Falsification Protocol

A scientific claim is only meaningful if there is an experiment whose outcome would refute it. This page collects the falsification criteria for every non-trivial claim scpn-quantum-control currently makes, so a reader can locate the break point without reverse-engineering the source.

Each claim has four fields:

• Claim — what we assert.
• Domain of validity — the regime where the claim is supposed to hold.
• Falsifier — the observable result that would refute the claim.
• Current evidence — the experiment or computation on which the claim currently rests.

C1 — DLA dimension formula

• Claim. For the heterogeneous XY Hamiltonian $H = -\sum K_{ij}(X_i X_j + Y_i Y_j) - \sum (\omega_i / 2) Z_i$ with generic (non-degenerate) frequencies on $N$ qubits, the dynamical Lie algebra has dimension $\dim(\mathrm{DLA}) = 2^{2N-1} - 2$ and decomposes as $\mathrm{DLA} = \mathfrak{su}(2^{N-1}) \oplus \mathfrak{su}(2^{N-1})$ acting on the even- and odd-parity subspaces.
• Domain. $N \ge 2$, all $\omega_i$ pairwise distinct, all $K_{ij} \neq 0$ for $i \neq j$.
• Falsifier. Computing the DLA by nested commutator closure at any $N \ge 2$ and getting a dimension different from $2^{2N-1} - 2$. Or finding a non-trivial symmetry beyond$\mathbb{Z}_2$ parity (which would split the DLA further).
• Evidence. Verified computationally for $N = 2, 3, 4, 5$ in analysis/dla_parity_theorem.py and tests/test_dla_parity_theorem.py. Representation-theoretic argument for all $N$ (not yet formalised in Lean 4 — the internal gap audit §C Lean 4 entry).

C2 — DLA parity asymmetry on hardware

• Claim. On a real superconducting processor, the even-magnetisation sector's post-Trotter leakage is larger than the odd-magnetisation sector's, by a few per cent, and the gap grows with Trotter depth.
• Domain. IBM Heron r2 class hardware at $n = 4$ qubits, Trotter depths 2–14, XY Hamiltonian with the same $K_{nm}$ matrix as the classical simulator.
• Falsifier. Any of: (i) mean relative asymmetry for depths $\ge 4$ drops to $\le 2\%$ on a new hardware run on the same backend; (ii) the sign flips (odd > even); (iii) Welch's two-sample $t$-test returns $p > 0.05$ on 7 of 8 depths.
• Evidence. data/phase1_dla_parity/*.json (342 circuits across 4 sub-phases on ibm_kingston, April 2026). Mean asymmetry $+10.8\,\%$ for depth $\ge 4$, peak $+17.48\,\%$ at depth 6, Welch $p < 0.05$ on 7/8 depths, Fisher combined $\chi^2 = 123.4$ ($p \ll 10^{-16}$). Reproducer: tests/test_phase1_dla_parity_reproduces.py.

C3 — $K_{nm}$ topological mapping

• Claim. The SCPN coupling matrix $K_{nm}$ (exponential-decay, all-to-all, with anchor overrides from Paper 27) correlates strongly with the effective coupling topology of at least two measured physical systems (photosynthesis FMO, EEG alpha-band, ITER MHD modes, IEEE power grid). Josephson junction arrays remain an illustrative comparison until calibration-sourced parameters and coupling edges are supplied.
• Domain. Systems with a natural distance-dependent coupling on a complete graph.
• Falsifier. Spearman $\rho < 0.5$ on every listed system.
• Evidence. EEG alpha $\rho = 0.916$, IEEE 5-bus $\rho = 0.881$, ITER MHD $\rho = 0.944$, FMO $\rho = 0.304$. Josephson array comparisons must be labelled illustrative unless backed by measured calibration parameters and coupling edges. See GAP_CLOSURE_STATUS.md.

C4 — Rust acceleration factors

• Claim. Measured Python↔Rust speedups for the functions in pipeline_performance.md §21 stay within a factor of 2 of the published values on a comparable-class runner (Linux x86_64, ≥ 8 cores, ≥ 16 GB RAM).
• Domain. The exact five paired benchmarks listed in §21 (build_knm, kuramoto_euler, correlation_matrix_xy, lindblad_jump_ops_coo, lindblad_anti_hermitian_diag).
• Falsifier. The next green CI run of tests/test_rust_path_benchmarks.py reports any paired speedup drop of more than 50 % from the published figure.
• Evidence. Section §21 of pipeline_performance.md (measured 2026-04-17 on ML350 Gen8 via test_rust_path_benchmarks.py).

C14 — Analog-native Kuramoto primitive accounting

• Claim. On the fixed S10 readiness benchmark, analog-native Kuramoto compilation uses fewer native coupling primitives than the digital Trotter compilation uses two-qubit gates at the same declared tolerance.
• Domain. The committed S10 readiness benchmark and compiler accounting only; this is not a hardware-performance or analog-advantage claim.
• Falsifier. Digital Trotter compilation reaches a lower two-qubit gate count at the same declared tolerance, or provider validation fails to preserve the native coupling model.
• Evidence. data/s10_analog_native/analog_native_readiness_2026-05-20.json, docs/analog_native_readiness.md, and tests/test_analog_native_readiness.py.

C15 — Sync-order quantum-sensing gain

• Claim. On a preregistered perturbation benchmark, QFI-based sync-order-parameter sensing beats the classical Fisher-information baseline.
• Domain. The committed S11 readiness benchmark records only a no-submit estimate. Hardware or applied-target promotion requires raw counts, uncertainty intervals, and the preregistered classical Fisher estimator.
• Falsifier. The QFI/classical-Fisher ratio is below 1 on the benchmark mean, or the uncertainty interval overlaps or falls below 1.
• Evidence. data/s11_quantum_sensing/quantum_sensing_readiness_2026-05-20.json, docs/quantum_sensing.md, and tests/test_quantum_sensing_readiness.py.

Open questions (no claim yet)

The following items are not claims — they are open problems. Nothing in scpn-quantum-control depends on any of them being true. They appear here so a reader knows they are known.

• Gap 2 — quantum result beyond classical. Two readings now distinguished (see classical_irreproducibility.md): the narrow reading (no ideal-Hamiltonian classical simulator can reproduce the observed asymmetry) is closed — every Hamiltonian term commutes with the total-parity operator, so classical leakage is identically zero; the observed hardware asymmetry is therefore a hardware-noise signature, not a property of the Hamiltonian. The broad reading (no efficient classical algorithm at any $N$) remains open: classical simulation cost still scales as $O(\mathrm{poly}(N))$ at $N \le 16$, so this is not yet a complexity-class claim.
• Gap 3 — p_h1 = 0.72 first principles. The hypothesis that $p_{h1}$ equals $A_{\mathrm{HP}} \sqrt{2 / \pi}$ (Hasenbusch-Pinn amplitude times the Nelson-Kosterlitz ratio) is 3 % off the observed value and was initially motivated by a square-lattice coincidence that is independently falsified. It is listed in bkt_universals.py as the best numerical fit among seven candidate combinations; it is not a derived claim.

When either of these is promoted to a claim, an entry goes in the Claims section above with its own falsifier.