A Conditional Height-Dominance Architecture for Beal's Conjecture: A Zookeeper-Style Reduction with a Power-Residue Sieve Companion (DRAFT)

This corrective preprint presents a conditional reduction architecture for Beal's conjecture and an asymptotic power-residue sieve companion. It does not prove Beal's conjecture. The problem is $A^x+B^y=C^z$ for positive integers with $\gcd(A,B,C)=1$ and exponents at least three. Part A separates elementary height cancellation (HD1) and power compression (HD-PC) from the open coercive verifier-complement HD3'. The latter is a Beal-strength local-global conjecture: the conditional closure packages the missing arithmetic exclusion and is not an independent proof advance. Formal fixed-exponent entropy estimates establish no global root identity. Part B reconstructs the positive-row additive-large-sieve argument on classical Jacobi/Weil and fixed-progression inputs. For fixed $K\ge4$, $3\le x,y,z\le K$, excluding $(3,3,3)$, it gives $T_K(H)\ll_{K,\varepsilon}H^{2/3}/\Sigma(Q;K)$ only for sufficiently large $H$ and $(\log H)^{2+\varepsilon}\le Q\le H^{1/(2K)}$. The lower cut is sufficient, not necessary. Zero integer rows are excluded; zero residue rows, empty classes and a zero exclusion budget are treated explicitly. This version certifies neither an explicit height threshold nor an effective constant package. The stronger exponential estimate for the cumulative exact solution count would force that count identically to zero and, over all fixed $K$, is already Beal-strength. (i) External inputs: Classical character-sum and additive-large-sieve results; the classical $(3,4,5)$ theorem is restricted to its exact primitive equation. Chocian's $(3,5,7)$ exclusion is source-reported without independent computational replay. Pasten's Faltings-height/conductor result supplies no general Szpiro or Beal transfer. Sahoo's number-field statements retain their coefficient, field, prime-exponent and conditional hypotheses. (ii) Internal component: Elementary power compression and corrected local/asymptotic reconstruction in the stated domain. The elementary $\Xi\ge\log4$ identity supplies no IUT or gcd bridge. (iii) Diagnostic evidence: Historical near-miss, variable-prime-bound and root-branch tables; synthetic local passes are negative controls. Their ranks, fitted scores and hard-coded gates establish no Beal exclusion, statistical significance or HD3'. (iv) Open bridge: HD3', typed root/height/prime transfers, effective constants, independent method validation and complete source/proof review remain open. English and German editions state the same correction scope. The public curated source/data package contains both manuscript sources, disclosures, eight unchanged historical producers, seventeen unchanged CSV tables, a hash manifest and seven bounded offline verification tests. It excludes internal working notes and third-party PDFs. This is a corrective version of an advanced research draft. Historical diagnostic evidence and the existing claim register are not promoted. Version 1.1 replaces the earlier genus assignment, universal metric-exclusion interpretation, unrestricted sieve language and overbroad literature transfers. Changes in Version 1.1 (October 2026) Corrective implementation of the R25 inventory findings; no claim of a proof of Beal's conjecture. Genus and height corrections: Removes the invalid signature-to-genus formula and the claimed universal genus certificate. Treats the elementary height inequality as an identity without an IUT/gcd transfer; diagnostic negativity and the 0/11 gate score provide no exclusion theorem. Sieve domain: Corrects the null-row direction, resonant character contributions, positive-row transposition, prime budget and sufficiently-large-height domain. No explicit threshold or effective constant certificate is asserted. Claim boundaries: Distinguishes scalar-family monodromy from stronger global statements, corrects the July holomorphy claim and restricts the classical $(3,4,5)$ input. The exponential cumulative-count conjecture is explicitly Beal-strength and open. Literature: Retains Chocian as source-reported, restricts Pasten to Faltings height/conductor, and restores Sahoo's field, coefficient, common-prime-exponent and conditional hypotheses. Bibliographic identities of all 27 entries were checked with documented access limitations; this is not a complete external proof review. Reproducibility and bilingual release: Publishes EN/DE sources, eight original producers, seventeen original CSVs, manifest and seven bounded verification tests at the linked public source package. Uploads the two corrected standalone PDFs only; earlier combined files remain attached to the predecessor. Changes in Version 1.0 (July 2026) Initial preprint release. Deterministic Architecture (Part A): Formulates the Zookeeper-style Height-Dominance reduction and the coercive complement HD3' for Beal's conjecture. Sieve Companion (Part B): Derives an unconditional, effective uniform bound $T_K(H) \ll H^{2/3}/\Sigma(Q;K)$ for primitive solutions using power-residue verifiers. Diagnostic Evidence: Includes a 1000-row empirical near-miss dataset and diagnostic calibrations. DE/EN: English and German PDFs published synchronously; combined PDF generated from EN plus DE.