radius 1.880 with no evidence of proximity to singularity in the bare nodal 2-norm — while the well-posedness of the direct system is NOT DERIVED [F4]. The natural half-domain reduction of the same problem is closed at order λ⁰ because the frozen one-body background violates the exchange condition on the genuine fixed set of the exchange map [E3]. A refinement-stability gate for the direct branch is shown to be not operationalisable as a pass/fail gate by the present construction, so that physical evaluation of that branch is not licensed [G2]. Finally we trace, from source, a coefficient clamp in the frozen implementation and characterise its entry into the discrete operator on three paths; its causal responsibility for the non-convergence is NOT DERIVED in either direction [I8]. The decision not to continue the direct branch is a programme-level allocation decision, not a mathematical rejection of it and not a physical result [J1]. No m4 value, m4 sign, Link-2 sign, channel-energy sign or Axiom-V classification exists; Output-0 items 5–6 are NOT EXECUTED, NOT REACHED; G4-2 is NONE DERIVED / NOT REACHED — BLOCKED.