Simple Young modules with nonprojective polynomial injective hulls

For every odd prime p over an algebraically closed field of characteristic p, at parameter q=1, degree r=2p-1 and partition lambda=(2p-2,1), the source-convention Young module is simple of dimension2p-2, but the corresponding polynomial injective I_n(lambda) is nonprojective for every permitted rank n>=2. Thus p=3,lambda=(4,1) already refutes the broad first bridge in Miyachi's printed2009 Conjecture7. The subsequent index-set proposal is stronger, not an assumed established equivalence; its sufficient projectivity implication also gives a negative answer. The separate DeVisscher-Donkin projective-injective classification and characteristic-zero nontrivial-root variants are not resolved or refuted. The proof uses classical natural permutation/Young structure, explicit algebraic-group coefficient calculations, credited DeVisscher-Donkin reciprocity/tilting/labelled-truncation and symmetric-power injective multiplicities, and the stable FI convention recorded by Cox-Parker. Erdmann-Law2021 Proposition3.1's classical analogue and Theorem3.3 supply published local nonsplitting/simplicity inputs, pointing to older2002 machinery. The full all-rank dominance and labelled-truncation deduction is explicit; arbitrary projectivity preservation under idempotent truncation is not asserted. No new local GL2/Young classification is claimed. Two independently positioned priority reviews, a later adversarial peer challenge and root primary-source checks identified no full predecessor in inspected statements. Priority remains unresolved: exact older two-row papers/tables, Fang2014, Fang-JunHu2025online/2026issue and incomplete citation/version coverage remain material gaps. No historical firstness, novelty certification, complete absence theorem or current worldwide open-status claim is made. Source ledgers distinguish actual body passages from metadata and inaccessible versions. The companion archive preserves all41 frozen candidate files/threeZIPs, two independent mathematical families, two priority reviews, full selected-record and source identities, exact finite coefficient/polarization/tensor-orbit checks and root reproduction receipts. Core verification uses Python's standard library; the optional independent56-basis Schur computation was verified with Python3.12.14/NumPy2.3.5. No full third-party PDF/text/image bodies are redistributed, and their optional exact custody replay is explicitly distinguished from core package verification. Finite computations support, rather than formally certify, the universal proof. AI tools were used extensively in development, literature investigation, drafting, computation, reproduction and adversarial review. This is an unrefereed preprint without external human peer review or proof-assistant certification. The note and authored companion material are CC BY4.0.