The Joint Observer Manifold: Field Geometry in the Relationship Between Observers

SFE-05. 12b proved that a self-referential observer cannot detect its own field regime through its estimation residual — the information is structurally erased by the matched filter. SFE-05. 13b showed that this information survives in position space, recoverable by a decoupled null-predictor channel. This work addresses the next question: where does field information live when no individual observer can access it? We construct a two-observer architecture in which both agents use null predictors (no adaptive estimation) and measure their cross-correlation in a sliding window. We show that the joint observer manifold — the geometry of the shared state space (xₐ, xb, ρₐb) — encodes field confinement strength k in a form inaccessible to either observer individually. Four results are established: Early detection. Cross-correlation between two null-predictor observers detects field confinement 80 cycles before either single observer crosses its own threshold (k = 0 → k = 1, extended domain). Geometric collapse. The joint manifold undergoes a measurable shape transition: background geometry is volumetric (eigenvalues 0. 41, 0. 39, 0. 20) ; burst geometry is linear (eigenvalues 0. 89, 0. 06, 0. 04), with the dominant axis aligning entirely with the correlation dimension (weight = 1. 000). Relational gap with confirmed ordering. Control experiments (SFE-06. 6) at 0. 001 resolution confirm that ρ dominance locks at k ≈ 0. 002 while spatial geometry has not collapsed by k = 0. 030, establishing a minimum relational gap of Δk > 0. 028. This is not a resolution artifact. e₂/e₃ asymmetry is stable under all tested configurations. The ratio e₂/e₃ rising from 1. 36 to 3. 41 is empirically stable under both observer offset (δ ∈ 0, 2, 5, SFE-06. 6) and window size (W ∈ 20, 40, 80, SFE-06. 7), with spread < 0. 003 across all tested configurations. Within this architecture, W behaves as a lens rather than a dimension: varying it does not change the eigenvalue structure. Whether this stability constitutes a true field invariant in the analytical sense is the primary open question for SFE-07. The collapse axis is purely relational: at k ≥ 0. 05 the dominant principal component has spatial weights |wₓₐ| ≈ |wₓb| < 0. 04 and correlation weight |w_ρ| = 1. 000. Within the tested configurations, field confinement is encoded in the coupling between observers, not in their individual positions, and the eigenvalue structure is stable across observer offset and window size.