Anchored Sparse-Offset Screening of Semiprimes: An Exact Sieve Null Model, Two-Adic Saturation, and Positive-Control Benchmarks up to 2048 Bits

This release presents Version 11.0.3 of the preprint “Anchored Sparse-Offset Screening of Semiprimes: An Exact Sieve Null Model, Two-Adic Saturation, and Positive-Control Benchmarks up to 2048 Bits”. The paper studies structured semiprimes whose weighted arithmetic centre lies in a public anchored sparse set 2^r + Z, certified exactly by the Lehman–Hart-type identity A^2 − abn = ((ap − bq)/2)^2. It proves an exact pass fraction 1/2 + χ_ℓ(N)/(2ℓ) for the quadratic-residue sieve (and a resulting prime-selection rule), proves that two-adic filtering saturates, introduces a lazily generated representation of offset sets of arbitrary span, and reports benchmarks on planted 1024- and 2048-bit moduli with up to 3.3×10^8 offsets. A pre-specified audit of 2,355 public RSA moduli (about 1.9×10^10 centre hypotheses) found no modulus in any tested family and no shared prime, while all 88 planted controls were recovered; this is a negative result that validates the pipeline rather than a finding about keys. The work is not a general attack on RSA. All positive controls are planted by the author; no experimental comparison with lattice-based methods is included. The release contains the preprint (PDF), a README, and a source package with the LaTeX source, the scripts (scan, benchmarks, corpus collector and audit) and the aggregate audit results. The key corpus itself is not redistributed. This preprint is part of the continuing dyadic-shell research programme on structural diagnostics in semiprime arithmetic and weak-key analysis.