The Vertical Ladder: Observer-Invariance as a Criterion for Distinguishing Intrinsic from Projected Structure [Unfinished working draft]

UNFINISHED WORKING DRAFT — Author status notice, 26 October 2026 This manuscript is an unfinished, exploratory working draft. Its analyses and interpretations remain subject to source verification, reproducibility checks and substantive revision. Claims of validation, universality or mechanism in the original manuscript should be treated as provisional rather than established conclusions. Outstanding work: The observer-invariance scoring and its examples require reconciliation with their underlying analyses and subsequent corrections. The proposed hierarchy of intrinsic structure remains an exploratory framework. The original deposited file is retained for provenance. This notice updates the record status; it does not certify completion of a new analysis. Original description (historical; subject to the notice above) How do we distinguish structure that exists in a system from structure created by the act of measuring it? We propose a falsifiable criterion: observer-invariance, operationalised as OI(m, r), where m counts independent methodologies and r counts independent replications that recover the same structure. We ground this in three empirical case studies. In constrained random walks, principal component analysis fabricates topological features that vanish under four projection-free tests (41,000 experiments). In radical pair magnetoreception, sensitivity shelves survive across nuclear configurations but their fine structure is parameter-dependent. In human EEG, a theta-to-alpha frequency ratio near 1.68 persists across three datasets (414 subjects), three brain regions, and three spectral methods (ANOVA: F(2, 411) = 0.87, p = 0.42). These cases form a vertical ladder of increasing observer-invariance that correlates with independently measurable constraint depth. We propose three independent proxies for constraint depth—number of interacting components, optimisation history, and functional consequence of violation—to avoid circularity, and draw implications for identifying genuine neural correlates of consciousness.