1 Introduction↩︎

The design of an industrial materials ontology faces three simultaneous challenges. None is new in isolation; what is new is that an ontology entering productive use today must answer all three at once.

The first challenge is the horizontal fragmentation of the materials-science ontology landscape. [1] identify 94 ontologies in the field, of which over 40 are structurally incompatible [2]. Within the German Platform MaterialDigital (PMD) consortium¹, more than a dozen projects — KnowNow [60], Mieller-Ferrit [27], SmaDi [34], KupferDigital, GlasDigital, StahlDigital, DiProMag, iBain [14] — each developed its own material-specific ontology, repeatedly re-modelling laboratory workflows, equipment, and measurement methods that are essentially identical across all of them. Only a fraction of the modelled knowledge is material-specific (the actual class hierarchy of ceramics, polymers, batteries, …); the largest part — workflow provenance, equipment, methods, identifier schemes — is material-agnostic and reusable.

The second challenge is the vertical convergence pressure driven by EU regulation. The Corporate Sustainability Reporting Directive (CSRD/ESRS), the Corporate Sustainability Due Diligence Directive (CSDDD), the Packaging and Packaging Waste Regulation (PPWR), the Carbon Border Adjustment Mechanism (CBAM), the Right-to-Repair Directive (R2R), the EU AI Act, the Construction Products Regulation (CPR), and the Ecodesign for Sustainable Products Regulation (ESPR) all require digital product passports (DPPs) that combine material with manufacturing and value-chain information. A materials ontology that addresses only horizontal fragmentation (per material class) without this vertical extension is incomplete for any consumer operating under contemporary EU regulation. The convergence is visible in the structure of the PMD programme itself: PMD Phase-3 explicitly incorporates the Wertschöpfungskette (value chain) as a programme requirement, anticipating integration with Manufacturing-X.

The third challenge is mechanistic explanation depth. A materials ontology that records that BNT-BT has \(d_{33} \approx 580\,\text{pC/N}\) at its morphotropic phase boundary stores a fact. An ontology that can also surface why — Bi-6s\(^2\) lone-pair stereo-activity, anomalous Born effective charges, soft-mode at the Brillouin-zone centre, R3c\(\leftrightarrow\)P4mm domain coexistence, V\(_\text{O}^{\bullet\bullet}\) defect chemistry, Hall-Petch grain-boundary mediation, Mn-acceptor pinning of domain-wall mobility — provides authoritativeness that a description-only vocabulary cannot. The challenge is to attach mechanistic explanation classes systematically without inflating the vocabulary into a textbook.

We answer these three challenges with a single integrated design: a multi-level, modular ontology with two independent classification axes plus a seven-tier mechanistic-explanation skeleton internal to the material-specific level. The first axis is the level of abstraction (L0 bridges, L1 material-agnostic laboratory-notebook, L2 material-class-specific, L3 categorical reasoning). The second is the consumer audience (material versus compliance). The material-specific level (L2) is internally organised by a seven-tier mechanistic-explanation skeleton applicable to any crystalline ionic oxide: Symmetry, Energy/DFT, Thermo/CALPHAD, Kinetics, Microstructure, Defect chemistry, Bonding. The two axes are independent — a module is placed on each at the level appropriate to its content, and consumers select which subsets they need — while the seven-tier skeleton structures the depth of mechanistic content within Level 2. The level-and-audience modularity dissolves the horizontal fragmentation, the compliance audience absorbs the vertical EU-regulation pressure, and the seven-tier organisation of the material-specific level delivers the mechanistic explanation depth — three challenges, three architecturally distinct answers, without collapsing them onto a single axis where they would compete.

We instantiate this design as the OntoCrafter Ceramics Ontology (OCO v0.94), the release engineered to enter productive use. OCO ships as a class-bearing module set with bridge mappings, SHACL shapes, a competency-question catalogue with executable SPARQL tests, and architecture decision records; the full metric inventory and method-of-measurement is in 4. Functional ceramics are the reference material domain, with BNT-BT as the end-to-end pilot demonstrated across all seven explanation tiers. v0.94 enters productive practice; corrections surfaced by that practice are the planned input for v1.0.

This paper contributes:

1. A formal description of the four-level modular architecture, driven by ten engineering design principles (modularity, adaptability, interoperability, purpose, equality, compatibility, functionality, authoritativeness, facetedness, portability), of which five go beyond the Norouzi REQ-canon (2.4, 3). The same modular pattern addresses horizontal material-domain fragmentation and vertical EU-regulatory convergence with one structural primitive.

2. The seven-tier mechanistic explanation skeleton formalised as the internal organising principle of Level 2 (material-specific knowledge), generic for crystalline ionic oxides, with cross-tier SHACL constraints that make the explanation chain auditable (3.4.2).

3. A reference implementation as the OntoCrafter Ceramics Ontology (OCO v0.94), realising the architecture across class-bearing material modules; a Neumann tensor engine that generates reified symmetry constraints algorithmically over the 32 crystallographic point groups; SPARQL-based phase-state coupling that derives the active point group from sample temperature and composition; a coordination-polyhedron module (oco-localstructure) that closes the mechanistic chain from composition through local geometry to tensor symmetry; multi-axis parameter classification along role, reference, and material-abstraction layer; an external-cache pattern for high-volume reference data (Shannon ionic radii, IUCr bond-valence parameters, pyxtal Wyckoff positions, Materials Project DFT corpus, Pauling electronegativities); and a disciplined reuse-before-invention bridge policy (4).

4. A vertical extension of the same architecture into the compliance and value-chain stack: modules for Life Cycle Assessment (with ecoinvent and EN 15804+A2 bridges), CSRD/ESRS reporting, supply-chain due diligence (CSDDD), packaging (PPWR), carbon-border adjustment (CBAM), right-to-repair (R2R), the EU AI Act, ODRL/trust, Manufacturing-X identifier and traceability infrastructure (AAS IEC 63278, Catena-X CX-0010/CX-0146), and laboratory automation (SiLA). The same modular level discipline absorbs these without restructuring the material core (4.8).

5. Validation against the Norouzi quality-requirement canon (REQ1–REQ9, all nine met), the OOPS! pitfall audit [61], a published catalogue of area-tagged competency questions with executable SPARQL tests, and a SHACL validator suite (counts in 4; reasoner/audit results in 5).

6. Discussion of limitations and the v1.0 roadmap, framed by the corrections expected from productive practice — including a second ceramic material system (ferritic high-performance ceramics) currently in active development (6).

The remainder of the paper is organised as follows. 2 surveys the MSE ontology landscape, positions the multi-level architecture against three established schools of design (BFO-aligned mid-level, EMMO-centric, and bottom-up domain-specific), and lays out the ten design principles that drive OCO (2.4). 3 presents the four-level architecture together with the material/compliance audience axis as the second classification dimension, plus the seven-tier mechanistic-explanation skeleton as the internal organisation of Level 2. 4 describes OCO as reference implementation — the material modules (including the Neumann engine, phase-state coupling, multi-axis parameter classification, the coordination-polyhedron module, and the seven-tier explanation skeleton with its external-cache pattern), the bridge inventory, and the vertical extension into the compliance and value-chain stack. 5 reports the validation results — all nine Norouzi requirements met. 6 discusses strengths, limitations, and the v1.0 horizon shaped by productive practice. 7 summarises and outlines the roadmap.

2 Background and Related Work↩︎

2.1 The State of MSE Ontologies↩︎

[1] provide the most comprehensive recent survey of MSE ontologies, evaluating 94 semantic artifacts (4 top-level, 8 mid-level, 60 domain-level, 2 application-level, plus 20 not openly evaluable) against nine quality requirements (REQ1–9) and an OOPS! pitfall audit. Their key findings frame the work presented here:

• Only 9 of 94 ontologies (10 %) publish competency questions.

• No ontology adopts user stories or personas as design anchors.

• Critical OOPS! pitfalls (P19 multiple-domain/range, P40 namespace-hijacking, P31 incorrect equivalentClass, P11 missing domain/range) are widespread, even in established ontologies such as QUDT (217 P11 hits).

• BFO is the most-reused top-level (16\(\times\)); EMMO follows (12\(\times\)); PMDco is reused only \(1\times\) directly despite being deployed in 13 BMBF projects.

2.2 Three Architectural Schools↩︎

Schule A — BFO-aligned Mid-Level. PMDco [45], MWO [62], MSEO, NFDIcore. Strict ISO/IEC 21838-2 conformance, mid-level material-science vocabulary above BFO, formal reasoner-friendly. Cost: high BFO learning curve, “portion-of” constructs awkward for non-philosophers.

Schule B — EMMO-centric. BattINFO, CHAMEO [63], GPO, EMMO Crystallography, domain-electrochemistry. Adopted in EU projects (EMMC, BIG-MAP, OntoTrans). Cost: each subdomain imports the full EMMO top-level; many subdomains are at v0.x maturity.

Schule C — Bottom-up domain-specific. KnowNow [60], MaterialDigital project ontologies, NanoMine, MatKG. Pragmatic and fast, but inter-project interoperability weak.

2.3 Specific Gaps in the Current Landscape↩︎

Beyond the methodological pitfalls flagged by [1], two content gaps emerge from a systematic reading of the recent literature:

No deep functional-ceramics modeling. KnowNow is restricted to LTCC multi-layer components; Mieller et al. cover only NiCuZn ferrite [27]; BattINFO addresses batteries; SmaDi [34] models four smart-material classes but at the level of constitutive parameters, not microstructure or defect chemistry. The combination of 230 space groups, Kröger-Vink defect notation [64], Newnham composite connectivity [65], and a full coupled-effects family (piezoelectric, pyroelectric, magnetostrictive, …) is absent from all surveyed ontologies.

Integrity constraints not delivered alongside the TBox. OWL’s open-world semantics interprets missing triples as unknown rather than as violations — a deliberate and correct design choice for an open-world reasoning language, but one that leaves enforceable integrity constraints (mandatory fields, value ranges, cardinality caps) outside what TBox axioms can express. The standard remedy is SHACL, which adds closed-world shape validation as an independent artifact type alongside the TBox; [35] demonstrate the pattern with their SHACL-OBDA validator. The gap in the current MSE ontology landscape is not the Open-World Assumption itself — it is the correct semantics for what OWL is for — but that most surveyed MSE ontologies ship a TBox without accompanying SHACL shapes, leaving consumers without a standard way to validate ABox compliance.

2.4 Positioning of OCO↩︎

OCO’s architecture is governed by ten design principles drawn from engineering practice (platform strategy, construction catalogues), quality management (SIPOC), and the materials-science domain itself. These principles, not the Norouzi requirement canon, are the primary design drivers; the canon is a verification surface that the principles must clear, not a brief from which they derive. Two emphases run through the principle set: a lessons-learned dimension that distills what worked and what did not in the PMD Phase-1 ontology cohort (2), and a forward-looking dimension that anticipates the EU-driven convergence of MaterialDigital with Manufacturing-X — the second axis of fragmentation introduced in 1. We list the principles here because they explain the architectural choices that follow in 3, and because five of them go beyond what REQ1–9 demand.

2.4.1 Ten Design Principles↩︎

1 organises the ten principles below as a causal chain: each principle cluster enables the next phase of what an industrial materials ontology must deliver, from consumer-side modular choice all the way through to sister-domain extension. The detailed list that follows is grouped in the same order.

1. Modularity. A materials ontology should follow the same logic as engineering platform strategy: classes and properties are organized into reusable modules that can be combined per consumer, analogous to the construction catalogues used by automotive platforms. A consumer who needs only equipment and method vocabulary imports two modules, not the whole ontology.

2. Adaptability. Bridges to external ontologies are isolated in a dedicated level (L0), and the imported external sources are versioned and cached locally. When an external ontology releases a new version, only the bridge file changes — no class definitions in OCO break, and the cache makes the build reproducible. The same mechanism extends forward: standards that are still consolidating (EU Construction Products Regulation 2024/3110, Critical Raw Materials Act, evolving DPP-XBRL schemas) can be tracked via provisional bridges that mature alongside the upstream release, without forcing rework in the material core.

3. Interoperability. An ontology is not a free-standing artifact but a vocabulary embedded in a workflow. For a materials ontology this requires concrete anchoring in the open-source materials stack: ELN/LIMS, machine-learning datasets (Croissant), materials databases (OPTIMADE), and provenance tooling (PROV-O).

4. Purpose. Vocabularies without a stated purpose accumulate dead classes. OCO binds its scope to a published catalogue of competency questions, each tagged with an area (tensor symmetry, phase state, route, lifecycle, …) and accompanied by an executable SPARQL test where possible.

5. Equality. Experimental documentation is never complete; any record is an SIPOC fragment — who was the supplier of the inputs, what was the process, what was the output, who is the customer. Scientific publications are treated identically: a paper is an SIPOC fragment of one or more experiments. The same provenance pattern applies to both, which removes the artificial line between raw experimental data and published results.

6. Compatibility. OCO is the architectural successor of two earlier PMD-Phase-1 ontologies (KnowNow for LTCC multi-layer ceramics, SmaDi for smart materials including piezo-ceramic) and the EU-regulatory peer of the Manufacturing-X ecosystem (AAS asset administration shells, Catena-X BPN identifiers, ESPR-driven sector DPPs). Backward compatibility — ingesting Phase-1 ontologies via bridges rather than re-modelling — and forward compatibility — anchoring in Manufacturing-X identifier and traceability infrastructure via bridges to the same kind of pattern — are the same requirement under the same kit (4.8).

7. Functionality. Beyond reusable modules, OCO is organized into four functional layers — L0 (bridges), L1 (laboratory-notebook level, material-agnostic, ELN/LIMS-ready), L2 (material-specific knowledge), L3 (reasoning axioms) — each addressing a different consumer concern. Maintenance becomes localized: a PMDco update touches only L0; a new material adds only L2.

8. Authoritativeness. For functional ceramics the full mechanistic-explanation chain — from local structure and bonding through symmetry, energy landscape, thermodynamic phase regions, kinetics, microstructure, and defect chemistry to the resulting tensor-component symmetry — is load-bearing knowledge. The seven-tier skeleton (3.4.2) is the systematic carrier of that chain. A central traversal through it is phase diagram \(\to\) active crystallographic phase \(\to\) tensor-component symmetry: without that traversal an ontology cannot answer “which piezoelectric coefficients are non-zero for BNT-BT at room temperature near the morphotropic phase boundary?” But this is one path of several — defect chemistry to Mn-acceptor pinning of domain-wall mobility, soft modes at the Brillouin-zone centre to incipient ferroelectricity, microstructure to Hall-Petch toughening — and a vocabulary that cannot deliver any of them along its central domain questions is not authoritative. OCO models the entire seven-tier chain explicitly, with the Neumann tensor engine, phase regions, and point-group bindings carrying the symmetry-to-tensor edge as one example implementation. The chain is not ceramics-specific: Neumann’s principle and the layered explanation pattern hold for every crystalline material, so the same mechanism governs metals (martensitic transformations in shape-memory alloys, soft-magnetic alloys across their Curie transition) and crystalline organics (pharmaceutical polymorphs, organic semiconductors). A sister-domain L2 replacement (5.4) inherits this entire infrastructure unchanged — only the concrete phase-region populations and the domain-specific seven-tier content differ.

9. Facetedness. A material parameter is not adequately described by a single classification axis. OCO classifies every parameter along three independent axes simultaneously: role (state, response, transport, structure, statistical, topological, fit), reference (fundamental, material, interface, defect, measurement, specimen, process, environment), and layer (atomic, crystalline, microstructural, mesoscopic, macroscopic). The axes are populated by reasoner-classified rdfs:subClassOf relations, so SPARQL queries can navigate any subset of facets without bespoke join logic.

10. Portability. The architecture must support replacement of the material-specific level without touching L0, L1, or L3. A metallurgy ontology adopting the same L0/L1/L3 need only contribute its own L2 module to deliver a fully reasoner-ready ontology for its domain.

2.4.2 Where OCO Goes Beyond the Landscape Canon↩︎

The Norouzi REQ1–9 canon emphasizes reasoning, modularity, bridges, and documentation — necessary but not sufficient for a working materials ontology. Five of the ten principles above are not captured by the canon and reflect requirements that surfaced from real consumer use cases rather than from the survey methodology:

• Adaptability is not explicitly in REQ1–9. The canon recognizes the importance of reuse but treats external version drift as a documentation matter. OCO’s strategy (bridge-isolation plus external version cache) is an engineering response to the empirical observation that bridge files are the only component routinely broken by external releases.

• Equality is absent from the canon. The canon implicitly distinguishes experimental data from literature; OCO unifies both as prov:Activity instances with the same provenance pattern. This is the architectural prerequisite for the SIPOC-Extractor companion tool and for cross-paper aggregation without forcing premature reconciliation of conflicting reports.

• Compatibility with predecessor projects (KnowNow, SmaDi) addresses a fragmentation problem the canon identifies but does not solve: even within a single consortium, every project re-models the same laboratory concepts. OCO’s bridge level ingests both predecessors verbatim, allowing their concepts to coexist with OCO’s deeper modeling.

• Authoritativeness in the functional-ceramics sense (the full seven-tier mechanistic-explanation chain, of which phase \(\to\) tensor coupling is one central traversal) is a domain requirement that the canon — being domain-neutral — cannot generate. Without it, a ceramics ontology cannot stand behind its own competency questions about coupled effects.

• Facetedness generalizes what the canon calls “rich semantics” into a concrete multi-axis classification with reasoner-supported navigation. The closest the canon comes is requiring “more than rdfs:label” — a much weaker bar.

The remaining five principles (modularity, interoperability, purpose, functionality, portability) align with REQ1–9 but are realized with engineering rather than compliance intent: modularity is platform strategy, not a list of files; functionality is level separation by consumer concern, not just file count; purpose is bound to executable tests, not free-text statements.

2.4.3 Architectural Consequence↩︎

The four-level architecture that the remainder of this paper describes is the synthesis of these ten principles, not a direct answer to REQ1–9. Modularity, functionality, and portability dictate the multi-level structure itself; adaptability dictates the bridge-level isolation; interoperability and compatibility dictate the bridge inventory; purpose dictates the area-tagged competency catalogue; equality dictates the unified prov:Activity treatment of experiments and publications; facetedness and authoritativeness dictate the depth of the material-specific level. The Norouzi canon is satisfied by this architecture (5), but as a verification rather than a brief — and the architecture extends to requirements the canon does not raise. The reference implementation for ceramics demonstrates that the pattern is viable; the modular structure invites sister-domain implementations (metallurgy, polymers, batteries) that would share L0 and L1 with OCO while replacing L2.

3 The Multi-Level Architecture↩︎

The architecture introduced in 1 comprises two independent classification axes plus a mechanistic-explanation skeleton internal to the material-specific level. The first and primary axis is the level of abstraction — L0 bridges, L1 material-agnostic laboratory-notebook level, L2 material-class-specific knowledge, L3 categorical reasoning — governed by the architectural principles in 3.1 and detailed level-by-level in [sec:level0,sec:level1,sec:level2,sec:level3]. The second axis is the consumer audience (3.6), which separates the material core from the compliance and value-chain modules without restructuring either. The two axes are independent: every module is placed on each at the level appropriate to its content, and consumers select the subsets they need. Within L2 (the material side), the content is organised internally by the seven-tier mechanistic-explanation skeleton (3.4.2), which lets the ontology surface why a property holds, not only that it does. Compliance modules have no analogous internal structure — they are regulatory rather than mechanistic — which is why the seven-tier skeleton is the internal organisation of one specific level rather than a third independent axis.

3.1 Architectural Principles↩︎

The architecture rests on five design principles:

1. Level separation. Each level has a clearly bounded scope: L0 bridges to external standards, L1 carries the material-agnostic vocabulary, L2 the material-specific vocabulary, L3 the categorical reasoning. Consumers select their import depth.

2. Modularity within levels. Each level decomposes into independently maintainable modules. Consumers can import single modules (e.g., oco-equipment alone) without pulling the entire level.

3. Opt-in reasoning. Categorical reasoning (L3) is not part of the default distribution. Consumers without reasoning needs do not pay the OWL-DL reasoner cost.

4. Bridge localization. External version changes (PMDco v3.1, QUDT v3.3) are confined to a single level (L0). Internal modules reference only bridge:* classes, which remain stable under our control.

5. Cache pattern for external reference data. Large externally-curated bodies of reference data — mid-level ontology versions consumed by L0 bridges, structural and thermodynamic constants consumed by the mechanistic tiers of L2 — are not embedded in OCO’s TBox but cached locally as versioned snapshots, pinned via SHA in bridge/external_versions.yaml. This separates reference-data scale from ontology scale: the TBox stays compact, while consumers query large reference corpora (Materials Project DFT entries, IUCr bond-valence parameters, pyxtal Wyckoff positions, Shannon ionic radii, Pauling electronegativities) with reproducible version pinning. Concrete instances appear in 3.2 (external ontologies) and 3.4.2 (mechanistic-tier reference data).

These five principles separate the architecture concretely from the two dominant schools introduced in 2. PMDco offers five distributions (full, base, simple, minimal, main), but these are vertical slices through the same mixed vocabulary — modular by class count, not by architectural level. The L1/L2 split that isolates “laboratory workflow without material classes” from “material description without workflow classes” along the consumer-concern axis cannot be expressed in PMDco’s distribution scheme. EMMO sub-domain ontologies (BattINFO, CHAMEO, GPO, the EMMO crystallography and electrochemistry modules) inherit the full EMMO top-level (700+ classes) and pay the corresponding reasoner cost regardless of which classes a given consumer actually uses; the opt-in reasoning principle realized here via a separate L3 distribution cannot be retrofitted onto an EMMO sub-domain without breaking its EMMO inheritance. The contrast is therefore not over rival mid-level vocabularies but over the modularity axis (class count versus consumer concern) and the reasoning posture (mandatory inheritance versus opt-in distribution).

3.2 Level 0 — Bridge to External Standards↩︎

L0 is the level at which OCO’s interoperability claim is made concrete. Its content is a curated set of bridge:* classes that act as named anchors between OCO’s internal vocabulary and external mid-level ontologies. Internal modules reference only these anchors, never the external IRIs directly — this isolates external-version churn (a PMDco v3.1 release, a QUDT update) to a single level that is small enough to audit class-by-class.

The selection of bridge targets is not opportunistic: a target is admitted only if it satisfies all of the following criteria.

1. OWL/RDF format. The target must be available as a machine-readable ontology in a standard W3C format. Industrial classification schemes published only as proprietary XML or catalog formats are excluded.

2. Mid-level granularity. Targets must occupy the mid-level between abstract foundations and instance data. Direct alignment to upper-level foundations is achieved transitively via the mid-level targets that already commit to them (e.g., BFO via PMDco), avoiding redundant philosophical commitments at the OCO surface.

3. Established adoption. The target must be in active use within the materials-science or research-data-management community, with a versioned release history.

4. Bounded import cost. A bridge entry adds at most a handful of anchor classes to OCO. Targets whose useful adoption requires importing hundreds of unrelated upper classes are inadmissible by this criterion — it would defeat the modular multi-level design.

5. License compatibility. Targets must permit redistribution under terms compatible with OCO’s CC-BY/CC-BY-SA scheme.

1 lists the eleven bridge targets with substantial class-level coverage (each anchored to \(\geq\)​14 OCO classes). A further six targets (IAO, m4i, SOSA, DCAT, W3C-Org, IUCr-Wiki) are present as minimal anchors (1–2 classes each), and the explicit cross-ontology mapping inventory in bridge_mappings.yaml contributes 467 further mappings, including bridges to the predecessor PMD ontologies KnowNow and SmaDi, to OPTIMADE, Croissant and the ELN-Filetype standard, and to the EMMO sub-modules ISQ, chemistry, and materials (4.7).

3.2.0.1 Targets explicitly not bridged, and why

A second list of candidate targets has been screened and rejected. The rejection categories are themselves part of the architectural argument.

• Foundational ontologies (BFO [74], UFO-A [75]). OCO is BFO-aligned transitively via PMDco; re-asserting BFO at the OCO surface would duplicate that commitment without adding classes. UFO-A’s rigid Kind/Role/Phase distinctions would force the reclassification of all existing OCO classes into a meta-typology that the materials community has not adopted — a change with high cost and no demonstrated benefit for our competency questions.

• Centralist mid-level competitors (EMMO [76] and its sub-domain ontologies such as the EMMO quantity, electrochemistry, and atomistic modules). EMMO sub-domain ontologies require importing the full EMMO core (700+ classes), which contradicts the bounded-import-cost criterion above and forecloses the opt-in reasoning principle: every consumer pays the full EMMO load regardless of need. We discuss the centralist-versus-multi-level contrast further in 6.

• Mid-level MSE competitors to PMDco (Fraunhofer MSEO). PMDco v3 has emerged as the consortial convergence target for the BFO-aligned mid-level MSE space, with active maintenance and broad German-ecosystem adoption. Maintaining a second mid-level MSE anchor in parallel would reintroduce the dual-anchor ambiguity in the very level whose purpose is to provide a unique external anchor per concept; the concepts MSEO covers are reachable via PMDco.

• Quantity/unit competitors to QUDT (OM [77], EMMO domain-quantity). PMDco has standardized on QUDT as its unit anchor. Maintaining a second quantity bridge would introduce ambiguity in the very level whose purpose is to provide a unique external anchor per concept.

• Non-OWL industrial classification schemes (ETIM [78], eCl@ss [79], ISO 15926-14 [80], NAMUR NE 100 [81]). These are widely adopted in industry but are distributed only as BMEcat-XML, proprietary catalogs, or non-OWL formats. No semantic mapping path exists that does not first require the external community to publish an OWL representation.

• ELN/LIMS tool ontologies (Chemotion, eLabFTW, openBIS, Kadi4Mat, NOMAD-Oasis, …). These systems are consumers of OCO’s L1 schema, not peer ontologies: their concepts (user sessions, folder permissions, signature workflows) are deliberately outside OCO’s modeling scope.

3.2.0.2 One known gap in the present roster

MeSH (Medical Subject Headings, U.S.National Library of Medicine) is published in SKOS/RDF and qualifies under our criteria; it is not bridged because the pharmaceutical sister domain is not currently a consumer, but no architectural obstacle exists.

The discipline of writing down both the inclusion criteria and the explicit rejections — and of naming the known gaps — turns L0 into the documented contract between OCO and the surrounding ontology landscape, rather than a loose collection of opportunistic mappings.

3.3 Level 1 — Material-Agnostic LIMS/ELN Level↩︎

L1 contains all concepts that are independent of the specific material under investigation: a spray dryer dries pharmaceutical suspensions as well as ceramic slurries; an XRD measures metals as well as ceramics; a poling station works on PVDF polymers as well as on BNT-BT. The level decomposes into fourteen pure-L1 modules plus the L1 fragments of two modules whose classes span L1 and L2 via the multi-axis classification (4.6). Consumers import only the parts they need — an asset-management tool may load oco-equipment alone; an LIMS may bundle oco-investigation, oco-process, oco-equipment and oco-measurement and skip the rest. 2 lists the modules and the architectural reason for each.

A core L1** pattern: literature and laboratory data as semantically equivalent sources.** OCO treats published-literature extractions and own-laboratory experiments as first-class equivalent ABox contributors. Both are modelled as prov:Activity instances and share the same provenance, quality, and uncertainty annotations — distinguished only by their activity class (Investigation vs. LiteratureExtraction) and their verification status, not by a separate vocabulary. A SPARQL query asking “what is the \(d_{33}\) of BNT-BT?” returns both validated lab measurements and extracted literature values, ranked by data-confidence level, without the schema forcing one source to be preferred a priori. This unification is the operational consequence of the equality principle (2.4, principle 5) and is the architectural prerequisite for using large-scale literature corpora alongside in-house experimentation; it also enables the SIPOC-fragment data model (4.9) to accommodate incomplete records uniformly across both source types.

The level is explicitly designed to be ELN-/LIMS-importable. Beyond the module structure, four cross-cutting features make L1 operational for laboratory-data systems:

• Data confidence levels (DCL 0–5): a mandatory annotation on every MeasurementResult or ExtractedValue, ranging from Unknown (DCL 0) to Validated (DCL 5). This separates raw entries, peer- reviewed values, and gold-standard data within the same knowledge graph.

• ExperimentStatus lifecycle: planned \(\rightarrow\) in-progress \(\rightarrow\) completed \(\rightarrow\) archived, with a separate StatusArchived terminal state. Required for any LIMS that distinguishes intent from execution.

• GUM uncertainty fields: CombinedStandardUncertainty with the five datatype properties prescribed by JCGM 100:2008, attached to existing MeasurementUncertainty classes rather than introduced as a parallel hierarchy.

• LiteratureExtraction as first-class prov:Activity: extraction from publications and patents is a tracked activity with its own VerificationStatus, so SIPOC-fragment data (4.9) carries its own provenance trail rather than being silently merged with laboratory data.

Substitutability. The level’s existence as a separate artefact is the architectural lever that distinguishes OCO from a monolithic ceramics ontology: a sister project (metallurgy, polymer science, pharmaceutics) imports L1 unchanged together with its own L2, replacing only the material-class-specific content. This is the structural mechanism by which the “\({\sim}70\) % workflow duplication across PMD-consortium projects” problem identified in [1] is dissolved.

3.4 Level 2 — Material-Class-Specific Level↩︎

L2 contains the material-class-specific knowledge — the part of OCO that a sister project (metallurgy, polymer science, pharmaceutics) would replace while keeping L0+L1 unchanged. For ceramics it has two internal facets: the material modules themselves (3.4.1), and the seven-tier mechanistic-explanation skeleton (3.4.2) that structures how the material content can be queried for cause-chain explanations rather than only for property values.

3.4.1 Material Modules↩︎

For ceramics, L2 decomposes into nine architecturally significant modules (3) that together cover the structure-property-defect chain that distinguishes functional-ceramic modelling from generic materials description. Four additional smaller modules (dataquality 17, dimension 14, application 12, calc 10) carry support vocabulary for the same level and total 53 further classes. A fifth module, oco-role, holds the abstract Role class plus 14 named individuals (solvent, binder, precursor, reactant, dopant, plasticizer, …) that are attached to process steps rather than to material classes — the pattern mentioned alongside the material module (2). The oco-localstructure module listed below additionally contributes 7 L1-frame classes (CoordinationPolyhedron root + family abstracts Tetrahedron / Octahedron / Cuboctahedron) alongside its 12 L2 polyhedra.

A cross-cutting feature spans L2 and L1: the coupled-effect family (32 effect classes: piezoelectric, pyroelectric, electrostriction, magnetostriction, magnetoelectric, thermoelectric, Verdet, Cotton-Mouton, plus 24 diagonal/cross effects following Nye’s convention [82]). The effect classes themselves are physical quantities and live in oco-property at L1; the symmetry constraints that connect each effect to its allowed crystallographic point groups live at L2 via the oco-tensor module and the reified oco:NeumannConstraint instances generated programmatically by the Neumann tensor engine (4.5). This split keeps the universal physical-quantity hierarchy in the agnostic level while the material-bound symmetry constraints stay where they belong — and replaces what would otherwise be hundreds of manually curated cross-axioms with a single algorithm.

Substitutability. The nine principal modules in 3 are the surface that a sister project replaces. The ferritic-high-performance-ceramics implementation currently in development is the first concrete test of this substitutability within the ceramics family; cross-domain substitutability (metallurgy, polymers) is on the validation roadmap (6).

3.4.2 Seven-Tier Mechanistic-Explanation Skeleton↩︎

The material-specific content of L2 is organised internally by a seven-tier mechanistic-explanation skeleton that distinguishes an authoritative materials ontology from a vocabulary that only describes. Every material property recorded in OCO sits within a chain of physical mechanisms; for industrial use that chain must be queryable from the same knowledge graph as the property value itself. OCO formalises this chain as a fixed skeleton of seven explanation tiers, each answering one fundamental materials-science question and contributing dedicated modules and (where applicable) an external reference-data cache (4).

3.4.2.1 Why “tiers” — five material-abstraction layers vs.seven mechanistic-explanation tiers

We deliberately call the seven mechanistic-explanation stages tiers, not layers, to keep them terminologically distinct from the five material-abstraction layers (Atomic, Crystalline, Microstructural, Mesoscopic, Macroscopic) carried by the oco-layer module listed in 3. The two concepts answer different questions. The material-abstraction layers describe the scale and governing-law regime at which a property is observed — each is a distinct tuple of state variables and governing laws used as a classification axis for parameters (4.6). The mechanistic-explanation tiers describe the causal mechanism stack that links composition through symmetry, energy, thermodynamics, kinetics, microstructure, defects, and bonding to the observed property. Microstructure appears in both lists by name only: in the material-abstraction sense (layer) it is a description scale (grain-sized features); in the mechanistic-explanation sense (tier) it is the cause-chain stage that supplies polycrystalline averaging, Hall–Petch coupling, and texture effects.

3.4.2.2 Generic skeleton, not material-specific

All seven tiers apply to every crystalline ionic oxide — the central material class for functional ceramics (ferroelectrics, magnetics, ion conductors, high-\(T_c\) superconductors). BNT-BT is the pilot material on which the skeleton was concretised; it is not the reason the skeleton has these seven tiers. The same skeleton applies without restructuring to NiCuZn ferrite, yttria-stabilised zirconia, , and any related material domain — only the per-tier instance content changes.

3.4.2.3 External reference-data caches

Each tier that draws on a large external reference corpus does so through the cache pattern formalised as Principle 5 in 3.1: a versioned local snapshot rather than embedded TBox classes. The per-tier cache totals appear in the right-most column of 4; all caches are SHA-pinned in bridge/external_versions.yaml. The OWL TBox stays compact; the externally curated data scales independently.

3.4.2.4 Cross-tier validation

The chain of explanation is auditable. Cross-tier references are formalised as seven SHACL NodeShapes () that flag incomplete annotations: a morphotropic phase boundary (Tier 3 Thermo) must reference a domain-state set (Tier 1 Symmetry); a soft mode (Tier 2 Energy/DFT) must reference a subgroup relation (Tier 1 Symmetry); a Brouwer diagram (Tier 6 Defect chemistry) must reference a chemical-potential diagram (Tier 3 Thermo); an aging-kinetics model (Tier 4 Kinetics) must reference a Kröger–Vink defect (Tier 6 Defect chemistry); a Hall–Petch model (Tier 5 Microstructure) must reference a grain-boundary classification (Tier 6 Defect chemistry, via grain-boundary defect types); a Born effective charge (Tier 2 Energy/DFT) must reference a bonding-character annotation (Tier 7 Bonding chemistry); a spinodal decomposition (Tier 3 Thermo) must reference a Cahn–Hilliard model (Tier 4 Kinetics). The constraints are deliberately lightweight (sh:Warning severity, not sh:Violation) because cross-tier annotation grows evolutionarily; missing references should attract modeller attention, not block the pipeline.

3.4.2.5 End-to-end pilot

The BNT-BT pilot ABox () carries concrete instances on each of the seven tiers with explicit cross-tier annotations: a soft mode at the \(\Gamma\) point linked to the R3c\(\to\)P4mm subgroup relation; a Born effective charge \(Z^*_{33}(\text{Ti}) \approx +7.2\) explained by Bi-6s\(^2\) lone-pair stereo-activity; a morphotropic phase boundary at \(x_\text{BT} \approx 0.06\) linked to the R3c/P4mm/Cm domain-state set; an aging-kinetics model linked to the V\(_\text{O}^{\bullet\bullet}\) / Mn\(_\text{Ti}^{''}\) defect-dipole chemistry; a Hall–Petch parameterisation with \(\sigma_0 \approx 3\,\text{GPa}\), \(k_{HP} \approx 0.8\,\text{MPa}\sqrt{\text{m}}\) at \(d = 2\,\mu\text{m}\); and a complete DFT-workflow provenance (PBEsol functional, PAW pseudopotentials, \(8\times8\times8\) Monkhorst–Pack mesh, \(600\,\text{eV}\) cutoff). The pilot demonstrates that the skeleton holds together operationally, not only conceptually — a query for “why does BNT-BT achieve \(d_{33} \approx 580\,\text{pC/N}\) at the MPB” traverses all seven tiers along the cross-tier annotation chain.

3.5 Level 3 — Categorical Reasoning Level↩︎

L3 carries the categorical (boolean-logical) reasoning that crosses module boundaries — the truths that hold always, never, or under condition X, and that have no natural home in any single L1/L2 module because they connect classes from several. Quantitative mathematics (functions, scaling laws, calibration curves) is not part of L3; it lies outside this release entirely (6.4). L3 ships as two TTL distributions, oco-domain.ttl (categorical axioms and compatibility tables) and oco-routes.ttl (ordered process-step templates and their state-sequence entries), compiled from YAML axiom sources under the axioms/ directory. Their combined contribution to the merged distribution, measured as the ROBOT measure [83] delta between oco_merged_l12.ttl (L1+L2) and oco_merged.ttl (L1+L2+L3), is 1 400 OWL axioms / 404 logical axioms / 248 ABox axioms. The content decomposes into four families (5).

A characteristic example is the symmetry-effect axiom \[\textit{Pyroelectricity} \sqsubseteq \textit{requires\_pointgroup} \mathbin{\textit{only}} \textit{PolarPointGroup},\] which encodes the categorical fact that a material can show pyroelectricity only if its crystallographic point group is one of the ten polar groups. This is the kind of axiom whose evaluation requires the universal restriction (only) construct — which is exactly the construct that lifts the OCO-with-L3 profile from OWL 2 EL to OWL 2 DL (8). Consumers without this reasoning need neither load L3 nor pay the OWL 2 DL reasoner cost.

The decisive architectural feature of L3 is not the axioms themselves but their separation from the rest of the schema and their binding to published competency questions. This makes the scope of the ontology — which questions it intends to answer — explicit, auditable, and testable: a CQ that loses its SPARQL test is a visible regression, and a proposed new axiom that cannot point to a CQ has no architectural justification for being admitted.

3.6 The Material / Compliance Audience Axis↩︎

A second classification axis is independent of the level hierarchy: every module carries an audience marker, with value material, compliance, or both. Twenty-nine modules constitute the material-audience-only set — the materials-science vocabulary proper, including oco-localstructure (the mechanistic bridge from composition through coordination polyhedra to symmetry, 3.4.2). Eleven modules form the compliance-audience-only set and carry the EU-regulatory and value-chain vocabulary detailed in 4.8: Life Cycle Assessment, CSRD/ESRS reporting, supply-chain due diligence (CSDDD), packaging (PPWR), carbon-border adjustment (CBAM), right-to-repair (R2R), the AI Act, Manufacturing-X identifier and traceability infrastructure, regulated substances, recycling, and Safe-and-Sustainable-by-Design. Four further modules are dual-audience — they serve both sides simultaneously: oco-format (industrial data formats), oco-odrl (W3C ODRL policy and Verifiable Credentials trust layer), oco-time-event (temporal extents per W3C Time), and oco-automation (SiLA 2.0 laboratory automation). These appear in 9 marked with \(\dagger\).

The two audiences are independent of the four levels. Every compliance module has its own L1/L2/L3 internal structure, just as the material modules do. A consumer who needs only the material core can ignore the compliance audience entirely; the audience marker drives module-selection profiles in the distribution. A consumer building a Manufacturing-X data pipeline loads both audiences. The independence is what makes the same architectural primitive — modular layering — absorb a second class of requirements without restructuring the material core.

4 Reference Implementation: OCO↩︎

4.1 Quantitative Description↩︎

The OntoCrafter Ceramics Ontology (OCO) is the reference implementation of the architecture introduced in 3 — two independent classification axes (level and audience) plus the seven-tier mechanistic-explanation structure of the material level. Metrics for the v0.94 release — the version entering productive practice — are measured with ROBOT 1.9.10 [83] and rdflib on the merged distribution distribution/oco_merged.ttl extended by the Neumann-constraint sub-distribution:

• Classes: 5 196 named, distributed across 44 class-bearing modules (45 in the namespace registry). 29 modules carry the material audience and 15 carry the compliance audience, four of them dual-audience (4.8). Every module carries its own L1/L2/L3 internal structure independent of the audience axis, and every material-audience module sits on one or more of the seven mechanistic explanation tiers (3.4.2).

• Properties: 1 674 total — 574 ObjectProperties, 1 051 DatatypeProperties, and 49 AnnotationProperties.

• Axioms: 167 348 OWL/RDFS axioms in the merged distribution, of which 40 454 are logical axioms (the remainder are annotations and bare entity declarations); per ROBOT measure [83]. The largest single contribution is the 5 920 reified oco:NeumannConstraint instances — one per (tensor \(\times\) point-group) pair, 4.5.

• Bridges: 11 L0 targets with substantial class-level coverage (\(\geq\)​14 anchors each, 1); a further 829 explicit cross-ontology mappings across 40 sections in bridge_mappings.yaml and mwo_mappings.yaml cover the material-side standards (PMDco, PROV-O, NFDIcore, MADO, OBI, CIF Core, EMMO sub-modules, QUDT, Croissant, KnowNow, SmaDi), the compliance-side standards (EN 15804, EU PEF, ecoinvent, BONSAI, EFRAG XBRL, CRMA, NZIA, PACT, Catena-X, CSDDD-UNGP, CBAM, R2R, AI Act, AAS, …), and the policy/trust layer (W3C ODRL, W3C Verifiable Credentials, SiLA) — 4.7, 4.8.

• Competency questions: 163 published, each tagged with one of ten reasoning areas (tensor symmetry, phase state, route, lifecycle, …); 52 carry executable SPARQL test queries against gold-standard ABoxes (52/52 PASS).

• SHACL shapes: 1 172 mandatory shapes validated via pyShacl; dominated by the machine-generated Neumann (768) and CIF-Core (270) subsets, complemented by 7 Cross-Tier NodeShapes (3.4.2) and per-domain hand-curated sets for material-class identifiers, MPB coexistence, and the compliance audience.

• Architecture decision records: 132, including explicit negative decisions for rejected bridge targets and rejected modelling alternatives.

• External reference-data caches: 5 productive caches under the seven-tier explanation skeleton (3.4.2), pinned to upstream versions in bridge/external_versions.yaml: Shannon ionic radii (497), IUCr bond-valence parameters (1 934), pyxtal Wyckoff positions (1 731), Materials Project DFT corpus (\(\sim\)​155 000), Pauling electronegativities (91).

• Expressivity: the full distribution sits in OWL 2 DL; the L0+L1+L2 bundle (without L3) reduces to OWL 2 EL — 8 gives the underlying ROBOT measurements.

4.1.0.1 Comparison with PMDco and EMMO

To place these metrics in landscape context, 6 compares OCO v0.94 against PMDco v3 (OCO’s primary mid-level bridge target, 3.2) and EMMO Crystallography (the EMMO sub-module closest in scope to ceramics). The base-metric values for the comparators are taken from Norouzi et al. [1], Tab. 9. OCO is roughly an order of magnitude broader than PMDco in classes and properties and almost two orders of magnitude broader in axioms; this is expected because PMDco is a mid-level vocabulary that OCO extends downward into a full material domain. EMMO is federated across 40+ sub-modules, each with its own per-module metrics; we report the Crystallography sub-module as the most analogous single point of comparison.

4.2 Distribution Variants↩︎

The OCO distribution is structured so that consumers select only the depth they need (see 7). Both bundle files —  and  — are thin owl:Ontology hulls carrying only owl:imports directives; the actual content lives in 17 per-module files plus . The two master variants are alternatives, not additive: importing the full variant subsumes the standard one.

The reasoner-profile assignment is empirical, not assumed: ROBOT classifies the description-logic constructs actually used in each bundle (8). The decisive contrast is that adding L3 introduces universal restrictions (\(\forall\), owl:allValuesFrom, used in route-template completeness constraints) and complex concept negation, both of which lift the profile from OWL 2 EL into full OWL 2 DL. The L0–L1–L2 bundle stays in EL-tractable territory — a polynomial-time reasoner (e.g.ELK) is sufficient. This is the multi-level-architecture promise made operational: reasoning cost is a consequence of the level chosen, not a property of the ontology.

4.3 Bilingual Definitions as Mandatory Field↩︎

Each class carries both a German (definition_de) and an English (definition_en) definition. This is enforced as a hard schema-validator constraint. Among the surveyed MSE ontologies [1], [84], [85], none mandates bilingual definitions; OCO is to our knowledge the only MSE ontology that does so as a hard constraint. This matters specifically for German-speaking industrial partners, BMBF projects, and the NFDI-MatWerk consortium.

4.4 Source Lifecycle and Quality Assurance↩︎

The distribution is generated from human-readable YAML sources rather than maintained directly as Turtle, which keeps source files git-diffable and review-friendly. Consistency of the distribution is verified against standard tooling: HermiT for OWL-DL reasoning, SHACL validators for shape constraints, and the OOPS! pitfall scanner [61] for ontology-engineering hygiene. All build steps and quality checks are reproducible from the source repository, ensuring that the published distribution can be regenerated and audited independently.

4.5 Authoritative Reasoning: Neumann Engine and Phase-State Coupling↩︎

The authoritativeness principle (2.4, principle 8) operationalizes the chain phase diagram \(\to\) active crystallographic phase \(\to\) tensor-component symmetry as a two-step inference. Two implementation components carry it.

4.5.0.1 Neumann tensor engine

A dedicated module oco-tensor carries 190 material-tensor root classes (Voigt families, polarization, conductivity, elasticity, piezo-, pyro-, magnetoelectric, …), each annotated with tensor order, symmetry class, and the axial/polar flag. A subprocess engine implements Neumann’s principle as a stabilizer-subgroup computation in sympy over the 32 crystallographic point groups, generating for every (tensor \(\times\) PG) pair the set of independent non-zero components. The engine is validated against [82] and IEEE Standard 176 on a 30-case gold standard (30/30 pass) and emits 5 920 reified oco:NeumannConstraint instances together with 768 sh:NodeShape validators. A hash-keyed cache keeps regeneration cheap: a full re-run after an engine fix completes in 5:30 min wall-time (cache-warm) versus 46 min for the cold first run.

4.5.0.2 Phase-state coupling

A symmetry library is only useful when the active point group can be derived, not assumed. Phase regions are therefore modeled as sub-classes of oco-phase:CrystalPhase with temperature and composition bounds expressed in the QUDT QuantityValue pattern, and each region carries a has_point_group restriction. Two reference phase diagrams are populated: BNT-BT (four regions, including the morphotropic phase boundary as a 3m+4mm coexistence region) and NiCuZn ferrite (ferrimagnetic / paramagnetic across the Curie transition). A SPARQL-INSERT pass over the sample ABox infers the active region from \((T, x)\), propagates the point group, and triggers the Neumann constraints — without OWL reasoning, which cannot express numeric intervals. End-to-end inference is gold-standard tested on six cases (6/6 pass). Together, the two components answer the central authoritativeness competency question — “which piezoelectric coefficients are non-zero for BNT-BT at room temperature near the morphotropic phase boundary?” — without any manual point-group assignment by the user.

4.6 Multi-Axis Parameter Classification↩︎

Implements the facetedness principle (2.4, principle 9). Every parameter class in OCO now carries three independent classification axes simultaneously, each encoded as rdfs:subClassOf so that an OWL 2-DL reasoner navigates them without bespoke join logic:

• Role (what the parameter does physically): StateVariable, ResponseParameter, TransportParameter, StructureParameter, StatisticalParameter, TopologicalParameter, FitParameter.

• Reference (the semantic anchor): FundamentalConstant, MaterialParameter, InterfaceParameter, SpecimenParameter, ProcessParameter, MeasurementParameter, EnvironmentParameter.

• Layer (abstraction level at which the parameter is defined): AtomicLayer, CrystallineLayer, MicrostructuralLayer, MesoscopicLayer, MacroscopicLayer — five classes housed in a separate module oco-layer. Each carries its own state variables (e.g.lattice parameters at the crystalline layer; effective permittivity at the mesoscopic layer) and governing laws (Schrödinger / DFT at the atomic layer; Maxwell-Garnett / Bruggeman at the mesoscopic layer). Layers are not spatial partitions but coexisting descriptive views of the same material.

A bulk classification pipeline populates all three axes for the \(\sim\)​950 MaterialParameter subclasses through family-default plus outlier-override rules. The tensor-rank and symmetry-class annotations from oco-tensor (4.5) provide a fourth independent hook that connects the parameter taxonomy to the Neumann engine. The resulting query granularity is illustrated by competency questions of the form “which response parameters at the crystalline layer are non-zero for the trigonal point group 3m?”, which become single rdfs:subClassOf traversals.

4.7 Extended Interoperability and Predecessor Bridges↩︎

Realizes the adaptability, interoperability, and compatibility principles (2.4, principles 2, 3, 6) through a disciplined bridge-expansion process. The discipline is captured in a reuse-before-invention checklist applied before any new class or property is proposed: (a) does OCO already have a fitting class? (b) external identifier? \(\to\) subclass of oco-identifier:Identifier; (c) provenance? \(\to\) PROV-O; (d) unit? \(\to\) QUDT QuantityValue. In the most recent interoperability wave, applying this checklist reduced eighteen candidate new properties to zero and fifteen candidate classes to five.

The expanded bridge inventory now contains 829 mappings across 40 sections in the bridge_mappings.yaml and mwo_mappings.yaml single sources of truth:

• Materials databases: OPTIMADE, via a lookup table for the structure-search-API field vocabulary.

• Machine-learning datasets: Croissant (MLCommons) for ML-ready dataset metadata.

• Electronic lab notebooks: the ELN-Filetype standard, a cross-vendor RO-Crate-based export format adopted by 14 ELN/LIMS systems — bridging to the format covers the entire set without per-vendor mappings.

• EMMO sub-modules: ISQ (the ISO/IEC 80000 quantity vocabulary, 93 mappings), chemistry, and materials, each in its own bridge section so that sub-module versioning can be tracked independently.

• Predecessor PMD ontologies: KnowNow [60] contributes 14 process- and property-class mappings (LTCC-multilayer-specific classes are deliberately excluded, as they belong to a material-specific route rather than the agnostic L1); SmaDi [34] contributes 15 mappings restricted to the piezoelectric-ceramic subset, with the shape-memory and elastomer concepts excluded as out of ceramic scope.

Three thin application profiles — , , and — bundle the modules each consumer class typically needs as owl:imports wrappers, avoiding the maintenance load that subset-extracted distributions would incur. External sources are versioned and cached locally, so that a release change in any external target breaks only the corresponding bridge file — the adaptability principle made operational.

4.8 Compliance and Value-Chain Modules↩︎

The audience axis introduced architecturally in 3.6 carries the value-chain and EU-regulatory vocabulary on the compliance side. The same construction-kit absorbs the vertical-convergence pressure of 1 — EU-driven integration of materials, manufacturing, supply-chain, and sustainability data — without restructuring the material core or the agnostic laboratory level. 3 captures the architectural relationship: while the material-science audience is organised by level, the compliance/value-chain audience cuts across levels — each compliance module carries classes on several of L1, L2, and L3 simultaneously (9).

4.8.0.1 Modules

9 lists the fifteen modules carrying the compliance audience: eleven compliance-pure modules (LCA, CSRD, CSDDD, PPWR, CBAM, R2R, AI Act, Manufacturing-X, regulated substances, recycling, SSbD) and four dual-audience modules (format, odrl, time-event, automation) shared with the material side. Each module has its own L1/L2/L3 internal structure — the two axes (audience and level) are independent.

4.8.0.2 Modules

The compliance-audience modules cover the EU-regulatory wave that will reshape materials-data practice over the next five years.

4.8.0.3 The joining concept: Digital Product Passports

Across the new modules, the architecturally load-bearing concept is the Digital Product Passport. The oco-lca module contributes material-DPPs (per-material passport profiles attached to specific material classes such as BNT-BT); the oco-mfgx module contributes sector-DPPs (per-industry passport profiles tied to specific EU regulations: Battery DPP, Construction-Products DPP under CPR 2024/3110, Generic-ESPR DPP). A concrete product instance inherits from both via multiple-inheritance: a BNT-BT actuator in a battery assembly is simultaneously a BNTBT-DPP and a Battery-DPP. This is the same multi-axis pattern used for material parameters (4.6), applied across the material/regulation divide.

4.8.0.4 The supplier module as Wertschöpfungs-Akteur anchor

The oco-supplier module is the connecting tissue between the material side and the compliance side: every supply-chain tier (CSDDD), every BPN identifier (Manufacturing-X), every CoA reference (material side) routes through this single module. oco-supplier is delivered as a public stub (skeleton classes for cross-module referencing) plus a proprietary body (full catalogues, vendor specifications); see 6.2.

4.8.0.5 Reified-constraint pattern generalized

The reified oco:NeumannConstraint pattern (4.5) and the reified oco:RouteTemplate pattern (3.5) generalize to oco:LCA_Result_Reified in the LCA module: domain constraints that are not OWL axioms but ABox instances of named constraint classes, SPARQL-evaluable but not reasoner-evaluable. This pattern — named constraint instances as SPARQL-queryable knowledge anchors — is what makes the construction-kit absorb domains (Neumann tensor symmetry, route templates, LCA results) whose semantics escape OWL 2 DL while keeping the categorical TBox clean.

4.9 ABox Data Model: SIPOC Fragments↩︎

A central pragmatic decision: OCO does not assume that ABox data are complete experiment descriptions. Instead, data are ingested as SIPOC fragments (Suppliers / Inputs / Process / Outputs / Customers).

The reason is empirical: real-world experiment documentation is never complete. With own experiments, completeness can at least be aspired to. With published literature and patents, incompleteness is often deliberate (competitive or patent strategy). A schema that mandates complete fields would either reject most real-world data or force the fabrication of placeholder values — both unacceptable. The SIPOC granularity, combined with the three-tier identifier hierarchy (mandatory/recommended/optional), accommodates incomplete data without breaking the schema. This makes OCO practically usable for the two dominant data sources — own lab data and literature extraction.

4.10 Companion Software (out of scope of this paper)↩︎

Two independent software components work with OCO; they are not the subject of this paper:

• OCO-Workbench (Pannek): GUI for data import, process modeling, and ABox population. Operative interface for laboratory personnel.

• SIPOC-Extractor (Grond): Pipeline for SIPOC-fragment extraction from scientific literature and patents. Augments own experiments with published-bestand coverage.

Both tools use the OCO TBox as schema; the modular L0–L3 granularity allows them to operate against sub-bundles rather than the full distribution. There is no publication schedule for the tools at this time — this paper focuses exclusively on the architectural pattern.

5 Validation↩︎

5.1 Coverage of the Norouzi Quality Requirements↩︎

10 maps the nine quality requirements of [1] against the OCO implementation.

REQ4, REQ6, and REQ9 are over-delivered: REQ4 by the disciplined reuse-before-invention bridge policy (4.7); REQ6 by the combination of data-confidence levels, GUM uncertainty, and ADR-documented architectural decisions; REQ9 by the two independent classification axes together with the seven-tier internal organisation of L2, which give consumers a four-dimensional subset choice (level, audience, mechanistic depth, and per-module composition) that a one-axis modular ontology cannot match.

The availability dimension shared by REQ1, REQ2, REQ4, and REQ9 is met for the publicly distributed portion of OCO (L0 and L1 excluding oco-supplier; 6.2). The proprietary modules (oco-supplier, L2, L3) contribute to the metrics reported here but are not externally inspectable in the present release; the architectural pattern itself remains fully described in 3 and 2.4 and is independent of access to those modules.

5.2 Quality Audit↩︎

OOPS! self-audit. All twelve OOPS! pitfalls have been audited. Critical pitfalls (P19, P40, P31, P05, P29, P27) are absent. Important pitfalls (P11, P24, P30) are absent or addressed through documented architecture decisions (P11 eliminated by the CIF-Core domain-class consolidation). Two minor pitfalls (P10 class disjointness, P20 cross-source annotation style) are explicitly accepted with documented rationale rather than reflexively eliminated, because the alternative would compromise either reasoner performance (P10) or annotation comprehensibility for human readers (P20). Minor pitfall P08 (naming convention) is addressed by an explicit architecture decision documenting eight deliberate lower-case exceptions for domain notation (pH, pT, pO2, nPropanol, d33).

Reasoner consistency. The full L0+L1+L2+L3 bundle — together with the Neumann-constraint sub-distribution — classifies in Pellet with zero unsatisfiable classes; ROBOT validate-profile reports no OWL 2 DL violations on the merged distribution.

Competency-question execution. 163 competency questions are published, each tagged with one of ten reasoning areas (tensor symmetry, phase state, route, lifecycle, multi-axis, interoperability, quality, crystal structure, BNT-BT, and an NCZF placeholder for the second ceramic material). 52 carry an executable SPARQL test against gold-standard ABoxes; 52/52 PASS. The remaining questions are either meta-discourse without an axiomatic answer requirement, or their test is pending the corresponding gold-standard ABox.

SHACL validation. The mandatory shape suite (count in 4) is validated via pyShacl, dominated by the machine-generated Neumann (768) and CIF-Core (270) subsets and complemented by per-domain hand-curated sets: 28 in the core oco_shapes.ttl (raw-material identifier sets, sintering atmosphere, process-step sample states, literature extraction, material-class identifiers), 25 for morphotropic phase-boundary coexistence regions, 7 Cross-Tier NodeShapes (3.4.2) that audit the seven-tier explanation-chain annotations, plus the compliance-side shape sets for LCA, CSRD, CSDDD/PPWR, AI Act / CBAM / R2R cross-cutting, Manufacturing-X traceability, regulated substances, SSbD, and ODRL policy. Adopting the SHACL-OBDA validator of [35] for relational-database back-ends is on the roadmap.

5.3 Architecture-Pattern Validation↩︎

The architecture has been operationally validated along both axes plus the seven-tier internal organisation of L2:

• Level axis (L0–L3): both distribution variants (oco_master.ttl and oco_master_full.ttl) parse and reason within their designed reasoner profiles (OWL 2 EL for L0+L1+L2, OWL 2 DL with L3 added). Individual modules of L1 (e.g., oco-equipment) can be imported without pulling the full bundle. L0 bridge re-emissions during development have not propagated changes into L1– L3 modules, demonstrating the version-localisation promise.

• Audience axis (material / compliance): three application profiles (oco_eln_profile.ttl, oco_materials_db_profile.ttl, oco_ml_profile.ttl) load only the modules each consumer class typically needs as owl:imports wrappers — the material-audience modules are reachable without the compliance modules, and conversely. The four dual-audience modules (format, odrl, time-event, automation) appear in both profile families without duplication.

• Seven-tier internal organisation of L2**** (the material-specific level’s internal mechanistic-explanation skeleton): the BNT-BT end-to-end pilot (examples/abox_pilots/bnt_bt_pilot.ttl) instantiates concrete classes on every one of the seven layers with explicit cross-tier annotations; the seven Cross-Tier SHACL NodeShapes pass with zero violations on the pilot’s 452-triple ABox, demonstrating that the explanation chain is operationally auditable rather than only conceptual.

5.4 Reusability — Work in Progress↩︎

A second ceramic material system, ferritic high-performance ceramics, is in active development as a second L2 instance on top of the unchanged L0+L1. Strategically, this choice tests architectural reusability across structurally distinct ceramic families: BNT-BT populates the perovskite branch of the oco-crystal hierarchy and exercises the piezoelectric/pyroelectric subset of the coupled-effect family; ferritic ceramics populate the spinel/garnet/hexaferrite branches and exercise the magnetic subset (magnetostriction, magnetoelectric coupling, Verdet effect). L1 remains unchanged across both; L2 oco-crystal, oco-phase, and oco-element are largely reused, while oco-material and oco-defect are extended with ferrite-specific classes. This is genuine L1-reuse and L2-extension validation within the ceramics family.

We emphasize what this is not: it is not cross-domain validation. Validating that L1 truly transfers to metallurgy, polymers, or batteries requires sister-project implementations that share L0+L1 with OCO — that work has not been undertaken and is left as an explicit roadmap position (7).

A parallel reusability claim is open at the mechanistic-explanation axis: the seven-tier skeleton is designed as a generic framework for crystalline ionic oxides (ferroelectrics, magnetics, ion conductors, high-\(T_c\) superconductors), not as a BNT-BT-specific construction. The skeleton has been concretised on BNT-BT; its claimed universality for the broader oxide class will be empirically established by the ferritic high-performance-ceramics second instance, whose magnetic phenomenology (Bloch / Néel walls, superexchange, magnetic anisotropy) exercises layers the BNT-BT pilot does not.

6 Discussion↩︎

6.1 What the Architecture Delivers↩︎

Compared with a flat ontology that bundles workflow, material, regulation, and reasoning concerns in a single TBox, the architecture (3) — with its two independent classification axes plus the seven-tier internal organisation of L2 — delivers five concrete benefits.

1. Fine-grained consumer choice. Each consumer imports only the depth they need. An ELN/LIMS integrator without material focus pays neither the ceramics-specific overhead nor the OWL-DL reasoner cost; a regulatory-reporting consumer loads the compliance audience without the materials-physics depth; a materials physicist loads L2 on the material audience and selects the mechanistic-explanation tiers (Symmetry alone, all seven, or any subset relevant to a specific question). The independence of the two axes plus the explicit seven-tier organisation of L2 permits subset choices along four dimensions (level, audience, mechanistic depth, and per-module composition) that a one-axis modular ontology cannot offer.

2. Sister-project reuse. A metallurgy or polymer ontology can replace L2 while sharing L0+L1, avoiding the duplication of laboratory, equipment, and measurement vocabulary that currently happens across PMD-consortium projects. The mechanistic-explanation skeleton (3.4.2) is designed to remain unchanged through this substitution — only the per-tier instance content changes.

3. Localized version updates. An external-standard release (PMDco v3.1, an EFRAG XBRL Taxonomy update, an updated Catena-X aspect model) requires changes only in L0 or the relevant bridge section — the material and compliance modules remain untouched.

4. CQ-bound reasoning scope. L3 makes the ontology’s intended question scope auditable: a published catalogue of competency questions with executable SPARQL tests (counts in 4) documents what the ontology is meant to answer, separately from what it can describe. Cross-Tier SHACL constraints (3.4.2) extend the same audit discipline to the explanation chain.

5. Mechanistic-explanation depth without TBox inflation. The external-cache pattern (3.4.2) keeps the TBox compact while letting consumers query against the Materials Project DFT corpus, the IUCr bond-valence parameters, the pyxtal Wyckoff positions, the Shannon ionic radii, and the Pauling electronegativities (cache totals in 4). A flat-vocabulary alternative would either embed those reference data as TBox classes (intractable for the reasoner) or leave them outside the knowledge graph altogether (loss of provenance).

6.2 Open- vs. Closed-Source Mix as Architectural Argument↩︎

A non-obvious benefit of strict level separation: the architecture enables a mixed open/proprietary distribution model that flat ontologies cannot offer. In the present release this is realized as follows. L0 is released under CC-BY 4.0, mirroring the licenses of the bridge targets it anchors to (PMDco, EMMO, PROV-O, and FaBiO are CC-BY; QUDT is Apache-2.0) and maximizing bridge adoption in third-party stacks. The publicly released portion of L1 — which excludes the oco-supplier module and the L1 portions of the compliance and value-chain modules listed in 9 (oco-csrd, oco-mfgx, oco-lca, oco-csddd, oco-ppwr, oco-cbam, oco-r2r, oco-aiact, oco-regulation, oco-recycling, oco-ssbd, plus the four dual-audience modules oco-format, oco-odrl, oco-time-event, oco-automation) — is released under CC-BY-SA 4.0, with dual-licensing to CC-BY available on request for commercial integrators that cannot adopt copyleft. The oco-supplier module, the L1 portions of the compliance and value-chain modules, the entire L2, and the entire L3 are developed under project confidentiality and remain proprietary in the present release. The same modular boundaries that make this split clean would, in a future configuration, also enable a per-module choice: a sister project working under different commercial constraints could open or close a different subset without restructuring.

This mix is structurally impossible in monolithic ontologies (everything-or-nothing open) and in purely proprietary industrial schemas (no external adoption). The architecture being modular along two independent axes plus the seven-tier internal organisation of L2 is exactly what makes the licensing choice fine-grained. The quantitative metrics and validation results in 4 and 5 are measured on the full distribution; the architectural contribution of this paper — the two-axis modular pattern, the ten design principles, the seven-tier mechanistic-explanation skeleton organising L2, the Neumann tensor engine, the phase-state coupling, the multi-axis parameter classification, and the external-cache pattern for reference data — is independent of which particular modules a given consumer can access.

6.3 Limitations↩︎

• Equipment module rests partly on textbook anchors. While the equipment module now bridges to PMDco, CHMO, OBI, and schema.org, a substantial portion of its class definitions still rest on textbook rather than formal-norm anchors. A systematic norm-anchor sweep is open work.

• Neumann engine validated on a 30-case gold standard. The 5 920 (tensor \(\times\) point-group) constraints (4.5) have been checked against [82] and IEEE Standard 176 on a 30-case sample (30/30 PASS). This covers the principal piezoelectric and elasticity cases; a larger reference set with independent textbook verification across all tensor-class \(\times\) point-group combinations is open work.

• Phase-state coupling instantiated for two materials. The Sample \(\to\) Region \(\to\) point-group inference (4.5) has been populated only for BNT-BT and NiCuZn ferrite (six gold-standard cases, 6/6 PASS). Extending the pattern to a third material with substantially different phase phenomenology — e.g.a martensitic or order–disorder transition — is the next coverage test.

• Multi-axis classification is heuristic-based. The bulk-classification pipeline (4.6) reaches \({\sim}99\,\%\) coverage via family-default plus outlier-override rules; the residual is conservatively over-approximated as ResponseParameter. Targeted manual review is open work.

• ****L1** cross-domain transferability is architecturally argued, not empirically proven.** See 5.4; only within-ceramics-family L2 substitutability has been tested so far.

• Seven-tier skeleton universality not yet empirically validated across the oxide class. The mechanistic-explanation skeleton (3.4.2) is designed as generic for crystalline ionic oxides and has been concretised on BNT-BT. The ferritic high-performance-ceramics second instance (5.4) is the first test of whether tiers such as Magnetic-Microstructure (Bloch / Néel walls) and Magnetic-Bonding (superexchange, Jahn–Teller distortion) can be added as Tier-5 / Tier-7 extensions without restructuring the skeleton itself; that test is in progress.

• External-cache provenance carries a maintenance contract. The five reference-data caches (3.4.2) are pinned to upstream versions via SHA. Upstream releases of the Materials Project, IUCr bvparm, Shannon compilations, pyxtal, and Pauling revisions will require periodic re-sync and re-validation. This is operational overhead the cache pattern explicitly takes on in exchange for keeping the TBox compact.

6.4 Scope Boundary and Roadmap Position — OCO v0.94↩︎

The architecture defines what OCO covers and, with equal discipline, what it does not. Within OCO the boundary is internal: L3’s categorical reasoning is opt-in (3.5), and even the bilingual definitional discipline (3.3) is a feature consumers can ignore if they wish. The external boundary — between OCO and the surrounding materials-data stack — is the architecturally load-bearing one, and we state it explicitly here.

6.4.0.1 The categorical/quantitative split

Quantitative mathematics (calibration curves, scaling laws, arbitrary numerical functions) lies outside this release entirely. This is a principled separation, not an oversight. OWL 2 DL can evaluate subsumption, existence, and restriction, but it cannot evaluate a function such as \(d_{33}(x) = a + b\,x\) on the interval \([0.04, 0.08]\) for the BNT-BT solid-solution series; SHACL can perform range checks but is equally not a function evaluator. Embedding such functions into OWL classes produces a TBox in which neither categorical nor quantitative reasoning works correctly: the reasoner cannot reason about the function, and the function cannot consult the rest of the OWL graph. Whatever takes responsibility for quantitative mathematics in the surrounding stack must therefore be a separate level with its own evaluator, coupled to OCO classes as anchors but not embedded in them.

6.4.0.2 Today’s workaround, tomorrow’s level

Consumers that already need quantitative computation handle this externally: a Python/SymPy/MATLAB compute level holds the equations and queries OCO classes by IRI. This works in practice and is the intended pattern for the present release. A future OCO release will formalize a quantitative-mathematics level above the present categorical levels; the architectural commitment is that the new level will respect the categorical/quantitative split rather than violating it. The categorical levels (L0–L3) will not change in the process.

6.4.0.3 The v0.94 framing

This paper describes OCO v0.94: the release engineered to enter productive practice. The version number is deliberate. v0.94 means: the architecture is complete along both classification axes, the categorical levels are populated, the seven-tier mechanistic-explanation skeleton organising L2 is in place, the compliance modules cover the EU-regulatory wave currently in force, the test suite passes, and the BNT-BT end-to-end pilot demonstrates the skeleton operationally. What v0.94 does not yet have is the corrective feedback that only productive use can deliver — conflicts between intended modelling and what actual data exposes, modules that turn out to need refactoring, bridge mappings that upstream releases break, cache contracts that real consumer queries strain. The v1.0 release is reserved for the state after that feedback cycle. Until then v0.94 is the deliberate label for a complete-and-ready-for-practice release that has not yet been corrected by practice.

6.4.0.4 Other deliberate non-inclusions

For clarity, the following are also outside the scope of this release:

• Workflow execution level. Executable workflow orchestration (e.g.pyiron, SimStack) is platform work, not ontology work; OCO provides class anchors that such systems can target.

• Own ML/AI classes. OCO does not introduce a machine-learning vocabulary of its own; bridging to existing community efforts (MDO, CMSO) is the chosen path when the need arises.

• Companion software tools. The OCO-Workbench and SIPOC-Extractor (4.10) use OCO as their schema but are outside the scope of this paper.

7 Conclusion and Outlook↩︎

We have argued that an industrial materials ontology entering productive use today must answer three simultaneous challenges: horizontal fragmentation across material domains, vertical convergence pressure driven by EU regulation, and mechanistic explanation depth that lets the ontology surface why a property holds, not only that it does. The architecture proposed here answers all three with a single integrated design — a multi-level, modular ontology with two independent classification axes (the level of abstraction, from L0 bridges through L3 categorical reasoning; and the consumer audience, material versus compliance, with four dual-audience modules at the join) in which the material-specific level (L2) is internally organised by a seven-tier mechanistic-explanation skeleton applicable to any crystalline ionic oxide. The level-and-audience modularity dissolves the horizontal fragmentation, the compliance audience absorbs the vertical regulation pressure, and the seven-tier organisation of L2 delivers the mechanistic-explanation depth.

The OntoCrafter Ceramics Ontology (OCO v0.94) instantiates the architecture for functional ceramics with BNT-BT as the end-to-end pilot: 5 196 classes across 44 class-bearing modules; 167 348 OWL axioms (40 454 logical, per ROBOT) including 5 920 reified Neumann tensor constraints; 1 674 properties; 829 cross-ontology bridge mappings across 40 sections; 1 172 SHACL shapes including 7 Cross-Tier NodeShapes that audit the explanation chain; 163 published competency questions with 52 executable SPARQL tests (52/52 PASS); 132 architecture decision records; and an external-cache pattern that lets the compact TBox query against approximately 155 000 Materials Project DFT entries, 1 934 IUCr bond-valence parameters, 1 731 Wyckoff positions, 497 Shannon ionic radii, and 91 Pauling electronegativities without inflating the OWL vocabulary itself.

The publicly available portion of the distribution (L0 under CC-BY 4.0, the public modules of L1 under CC-BY-SA 4.0) is hosted at https://w3id.org/oco/. The supplier module, the full L2, and L3 are developed under project confidentiality, as discussed in 6.2.

The v0.94 designation is deliberate: the release is engineered to enter productive practice. The v1.0 release is reserved for the state after that practice has fed back corrections — conflicts between intended modelling and what actual data exposes, modules that turn out to need refactoring, bridge mappings that upstream releases break, cache contracts that real consumer queries strain. The shape of the v0.94\(\to\)v1.0 roadmap, stated without promises:

• Practice-feedback cycle. Productive use of OCO in materials-research and compliance-reporting pipelines, with structured intake of corrections through the existing ADR process. Decisions taken on the basis of that feedback are the substance of v1.0.

• Completion of the second ceramic material instance (ferritic high-performance ceramics), validating L1 reusability and L2 extension within the ceramics family (5.4). The ferritic instance also stresses the seven-tier skeleton on the magnetic side (Bloch / Néel walls, superexchange, Jahn–Teller distortion) that the BNT-BT pilot does not exercise.

• Discoverability channels. Listing on MatPortal, IndustryPortal, and OSF, to enter the channels surveyed by [1].

• Open invitation to sister-domain projects (metallurgy, polymers, batteries, pharmaceuticals) to share L0+L1 with OCO and contribute their own L2 instance — the first genuine cross-domain validation of the architecture.

The deeper claim of this paper is not that OCO is the right ontology for ceramics. It is one possible implementation of a broader idea: that the materials-science community can stop re-modelling the same workflow, equipment, measurement, compliance, and mechanistic-explanation concepts in every new domain ontology. The architecture proposed here — two independent axes plus the seven-tier internal organisation of L2 — is one way to do that. We hope others follow.

Author Contributions (CRediT)↩︎

T. Pannek and W. Grond (both): Conceptualization (ontology architecture), Methodology (bridge stack, pipeline), Validation, Writing.

T. Pannek (additionally): OCO-Workbench (companion software for data import and ABox population).

W. Grond (additionally): Materials Science (L2 ceramic material modeling for BNT-BT and ferritic high-performance ceramics), SIPOC-Extractor (companion software for literature extraction).

Both authors appear on all Numberland publications related to the OCO suite (ontology and two companion software tools), reflecting the close collaboration between the materials-science and architecture/implementation domains.

Acknowledgments↩︎

Data and Code Availability↩︎

The publicly available portion of the OCO distribution — L0 (CC-BY 4.0) and L1 excluding the oco-supplier module (CC-BY-SA 4.0) — is hosted at https://w3id.org/oco/. Dual-licensing of the public L1 modules to CC-BY 4.0 is available on request for commercial integrators that cannot adopt copyleft. The oco-supplier module, L2, and L3 are developed under project confidentiality and are not available under an open license in the present release; the rationale and architectural consequences are discussed in 6.2. Quantitative metrics and validation results in this paper are reported from internal validation against the full distribution. Academic-collaboration and commercial-license enquiries can be addressed to the corresponding author.

References↩︎

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1. The PMD Phase-1 publication portfolio sets the practical context for this work: [3]–[59].↩︎