Noncommutative quantum sequential growth under state-level covariance: existence, fixed-seed rigidity, and geometric limits

We give an explicit cyclic irreducible two-dimensional noncommutative quantum sequential-growth model satisfying operator Markov normalization, the full abstract marked-core causal-past-ordered Bell comparisons, and strict covariance of history state vectors. The model fails covariance of operator words; consequently the antichain commutator associated with operator-covariant rigidity does not follow from the weaker state-covariant assumptions. We reconstruct algebraic classical-sequential-growth couplings for any invertible commuting shadow on its reachable module and exhibit a positive five-birth Gram invariant excluding such a shadow for our model. An inductive common-precursor recursion extends the noncommutative seed to all finite births, with invertibility guaranteed by a recursive admissible choice of scales. For a specified geometric tail, uniform variation bounds yield a finite-variation vector measure on naturally labelled infinite histories, whose total variation is absolutely continuous with respect to a finite mixture of conditional transitive-percolation reference laws. For the fixed irreducible seed, marked-core Bell identities and state covariance enforce the common-precursor form up to parent-size scales; bulk precursor weights are blind to detailed order shape. That particular geometric tail is almost surely chainlike on large anchored intervals, excluding four-dimensional flat Alexandrov scaling in that regime. To our knowledge, the combination of an exact state-covariant noncommutative all-stage construction and these operational and geometric boundary results addresses a case identified as open in recent operator-covariant rigidity work. No spacetime dimension or gravitational field equation is derived. Supplementary package: exact-arithmetic certificates (Python standard library only), one per theorem, plus claim and statement ledgers. Run: python3 certificates/run_all.py