Operationalising the Shear–Form Coupling Ratio χ: A Pre-Registered Numerical Probe of Conjectured Dimensionless Invariance Across Mechanochemical and Phase-Transformational Systems

The companion philosophy-of-science paper on shear as efficient cause and internal transformation grammar as formal cause introduces a dimensionless ratio χ = τeff/τF relating applied shear to an internally defined form-threshold stress, and raises the question of whether χ admits a characteristic value across heterogeneous systems. The main paper is explicit that the value 2√2, which appears in that discussion, is a conjectured structural coefficient rather than an empirically established invariant. The present technical note pre-registers a numerical protocol designed to test that conjecture honestly. Operational definitions of τeff, UF, γc, Veff are fixed in advance for three case classes: Silicon under non-hydrostatic compression and shear; The zirconium α–ω transformation under tensorial-kinetic loading; Shear-activated molecular mechanochemistry. Decision criteria for convergent, clustered near 2√2, and disconfirmed are specified in advance and apply uniformly across cases. Cases are partitioned into a confirmatory set (all quantities extracted under primary rules) and an exploratory set (including cases requiring fallback rules), with the main convergence judgment based on the confirmatory set alone. A sensitivity-analysis protocol reports the full range of χ consistent with the admitted operationalisation variability, including rule-switching variation between primary and fallback extraction. Results are deferred to v1.0. This record is the pre-registration stage: Sections 1–6 and 9 of the document are locked at v0.2 and will not be revised in subsequent versions except for clerical corrections. Companion to the main paper: Takagi, T. "Shear as Efficient Cause, Structure as Formal Cause: Internal Transformation Grammar in Shear-Activated Matter" (working draft, target venue: Synthese).