BOTTOM-UP MOLECULAR CONSTRUCTION FROM CONSTITUENT RELATIONS

BOTTOM-UP MOLECULAR CONSTRUCTION FROM CONSTITUENT RELATIONS An Extension of PAST-Mol for Generative Reconstruction of Molecular Structure Cláudio Vicente da SilvaIndependent Researcher — Londrina, Paraná, BrazilSeptember 26, 2026 DESCRIPTION This work presents a formal extension of the PAST-Mol framework for bottom-up molecular structure reconstruction from LC-MS/MS spectra. The central architectural transition is from direct spectrum-to-structure identification toward an explicit constructive process in which molecular structures are generated through a sequence of constituent selection, relational construction, opposition, equilibrium, configuration, validation, expansion, closure, forward spectral reconstruction, ranking, and audit. The proposed architecture is expressed by the sequence CONSTITUENT → RELATION → OPPOSITION → EQUILIBRIUM → CONFIGURATION → MOLECULAR STRUCTURE and, in its complete computational form, S → Λ → R → O → E → C₀ → C₁ → ... → Cₙ → G → F(G) → Ŝ → D(S,Ŝ) → K → A → SMILES. Here, S denotes the observed LC-MS/MS spectrum, Λ the spectral latency and unresolved structural information, R the relational representation extracted from the spectrum, O the comparative opposition between candidate configurations, E the compatibility or equilibrium criterion, C₀ the structural root, C₁,...,Cₙ the successive molecular configurations, G the resulting molecular graph, F(G) the forward spectral reconstruction, Ŝ the predicted spectrum, D(S,Ŝ) the spectral discrepancy, K the ranking operation, and A the final structural and computational audit. The extension makes the intermediate construction states explicit: C₀ → C₁ → C₂ → ... → Cₙ = G. Each configuration is represented as a structured molecular state containing constituents, relations, attributes, and structural constraints. Candidate relations may include atom addition, bond formation, bond-order modification, charge assignment, ring closure, substructure extension, and alternative fragment-compatible transformations. The construction process is therefore not restricted to selecting an already existing molecular structure. Instead, it defines a finite computational search over possible structural configurations generated from information contained in the observed spectrum and constrained by mass relationships, neutral losses, isotope relations, precursor information, charge and adduct states, structural validity, and spectral compatibility. The PAST-Mol extension introduces a structural root: C_root ∈ 𝒞_root, where the root may correspond to a constituent, bonded pair, small connected subgraph, fragment-derived substructure, precursor-supported substructure, or recurrent molecular motif. Multiple roots may be retained when the available spectral information does not uniquely determine the initial configuration. For each configuration Cᵢ, a relation-generation operator produces a finite set of admissible structural relations: 𝓡(Cᵢ,S) = {r₁,...,r_b}. Each relation generates a new configuration through the transformation operator Φ(Cᵢ,rⱼ,S) → Cᵢ₊₁^(j). The resulting configuration space is explored through controlled branching and beam selection. Configurations that are temporarily excluded are retained in a discarded-state structure and may subsequently be recovered. The operational search therefore follows the form 𝒞ᵢ₊₁ = Expand(𝒞ᵢ) ∩ Filter(𝒞ᵢ,S) ∪ Recover(𝒟ᵢ). This prevents the computational funnel from becoming an irreversible elimination process and provides an explicit mechanism for structural recovery. Each configuration is evaluated through a compatibility function of the form E(Cᵢ|S) = w₁E_mass + w₂E_fragment + w₃E_loss + w₄E_isotope + w₅E_precursor + w₆E_condition + w₇E_structure, with non-negative weights satisfying Σwⱼ = 1. Structural validity is independently evaluated through constituent, valence, charge, connectivity, formula, and other predefined constraints. The architecture also introduces explicit forward verification. A candidate molecular graph G is transformed into a reconstructed spectrum Ŝ = F(G), and spectral compatibility is measured through D(S,Ŝ). This establishes a bidirectional computational structure: S → G for reconstruction and G → Ŝ for forward verification. The final candidate ranking combines structural compatibility, forward spectral consistency, structural quality, and permitted memory information. Candidate structures are then subjected to a final audit covering graph integrity, constituent validity, structural relations, valence and charge, precursor compatibility, spectral consistency, duplicate control, provenance, ranking, and molecular representation. The framework explicitly records the complete construction trajectory: Mⱼ = (Sⱼ,C₀ⱼ,C₁ⱼ,...,Cₙⱼ,Gⱼ), allowing structural memory to preserve not only the final molecular graph but also the sequence of configurations through which that graph was constructed. The resulting computational cycle is: IDENTIFY → RELATE → CONSTRUCT → VALIDATE → EXPAND → CLOSE → SIMULATE → COMPARE → RANK → AUDIT. TESTABLE ALGORITHM The proposed algorithm receives an LC-MS/MS spectrum S = (P,{(mᵢ,Iᵢ)}ᵢ₌₁ᴺ,A,C,Q) together with a fixed parameter set Θ. The algorithm computes spectral latency, extracts mass and intensity relations, generates constituent candidates, identifies structural roots, generates successive molecular configurations, applies structural and spectral constraints, controls branching through beam selection, stores discarded states, performs recovery operations, closes valid molecular graphs, reconstructs their spectra, computes spectral discrepancy, ranks candidates, and performs a final audit. The output is an ordered candidate set 𝒪(S) = [(G₍₁₎,q₁),...,(G₍ₖ₎,qₖ)], with K ≤ 25. For each candidate, the computational record may contain the molecular graph, canonical molecular representation, final score, complete construction trajectory, reconstructed spectrum, spectral discrepancy, provenance information, and audit status. EXPERIMENTAL VALIDATION The architecture is designed to be tested through controlled computational experiments. The principal comparison separates three conditions: A. Retrieval baseline S → Retrieval → Ranking B. PAST-Mol S → Λ → R → O → E → G → F → M → C → B → R_c → K → A C. PAST-Mol with explicit bottom-up construction S → Λ → R → O → E → C_root → C₁ → ... → Cₙ → G → F → M → C → B → R_c → K → A The contribution of the bottom-up construction mechanism can therefore be evaluated through controlled ablation experiments. The evaluation framework includes: Top-1, Top-3, Top-5, Top-10, and Top-25 structure recovery; MRR@25; construction success rate; valid-structure rate; molecular formula accuracy; graph similarity; fingerprint similarity; spectral reconstruction similarity; candidate-space coverage; recovery rate; failure rate; mean spectral reconstruction error; complete trajectory reproducibility. The mean reciprocal rank at 25 is defined as MRR@25 = (1/N) Σᵢ RR₂₅,ᵢ, where RR₂₅,ᵢ = 1/rᵢ when the correct structure occurs at rank rᵢ ≤ 25, and RR₂₅,ᵢ = 0 otherwise. No experimental performance value is assumed by the formulation itself. Numerical results are properties of the implementation and evaluation dataset and must be obtained through execution of the defined computational protocol. REPRODUCIBILITY The algorithm is specified so that each computational trajectory can be recorded and reproduced. The experimental record includes: dataset and version; spectrum identifiers; precursor information; parameter values; mass tolerance; equilibrium threshold; beam size; branching limits; maximum construction depth; ranking coefficients; forward-model parameters; software versions; molecular databases; random seed where applicable; hardware and execution date; complete construction trajectories; discarded configurations and exclusion reasons; recovered configurations and recovery conditions; final audited candidates. Training, reference, validation, and test information are to be separated according to the experimental protocol so that structural information from evaluation data does not enter the construction or memory mechanisms in an uncontrolled manner. SCIENTIFIC SCOPE The work defines a computational architecture and a testable generative procedure. The Primitive Architecture concepts used in the framework constitute the conceptual and mathematical organization of the proposed reconstruction process and are not presented as established chemical laws. The Spiral Geometry component of the broader Primitive Architecture framework is treated as a procedural representation and is not assumed to constitute an intrinsic geometric law of molecular structure. The proposed bottom-up construction framework does not assume that every LC-MS/MS spectrum uniquely determines a molecular graph. Multiple structural configurations may remain compatible with the same observed information, and the algorithm therefore maintains candidate multiplicity, branching, recovery, and ranking. The principal methodological objective is to transform molecular reconstruction into an explicit sequence of computationally testable operations rather than treating spectrum-to-structure reconstruction as an opaque direct mapping. COMPLETE ARCHITECTURAL FORM The complete extended PAST-Mol architecture can therefore be represented as S → Λ → R → O → E → C_root → C₁ → C₂ → ... → Cₙ → G → Ŝ → D(S,Ŝ) → K → A → SMILES. The construction component is C_root → C₁ → C₂ → ... → Cₙ = G, while the verification component is G → F(G) → Ŝ → D(S,Ŝ). The resulting framework provides a unified computational sequence for spectral interpretation, constituent generation, relational construction, structural expansion, recovery, molecular closure, forward verification, ranking, and audit. This work e