BandReal v1.1: A Digital-Space Reference Implementation and Verified Evidence for the Direction–Structure Divergence Hypothesis

BandReal v1 proposed a reality operating layer that projects BandOS's non-semantic internal physics -- directional intent, structural memory, and predictive proto-structure -- into physical AR space, defining a Reality Mapping R_t = Φ(U_t, X_t), per-modality projections (directional, structural, intuition-based), worldline assignment for persistent AR objects, and three evaluation metrics (A_dir, A_struct, S_obs). No implementation accompanied that paper. This report closes that gap in digital space, ahead of any physical hardware, for two of its three metrics and for its worldline-persistence claim, reusing three pieces of existing project infrastructure (a raf_laa Field as the substrate, the D-Operator as the following dynamics, and StructureCache as the worldline ledger) without writing a new physics layer. The motivating question was concrete: if a VLM/LLM guides a physical fabrication process (e.g. a 3D printer) from visual direction alone, can it look correct while a structural defect goes undetected? We reproduce exactly this failure mode digitally -- a guideline-following trajectory that skips one waypoint scores A_dir=0.9989 (direction still looks natural) while A_struct collapses from 1.0000 to 0.0000 (the realized transition matches no edge of the intended path graph) -- giving concrete quantitative support to the hypothesis that an independent structural check catches defects a direction-only check misses. We further verify, on a separate five-worldline scenario, that persistence across sessions, shared observation by independent users, and rejection of unplaced ("hallucinated") anchors all hold under a file-backed ledger, and, on a third scenario, that worldlines confined to a real FieldMap's graph edges never traverse a non-existent path. We document one honest scope gap between the first and third scenario: the first has no literal environment graph G and stands in an intended-edge set in its place, a gap the third scenario closes by supplying a real one. Separately, motivated by a question about whether a fixed FieldMap anchor drifts under Earth's rotation (it does not, since geographic coordinates are defined in an Earth-fixed rotating frame), we implement and verify a differential-correction scheme in the style of Differential GPS: a single noisy measurement at a known-accurate "ground zero" node reduces mean positional error from 0.4154 to 0.0411 (a systematic bias of magnitude 0.4134 is nearly eliminated, leaving only irreducible independent noise at scale 0.03), and averaging independent corrections from N peers reduces the residual error by a measured factor close to the 1/sqrt(N) scaling law's prediction (0.1219 measured against 0.125 theoretical at N=64) -- an emergent crowd-sourced-correction property that was not an explicit design goal. Finally, motivated by a live-AR use case (a rendered effect tracking a moving hand rather than a fixed anchor), we show that a dynamic worldline needs an identity source independent of position: reusing the same Ed25519 primitive WHFE v0.2 (https://doi.org/10.5281/zenodo.22980658) uses for its Origin Signature, an impostor positioned only 0.0361 from a genuine worldline's last known location -- close enough to pass any proximity-only check -- is correctly rejected once identity is checked against the worldline's expected signer rather than its coordinates.