This isn't quantum buzzword soup. Falsify it.

the thirty-two proof rows · each checked against a published anchor

• hadamard-involution‖H·H − I‖_F (Frobenius residual)· cite: Nielsen & Chuang §4.2 · doi:10.1017/CBO9780511976667
• pauli-involution‖X·X − I‖_F (Frobenius residual)· cite: Nielsen & Chuang §4.2 · doi:10.1017/CBO9780511976667
• cnot-involution‖CNOT·CNOT − I⊗I‖_F (Frobenius residual)· cite: Nielsen & Chuang §4.2 · doi:10.1017/CBO9780511976667
• grover-optimal-ksin(13·arcsin(1/8)) at n=6, w=42· cite: Grover STOC 1996 · doi:10.1145/237814.237866
• multi-marked-grover-closed-formsin(7·arcsin(√(3/64))) at n=6, M=3, W={0,4,7}· cite: Grover STOC 1996 §3 / NC §6.1.4 · doi:10.1145/237814.237866
• teleportation-fidelity-1993|⟨ψ_in|ψ_out at qubit 2⟩|² = 1 EXACT (Theorem 1)· cite: Bennett, Brassard, Crépeau, Jozsa, Peres, Wootters 1993 · doi:10.1103/PhysRevLett.70.1895
• bit-flip-channel-superoperatorleading linear-in-p coefficient: E[fidelity] = 1 − 1·p· cite: Daley 2014 / NC §8.3.4 · doi:10.1080/00018732.2014.933502
• bit-flip-repetition-codeleading p² coefficient: corrected fidelity = 1 − 3·p² + 2·p³· cite: Shor 1995 / NC §10.2 Eq. 10.7 · doi:10.1103/PhysRevA.52.R2493
• stabilizer-clifford-conjugationstructural identity: H · Z · H = X (row count) — 1 indicates the load-bearing rule matches Table I· cite: Aaronson & Gottesman 2004 Table I · doi:10.1103/PhysRevA.70.052328
• stabilizer-measurement-born-ruleBorn-rule anti-commuting-Pauli outcome probability = 0.5 EXACT· cite: Born 1926 / Aaronson-Gottesman 2004 §III Lemma 3 · doi:10.1103/PhysRevA.70.052328
• grover-dim7-k15-recurrence-closuresin²(31·arcsin(1/4)) at n=6, M=4, k=15 (the cited 'glassy' recurrence-closure)· cite: Grover STOC 1996 §3 / CircuitExploration §1 · doi:10.1145/237814.237866
• grover-whole-tone-hex-k2-closuresin²(5·arcsin(√(6/64))) at n=6, M=6, k*=2 (cited cleanest small-M rounding, distance 0.021)· cite: Grover STOC 1996 §3 / CircuitExploration §2 · doi:10.1145/237814.237866
• grover-cleanness-monotonicityargmax_M P_peak(M) over M ∈ {1..12} at n=6 = 6 (cited whole-tone hexachord)· cite: Grover STOC 1996 §3 / CircuitExploration §2 · doi:10.1145/237814.237866
• grover-recurrence-lattice-dim7groverClosedFormProb(6, 15, 4) — cited CircuitPurityDial 'glassy' anchor (k=15 near-closure on the dim7 cleanness ladder)· cite: Grover STOC 1996 §3 / CircuitExploration §1+§3.3 · doi:10.1145/237814.237866
• grover-off-peak-leakage-spectrumcos(7·arcsin(1/4))/√60 — cited per-index leakage amplitude at dim7 k=3 (the cited uniform spectral shape)· cite: Grover STOC 1996 §3 / CircuitExploration §3.4 · doi:10.1145/237814.237866
• qft-unitarity‖QFT_8† · QFT_8 − I‖_F (Frobenius residual at n=3, cited Vandermonde Plancherel)· cite: Coppersmith 1994 / Nielsen & Chuang §5.1 · doi:10.48550/arXiv.quant-ph/0201067
• phase-estimation-eigenvaluePr(measured estimator = m | φ = m/2^n) = 1 EXACT (n=4 estimator qubits)· cite: Kitaev 1995 / Nielsen & Chuang §5.2 Eq. 5.23 · doi:10.48550/arXiv.quant-ph/9511026
• trotter-suzuki-error-bound½·Δt²·‖[X, Z]‖_op = Δt² at Δt = 0.05 — cited Lloyd 1996 1st-order Lie-Trotter per-step bound· cite: Lloyd 1996 / Suzuki 1990 / Childs-Su 2019 · doi:10.1126/science.273.5278.1073
• transverse-field-ising-commutatorΣ_{j<k} ‖[T_j, T_k]‖_op = 12 EXACT at TFIM n=4, J=h=1, open chain — cited Pauli symplectic anticommute count· cite: Sachdev 2011 §1.2 / Aaronson-Gottesman 2004 Theorem 3 · doi:10.1103/PhysRevA.70.052328
• shor-nine-corrected-fidelityC(9, 2) = 36 EXACT (leading p² coefficient of the corrected ensemble fidelity under depolarizing noise — Shor 1995 / NC §10.3 Eq. 10.16)· cite: Shor 1995 / Nielsen & Chuang §10.3 Box 10.3 · doi:10.1103/PhysRevA.52.R2493
• steane-seven-transversal-cliffordC(7, 2) = 21 EXACT (leading p² coefficient of the corrected ensemble fidelity under depolarizing noise — Steane 1996 / NC §10.4.3 distance-3 [[7, 1, 3]] property)· cite: Steane 1996 / Nielsen & Chuang §10.4.3 Table 10.5 · doi:10.1098/rspa.1996.0136
• surface-code-d3-stabilizer-countd² − 1 = 8 EXACT (stabilizer generator count for the rotated distance-3 surface code on 9 data qubits — Fowler 2012 §II.A: 4 X-plaquettes + 4 Z-plaquettes)· cite: Fowler, Mariantoni, Martinis, Cleland 2012 / Kitaev 2003 · doi:10.1103/PhysRevA.86.032324
• cross-code-logical-observable⟨+_L|X_L|+_L⟩ = +1 EXACT across all 3 codes (Shor 9 / Steane 7 / surface-d3) — the cross-code logical-qubit X-basis +1 eigenvector identity, the C.12 enabler· cite: Nielsen & Chuang §10.5 / Knill 2005 · doi:10.1038/nature03350
• joint-observable-partial-tracemax |Tr(Z · ρ_sys) − (1 − 2p)| over Stinespring p ∈ {0.05, 0.2, 0.4} via shared clean GATE_CNOT (substrate-ULP module-load anchor)· cite: Stinespring 1955 / Nielsen & Chuang §2.4.3 + §8.2 · doi:10.1090/S0002-9939-1955-0069403-4
• joint-rabi-frequencyΩ_1 = 2·g·√(n+1) at (g=0.05, n=1) = 0.1·√2 ≈ 0.14142 — cited Cummings 1965 √(n+1) Rabi-frequency ladder at the single-Fock anchor (Wave C.13 first cross-engine algebraic milestone)· cite: Jaynes & Cummings 1963 / Cummings 1965 / Walls & Milburn §10 · doi:10.1109/PROC.1963.1664
• amplitude-damping-population-decayleading linear-in-γ coefficient: E[|amp₁|²] on |1⟩ = 1 − 1·γ (single step) → (1−γ)^k after k steps· cite: Nielsen & Chuang §8.3.1 / Daley 2014 · doi:10.1080/00018732.2014.933502
• thermal-relaxation-steady-statethermal steady-state excited population n̄/(2n̄+1) at n̄=0.5 = 0.25 (Lindblad detailed-balance fixed point)· cite: Lindblad 1976 / NC §8.3.1 · doi:10.1007/BF01608499
• grover-n8-magic-cardinalityargmax over the n=8 M-sweep of cleanest large-M peak prob = 24 (magic cardinality absent at n=6)· cite: Grover STOC 1996 §3 · doi:10.1145/237814.237866
• phase-oracle-amplitude-amplificationBHMT P_k = sin²((2k+1)·arcsin(√a)) at a=3/64, k=3 ≡ Grover triad peak ≈ 0.99790· cite: Brassard-Høyer-Mosca-Tapp 2002 · doi:10.1090/conm/305/05215
• solovay-kitaev-contractionempirical worst-case 3/2-contraction prefactor c_approx ≈ 1.74 in ε_{n+1} ≤ c_approx·ε_n^{3/2} at the depth-14 Clifford+T base net (Dawson-Nielsen 2006 accuracy contraction)· cite: Dawson & Nielsen 2006 / Kitaev 1997 / Nielsen & Chuang §4.5.3 · doi:10.48550/arXiv.quant-ph/0505030
• surface-code-d5-distancerotated distance-5 surface code: d² − 1 = 24 stabilisers (12 X + 12 Z), code distance d = 5 EXACT via CSS coset minimisation (structural-only — no 2^25 state vector)· cite: Fowler 2012 / Kitaev 2003 · doi:10.1103/PhysRevA.86.032324
• braid-fibonacci-yang-baxter‖σ₁σ₂σ₁ − σ₂σ₁σ₂‖_F — the Fibonacci-anyon Yang-Baxter residual (the B₃ representation certificate, ≈ 0 EXACT)· cite: Nayak 2008 §IV.B / Freedman-Kitaev-Larsen-Wang 2003 · doi:10.1103/RevModPhys.80.1083

tamper falsifiability — surgical, one row at a time

A proof page that can't fail isn't one. The radio below the rows perturbs one entry of the targeted row's load-bearing matrix (GATE_H[0,0], GATE_X[0,1], GATE_CNOT[2,2], the Grover loop's Hadamard, the C.8 cleanness-lattice's higher- entry H clones, a marked-set cardinality nudge, a mass- preserving state perturbation, the C.9 algorithm-gateway pair's QFT round-trip H or phase-estimation pipeline H, a local PauliGateBundle clone threading a perturbed GATE_X / GATE_Z through the Trotter step while the Taylor reference stays clean for the C.10 Hamiltonian-engine pair, or — for the C.11 Sessions A + B + C + D QEC code library — a local GATE_H[1,1] (entry 3) clone threaded through the Shor 9 encoder + decoder via the hGate parameter, a local GATE_H[0,1] (entry 1) clone threaded through the Steane 7 decoder's two transversal-Hadamard basis-change layers, a local GATE_H[1,0] (entry 2) clone threaded through the surface-d3 decoder's two transversal-Hadamard basis- change layers, or — for the cross-code logical-qubit observable closer — a local GATE_H[0,0] (entry 0) clone threaded through all three QEC decoders simultaneously via the hGate parameter, with the encoders left on the SHARED clean GATE_H singleton so the per-code Path A / B / C eigenvector anchors stay bundle-independent; or — for the C.12 Phase III bridge joint-observable row — a local GATE_CNOT[3,0] (entry 12) clone threaded through entangleWithSharedRegister's couplingUnitary parameter, breaking the Stinespring bit-flip dilation while Paths A / B (direct- amplitude entangled-state construction and shared-side Pauli sweeps, no CNOT involved) and Path C (Stinespring via the SHARED clean GATE_CNOT singleton) stay bundle-independent; or — for the C.13 first cross-engine algebraic milestone (joint Rabi-frequency row) — a local GATE_CNOT[3,1] (entry 13) clone threaded through the same couplingUnitary parameter on the Stinespring- analog absorption leg, breaking ⟨σ_z ⊗ I⟩ = 2p − 1 while Paths A (Cummings 1965 Rabi-frequency anchor) + B (n=0 doublet cross-pin) + C (bipartiteJCState via the C.12 surface yielding ⟨σ_z⟩ = −1 EXACT at the half-period) + Path D Leg 1 (multi-Fock pure-|↑,n⟩ aggregate, n ∈{0, 1, 2, 3}) stay bundle-independent — the four CNOT-tamper rows now span the full row-3 = "output |11⟩" band of the row-major CNOT matrix at entries{10, 11, 12, 13}) by a quantised ε — or, for the V1.5 Wave 2 larger-N lattice row (n=8 magic cardinality), a marked-set-push lever that grows the M=24 marked set 24 → 25 through the offline Grover loop (NOT a matrix entry — the Hadamard's four real entries are all claimed by earlier Grover-family rows) while the closed-form argmax / integrity / preset cross-pin legs stay green; or — for the V1.5 Wave 3 amplitude-amplification row (BHMT 2002) — a local GATE_H[0,1] (entry 1) clone threaded through the amplitude-amplification loop's diffuser, drifting only the LOAD-BEARING phase-oracle AA loop while the BHMT↔Grover prob cross-pin, optimal-k agreement, and phase-oracle ≡ diagonal- phase byte-identity legs stay green; or — for the V1.5 Wave 4 Solovay-Kitaev gate-compilation row (Dawson-Nielsen 2006) — a local GATE_S[1,1] (entry 3) clone (the FIRST row to tamper GATE_S, an honest lever since S is in the Clifford+T alphabet the base net is built from) threaded only through the compiled word's reconstruction, drifting the LOAD-BEARING ‖U − SK_3(U)‖ off its clean value while the base-net unitarity + covering radius, the group-commutator exactness, and the 3/2-power contraction profile (all computed on the clean net) stay green; or — for the V1.5 Wave 5 surface-code-scaling row (distance-5 rotated surface code) — a STRUCTURAL lever rather than a matrix entry: perturbGeneratorMask flips one plaquette support bit of one X-type stabiliser generator on a fresh clone of the d=5 generator set, breaking abelianness so the runtime symplectic anti-commute count jumps above 0 while the stabiliser-count, CSS coset-min distance, and d=7 counts legs (all computed on the clean generators) stay green — a documented discipline fork, since a pure-combinatorics row has no state-vector amplitude to perturb; or — for the V1.5 Wave 6 Strand⊗Circuit braid row (Fibonacci-anyon Yang-Baxter) — a row-local R_τ-phase PARAMETER lever rather than a matrix entry: nudging the cited +3π/5 R-symbol phase keeps every braid generator unitary but breaks the hexagon consistency, so the runtime braid relation ‖σ₁σ₂σ₁ − σ₂σ₁σ₂‖_F jumps from 0 EXACT to O(ε) while the generator-unitarity, clean Yang-Baxter certificate, and F²=I / cited-phase / apply1q round-trip legs (all rebuilt from cited constants) stay green — no shared GATE_* singleton touched, no GATE_* slot consumed. Exactly ONE row flips red; the other thirty-one stay green by construction — the tamper is cross-row independent (every row builds its own local perturbed gate via perturbGateRealEntry / perturbTwoQubitGateRealEntry, never mutating the shared GATE_H / GATE_CNOT singletons; the QEC-code-library codes share H-entry slots {0, 1, 2, 3}with earlier rows, the C.12 row uses CNOT- entry 12 (distinct from cnot-involution's entry 10 and bit-flip-repetition-code's entry 11), and each row's clone is a fresh Float64Array, so the cross-row independence is structural). The substrate-ULP cited anchor on each row is a STATIC closed-form residual (GATE_H_SQUARED_RESIDUAL, et al.) computed at module load; the tamper expresses itself in the live state-vector measurements, not the cited chip.

chord-morphing axis — musical, not falsifiable

The multi-marked row pins the M-generalized closed form for a static marked set: per-w amplitude matches sin((2k+1)·arcsin(√(M/N))) / √M at every step, peak at k* = ⌊π / (4·arcsin(√(M/N)))⌋. The C.3 instrument also exposes a chord-morph axis — press Won a chord preset to swap the active marked set mid-loop. That morph breaks the simple closed form (the formula assumes the marked set stays constant across all k iterations); it's a musical chord-progression knob, not a load-bearing claim about the math. The proof above pins the static-set case; the morph is an additional gesture on top.

measurement-based axis — stochastic outcomes, deterministic closed form

The teleportation row pins Bennett 1993 Theorem 1: |⟨ψ_in|ψ_out at qubit 2⟩|² = 1 EXACT for every input |ψ⟩ AND every classical-bit outcome (c₀, c₁). Each Space trigger on the teleportation preset produces a different random (c₀, c₁) pair via mid-circuit Z-measurements; Bob's classically-conditional X^c₁ · Z^c₀ corrections deterministically cancel the randomness. The fidelity is closed-form-1 in expectation AND per-trial — the proof row asserts it across multiple input states and multiple RNG seeds. The tamper perturbs the Bell-pair prep Hadamard; the corrections no longer exactly cancel, fidelity drifts.

noise-as-substrate axis — Monte Carlo single-trajectory, cited claims hold in expectation

The bit-flip channel and 3-qubit repetition code rows are stochastic: at each trial, one Pauli per qubit per noise op is sampled from the per-voice seeded RNG and applied to the pure state — the Daley 2014 stochastic wave function method (NC §8.3.4). A density-matrix simulation would balloon storage from 2ⁿ complex amplitudes to 4ⁿ real numbers, which the state-vector substrate doesn't support; instead the cited NC §8.3.4 superoperator action and the NC §10.2 Eq. 10.7 corrected fidelity 1 − 3p² + 2p³ hold in expectationover the seeded RNG ensemble. The proof rows assert empirical convergence within the Bernoulli 4σ standard-error band at N seeded trials per p, backed by a deterministic anchor leg (p=0 round trip / p=1 full-flip) at substrate-ULP tolerance — that's where the tamper expresses itself first. The V1.5 open-system rows extend this axis to the first NON-UNITAL channels: amplitude damping relaxes population toward |0⟩ (so on |+⟩ it drives ⟨Z⟩ to +γ, a signature no Pauli channel can produce) and thermal relaxation adds a bath raising channel that drives the qubit to the cited n̄/(2n̄+1) detailed-balance occupation — each backed by a deterministic σ⁻ / σ⁺ jump anchor at substrate-ULP where the tamper lands.