Independent

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bounded_quotient_blocks_and_recentering: Unverified independent input; checked additions and superseded targets are recorded in the topical notes.

harmonic_bounds_and_common_shifts: Unverified independent input; checked conclusions and corrections are recorded in the topical notes.

harmonic_capacity_and_narrow_windows: Unverified independent input; the checked two-class result, moment certificate, and superseded targets are recorded in the topical notes.

profinite_shifts_and_long_windows: Unverified independent input; checked additions and superseded targets are recorded in the topical notes.

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These inputs are preserved as background, not endorsed wholesale. The root research index is the entry point to current progress. For the first record (harmonic_bounds_and_common_shifts), the comparison and corrections identify what was verified, strengthened, or rejected. Its mathematical text has been left unchanged.

For the second record (bounded_quotient_blocks_and_recentering), the comparison and corrections record the checked additions and distinguish its obsolete open targets from the estimates that remain unresolved. Its mathematical text is also preserved unchanged.

For the third record (profinite_shifts_and_long_windows), the comparison and corrections record the proved weighted and quantitative window bounds, the retained obstructions, and the already-refuted exact Dirichlet target. Its mathematical text is preserved unchanged; unavailable companion files were not used as evidence.

For the fourth record (harmonic_capacity_and_narrow_windows), the comparison and corrections retain a checked two-class positive result and a small moment certificate, and distinguish its obsolete exact finite targets from the unresolved conditioned-tail problem. Its mathematical text is preserved unchanged.