Reusable Block-Granular Units

• Reusable block-granular units are modular, independently addressable blocks embedded with formal metadata and unique identifiers, enabling precise citation and reuse.
• They support multi-level composition from atomic statements to compound units, facilitating fine-grained knowledge organization and system interoperability.
• Their implementation leverages persistent identifiers, automated composition directives, and formal ontologies to enhance performance, maintainability, and FAIR compliance.

A reusable block-granular unit is a modular, semantically meaningful, and independently addressable component within a larger data, software, or knowledge structure. This paradigm appears across domains—from learning object repositories and knowledge graphs to deep learning model architectures and programmable logic overlays—where the focus is on maximizing reusability, maintainability, and composability by decomposing systems into atomic or composite “blocks” endowed with formal metadata and unique identifiers (Vogt et al., 30 Sep 2025, Vogt, 2023, Vogt et al., 2023, Salas, 2020). Reusable block-granular units support the principles of Findability, Accessibility, Interoperability, and Reusability (FAIR), dynamic composition, provenance tracking, and efficient sharing both within and across projects.

1. Formal Definitions and Abstractions

Across domains, block-granular units are rigorously defined objects characterized by independent identity, encapsulation of structure, and self-descriptive metadata. In semantic knowledge modeling, a semantic unit (SU) is defined as an identifiable resource with a unique persistent identifier (GUPRI), an associated content graph, and a meta-graph with provenance, type, and schema declarations (Vogt et al., 30 Sep 2025):

$u = (id_u, M_u, C_u)$

where $id_u$ is the GUPRI, $M_u$ is meta-graph, and $C_u$ is content-graph. Compound units are sets of SUs (or other compound units) sharing a GUPRI and linkage metadata. This formal modularization yields a partition of the knowledge base:

$$\bigsqcup_{u \in SU} C_u = T \qquad \forall u_i \neq u_j: C_{u_i} \cap C_{u_j} = \varnothing$$

In computational and authoring environments (e.g., CourseGen, FPGA overlays), a block-granular unit may be as fine as a single Markdown file or a parametrized functional unit, with versioning and metadata headers that support inclusion, linking, and automated composition (Salas, 2020, Li et al., 2016).

2. Typology and Hierarchical Composition

Block-granular units support multiple levels of granularity, enabling modeling, authoring, and computation at varying abstraction levels.

• Atomic (Statement) Units: The minimal, independent proposition or building block. In knowledge graphs, these correspond to statement units that partition the graph's assertion triples (Vogt et al., 2023, Vogt, 2023). In learning object repositories, micro-learning objects may be as small as a paragraph or single line (Salas, 2020).
• Compound Units: Collections of atomic units sharing a common relation, subject, or pattern. These may encode item units (all statement units about one subject), item group units (semantically related sets), dataset units (user-defined arbitrary collections), or granularity tree units encoding hierarchical relationships (Vogt, 2023, Vogt et al., 30 Sep 2025).
• Hierarchy: Composition operators enable recursive nesting, forming granularity trees or DAGs:

$\text{compose}: \mathcal{P}(U) \rightarrow U_2$

with U the universe of semantic units.

Table 1. Typology of Block-Granular Units in Knowledge Organization

Unit Type	Definition	Example Context
Statement Unit	Minimal, semantically atomic assertion; partition of content	"Protein X has mass 24.76 g"
Compound Unit	Set of semantic units, possibly recursively composed	Measurement group, topic section
Item Unit	All SUs about a single subject (entity/class)	All assertions about a gene
Dataset Unit	Arbitrary user-defined SU aggregation	Table of blood values
Granularity Tree Unit	Hierarchical (tree-ordered) composition	Anatomy partonomy

3. Mechanisms for Reusability and Interoperability

Reusable block-granular units are engineered for independent citation, discovery, and combination. Key mechanisms include:

• Globally Unique Persistent Identifiers (GUPRIs): Every unit is issued a URI or analogous global ID at creation, ensuring dereferenceability and cross-system referencing (Vogt et al., 30 Sep 2025).
• Meta-Graph and Provenance: Each unit carries a structured meta-graph—fields include type/class, schema model, logical formalism, version, license, and provenance (e.g., prov:wasDerivedFrom). In learning repositories, YAML-style front matter with author, date, and title serves a similar role (Salas, 2020).
• Formal Ontology and Type System: Modular ontologies (via OWL, RDF, SHACL) define classes, inheritance, and allowed block relations—e.g., :SemanticUnit, :CompoundUnit with subtypes for statement, item, group, or dataset units (Vogt, 2023).
• Automated Composition and Reference: Directives ($include,$link_to in CourseGen) and graph composition operators support parameterless inclusion and linking without cut-and-paste, enforcing referential transparency and propagating edits automatically (Salas, 2020).
• FAIR Digital Object Packaging: Units map 1:1 to nanopublications or RO-Crate objects; each package encapsulates both content and metadata, supporting tool-independent reuse and migration (Vogt et al., 30 Sep 2025).

4. Implementation Paradigms and Architectures

Distinct applied architectures realize the block-granular principle:

• Knowledge Graphs: SUs structure KGs into referenceable subgraphs, supporting statements about statements, fine-grained provenance, versioning, and schema modularity. Example: each measurement or assertion yields a nanopublication with a content- and meta-graph, all indexed by GUPRI for direct cross-graph reuse (Vogt, 2023, Vogt et al., 2023, Vogt et al., 30 Sep 2025).
• Learning Repositories (CourseGen): Micro learning objects (CGLOs) are plain-text files with YAML metadata and embedded Marshal/Include directives. Version control (git) and build pipelines enforce atomicity, automated publication, and continuous integration across curricula (Salas, 2020).
• Visual Programming (Block Shelves): Blockly block shelves encapsulate any arbitrary block cluster as a named "shelf," exported/imported as XML fragments. Shelf operations (add, remove, activate, duplicate) operate on the whole unit, supporting cross-project reuse (Hsu et al., 2016).
• Software and Deep Learning Models: Weight tensors or layers are partitioned into fixed-size block units, each loaded, cached, or evolved independently. Block-level equivalence and sharing are core to multi-tenant and sparse-execution frameworks (Hu et al., 28 Apr 2024, Huang et al., 25 Nov 2025).
• FPGA Overlays: Time-multiplexed functional units (FUs) built on DSP primitives act as block-granular compute units, each pipelined for context-switched reuse across different data-flow graph stages; their granular allocation and minimal reconfiguration accelerate workload context switching (Li et al., 2016).

5. Advantages, Impact, and Empirical Evidence

The block-granular paradigm yields direct, measurable benefits for maintainability, reusability, and efficiency:

• Reusability: Units are reusable at multiple levels of granularity, enabling selective importation, precise citation, and zero duplication—all without tight coupling to the host schema (Vogt et al., 30 Sep 2025, Vogt, 2023).
• Versioning and Provenance: Fine-grained units permit atomic version tags, detailed change tracking, and provenance assertions at any abstraction level (Salas, 2020).
• Performance and Efficiency: In multi-task sparse model serving, block-granular weight reuse yields substantial reductions in memory movement and latency (e.g., 6.6–16× speedup and 46% GPU footprint reduction for on-demand edge deployment (Huang et al., 25 Nov 2025)). In learning objects, CourseGen avoids cut-and-paste and missing updates entirely (Salas, 2020).
• Cognitive Interoperability: Knowledge blocks are independently discoverable (e.g., by SPARQL, SQL, or vector search), and schema or UI layers can map these blocks across multiple user-facing views (Vogt, 2023, Vogt et al., 30 Sep 2025).
• Empirical Results: In visual programming, adoption of block shelves resulted in a twofold reduction in search time for code navigation, with no statistically significant increase in reading time (Hsu et al., 2016).

6. Use Cases, Applications, and Illustrative Examples

• Knowledge Graphs: Block-granular SUs allow fine-grained annotation, evolution, and reuse, enabling applications such as cross-domain data integration, subgraph pattern matching, and access control. Concrete RDF/Turtle examples demonstrate block-level citation and provenance (Vogt, 2023, Vogt et al., 30 Sep 2025).
• Learning Content: CourseGen supports assembling lectures by $include and$link_to directives; atomic blocks such as definitions, policy notes, and exercises propagate into every product (PDF, web, slides) without duplication (Salas, 2020).
• Software-Defined Hardware: FPGA contexts can be switched in sub-microsecond time by streaming only the new block’s instructions to the relevant functional unit, cutting resource usage by up to 85% over spatial overlays (Li et al., 2016).
• Model Serving and Edge Deployment: Systems like BlockLLM maintain a “block zoo,” reusing and substituting equivalent blocks on-the-fly for serving large ensembles, reducing memory and storage footprint by over 16%, and improving latency by over 30% at peak percentiles (Hu et al., 28 Apr 2024).

7. Limitations and Challenges

While block-granular reuse delivers substantial practical efficiency, several challenges remain:

• Granularity Tuning: Excessively fine-grained blocks can increase management overhead and fragment provenance, while coarse granularity limits composability and reusability (Salas, 2020, Vogt, 2023).
• Schema Evolution and Alignment: Ensuring semantic and operational compatibility among recomposed blocks, particularly in federated or rapidly evolving systems, requires sophisticated type systems, equivalence checking, and conversion pipelines (Hu et al., 28 Apr 2024, Vogt et al., 30 Sep 2025).
• Cognitive Cost: Although designed to enhance cognitive interoperability, the complexity of multi-level granularity and cross-referencing may increase onboarding friction without adequate UI/UX and documentation layers (Vogt, 2023).
• Performance Trade-Offs: In hardware overlays, latency and throughput can be impacted as a function of block size and allocation (e.g., increased initiation interval in time-multiplexed FUs (Li et al., 2016)).

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Reusable block-granular units constitute a cross-disciplinary framework for modular, versionable, and efficiently composable information and computation architectures. They are foundational to the scaling of FAIR data infrastructures, AI-ready scholarly communication, and robust multi-tenant software and hardware systems (Vogt et al., 30 Sep 2025, Salas, 2020, Vogt, 2023, Huang et al., 25 Nov 2025, Hsu et al., 2016, Li et al., 2016).