Apeiron: A Bounded Scientific-Feasibility Construction for a Fundamental Cosmological Carrier

Apeiron proposes one fundamental carrier whose states and organizations could underlie effective spacetime and matter descriptions. This article consolidates a bounded mathematical and physical feasibility result for one local realization, Variant B, and its uniquely named witness O049. The inherited construction supplies a common smooth homogeneous solution, a correlated renormalized source and state binding, admissible local dynamics, and a qualitative causal scalar and transverse-traceless response with a finite local stability bound. Its common feasibility domain is conformal time η ∈ [−1/125, 0] and wave number k ∈ [5/8, 5/4]. For the narrower non-flat θ-source problem at k = 1, a compatible initial-state variation cancels the first correlated portal initial logarithm, and the specified once-Duhamel-corrected source Ward test satisfies its frozen budgets. These results support SCIENTIFIC FEASIBILITY GO under the explicitly documented local criteria. They do not complete AP1_GO. Audits 058–060 leave the full quantitative raw/paired-data response undecided: the required executable O049 histories, transports, complete contact assembly, uniform operator errors, reference calculation and finite cost bound are not jointly available. The single-time reformulation is algebraically established at a common finite regulator, but is not production-ready. No full response calculation or new physical NONPASS is reported. The carrier ontology, global cosmology and observational predictions remain outside the established result.