Determinant-native matrix-free fermionic quantum chemistry: FCI-quality ground states at 8-26 qubits without instantiating the 2^M Hilbert space

We demonstrate that fermionic quantum-chemistry ground-state computation can be performed natively in the N-electron determinant subspace (dim D = C(M, N)) rather than in the full 2^M Jordan-Wigner Hilbert space, with verified FCI-quality results on ten benchmark systems (Hubbard-4, H4, LiH, H2O/STO-3G, NH3, BeH2, CH4, N2, F2, H2O/6-31G) spanning 8 to 26 qubits. Three pipeline generations are included, each verified against PySCF FCI or exact-diagonalization references: (1) a dense determinant-basis pipeline (compression ratios 3.66x to 16.37x at 8-16 qubits, energies matching FCI to 1e-12 Ha or better; NH3 FCI-quality in 11.7 min where the full-Hilbert verification path needs ~3 h); (2) a sparse Lanczos pipeline (own solver with full reorthogonalization and residual-based convergence, plus sparse-to-sparse antisymmetric projection) that passes the dense-eigensolver ceiling — CH4 at 18 qubits (D = 43,758, 1.3e-12 Ha vs FCI, dense infeasible at ~30 GB), N2 at 20 qubits (2.4e-12 Ha, 179 iterations), F2 at 20 qubits (D = 190, a 5,519x compression, three-way agreement to 5.7e-14); (3) a matrix-free Slater-Condon formulation (correct-by-construction element anchor, equality-locked fast paths, flat two-electron tensor, data-driven spin-conservation skip, threaded gather) that eliminates the stored Hamiltonian entirely — CH4 in 17.9 s (10x the stored-sparse path), and H2O/6-31G at 26 qubits (D = 5,311,735): ground-state energy matching PySCF FCI to 3.1e-12 Ha in 3.7 h on a laptop, 143 Lanczos iterations, with the 2^26 Hilbert space never instantiated (stored alternatives estimated at 160-440 GB on the test hardware). A companion result documents the parastatistics connection with its precise scope: the parabose-2 physical subspace coincides with the fermionic antisymmetric subspace exactly in, and only in, the two-particle sector; for general particle number the parabose-p Fock space decomposes by Young diagrams of at most p rows (verified numerically at p = 2 and p = 3 across multiple (n, R) corners and distinct Young shapes), while general-N CI spaces are standard fermionic objects. Order-1 parabosons are ordinary bosons. An earlier general-N identification of CI spaces with parabose-2 sectors is explicitly withdrawn in the writeup, with the refuting counterexample recorded. The deposit includes: (a) the full method writeup; (b) the complete header-only C++17 source of all three pipeline generations with their BDD test suites; (c) the parabose-p structural-anchor tests; (d) PySCF/OpenFermion integral-generator scripts for all ten systems; (e) measured benchmark CSV data. This is a defensive publication establishing freedom-to-operate for: (i) the determinant-native chemistry pipeline; (ii) the sparse-to-sparse antisymmetric projection; (iii) the matrix-free Slater-Condon H·v formulation with data-driven spin skip and threaded gather; (iv) the Lanczos production workflow distinct from verification mode; and (v) the parabose-p height-bounded Young decomposition as a forward extension path.