Local Two-Fragment Redundant Record Formation in Spectrum-Preserving ACRF-8: Counterfactually Separable Write-Retain-Read of a Common Source Distinction

This theorem note gives a reproducible local two-fragment redundancy result in the repository-selected spectrum-preserving ACRF-8 continuation of Registration Theory. An explicit admissible eight-node witness is partitioned into four two-node sectors A, B, C, and D. A single quotient-valid source distinction D_A writes nontrivially into two receiver sectors B and C through two independently removable checkerboard retained-boundary channels. Each receiver then writes a scalar retained log-ratio record into a disjoint retained-edge fragment. The global adaptive normalization cancels exactly from each log ratio. At the stated witness, both retained record maps have nonzero derivative with respect to the same source coordinate D_A, so each fragment locally determines D_A with all other witness coordinates fixed. Knocking out the A-to-B checkerboard channel preserves the fixed retained-edge budget, erases only the B receiver distinction and B retained record, and leaves the C branch exactly unchanged in the one-step construction; the reciprocal A-to-C knockout has the corresponding property. The note then holds the current state fixed and perturbs only one retained fragment in a budget-preserving antisymmetric direction. Each fragment has a nonzero first-order readout into its own receiver and zero first-order cross-read into the other receiver. Thus, the explicit witness supports write → retain → independently read twice from the same originating distinction. The result establishes local retained redundancy number at least two under the note’s stipulated recoverability, counterfactual-separability, and readout criteria. It is deliberately bounded. It does not derive a global multi-host quotient theorem, dynamical selection of the four two-node partition, quantum mutual-information redundancy, decoherence, Born probabilities, or macroscopic environmental objectivity. The accompanying Python certificate reconstructs the model and witness, verifies budget preservation and positivity, reproduces analytic and finite-difference derivatives, checks both channel knockouts, and verifies independent retained readout.