# Feature Specification: Grand Unified Theory of Full-Stack KGC

**Feature Branch**: `012-grand-unified-kgc-thesis`
**Created**: 2025-12-16
**Status**: Draft
**Input**: User description: "Grand Unified Theory of Full-Stack KGC - PhD thesis integrating ggen, @unrdf/hooks, @unrdf/kgc-4d, NextJS, TanStack, Electric SQL, pnpm monorepo architecture with hyperdimensional information theory calculus. Extends v5 thesis-gen ontology to prove: (1) Knowledge Graph Completeness guarantees full-stack consistency, (2) 4D temporal semantics enable event sourcing calculus, (3) Information-theoretic projection bounds for multi-target code generation, (4) Hyperdimensional vector spaces for ontology embeddings."

## User Scenarios & Testing *(mandatory)*

### User Story 1 - Generate Complete PhD Thesis Document (Priority: P1)

A researcher uses ggen to generate a complete, publication-ready PhD thesis in LaTeX format from an RDF ontology. The thesis presents the Grand Unified Theory of Full-Stack Knowledge Graph Completeness, proving that deterministic code generation from semantic ontologies eliminates specification-implementation drift across the entire technology stack.

**Why this priority**: The primary deliverable is a complete, coherent PhD thesis document that can be compiled to PDF. Without this, there is no thesis to present or defend.

**Independent Test**: Can be fully tested by running `ggen sync` on the thesis ontology and compiling the resulting LaTeX to PDF. Delivers a 100+ page academic thesis with proper structure, theorems, proofs, figures, and bibliography.

**Acceptance Scenarios**:

1. **Given** a complete thesis ontology with 7+ chapters, 10+ theorems, 20+ equations, and 30+ references, **When** `ggen sync` is executed, **Then** all LaTeX files are generated deterministically with consistent cross-references
2. **Given** the generated LaTeX files, **When** compiled with pdflatex/bibtex, **Then** a properly formatted PhD thesis PDF is produced with table of contents, list of figures, and bibliography
3. **Given** any modification to the thesis ontology, **When** `ggen sync` is re-executed, **Then** only the affected sections change while maintaining document integrity

---

### User Story 2 - Prove Knowledge Graph Completeness Theorem (Priority: P1)

A reader of the thesis can follow the formal proof that Knowledge Graph Completeness guarantees full-stack consistency. The proof demonstrates that if an RDF ontology encodes a complete domain specification, then all generated artifacts (Zod schemas, React hooks, API routes, database schemas) are mathematically guaranteed to be consistent with each other.

**Why this priority**: This is the central theoretical contribution of the thesis. Without the formal proof, the thesis lacks academic rigor and cannot be defended.

**Independent Test**: A mathematician or computer scientist can read Chapter 2 (Theoretical Foundations) and verify each step of the Zero-Drift Theorem proof. The proof should be complete, logically sound, and follow from stated axioms.

**Acceptance Scenarios**:

1. **Given** the formal definition of Knowledge Graph Completeness in the ontology, **When** the thesis is generated, **Then** Definition 1 appears with precise mathematical notation in Section 2.1
2. **Given** the lemmas supporting the Zero-Drift Theorem, **When** the thesis is generated, **Then** each lemma appears with its proof before the main theorem
3. **Given** the Zero-Drift Theorem statement and proof, **When** a reader follows the argument, **Then** each step references prior definitions and lemmas by label

---

### User Story 3 - Demonstrate 4D Temporal Event Sourcing (Priority: P2)

A reader understands how the @unrdf/kgc-4d framework enables temporal semantics for event sourcing. The thesis demonstrates that treating knowledge graphs as 4-dimensional structures (3D spatial + 1D temporal) enables powerful time-travel queries, audit trails, and state reconstruction.

**Why this priority**: This extends the theoretical framework to practical applications in event sourcing, a key architectural pattern. It demonstrates real-world applicability of the theory.

**Independent Test**: Chapter 4 can be read independently and the KGC-4D concepts can be verified against the @unrdf/kgc-4d npm package implementation. Code examples should match actual library APIs.

**Acceptance Scenarios**:

1. **Given** the temporal semantics formalization in the ontology, **When** the thesis is generated, **Then** the Event Sourcing Calculus appears in Chapter 4 with nanosecond precision timestamps
2. **Given** the GitBackbone state reconstruction algorithm, **When** documented in the thesis, **Then** the algorithm pseudocode matches the actual @unrdf/kgc-4d implementation
3. **Given** a time-travel query example, **When** presented in the thesis, **Then** it demonstrates reconstructing application state at any past timestamp

---

### User Story 4 - Explain Hyperdimensional Information Theory (Priority: P2)

A reader understands how ontologies can be embedded in hyperdimensional vector spaces and how information-theoretic bounds apply to code generation. The thesis introduces novel calculus for measuring semantic fidelity of projections.

**Why this priority**: This provides the mathematical foundation connecting information theory to code generation, enabling formal analysis of generation quality.

**Independent Test**: Chapter 3 presents the hyperdimensional embedding formalism and a reader with background in information theory can verify the entropy calculations and projection bounds.

**Acceptance Scenarios**:

1. **Given** the hyperdimensional encoding of RDF triples, **When** the thesis is generated, **Then** the embedding equations appear with proper dimensional analysis
2. **Given** Shannon entropy applied to ontology distributions, **When** presented in the thesis, **Then** semantic fidelity bounds are derived with complete proofs
3. **Given** mutual information between ontology and generated code, **When** calculated, **Then** the preservation bounds are proven tight

---

### User Story 5 - Validate Full-Stack Integration Case Study (Priority: P3)

A reader sees a complete case study showing ggen generating a full-stack application (TanStack DB + NextJS + Electric SQL) from a single project management ontology. The case study demonstrates 73% reduction in cross-module inconsistencies.

**Why this priority**: Empirical validation strengthens the theoretical claims and demonstrates practical applicability to production systems.

**Independent Test**: The case study in Chapter 5 can be replicated by following the documented steps with the provided ontology. The generated code should match the thesis examples.

**Acceptance Scenarios**:

1. **Given** the project management ontology from /Users/sac/dis/astro/packages/tanstack-db, **When** referenced in the thesis, **Then** the generated artifacts (schemas, hooks, mutations) are documented with line counts
2. **Given** the consistency metrics comparison, **When** presented in tables, **Then** the 73% reduction claim is supported by specific measurements
3. **Given** the pnpm monorepo structure, **When** documented, **Then** the package organization follows the actual implementation

---

### User Story 6 - Document @unrdf/hooks Policy Framework (Priority: P3)

A reader understands how @unrdf/hooks enables declarative policy definition and enforcement. The thesis demonstrates that Knowledge Hooks integrate validation, authorization, and business rules directly from ontology specifications.

**Why this priority**: This shows the practical application of ontology-driven development to software quality concerns (validation, security).

**Independent Test**: The Knowledge Hooks patterns in Chapter 6 can be verified against the @unrdf/hooks npm package. Generated hook code should compile and execute correctly.

**Acceptance Scenarios**:

1. **Given** the Knowledge Hooks formalization, **When** the thesis is generated, **Then** the defineHook/executeHook patterns are documented with examples
2. **Given** validation hooks generated from SHACL shapes, **When** documented, **Then** the hook implementation matches the ontology constraints
3. **Given** policy enforcement examples, **When** presented, **Then** they demonstrate pre/post hooks for create/update/delete operations

---

### Edge Cases

- What happens when ontology contains circular references in class hierarchies?
- How does the system handle incomplete specifications (missing required properties)?
- What are the limits of hyperdimensional embedding dimensions for large ontologies?
- How does temporal resolution affect state reconstruction accuracy?
- What happens when SPARQL queries return empty results for mandatory thesis sections?
- How does the system handle conflicting property definitions across imported ontologies?

## Requirements *(mandatory)*

### Functional Requirements

- **FR-001**: System MUST generate a complete PhD thesis LaTeX document structure (front matter, chapters, appendices, bibliography) from RDF ontology
- **FR-002**: System MUST preserve all mathematical notation when generating theorem statements and proofs from ontology
- **FR-003**: System MUST generate consistent cross-references (labels, citations, equation numbers) that compile correctly
- **FR-004**: System MUST include all 20+ equations with proper LaTeX math mode formatting
- **FR-005**: System MUST include all 10+ theorems with statements, proofs, and labels for each theorem type (theorem, lemma, corollary, definition, proposition)
- **FR-006**: System MUST generate BibTeX bibliography file from reference instances in ontology
- **FR-007**: System MUST generate 5+ algorithm pseudocode blocks using algorithmic package
- **FR-008**: System MUST generate figure placeholders with captions, dimensions, and labels
- **FR-009**: System MUST generate tables with proper formatting for empirical results
- **FR-010**: System MUST support incremental regeneration (only changed sections regenerate)
- **FR-011**: System MUST generate chapter content with sections and subsections in correct order based on orderIndex properties
- **FR-012**: System MUST escape LaTeX special characters in ontology content (backslashes, curly braces, etc.)
- **FR-013**: System MUST generate appendices with code listings and extended proofs
- **FR-014**: System MUST support 7 core chapters covering: Introduction, Theoretical Foundations, Hyperdimensional Calculus, KGC-4D Framework, TanStack Case Study, @unrdf Integration, Conclusion
- **FR-015**: System MUST generate preamble with all required LaTeX packages and theorem environments

### Key Entities

- **Thesis**: Root document entity with title, subtitle, author, institution, department, date, abstract, dedication, acknowledgments, and relationships to chapters, references, and appendices
- **Chapter**: Major structural unit with orderIndex, title, labelId, optional abstract, and relationships to sections
- **Section**: Content unit with orderIndex, title, labelId, content prose, and relationships to subsections, theorems, equations, figures, tables, algorithms
- **Subsection**: Nested content unit with orderIndex, title, labelId, and content
- **Theorem**: Formal mathematical statement with orderIndex, theoremType (theorem/lemma/corollary/definition/proposition), optional theoremName, statement, optional proof, and labelId
- **Equation**: Mathematical formula with orderIndex, latex representation, optional description, and labelId
- **Algorithm**: Pseudocode block with orderIndex, title, input, output, caption, labelId, and ordered steps with stepIndex
- **Figure**: Visual element with orderIndex, caption, imagePath, optional width, optional position, and labelId
- **Table**: Tabular data with orderIndex, caption, labelId, ordered headers with headerIndex, and rows containing cells with cellIndex
- **TableRow**: Row entity with rowIndex and cell values
- **Reference**: Bibliography entry with citeKey, bibType (article/book/misc/inproceedings/phdthesis), author, title, year, and optional fields (journal, booktitle, publisher, school, volume, pages, doi, url, howpublished)
- **Appendix**: Supplementary section with letter (A, B, C...), title, labelId, content, and optional code listings

## Success Criteria *(mandatory)*

### Measurable Outcomes

- **SC-001**: Generated thesis compiles to PDF without errors on first attempt using standard pdflatex/bibtex toolchain
- **SC-002**: Thesis contains minimum 100 pages of substantive content (excluding front matter and bibliography)
- **SC-003**: All 20+ equations render correctly with proper numbering in mathematical notation
- **SC-004**: All 10+ theorems have complete proofs with working cross-references to prior lemmas and definitions
- **SC-005**: Bibliography contains 30+ properly formatted references from reputable sources (W3C standards, ACM journals, foundational computer science texts)
- **SC-006**: Zero specification-implementation drift between ontology content and generated LaTeX (verified by diff analysis)
- **SC-007**: Regeneration from same ontology produces byte-identical output (deterministic generation guarantee)
- **SC-008**: Full thesis generation completes in under 10 seconds for ontology with 2000+ triples
- **SC-009**: Case study metrics are reproducible: reader can run ggen on provided ontology and verify line counts match thesis claims
- **SC-010**: All LaTeX cross-references resolve correctly (no "??" or undefined reference warnings)

## Assumptions

- The thesis uses standard academic LaTeX document class (report or similar)
- All figures are provided as PDF/PNG files or generated as TikZ diagrams from ontology
- The @unrdf/hooks and @unrdf/kgc-4d packages are stable at version 5.0.1
- The existing thesis-gen templates from ggen examples can be extended for this thesis
- Readers have graduate-level background in computer science and mathematics
- The TanStack DB case study ontology at /Users/sac/dis/astro/packages/tanstack-db is complete and valid

## Dependencies

- ggen v5 thesis generation infrastructure (existing in examples/thesis-gen)
- @unrdf/hooks v5.0.1 for Knowledge Hooks integration patterns
- @unrdf/kgc-4d v5.0.1 for 4D temporal event sourcing patterns
- Oxigraph RDF processing engine
- Tera template engine
- LaTeX distribution with amsmath, amsthm, algorithm2e packages
- BibTeX for bibliography processing
