A Noise-Invariant Determinism Theorem for Multi-Base Post-Processing in Shor's Order Finding (v0.5.1: nonstabilizerness / magic — coding-theory of marker sets + oracle-hiding as T-cost)

v0.5.1 extends the magic (nonstabilizerness) direction of v0.5.0 (DOI 10.5281/zenodo.20725965). The six order-finding theorems (T1-T6) are RETAINED unchanged; the magic direction is now integrated into the canonical paper as Section 9. NEW IN v0.5.1: (1) A coding-theory of marker sets for the flat state |flat_W> over a support W in F2^n: an additive-energy closed form M2 = -log2(M^-4 sum_x E(W cap (W+x))) (Prop 4), the exact zero-test M2=0 iff the autocorrelation A_W is two-valued ({0,M}) iff W is an affine subspace, a Sidon (B2) law M2 = log2(M^3/(7M-6)) -> 2 log2 M - log2 7 (Prop 5), and an exact expectation for a uniform random M-subset E[xi] M^4 = (7M^2-6M) + 7(M)_4/(N-3) + N(N-1)(N-2)(N-4)(M)_8/(N)_8 (Prop 5'). The minimum Hamming distance is shown NOT to determine magic ({0,1,2,3} vs {0,1,2,4} share d_min=1 but M2=0 vs 1.54). (2) Oracle-hiding = T-cost (Prop 6): M2(graph state of f) > 0 iff f has a degree>=2 ANF monomial iff the oracle U_f needs non-Clifford (Toffoli/T) gates, all zero iff f is affine; a fault-tolerant resource estimate (oracle_ftqc_estimate.py) converts the nonlinear ANF (degree-d monomial -> (2d-3) Toffolis -> 7T each) into a T-count, with the honest caveat that per-output-bit ANF synthesis is an UPPER bound (real modular exponentiation is far cheaper via windowed arithmetic; cf. Gidney-Ekera 2021). HONEST NOVELTY AUDIT (the headline of this release): full-text comparison of all four code<->magic literatures shows the flat-state closed form (Prop 4) is the uniform-support specialization of Tarabunga-Castelnovo's Rokhsar-Kivelson SRE formula (Quantum 8, 1347 (2024), Eq. 8) -- CREDITED, not claimed as new -- and the 2 log M growth rate is the saturation of the standard bound M_alpha <= 2 log R. The surviving defensible contributions are the Grover 3-bit ladder (carried from v0.5.0), the coding-theoretic SPECIALIZATION (zero-test, exact Sidon constant, exact random expectation, d_min refutation, Grover multi-marked application), and oracle-hiding = T-cost; differentiated from hypergraph-state magic (phase-encoded / RM(2): arXiv:2308.01886, 2602.23687), weight-enumerator SRE tools (arXiv:2308.05152), and permutation-invariant/Dicke magic (arXiv:2402.08551). Carried from v0.5.0: a verified stabilizer 2-Renyi entropy tool (XOR fast Walsh-Hadamard, cross-checked to 1e-15), the speedup ladder (Simon/affine -> 0; Grover quadratic -> bounded, density 0; Shor exponential -> growing), and a 42-assertion proposition checker (all pass). ALSO ADDED LATE IN v0.5.1 (JAMES-DISCOVER): an automated discovery loop (Generator -> Probe -> Miner -> Adversary -> Promoter, numpy-only, no LLM) layered on the existing magic infrastructure. The loop first passes a D1 sanity gate by re-deriving the Sidon constant and the additive-energy closed form from scratch (discover_poc.py), then yields a D3 finding (discover_d3_jensen.py) that PARTIALLY CLOSES one of v0.5.1's listed open items: defining the Jensen gap J(M,N) := E[M2] + log2 E[xi] >= 0, the loop discovers J ~ 1/N in the sparse regime M^2 << N (measured slope -0.96 across M in {6,8,10}, n in {10..13}), so Prop 5' (E[xi] closed form) is not merely a Jensen lower bound but an asymptotically tight estimate of E[M2] with absolute error O(1/N). The saturation boundary M^2/N -> 1 and the prefactor kappa(M) = J * N remain open. numpy + Python standard library only; no quantum libraries required.