Testing a Multilevel Oscillatory Hierarchy: A Finite-Work Toy Model, Negative Results, and Open Physical Bridges

Earlier work introduced a multilevel oscillatory hierarchy (MOH) as a conceptual architecture in which a lower cosmological order may collapse and renew from a history-bearing residue while a higher-order sector continues along its own trajectory. Here we test that architecture with a staged finite-work toy model. The construction does not yield a physically closed or predictive cosmological renewal model. The R channel carries the working concept of inherited sensitivity: prior history can change the later realized response of an otherwise comparable residue. In the tested model, history-correlated residue changes first-passage accessibility relative to matched shuffle controls. Within an expanded-state description, however, the implemented inherited sensitivity is representable as history-dependent hidden-state dynamics; the present test therefore does not establish independent physical content or predictive superiority for the R/H decomposition, and its physical carrier and readout law remain open. Within the chosen reciprocal-energy/positive-mobility model class, a reciprocal higher-order/formation functional generates formation work dynamically and satisfies an exact work identity. A scale-free relational map from premetric proto-organization to a traceless homogeneous shape variable provides a conditional candidate for newborn intrinsic geometry, with dimensionality and coframe promotion kept explicit as assumptions. When a positive homogeneous geometry burden is inserted into the same common work account, the predeclared strict no-retuning gate fails at every tested positive load at the frozen formation thresholds. This rejects the tested friction-like homogeneous-geometry bridge, not geometry emergence in general. No mechanism is obtained that generically produces a low-Weyl cosmological initial state: the homogeneous construction remains conditional and the inhomogeneous low-Weyl extension remains blocked. Subsequent normalization and stress-closure audits show that direct canonical continuation of the higher-order coordinate into the newborn scale factor fails, already-accounted higher-order work cannot be spent again, and the post-emergent mean stress required for accelerated expansion remains undetermined. The paper therefore reports a controlled model-development attempt, preserving both consistency checks and negative results, and identifies the independent physical bridges that would be required before stronger cosmological claims are justified.

The companion reproducibility package v1.1, dated 2 October 2026, contains retained source records and executable scripts, frozen protocols, archived and recomputed machine-readable outputs, a claim manifest, a provenance/status ledger, and SHA-256 checksums.

The archive distinguishes exact executable reruns, source-data audits, and analytic audits. Some historical simulators are not available as complete executable code; the README and verification report identify those limits. The package supports the retained claims and frozen negative results rather than the entire exploratory development history.

Data and code archive DOI: 10.5281/zenodo.23110906.