QILP-0: Constructing Observational Declarative Twins of Quantum Circuits

Motivation

• Quantum embeddings and trainable transformations can alter the representations seen by downstream learners, leaving the observable relation produced by the quantum pipeline unexplained by its final prediction alone.QXymb pursues a complementary goal to learned latent representations: reconstructing an explicitly scoped part of observable behaviour as a finite, traceable declarative theory.Source: §1 · p. 2

Framework and auditability

• QXymb is a replaceable framework whose QILP-0 specialization uses Pauli observables and LFIT/PRIDE to induce finite multi-valued propositional theories.Explicit provenance and certification trace symbolic literals to discrete states, numerical intervals or native values, and original observables, supports, and qubits.Source: §1 · p. 3

Scope and exactness

• An observational declarative twin reconstructs only the finite relation within a declared scope, not a circuit’s complete behaviour across all possible conditions.Coverage is relative to a declared observational reference horizon; logical exactness concerns the produced discrete relation, while sampling, numerical, backend, or provider uncertainty is recorded separately.Source: §1 · p. 3

Construction method

• QILP-0 builds its relation through target-independent observable generation, structural traversal, geometry, coverage, column selection, and admissible discretization before target-based auditing and induction.For continuous observations, it uses incremental exact-support blocks, SVD-based geometry, reference-relative coverage, and deterministic mapping from retained latent structure to original observable columns.Source: §1 · p. 3

Validation

• In every reported relation, QILP-0 achieved complete, conflict-free reconstruction with strict reconstruction accuracy equal to one.The validation covers exhaustive Bars & Stripes experiments and Low-Depth MNIST analyses of all 14,708 digit-0/1 instances.Source: §1 · p. 4

2.1. Explainability in QML

• VQCs pose quantum-specific explanation challenges, while classical surrogates, shadow models, observable-dynamics equations, and quantum logics pursue different outputs from QILP-0.Intermediate states may be unavailable, exact state descriptions scale exponentially, and probabilistic measurements and finite-shot noise affect predictions and explanations; classical methods may not transfer unchanged Pira and Ferrie (2024); Gil-Fuster et al. (2024). Surrogates yield predictive models, dynamics work yields generators, and formal logics specify or verify processes Schreiber, Eisert and Meyer (2023); Jerbi, Gyurik, Marshall, Molteni and Dunjko (2024); Cemin, Carnazza, Andergassen, Martius, Carollo and Lesanovsky (2024); Bauer-Marquart, Leue and Schilling (2023); Brunet (2016); Balu (2015).Source: §2.1 · pp. 4–5
• QML explainability includes feature attribution, circuit-component attribution, intrinsically interpretable models, and visual analytics, but these do not provide QILP-0’s declarative reconstruction.Examples include Q-LIME and related feature explanations Pira and Ferrie (2024); Tian and Yang (2024a); Kadian, Garhwal and Kumar (2025); Kottahachchi Kankanamge Don and Khalil (2025); Acampora and Vitiello (2026), gate-level Shapley scores Heese, Gerlach, Mücke, Müller, Jakobs and Piatkowski (2025), concept-driven models Tian and Yang (2024b), and VIOLET Ruan, Liang, Guan, Griffin, Wen, Lin and Wang (2024).Source: §2.1 · p. 4
• QDisc and related representation-learning methods seek compact, physically meaningful latent factors, whereas QILP-0 preserves the declared observable vocabulary and learns rules over it.QDisc combines a probabilistic variational autoencoder with symbolic regression de Schoulepnikoff et al. (2026); QILP-0 instead maps its target-independent geometry back to original observables before discretization and induction, making the approaches complementary.Source: §2.1 · p. 5
• QILP-0 combines target-independent observable traversal and geometry, reference-relative coverage, deterministic mapping to original observables, discretization, rule induction, and certification against the finite observed relation.Its declared reference horizon limits the coverage claim, and each rule literal remains traceable to an original observable, its qubit support, and a discrete state.Source: §2.1 · pp. 5–6

2.2. Formalization of quantum computations

• Quantum dynamic logics formalize and verify quantum programs, while QILP-0 proceeds inductively from an existing circuit’s observed behaviour to a declarative theory.LQP represents measurements, unitaries, locality, and entanglement in a dynamic-logical semantics Baltag and Smets (2006); later work extended probabilistic and decidable reasoning Baltag, Bergfeld, Kishida, Sack, Smets and Zhong (2014); Baltag and Smets (2022).Source: §2.2 · p. 6

2.3. Induction of propositional theories equivalent to datasets

• LFIT induces logic programs from discretized state transitions across several system semantics, including the finite multi-valued relation needed by QILP-0.Its addressed settings include memoryless deterministic, memory-bearing, probabilistic, multi-valued, and continuous time-series systems Inoue et al. (2014); Ribeiro, Magnin, Inoue and Sakama (2015a); Martínez Martínez, Ribeiro, Inoue, Alenyà Ribas and Torras (2015); Ribeiro, Magnin, Inoue and Sakama (2015b); Martínez, Alenyà, Torras, Ribeiro and Inoue (2016); Ribeiro, Tourret, Folschette, Magnin, Borzacchiello, Chinesta, Roux and Inoue (2018b). Annotated multi-valued logic programs support the required representation Ribeiro, Folschette, Magnin, Roux and Inoue (2018a); Ribeiro, Folschette, Magnin and Inoue (2022a).Source: §2.3 · p. 6

3.1. Condition 1: an observational behaviour matrix can be constructed

• QILP-0 represents each analysed input’s observable profile as a row in a real-valued matrix, preserving identifiable columns rather than constructing it from the supervised target.The matrix covers only the declared inputs and observables; target access begins at the later twin-admissibility audit.Source: §3.1 · p. 7

3.2. Condition 2: a semantically adequate observable family can be declared

• The full Pauli family can determine an n-qubit density operator, while QILP-0’s claims remain relative to the provider and observational horizon actually declared and evaluated.Other providers are admissible if their observables are semantically traceable, stably identified, reproducibly organized, and documented with provenance and uncertainty.Source: §3.2 · pp. 7–8

3.3. Condition 3: the observable family admits a reproducible structural grading

• Pauli support supplies a reproducible, target-independent order of exact-support blocks; other providers can be traversed if they define finite graded blocks and an explicit horizon.When the reference horizon is shorter than the provider’s physical horizon, claims do not extend to the unobserved remainder.Source: §3.3 · pp. 8–9

3.4. Condition 4: observable profiles admit a target-independent geometric representation

• SVD organizes observable-response redundancy and independent directions without target labels, then maps retained geometry back to original observable columns for symbolic provenance.Its structural-richness interpretation is limited to the declared dataset and reference horizon, not a universal measure of information or circuit complexity.Source: §3.4 · pp. 9–10

3.5. Condition 5: incremental geometric progress can be measured against a fixed reference

• Before incremental selection, QILP-0 fixes a geometric reference from every complete grade in the declared horizon, so early stopping does not change the reference denominator.The reference pass may evaluate or retrieve the required responses without keeping every observable column resident in memory.Source: §3.5 · p. 10
• Reference-relative progress uses a fixed horizon: local residual novelty is not coverage, and normalized geometric quantities are not physical energy, Shannon information, complexity, or target relevance.The reference is fixed before incremental selection, independently of the target, retained basis, selected observables, and stopping decision.Source: §3.5 · pp. 11–12

3.6. Condition 6: the traversal is monotone and admits explicit stopping conditions

• Traversal stops after a complete grade on reaching the coverage target, an enabled plateau, a downstream resource limit, or reference-horizon exhaustion; coverage concerns only the declared reference, not all quantum structure.A resource endpoint means the next complete layer cannot be processed under the configured budget, not that coverage has converged.Source: §3.6 · pp. 12–13

3.7. Condition 7: latent geometry can be mapped back to the original observable vocabulary

• QILP-0 maps retained geometry to deterministic score-ranked original observables, not latent symbolic variables; target-independent selection preserves a declared association threshold and source provenance.Geometric directions determine which original columns to retain, while selection metadata records each observable’s source identifier, grade, support, structural ordinal, association score, and provider provenance.Source: §3.7 · pp. 14–15

4. Declarative reasoning layer: from continuous observations to a finite relation

• The declarative layer fixes a target-independent finite representation first, then audits its compatibility with an exact deterministic input–target relation.Conditions 8 and 9 govern discretization and twin-admissibility; only after both are satisfied is the finite relation presented to the logic engine.Source: §4 · p. 15

4.1. Condition 8: each observable admits a target-independent finite discretization at a defensible resolution

• Each observable receives a finite domain at a defensible, target-independent resolution, preserving native discrete states and limiting continuous distinctions to those supported by observed profiles and available resolution information.Columns are classified as constant, native discrete, or continuous; the method records the resulting types, cuts or states, occupancies, tolerances, uncertainty metadata, and provenance.Source: §4.1 · pp. 16–17

4.2. Condition 9: the discretized representation is twin-admissible for the observed target

• Twin-admissibility is checked only after discretization: if identical discrete states require different targets, QILP-0 records the conflict and does not claim an exact twin.The failed consistency audit can terminate construction before PRIDE induction while retaining the non-deterministic relation and its provenance.Source: §4.2 · pp. 18–19

4.3. Condition 10: the declarative engine can reconstruct the observed finite relation

• Condition 10 requires the inductive engine to construct a finite logic program that completely and correctly reconstructs the observed relation while meeting rule-body minimality requirements.The engine receives the relation established by the preceding conditions; it does not determine the vocabulary or resolution or repair target inconsistencies.Source: §4.3 · p. 19

PRIDE as inductive propositional logic engine

• PRIDE (Ribeiro, Folschette, Trilling, Glade, Inoue, Magnin and Roux (2022b)) serves as QILP-0’s LFIT engine, inducing complete and correct multi-valued propositional theories from the finite relation.Its role follows the target-independent vocabulary and compatibility stages.Source: PRIDE as inductive propositional logic… · p. 19, §4.3 · p. 19
• The PRIDE-style induction objective is a rule program that explains every observed feature–target transition correctly using minimal feature conditions.A rule body matching a feature state supplies a sufficient condition for its target conclusion in the learned relation.Source: PRIDE as inductive propositional logic… · p. 20

4.4. The observational declarative twin as a contractual object

• Twin rules must be sufficient and minimal for the observed relation, traceable to original observables and their values, grades, and qubits, with scope and uncertainty metadata recorded.The declared scope includes the dataset, observable provider and horizon, stopping and selection policies, discretization, backend or estimator, and relevant numerical metadata.Source: §4.4 · p. 20
• The twin’s equivalence is finite and observational: it does not assert complete-unitary equivalence, reproduction of every predictor behavior, or global minimality in rule count.Source: §4.4 · p. 20
• The pipeline builds a fixed reference, discovers and discretizes selected observables, forms the finite feature–target relation, then induces and certifies the theory.Source: §4.4 · p. 21

5.1. Constructive correctness

• Given a finite dataset and horizon, defined evaluations, finite traceable observables, admissible discretization, and a successful post-discretization audit, Algorithms 1–4 terminate with a finite QILP-0 twin.The resulting program satisfies Definition 8 within the declared observational scope.Source: §5.1 · p. 21
• The induced program completely and correctly reconstructs the finite discrete relation, while every rule literal remains traceable to its value, original observable, grade, qubits, and evaluation metadata.PRIDE’s rule bodies are minimal with respect to the supplied observations in the stated sense.Source: §5.1 · p. 21
• Exactness concerns the reported discretized relation: backend uncertainty qualifies its relationship to ideal expectations, while conflicting targets for identical states prevent an exact-twin claim.The certificate records scope, discretization, uncertainty, conflicts, reconstruction accuracy, theory properties, and literal-to-observable traceability.Source: §5 · p. 21, §5.1 · p. 22

5.2. Computational scope and scalability

• For fixed support bound K, the number of non-identity Pauli words is O(n^K), whereas an unrestricted traversal contains 4^n−1; 100-qubit runs do not establish comparable full-horizon cost.Those runs demonstrate construction of the complete declared support-≤2 reference for the embedding-specific providers under the reported policy.Source: §5.2 · pp. 22–23
• QILP-0 treats acquisition, geometry, discretization, and induction as distinct cost stages, reporting structural growth and stopping scope rather than installation-specific runtimes as general scalability evidence.Geometric selection can reduce downstream variables but cannot remove the acquisition cost of evaluated observable blocks.Source: §5.2 · pp. 22–23

• The evaluation tests whether QILP-0’s construction is practicable and its theories satisfy the observational-twin contract within their declared scope.Source: §6 · p. 25
• Bars & Stripes provides an exhaustive native-discrete setting for comparing two fixed quantum embeddings across increasing system sizes.Source: §6 · p. 25
• Low-Depth MNIST provides a continuous setting for comparing the same data representation before and after a trained variational transformation.Source: §6 · p. 25
• Together, the cases exercise both QILP-0 interface branches and audit geometric, discretization, symbolic, and certification stages under different conditions.Source: §6 · p. 25

6.1. Validation objectives and certificate criteria

• Validation reports the executed structural horizon, geometric coverage and retained dimension, discretization audit, discrete-relation consistency, and row-level reconstruction within the declared observational scope.Default geometric thresholds were 𝜏dir = 0.999 and 𝜏col = 0.999; constant-column, residual-zero, and rank tolerances were 10−12, 10−10, and 10−8. The explicit-residual and column-Gram paths implement the same target-independent selection contract, with configuration and source metadata recorded for audit.Source: §6.1 · p. 25
• An exact observational-twin certificate requires a target-consistent discrete relation that the induced theory reconstructs completely and correctly, with every row covered, no conflicting prediction, and strict accuracy equal to one.The certificate also preserves provenance linking symbolic literals to discrete states and original observables.Source: §6.1 · p. 25
• Backend or provider uncertainty qualifies correspondence between reported observables and ideal quantum responses, but does not make exact symbolic reconstruction of the reported discrete relation approximate.Uncertainty metadata makes the qualification explicit for domain experts.Source: §6.1 · p. 25

6.2.1. Community benchmark and controlled architectural comparison

• The exhaustive binary benchmark spans 28–2,044 patterns and 16–100 qubits, comparing a product embedding with the same local encoding followed by grid-neighbour CZ gates.The all-zero and all-one images are excluded because they satisfy both Bars and Stripes definitions; the controlled comparison changes only the addition of two-qubit interactions.Source: §6.2.1 · p. 25

6.2.2. Exact observable evaluation and executed supports

• Reference horizons for L=4,…,10 were 6, 4, 3, 3, 3, 2, 2, set prospectively using target-independent resource limits.Product-state Pauli words containing Y vanish exactly, while grid-CZ observables are evaluated by exact Clifford pullback; neither route adds approximation or sampling uncertainty.Source: §6.2.2 · p. 26

6.2.3. Incremental observational coverage

• At L=10, coverage was 1.000000 for product and 0.999874 for grid-CZ, while retained geometric dimensions were 109 and 248, respectively.Across sizes, product reached 0.99 coverage at support 3 for L=4–6 and support 2 for L=9–10; grid-CZ reached it at support 2 except L=8 (0.987322). Product L=7 and L=8 stopped at coverages 0.978420 and 0.977275 because the next selected-observable grade exceeded the feature budget, not because of convergence.Source: §6.2.3 · pp. 26–27

6.2.4. From continuous geometry to declarative reconstruction

• The rule set was stable at support 1 for every product size, while grid-CZ changed between supports 1 and 2 for L=4, 5, 7, and 8.For L=5, both embeddings’ theories covered all 60 patterns without conflicts and achieved strict reconstruction accuracy 1.0; adding support 2 did not change the product rules, and the grid-CZ change was localized to one Stripes condition.Source: §6.2.4 · pp. 27–28

6.2.5. Observational-twin certificate

• Minimum strict reconstruction accuracy was 1.0 across all reported native-discrete relations; every PRIDE program covered every analysed row without conflicting predictions.Every selected feature was audited as an exact native discrete observable state, so discretization preserved observed states without numerical cuts.Source: §6.2.5 · p. 28
• Sample-sufficiency warnings were retained as diagnostic metadata and did not alter observed native states or the exact observational-twin certificate.The certificate applies to each reported layer’s native-discrete relation under the declared observational scope.Source: §6.2.5 · p. 28

6.2.6. Methodological interpretation

• The results do not establish a universal advantage of entanglement: grid-CZ can approach product coverage while retaining greater geometric dimension, and added structure need not change the rule theory.Resource-limited endpoints are separated from convergence claims.Source: §6.2.3 · p. 26, §6.2.4 · p. 27, §6.2.6 · p. 28

6.3.1. Community dataset and experimental comparison

• The experiment retains 14,708 digit-0/1 instances on 11 qubits, and the depth-4 image preparation has mean FRQI fidelity 0.968639.The preparation uses 171 image-dependent rotations and 80 CNOT gates; fidelity is metadata only and is not supplied to the symbolic learner.Source: §6.3.1 · p. 28

6.3.2. Variational circuit and supervised training

• VQC validation accuracy rises from 0.465330 before training to 0.971108 after training on the fixed 80/20 split.Training uses five epochs, batches of 128, Adam at learning rate 0.01, and seed 0; after parameters are fixed, subsequent observable analysis and discretization do not use labels.Source: §6.3.2 · p. 29

6.3.3. Exact observable evaluation and executed supports

• Exact evaluation covers complete Pauli families at supports 1, 2, and 3 for both representations, retaining all rows and sampling no observable columns.Expectations come from exact simulated states, without finite-shot uncertainty or hardware noise; the support blocks contain 22, 275, and 2,310 non-constant columns, respectively.Source: §6.3.3 · p. 29

6.3.4. Incremental observational coverage

• Support-1 coverage rises from 0.355399 to 0.667402 and accumulated support-2 coverage from 0.809468 to 0.901905 after training.Final coverages are almost identical, while retained geometric dimension increases from 1,819 to 2,092 and selected original observables from 2,168 to 2,498; these are experiment-specific geometry results, not circuit-complexity measures.Source: §6.3.4 · p. 29, Table 3 · p. 30

6.3.5. Declarative reconstruction and theory structure

• Across every accumulated-support layer, QILP-0 reconstructs all 14,708 rows with strict accuracy 1.0 and no conflicting predictions.This certifies exact reconstruction of each finite discrete observational relation, not preservation of every metric distinction in the continuous matrices.Source: §6.3.5 · p. 29, §6.3.6 · pp. 30–31
• Post-VQC support-3 theories contain 2,361 rules versus 1,106 before training, despite available states decreasing from 350 to 216.Across the four observables used in final theories, used observable–state atoms decline from 244 to 215 and observable-level schemas rise from 21 to 24; rule bodies use only observables of q0 and q10.Source: §6.3.5 · pp. 29–30

6.3.6. Admissible-discretization and observational-twin certificate

• Across six accumulated-support datasets, all selected columns are continuous and non-constant, every effective bin is occupied, and no requested cut set collapses numerically.Sample-sufficiency warnings are diagnostics only; the target-independent discretization meets the declared resolution contract, while exactness applies to the resulting finite relation.Source: §6.3.6 · pp. 30–31, Table 6 · p. 31

6.3.7. Methodological interpretation

• The Low-Depth MNIST case demonstrates QILP-0 auditing and exactly reconstructing continuous observational relations before and after a supervised quantum transformation.Training improves held-out validation accuracy, changes low-support geometry and yields a larger declarative theory, whose final rule bodies remain restricted to observables of q0 and q10.Source: §6.3.7 · p. 31

6.4. Cross-experiment certification

• All four routes use exact observable evaluation, target-independent symbolic-vocabulary construction, complete row-level audits, and exact PRIDE reconstruction.These are the common certificate fields collected in Table 7.Source: §6.4 · p. 31
• Bars & Stripes exercises preservation of native discrete states, whereas Low-Depth MNIST exercises the continuous admissible-discretization contract.Source: §6.4 · p. 31
• Within each run’s finite observational scope, all four routes achieve exact PRIDE reconstruction of the resulting discrete relation.The certification applies to the corresponding reported discrete relations; coverage is reported separately relative to each run’s declared observational reference horizon.Source: §6.4 · p. 31

• Estimated observables with uncertainty metadata can yield exact reconstruction of the reported discrete relation, while correspondence to ideal quantum responses remains qualified by that uncertainty.The symbolic equivalence is exact with respect to the discretized relation, not necessarily the underlying ideal responses.Source: §6.5 · p. 31
• When identical discrete observational states carry incompatible targets, QILP-0 preserves the non-deterministic relation and provenance but makes no exact-twin claim.In the exact-twin branch, the consistency audit stops construction before PRIDE induction and records the conflicting states.Source: §6.5 · p. 31
• A resource-limited traversal changes the declared observational scope but does not itself make logical reconstruction approximate.Source: §6.5 · p. 31
• Certified approximate observational twins would require an explicit contract specifying admitted discrepancies and bounds; no such contract is claimed for the reported exact experiments.The contract could define bounds at the observational, discretization, or symbolic-reconstruction level.Source: §6.5 · p. 32

6.6. Additional implementation validation

• Exploratory checks across MQT Bench, small TFIM and Heisenberg configurations, and increasing-size Bars-and-Stripes circuits tested prototype invariants and exposed practical resource limits.Checks covered exact-support generation, incremental accumulation, target-independent geometry, coverage and stopping metadata, agnostic discretization, PRIDE induction, provenance, output handling, and backend consistency.Source: §6.6 · p. 32
• These exploratory executions are not comparative benchmarks; quantitative experimental claims are restricted to the Bars & Stripes and Low-Depth MNIST studies.The configurations were not all executed under a single controlled protocol.Source: §6.6 · p. 32

Contributions

• QILP-0 constructs a finite-scope declarative twin without letting the target determine the observational vocabulary or severing literals from their original observables.Continuous geometry guides reproducible selection, but retained structure is mapped back to original observable columns before symbolic processing; exactness applies to the resulting finite task-conditioned discrete relation.Source: §7 · p. 35

Results

• Every reported Bars & Stripes and Low-Depth MNIST relation received an exact-twin certificate with complete, conflict-free reconstruction.Bars & Stripes covered product and grid-CZ embeddings from 16 to 100 qubits. Low-Depth MNIST analyzed all 14,708 digit-0/1 instances and achieved strict reconstruction accuracy equal to one at every reported accumulated support in both representations.Source: §7 · p. 35

Limitations

• QILP-0 is an order-0 finite multi-valued propositional construction, and its certificates cover only finite datasets within declared observational reference horizons.When Kref < Kphys, coverage and certification are relative to Kref; no percentage of unobserved higher-support geometry is inferred.Source: §7 · p. 35
• Full Pauli traversal grows exponentially, and the reported 100-qubit Bars & Stripes runs rely on embedding-specific algebra and specialized providers.The support-bounded family is polynomial in qubit count only when maximum support is fixed; practical horizon limits also depend on provider, dataset, execution environment, and budgets.Source: §7 · p. 35

Future Work

• Future work will test finite-shot, noisy, and real-hardware execution and define an explicit contract for approximate twins.Uncertainty and calibration information would enter observable-resolution metadata, while logical exactness remains relative to the reported discrete relation; approximation criteria should specify admitted discrepancies and quantitative bounds.Source: §7 · pp. 35–36
• Future observational providers and resource-aware geometric processing should scale while preserving stable semantics, provenance, and reference-relative coverage.Proposed providers include locality-, circuit-, tensor-network-, classical-shadow-, and analytically structured approaches; streaming, matrix-free, and distributed processing plus improved resource assessment and adaptive stopping are also proposed.Source: §7 · p. 36
• Future work will compare admissible discretization criteria and develop richer QXymb specializations with explicit semantic and reconstruction guarantees.The paper proposes studying when alternative resolution criteria change the symbolic relation or induced theory, and exploring other declarative engines and more expressive logical representations.Source: §7 · p. 36
• Further work will broaden empirical validation, connect induced theories to formal verification, and test whether task-specific qubit footprints can guide circuit simplification.The paper cautions that footprint-based simplification requires separate causal or ablation analysis: absence from final rule bodies does not show a qubit is unnecessary for producing active observables.Source: §7 · p. 36

Reproducibility package

• The package executes the complete QILP-0 path, from target-independent observable acquisition and geometric analysis to PRIDE induction and row-level twin certification.It also covers preservation of original observables, discretization, and comparison against a fixed observational reference.Source: Data and code availability · p. 36

Didactic configuration

• The executable uses an exhaustive non-uniform 3×3 Bars & Stripes instance with declared K_ref = 2, demonstrating the contract after the reference horizon is supplied.This didactic configuration does not reproduce the prospective resource policy used to choose horizons for the larger experiments.Source: Data and code availability · p. 36

Scope and availability

• The didactic case is smaller than the paper’s L = 4,…,10 experiments and is not an additional quantitative benchmark; its outputs include the scope, coverage trajectory, audits, theory, and certificate.The broader QXymb codebase remains under active development; the package’s v1.0.0 release is archived in Zenodo (doi:10.5281/zenodo.22165888).Source: Data and code availability · pp. 36–37

Reproducibility result

• 12 rows are reconstructed without conflicting predictions, with strict accuracy equal to one and the reference theory hash reproduced in a clean Python environment.The run uses only package-declared dependencies; PRIDE is accessed through the external PyLFIT 0.5.1 package.Source: Data and code availability · pp. 36–37

Funding

• The European Union funded the research, but the authors’ views and opinions do not necessarily reflect the EU or ERCEA, and neither is responsible for them.Source: Funding · p. 37