Human–AI Collaborative Derivation of Tissue Regeneration: Established State Conditions, Exact Recovery Results, and an Open Microvascular-Chip Falsification Challenge

This preprint presents a documented human–AI calculation-to-test workflow for conditional tissue-regeneration research. Its outputs are an exact compatibility and graph-error calculation, a conditional recovery envelope, an inverse disturbance budget, and a structural and functional experimental handoff. Hailing Sheng defined the question, theoretical scope, acceptance rules, interpretation, and final claims. AI systems assisted with derivation, counterexample search, reproducible synthetic checks, literature organization, and drafting; AI agreement itself is not treated as proof. The research results reported in this paper are established under their stated assumptions and domains. They comprise an exact invariant-graph error identity, bounded-input recovery estimates, an observation bridge, a second-moment topology counterexample, a quotient-contraction theorem, an inverse calculation, and a reproducible calculation-to-test method. They do not await laboratory approval. A prospective first in-vitro study and an open falsification challenge are specified for a perfusable microvascular chip, using independent structural and functional endpoints, calibrated intervention, controls, frozen decision rules, and held-out experimental units. The supplementary material and reproducibility package retain detailed proofs, source-resolved comparisons, protocol worksheets, 29 archived synthetic checks, and six separately executed symbolic checks of selected identities. The revision also supplies an animal-to-human indicator mapping, explicit seed/location definitions, unit and metric transformations, and a conditional inverse budget for candidate experimental settings. No new tissue, animal, or human experimental outcomes are reported. Experiment therefore challenges the proposed biological realization of the established research results; it does not determine whether those proved results are valid. Biological realization, ADF-specific discriminatory predictions, organ-level efficacy, and clinical application remain open. Preprint, not peer reviewed. The experimental collaboration is proposed; no laboratory has contributed data to this version. The mathematical and software checks do not demonstrate human organ regeneration.