ELSD v4.0: Correction of a Metalloenzyme VQE Benchmark and an Independently Verified Correlated State for a Zn²⁺ Carbonic Anhydrase II Active-Site Model

ELSD (Electronic Landscape Stability Diagnostics) v4.0: Correction of a Metalloenzyme VQE Benchmark and an Independently Verified Correlated State for a Zn²⁺ Carbonic Anhydrase II Active-Site Model Supersession notice. This version supersedes v3.0 of this record (10.5281/zenodo.20318424, May 20, 2026) and corrects the ELSD benchmark datasets 10.5281/zenodo.19142883 (v1.0), 10.5281/zenodo.19163956 (v2.0) and 10.5281/zenodo.19212485 (v3.0). The chemistry interpretations in those datasets, and the verdicts in v3.0 of this record, are withdrawn for the reasons given in §3–§4. The original files remain available as a record of what the software produced. Plain Language Summary What we built. Software that simulates the electrons at the metal centers of enzymes that drugs target. It uses a quantum-computing algorithm (the variational quantum eigensolver, VQE), run on a GPU simulator, together with checks meant to tell whether each result can be trusted. What a stricter audit of our published benchmark found. We built a verification process that measures each saved result directly instead of relying on the software's own report. Applied to our earlier published benchmark, it showed that those simulations had stayed at their starting approximation. The differences we had reported between drug targets came from a defect in a penalty term inside the software, not from the chemistry. We traced this to specific defects in the code and corrected them. What the corrected engine does. We ran the corrected engine on a model of the zinc site of carbonic anhydrase II, an enzyme targeted by glaucoma drugs. It captured 74–80% of the extra accuracy available in the model, and 67–76% after keeping only the correct spin state. A second, independently built set of tools reproduced every reported number to ten or more decimal places and identified what is still unfinished: the runs did not fully converge, and part of each result is in the wrong spin state. What this does and does not mean. None of this tells anyone which drug will work. The zinc model was chosen to be small enough that the exact answer can also be computed by conventional means, and that is what makes it a fair test: a quantum method can only be checked where the right answer is already known. On that test, the engine recovered most of the available accuracy on a real metal-enzyme site, and its own safety checks flagged the remaining problems. The next step is to apply it, with the same checks, to problems where the exact answer is out of reach. Why it matters. A computational result can pass its own internal checks and still not measure what it claims to measure. We publish the full verification protocol, the evidence, and the corrected results so that others can check our work and apply the same tests to their own. Abstract We report a forensic re-examination of the ELSD (Electronic Landscape Stability Diagnostics) metalloenzyme benchmark, which used the seed-ensemble spread σ of penalized VQE energies as a measure of electronic-landscape stability for Cu, Zn and Fe active-site models. Evaluating the physical energy of all 110 deposited statevectors (22 systems × 5 seeds) shows that every state is the Hartree–Fock (HF) determinant of its target (N, S_z) sector to within 1.3 × 10⁻⁵ Ha. The published σ values are the seed-to-seed scatter of a constant offset, 3.75–6.25 Ha, introduced by an incompletely expanded S_z penalty. We identify the engine defects responsible, including a "UCCSD-like" double-excitation block that changes particle number and therefore cannot move the state within the target sector. A particle-conserving ansatz (spc) recovers 99.9% of the active-space correlation energy for H₂O/STO-3G and 74–80% (67–76% after singlet projection) for a 20-qubit Zn²⁺ carbonic anhydrase II active-site model. Two independently built toolchains agree on every reported quantity: energies to ≤ 2 × 10⁻¹² Ha and dimensionless quantities to ≤ 1.4 × 10⁻¹¹. We describe the verification protocol, state the limitations of the corrected result, and withdraw the chemistry interpretations of the earlier datasets. Key results [M] Deposited states. All 110 deposited statevectors are the HF determinant of their own (N, S_z) sector (max |E_sector − E_HF| = 1.3 × 10⁻⁵ Ha). The correlation energy available in each active space, 0.03–112 kcal/mol, was not recovered in any of them. [M] What σ measured. Each published σ equals the scatter of a penalty offset λ_sz·(n_orb/8 − t²), not scatter in physical energy. Across seeds, the physical energy varies by at most 4.1 × 10⁻³ kcal/mol. [M] Root causes. Four engine defects (§4) plus four data-handling and provenance issues. The decisive one (D2) is a double-excitation block that changes particle number, which leaves HF a strict local minimum. [M] Corrected method. The particle-conserving spc ansatz (engine v12.1.0 and later) recovers genuine correlation, verified from saved states: H₂O 99.9%, N₂ 56%, and the Zn²⁺ CA-II model 74–80%. [M] Independent verification. The Zn²⁺ result was produced with one AI-agent toolchain and verified by a second, independently built one, with measurements hash-sealed before the producing run's claims were read. All 30 numerical comparisons pass: energies agree to ≤ 2 × 10⁻¹² Ha and dimensionless quantities to ≤ 1.4 × 10⁻¹¹. Labels: [M] = measured and reproducible from the files in this record; [I] = inference. 1. Background and scope 1.1 Records covered Record Version Original claim Status in this version 10.5281/zenodo.19142883 Dataset v1.0 (Mar 2026) 10 locked systems; σ as landscape ruggedness; Cu²⁺ SOD 9.2× apo/bound ratio Interpretations withdrawn; data retained 10.5281/zenodo.19163956 Dataset v2.0 (Mar 2026) 16 locked results; three-part Cu mechanistic decomposition Interpretations withdrawn; data retained 10.5281/zenodo.19212485 Dataset v3.0 (Mar 25, 2026) 25 results; VAP-1 "Nitrogen Rule"; DOTA/NOTA ranking Interpretations withdrawn; data retained This record v3.0 (May 20, 2026) Audit: 12 of 13 systems pass; v1.0 σ reproduces exactly; 9.2× ratio verified Superseded and revised 1.2 How v3.0 of this record is revised v3.0 checked the deposited statevectors against the deposit's own gate criteria (sector cleanliness, dominant-determinant weight dom_p > 0.99, and identical dominant bitstring across seeds) and recomputed σ from the convergence histories. It explicitly left open whether σ reflects physical-energy scatter, pending an in-sector exact reference. This version supplies that reference and the physical-energy measurement, which changes several of v3.0's conclusions: v3.0 section v3.0 statement This version §2.1, §3 12 of 13 systems pass the locked-gate criteria The criteria are satisfied by any single determinant, so they cannot distinguish a converged correlated state from an HF-locked one. All 110 states are HF-locked (§3.1) §2.4 v1.0 σ reproduces exactly from history.csv; v2.0 divergences are a documentation gap The seven v1.0 values were computed from history-tail energies; the v2.0 values used the npz vqe_energy field, which is the deposit's documented recipe (§3.3). Both measure the penalty offset (§3.2) §2.5 The 9.2× Cu²⁺ SOD apo/bound ratio is audit-verified Withdrawn (§3.3, §6) §2.6 Canonical convention is qubit 2i = β The engine source defines α = qubit 2p, β = qubit 2p+1, with qubit 0 as the most significant bit. [I] The v3.0 convention is consistent with reading bitstrings in reversed order, which swaps even and odd positions §3 The geometry-axis and metal-identity decomposition rows survive Withdrawn (§6) §4 Three v1.0 systems unaudited; their values stand Resolved (§3.4) §5 Whether σ reflects physical ruggedness or optimizer behavior is open Answered: σ is penalty-offset scatter (§3.1–§3.2) §5 SCF root stability across rebuilds is untested Tested for Zn_CA2_imidazole: five builds, HF spread 4.5 × 10⁻¹² Ha, same root, internally unstable (§5.2). Not yet tested for the other systems (§8) 2. Methods: verification protocol Each phase of the work followed the same protocol: State-level measurement. The in-sector physical energy ⟨ψ|H|ψ⟩ of each saved statevector is evaluated in float64 from the physical (unpenalized, untruncated) Hamiltonian, together with out-of-sector weight, dominant-determinant weight and, for the Zn²⁺ result, the total-spin decomposition and overlap with the exact ground state. The software's reported energies are compared against these measurements, never used in their place. Exact references. Each system's exact in-sector ground state is computed by sparse Lanczos on the same qubit Hamiltonian, without constructing the full 2²⁰-dimensional operator. Fixtures before data. Every measuring tool passed test cases with known answers before touching real data: 43/43 for the physical-energy auditor, 22/22 spin and sector checks, and 24/24 for the D2 diagnostic bench. When a fixture failed, the tool was corrected, not the test. Byte-level provenance. 385 deposited npz files were matched by SHA-256 to files in the original compute-machine backup (v1: 132, v2: 154, v3: 99), and the engine build that produced them was identified. Fail-closed execution. New runs used no Hamiltonian truncation, no overridden guards and no substituted SCF roots. When a guard tripped, the run stopped and reported what it had established. Separation of production and verification. The Zn²⁺ result was produced and verified by separate toolchains with separately sourced code. The verifier's measurements were hash-sealed before it read the producing run's claims. 3. Results I: the deposited benchmark 3.1 Every deposited state is the HF determinant [M] Scope: all 22 deposit systems with saved statevectors, 5 seeds each. All 22 reproduce the deposit hf_energy; for 7 of them this requires replicating the engine's SPIN-FIX behavior (§4). Result: max |E_sector − E_HF| = 1.3 × 10⁻⁵ Ha. The dominant determinant is the HF occupation in all 110 files. The orbital-sign-gauge envelope over all systems and seeds is −3.4 × 10⁻⁵ … +3.5 × 10⁻⁵ Ha. Available correlation: the exact in-sector ground state lies 0.03–112 kcal/mol below E_HF, depending on the system. 3.2 What σ measured [M] The deposit vqe_energy lies above the physical energy of the saved state by a constant: 5.000 Ha for the 20-qubit Cu doublets, 3.750 Ha for the 16-qubit DOTA/NOTA systems, 6.250 Ha for Cu_AOC3_minimal_hydroxide, and ≈0 for the Zn systems (λ_sz = 0). This equals λ_sz·(n_orb/8 − t²), the value on the HF determinant of the engine's hand-expanded S_z penalty, which omits the same-orbital Z_αZ_β term of Ŝ_z². A free fit across 20 seed-points gives λ_sz = 4.9998. σ_npz equals the σ of this offset in every system. Its seed-to-seed variation tracks out-of-sector leakage (correlations up to 0.99) and float32 quantization (grid spacing 0.0383 kcal/mol for |E| of 512–1024 Ha). 3.3 Energy sources in the published tables [M] Seven v1.0 values come from history.csv tail energies (Zn_CA2_imidazole, Zn_CA2_sulfonamide, Cu_SOD_minimal, Cu_SOD_2imidazole, Cu_SOD_2imidazole_water, Cu_SOD_protonated, Cu_SOD_acetate). The other fifteen come from the npz vqe_energy field, which the deposit README's own energy.min() recipe reproduces. Example: Cu_SOD_2imidazole σ is 0.0803 as published and 0.1383 from npz. The 9.24× apo/bound ratio becomes 3.46×. Both values measure the offset of §3.2. 3.4 Systems without deposited per-seed data [M] System Finding Zn_CA2_minimal (σ 0.0933) No source found in the deposits or the compute-machine backup; no five-seed set reproduces it. FePorphyrin_FeII_ls (σ 0.3375) Reproduced from seed logs only; its one saved statevector lies mostly outside the target sector. Zn_squareplanar (σ 43.29) Files found in the backup, not in the deposits; σ is their sample (ddof=1) standard deviation. This is the only published σ that reflects physical-energy scatter: the seeds land on different single determinants, three of them 63–110 mHa below the aufbau HF determinant. [I] This indicates that the SCF reference is not the lowest single determinant in that active window, rather than correlation recovery. 3.5 Other campaigns on the same engine [M] Of 262 audited seeds across all campaigns in the backup, the only states below HF are the three Zn_squareplanar seeds above, each a single determinant. The never-deposited IDE, NEP and ECE1 campaign states are HF-locked as well. 4. Results II: root causes in the engine [M] The 385 deposited data files are byte-identical (SHA-256) to files in the compute-machine backup. [I] The engine that produced them is attributed to the March 17–30, 2026 prometheus_vqe_engine_penalized.py lineage on two lines of evidence: the penalty offsets of §3.2 match its penalty function, which is the same in all 40 archived March versions; and the SPIN-FIX messages in the run logs match its code. # Defect Effect D2 The "UCCSD-like" ansatz's double-excitation block is cry(occ, virt) with an occupied control and an empty target. This is a bare RY on an empty qubit, which changes particle number (ΔN = +1). No gate in that ansatz moves an electron within the (N, S_z) sector. HF is a strict local minimum: on H₂/6-31G all 105 gradients at θ = 0 are exactly 0.0 and the Hessian has no negative eigenvalue. Adam and L-BFGS, initialization scales 0.01–0.3, and penalties on or off all return to HF, in every engine version through v12.3.2. The "UCCSD-like" label in the deposits is inaccurate. D1 n_occ = min(n_electrons, n_qubits//2) compares electron count to spatial-orbital count. For 10–12 electrons in 10 orbitals, n_virt = 0 and the double block does not execute. Secondary to D2. D3 Hand-expanded S_z penalty omitting the same-orbital Z_αZ_β term. Produces the offset of §3.2. Fixed in the engine on 2026-05-14. D4 "SPIN-FIX": when PySCF rejected a requested spin as parity-inconsistent, the engine changed mol.spin without stopping. Seven systems were computed in an active window with a mismatched electron count. Since v12.0.0 the engine refuses instead. — Hamiltonian truncation to about 3,100 terms. The optimizer worked on a reduced operator (e.g. 14,247 → 3,100 terms, 0.88 Ha of coefficient weight dropped for Cu_SOD_2imidazole). — Mixed energy sources in published tables. §3.3. — A May 2026 exact-reference comparison reported gap_std = σ as verification. std(E_i − E_ref) = std(E_i) for any constant E_ref, so this comparison carries no verification content; the informative quantity is the mean gap. The solver's engine-independence check was disabled, and its Hamiltonian builder shares 74% of its code with the engine. — Release provenance. The release manifest lists 112 files, 28 of them absent; an audit script dated after the seal was present in the tree, unsigned. Candidate fix for D2 [M]. Replacing the CRY block with the engine's own α–β pair-double gate makes the uccsd path leave HF (H₂/6-31G: −16.679 mHa, 66.9% of the available correlation; H₂O/STO-3G at depth 3: −25.090 mHa, 50.6%, matching spc at the same depth). It remains a candidate pending independent verification. The results in §5 use the spc ansatz. 5. Results III: corrected method, independently verified 5.1 Small molecules (spc and ADAPT, engine v12.1.0 and later) [M] System Qubits Best E_phys − E_HF Exact available Recovered Evidence H₂O / STO-3G 14 −49.55 mHa 49.58 mHa 99.9% 32 saved superposition states below HF H₂ / 6-31G 8 −16.68 mHa 24.92 mHa 67.0% ADAPT and spc N₂ / STO-3G 20 −88.2 mHa 156.94 mHa 56.2% 21 checkpoint replays reproduce their run's claim to ≤ 1.5 mHa These are standard correctness tests. They establish that the corrected ansatz recovers genuine correlation; they are not a claim of advantage over classical methods. 5.2 Zn²⁺ carbonic anhydrase II active-site model [M] Setup. Zn_CA2_imidazole: charge 0, singlet, 10 electrons in 10 active orbitals (20 qubits), LANL2DZ/ECP on Zn and 6-31G on light atoms. Engine v12.3.2 (SHA-256 600b7727…57999), spc depth 2, Adam lr 0.02, 40 iterations, initialization scale 0.001, seeds 0–2. The full Hamiltonian was used (10,299–11,939 Pauli terms across the three production builds) with zero terms dropped, measured with a float64-accumulating backend. Five independent SCF-reproducibility builds agree on E_HF to 4.5 × 10⁻¹² Ha, while their term counts span 10,235–11,939 (about 15%). Because the term count is not build-invariant, every seed's gate and exact reference use that seed's own saved operator. Exact reference. E_HF − E_exact = 80.99 mHa (50.82 kcal/mol), cross-checked four ways: the engine's CASCI, two independently written sparse-Lanczos implementations, and each seed's own frozen operator. The exact sector ground state is nondegenerate and essentially pure singlet (⟨S²⟩ ≈ 10⁻¹²); the next level lies 3.77 mHa higher. Seed E_phys − E_HF (mHa) Recovered Singlet weight Singlet-projected E − E_HF (mHa) Singlet correlation recovered ⟨S²⟩ Overlap² with exact ground (singlet-projected) 0 −60.21 74.3% 46.6% −54.08 66.8% 1.067 0.358 (0.767) 1 −64.54 79.7% 41.6% −59.69 73.7% 1.169 0.321 (0.773) 2 −62.26 76.9% 45.3% −61.75 76.2% 1.095 0.294 (0.648) Verification. All three states are genuine superpositions, in sector (out-of-sector weight ≈ 10⁻¹⁷), and below HF. The physical-energy spread across seeds is 1.11 kcal/mol (ddof=0), which is real scatter in physical energy, in contrast with the deposited σ. Singlet content. Projection onto S = 0 retains 90–99% of each state's lowering below HF, so the recovered correlation is not an artifact of triplet admixture. Engine safeguards. The engine's own guards blocked the result as not decision-grade (S2_sector_violation, scf_internal_instability) and recorded further abstain reasons (sector_evidence_incomplete, variational_bound_unchecked, optimizer_budget_exhausted). These verdicts were recorded, not overridden; the independent references check the variational ordering separately. 6. Status of earlier claims Withdrawn (all interpretations built on σ in ELSD v1.0–v3.0 and in v3.0 of this record): the Cu²⁺ SOD 9.2× apo/bound ratio and the SOD perturbation series the three-part Cu mechanistic decomposition, all three axes the Zn²⁺ CA2 warhead ladder and the Rigid Stability / Coherent Open-Shell classifications the VAP-1/AOC3 "Nitrogen Rule" the DOTA vs NOTA chelator ranking (also not statistically resolved on the published numbers: F-test p = 0.83 with 5 seeds each) the IDE/NEP catalytic-state maps the May 2026 gap_std = σ exact-reference verification the published values of Zn_CA2_minimal and FePorphyrin_FeII_ls Retained: the deposited files, as an accurate record of what the March 2026 engine produced; the determinant-switching finding for Zn_squareplanar (§3.4); and v3.0's finding that the Cu_SOD_minimal_CuI d⁹ → d¹⁰ comparison does not hold. 7. Discussion [I] Reference-side checks are not sufficient. The original pipeline included SCF stability tests, sector-purity gates, an exact in-sector reference and a variational-bound check. Each was correctly implemented, and every one is satisfied by a state that never leaves HF. The check that distinguishes a correlated state from the reference, the physical energy of the saved state relative to E_HF, was absent. We recommend it as a required gate for any VQE result, alongside a total-spin check for open-shell or singlet targets. [I] Seed-ensemble σ is fragile as a stability metric. σ is sensitive to constant penalty offsets, out-of-sector leakage and floating-point quantization, and it is small whenever every seed is trapped at the same point. If σ is reported, it should be computed from the physical energy of the saved states and reported together with the mean gap to an exact reference. [I] Independent verification found what self-checking did not. The earlier work was built and checked within one workflow, and the checks inherited the workflow's assumptions. The audit that found the problem, and the verification of the corrected result, used separately sourced tools with fixtures run first and measurements sealed before claims were read. That separation is what made both the correction and the new result checkable. What the corrected engine contributes. The engine now runs metal-enzyme active-space problems as quantum circuits that conserve particle number, recovers most of the available correlation on a 20-qubit transition-metal model with the full Hamiltonian, refuses invalid inputs and oversized runs instead of silently altering them, and saves every run's Hamiltonian, orbitals and state in a form that a third party can verify. The exact answer for this model can also be computed classically; that is what makes it a usable benchmark. The value of the engine lies in carrying the same verified workflow to systems where the exact answer is not available. 8. Limitations and open items Spin contamination. The Zn²⁺ states have majority triplet weight. The singlet figures are post-processing, not a spin-pure run. Next: S²-penalized or spin-adapted runs. Convergence. 40 iterations did not converge (optimizer_stationary = false). Next: longer runs. Wavefunction fidelity. Overlaps with the exact ground state are 29–36% (65–77% after singlet projection); energy recovery is ahead of state quality. SCF root. The selected root is internally unstable (lowest Hessian eigenvalue −0.0327). Following it lowers E_HF by 0.457 mHa, which bounds orbital-relaxation contamination along that path. Next: repeat on the stable root. Precision. State preparation is complex64 with float32 parameters; measurement and verification are float64. Spin symmetry of the operator. The saved operators carry a small H/S² commutator defect: ‖[H, S²]r‖ = 1.8–2.0 × 10⁻⁶ Ha for normalized random probe vectors r (probes, not operator-norm bounds), present in both independently built operators. The resulting cross-spin contribution to each VQE energy, E − Σ_S w_S E_S, is −1.2 × 10⁻¹⁰, −1.3 × 10⁻¹⁰ and +3.8 × 10⁻¹¹ Ha for seeds 0–2, which is negligible at the precision reported here. Its origin is not yet diagnosed. [I] Low-lying level. The first excited level of the Zn²⁺ model lies only 3.77 mHa above the ground state, which may relate to active-space orbital selection and to the SCF instability. Scope. A reduced 10e/10o active-space model. It says nothing about inhibitor binding, drug activity or chemical adequacy. D2 fix. The candidate fix is untested on open-shell and transition-metal systems; retiring or rerouting the uccsd path is preferred. Related records. 10.5281/zenodo.20264767 (Fe₄N₂), 10.5281/zenodo.20279079 (LLZO) and 10.5281/zenodo.20298089 were built on the same engine family and are under the same review. 9. Files in this version ELSD_v4_correction_bundle.zip contains a top-level README.md mapping each claim above to its supporting file, and these folders: 01_sigma_audit/: 25-system σ re-derivation, energy-source attribution, float32 floor and pair analysis 02_lanczos_gap_audit/: the gap_std = σ identity; physical-energy diagnostic 03_physical_energy_audit/: all 110 deposited states; penalty-offset identification; SPIN-FIX replication results (the replication tool itself is not included) 04_ganymede_backup_audit/: engine-build identification, byte matching to the deposits, missing-data search 05_postmay_engine_audit/: engine timeline; spc/ADAPT recovery on small molecules 06_d2_diagnosis/: D2 root cause, tests, candidate-fix results, LLM call ledger 07_zn_ca2_spc_pilot/: production run, saved statevectors, frozen Hamiltonians, exact references, gate results 08_zn_ca2_independent_verification/: sealed independent measurements, spin decomposition, overlap, line-by-line comparison MANIFEST.sha256: SHA-256 of every file in the bundle Each folder includes its findings document (FINDINGS.md; SUMMARY.md in folder 01), its results tables and its tools, and fixture outputs for the phases that ran fixtures. The proprietary engine source is not included, nor are large reproducible intermediates. Five staged audit files that originally quoted engine source have had the quoted block replaced by a placeholder; each is listed in REDACTIONS.csv. The original deposit files remain available in the records listed in §1.1. 10. Citation Cite this version for the audit, the root-cause analysis and the Zn²⁺ CA-II result (§5.2, with its stated limitations). The σ values in ELSD v1.0–v3.0 should be cited, if at all, as "seed-ensemble scatter of a penalty-term offset on Hartree–Fock-locked states (Zenodo 10.5281/zenodo.23933642, v4.0)", not as measures of electronic-landscape stability. Quantum-Clarity LLC · November 2026 · Data: CC BY 4.0