Textbook Grounding

Textbook Grounding v2.0

λ: Query → Tensor Activation → Syntopical Analysis → Grounded Response with Citations

Generate examination-optimized responses grounded in systematic cross-textbook analysis using Hegelian dialectical synthesis with orthogonal tensor integration.

Core Philosophy

Syntopical Reading (Mortimer Adler)

The highest level of reading—comparing multiple authoritative sources on the same topic to synthesize understanding unavailable from any single source.

Hegelian Dialectic

"A higher level of understanding and insight could be achieved by creating the two most diametrically opposed viewpoints, the mutual contradiction being reconciled on a higher level of truth." — Model of Dialectical Learning

• Thesis: Each textbook's interpretation/claim
• Antithesis: Contradictions, variations, nuances across sources
• Synthesis: Universal principles emerging from resolved tensions

Orthogonal Tensor Integration

This skill participates in the 5D tensor routing space:

• S dimension: Activates [saq, dialectical, critique, constraints]
• T dimension: Integrates [pdf-search, perplexity, relate]
• L dimension: Leverages [pdf-brain, docling, qmd]
• Cross-dimensional synergy: S×T×L = 0.95

Architecture v2.0

┌─────────────────────────────────────────────────────────────────────────────┐
│                  ORTHOGONAL TEXTBOOK GROUNDING PIPELINE                     │
├─────────────────────────────────────────────────────────────────────────────┤
│                                                                             │
│  Φ0: TENSOR ACTIVATE ─────────────────────────────────────────────────────  │
│      └─ Score dimensions, detect synergies, compose execution plan          │
│                                                                             │
│  Φ1: QUERY DECOMPOSE ─────────────────────────────────────────────────────  │
│      └─ Parse topic, domains, complexity; route to skill stack              │
│                                                                             │
│  Φ2: PARALLEL SEARCH ─────────────────────────────────────────────────────  │
│      └─ Multi-query semantic search across pdf-embeddings + web             │
│      └─ Execute via T×L synergy: pdf-search × pdf-brain × docling           │
│                                                                             │
│  Φ3: THESIS EXTRACTION ───────────────────────────────────────────────────  │
│      └─ Extract T_i from each source with page-level citations              │
│      └─ Classify: definitional | mechanistic | quantitative | clinical      │
│                                                                             │
│  Φ4: ANTITHESIS DETECTION ────────────────────────────────────────────────  │
│      └─ Compare thesis pairs for tensions A_ij                              │
│      └─ Classify: contradiction | refinement | extension | context_dependent│
│                                                                             │
│  Φ5: DIALECTICAL SYNTHESIS ───────────────────────────────────────────────  │
│      └─ Invoke dialectical skill for α-β-γ structure                        │
│      └─ Apply constraints skill for deontic obligations                     │
│                                                                             │
│  Φ6: MULTI-LENS CRITIQUE ─────────────────────────────────────────────────  │
│      └─ STRUCTURAL × EVIDENTIAL × SCOPE × ADVERSARIAL × PRAGMATIC           │
│      └─ Per-thesis evaluation with aggregate scoring                        │
│                                                                             │
│  Φ7: ABDUCTIVE SYNTHESIS ─────────────────────────────────────────────────  │
│      └─ Abduce minimal universal principles S resolving tensions            │
│      └─ Validate: ∀T_i. ∃s ∈ S. subsumes(s, T_i)                            │
│                                                                             │
│  Φ8: RESPONSE GENERATION ─────────────────────────────────────────────────  │
│      └─ Invoke saq skill for template routing                               │
│      └─ Apply symbol lexicon, word count constraints                        │
│                                                                             │
│  Φ9: CITATION WEAVING ────────────────────────────────────────────────────  │
│      └─ Systematic footnote generation with page references                 │
│      └─ Apply deontic constraints: O(cite), O(page), F(uncited)             │
│                                                                             │
│  Φ10: VALIDATION & QA ────────────────────────────────────────────────────  │
│       └─ Coverage, parsimony, confidence floor checks                       │
│       └─ Examiner expectation alignment                                     │
│                                                                             │
└─────────────────────────────────────────────────────────────────────────────┘

Phase Execution Details

Φ0: Tensor Activation

When invoked via /m, this skill receives tensor context:

tensor_context:
  prompt: "{original_query}"
  activated_dimensions:
    C: sc:document (0.70)
    A: researcher (0.75)
    S: textbook-grounding (0.95), saq (0.90), dialectical (0.80), critique (0.75)
    T: perplexity (0.65), pdf-search (0.90)
    L: pdf-brain (0.90), docling (0.75), qmd (0.70)
  synergies:
    S×T×L: textbook-grounding × pdf-search × qmd = 0.95
    S×S×S: saq × dialectical × critique = 0.90
  execution_mode: sequential

Synergy Exploitation:

IF synergy(S×T×L) > 0.9:
    activate_parallel_search()  # pdf-brain + pdf-search + perplexity
IF synergy(S×S×S) > 0.85:
    chain_skill_stack()  # dialectical → critique → saq

Φ1: Query Decomposition

inputs:
  query: "Describe the pharmacology of propofol with textbook citations"
  context: ANZCA_primary | CICM_primary | VIVA | concept | academic

outputs:
  topic: "propofol pharmacology"
  domains: [pharmacology, anaesthetics, sedation, critical_care]
  question_verb: describe
  estimated_sources: 8-12
  complexity: standard | deep | comprehensive
  skill_stack: [textbook-grounding, dialectical, saq, critique]
  tool_stack: [pdf-search, pdf-brain, perplexity]
  cli_stack: [docling, qmd]

Complexity Routing:

IF context = VIVA OR context = comprehensive:
    complexity = deep
    search_depth = 25
    skill_chain = [dialectical, critique, constraints, saq]
ELIF context ∈ {ANZCA_primary, CICM_primary}:
    complexity = standard
    search_depth = 15
    skill_chain = [dialectical, saq]
ELIF context = academic:
    complexity = comprehensive
    search_depth = 30
    skill_chain = [dialectical, critique, deep-research]
ELSE:
    complexity = standard
    search_depth = 10
    skill_chain = [saq]

Φ2: Parallel Search (T×L Synergy)

Execute multi-query semantic search across sources:

# Primary searches (parallel via T×L synergy)
pdf-search "{topic} {key_terms}" --limit {search_depth} &
pdf-brain search "{topic}" --semantic --top-k 10 &
docling convert *.pdf --extract-sections "{topic}" &

# Secondary enrichment (sequential)
perplexity search "{topic} latest research 2024 2025"

Search Strategy Matrix:

Multi-Query Expansion:

Primary: "{topic} {domain_terms}"
Mechanism: "how {topic} works mechanism"
Clinical: "{topic} clinical application"
Comparison: "{topic} vs alternatives"
Exceptions: "{topic} exceptions limitations"

Φ3: Thesis Extraction

For each unique source, extract claims with full provenance:

thesis:
  id: T_01
  source: "Middleton B et al. Physics in Anaesthesia. 3rd ed."
  page: 115
  chapter: "Fluid Dynamics"
  claim: "Reynolds number is dimensionless"
  claim_type: definitional | mechanistic | quantitative | clinical
  confidence: 0.95
  context: "The Reynolds number is a dimensionless quantity, i.e. it has no units."
  quote: true
  extraction_method: pdf-search | manual | perplexity

classification:
  definitional:
    description: "What something IS"
    priority: HIGH
    focus: "examine consensus across sources"
  mechanistic:
    description: "How something WORKS"
    priority: HIGH
    focus: "examine completeness of explanation"
  quantitative:
    description: "Numeric values/thresholds"
    priority: CRITICAL
    focus: "examine variation, cite ranges"
  clinical:
    description: "Application/relevance"
    priority: MEDIUM
    focus: "context-dependent, may vary by source"

Φ4: Antithesis Detection

Compare all thesis pairs for tensions:

antithesis:
  id: A_01_02
  thesis_1: T_01  # "Re < 2000 = laminar"
  thesis_2: T_02  # "Re < 1000 = laminar"
  tension_type: contradiction | refinement | extension | context_dependent
  description: "Threshold for laminar flow varies: 2000 vs 1000"
  resolution_candidates:
    - "2000 is generally accepted; 1000 is conservative"
    - "Context matters: ideal vs physiological conditions"
  evidence_weight:
    T_01: 0.85  # More sources agree
    T_02: 0.70  # Single source

tension_types:
  contradiction:
    definition: "Mutually exclusive claims"
    resolution: "Authority + recency + specificity + consensus"
  refinement:
    definition: "One claim more precise than other"
    resolution: "Accept refined version with acknowledgment"
  extension:
    definition: "One claim adds to another"
    resolution: "Merge with attribution to both"
  context_dependent:
    definition: "Both true in different contexts"
    resolution: "State conditions explicitly"

Φ5: Dialectical Synthesis (S×S Synergy)

Invoke dialectical skill for structured synthesis:

dialectical_structure:
  α_AGONAL:
    purpose: "Establish consensus with paradox awareness"
    content: "Synthesized universal principles from majority sources"
    citations: [highest_authority_sources]

  β_MAIEUTIC:
    purpose: "Guide through mechanisms with Socratic clarity"
    content: "Resolved tensions with evidence-weighted decisions"
    method: "Show reasoning process, not just conclusions"

  γ_APOPHATIC:
    purpose: "Acknowledge limitations with academic humility"
    content: "Noted variations, exceptions, context dependencies"
    tone: "Scholarship, not overconfidence"

Integration with Constraints Skill:

deontic_obligations:
  O(cite): "All claims MUST have at least one citation"
  O(page): "Page numbers OBLIGATORY for all citations"
  O(synthesis): "Must produce synthesis, not mere aggregation"
  P(multi_cite): "Multiple citations PERMITTED for consensus"
  P(quote): "Direct quotes PERMITTED for key definitions"
  F(uncited): "Uncited claims are FORBIDDEN"
  F(single_source): "Single-source claims FORBIDDEN for consensus"

Φ6: Multi-Lens Critique (S Synergy)

Apply critique skill's five lenses:

lenses:
  STRUCTURAL:
    question: "Are theses logically coherent?"
    weight: 0.20
    validation: [internal_consistency, logical_flow]

  EVIDENTIAL:
    question: "What's the evidence quality?"
    weight: 0.25
    validation: [source_authority, peer_review, recency]

  SCOPE:
    question: "Do claims overgeneralize?"
    weight: 0.20
    validation: [boundary_conditions, exceptions_noted]

  ADVERSARIAL:
    question: "What would examiners challenge?"
    weight: 0.20
    validation: [anticipate_objections, prepare_defenses]

  PRAGMATIC:
    question: "Does this work clinically?"
    weight: 0.15
    validation: [clinical_utility, practical_application]

per_thesis_evaluation:
  thesis: T_01
  lens_scores:
    S: 0.90  # Clear logical structure
    E: 0.95  # Peer-reviewed source
    O: 0.75  # May not apply to all fluids
    A: 0.80  # Standard examiner expectation
    P: 0.85  # Clinically applicable
  aggregate: 0.85
  issues:
    - "Scope: Applies to Newtonian fluids; blood is non-Newtonian"

Φ7: Abductive Synthesis

Generate minimal set of universal principles:

ABDUCTION PROTOCOL
──────────────────
1. Cluster theses by claim_type
2. For each cluster:
   a. Identify consensus claims (≥80% agreement)
   b. Resolve contested claims (40-79%) via critique lens priority
   c. Flag unique claims with high individual confidence (>0.8)
3. Compose synthesis S that:
   a. Subsumes all consensus claims
   b. Includes resolved contested claims with caveats
   c. Optionally includes unique claims as extensions
4. Validate: ∀T_i. ∃s ∈ S. subsumes(s, T_i)
5. Check parsimony: |S| ≤ min(|T|/2, 10)
6. Verify confidence floor: ∀s ∈ S. confidence(s) ≥ 0.60

Synthesis Schema:

synthesis:
  universal_principles:
    - id: S_01
      claim: "Reynolds number predicts flow type (laminar vs turbulent)"
      type: universal
      supporting_theses: [T_01, T_02, T_03, T_05, T_08]
      confidence: 0.95

  resolved_tensions:
    - antithesis: A_01_02
      resolution: "Re < 2000 generally indicates laminar; stricter thresholds exist"
      resolution_type: context_dependent
      caveats: ["ideal conditions", "physiological variation"]

  acknowledged_variations:
    - topic: "Critical threshold"
      range: "1000-4000 depending on source"
      recommendation: "Use Re < 2000 = laminar, Re > 3000 = turbulent"

Φ8: Response Generation (S Synergy with SAQ)

Route to saq skill for template-based generation:

template_routing:
  IF question_verb = describe AND domain = pharmacology:
    template = saq/references/pharmacology-template.md
  ELIF question_verb = describe AND domain = physiology:
    template = saq/references/physiology-template.md
  ELIF question_verb ∈ {compare, contrast}:
    template = saq/references/comparison-template.md
  ELIF context = VIVA:
    template = viva-extended-template.md
  ELSE:
    template = saq/references/physiology-template.md

generation_constraints:
  SAQ_mode:
    word_count: 180-220
    structure: 2-3 A4 pages handwritten
    time: 8 minutes
    format: dot points, symbols, minimal prose
  VIVA_mode:
    word_count: 500-800
    structure: extended mechanistic detail
    includes: [examiner_anticipation, deep_dive, edge_cases, clinical_vignettes]
  Academic_mode:
    word_count: 1000-2000
    structure: full scholarly format
    includes: [literature_review, methodology, discussion]

Φ9: Citation Weaving

Footnote Format:

[^n]: Author(s). *Title*. Edition. Publisher, Year; p. page. "Verbatim quote."

Citation Priority Weights:

Citation Density Requirements:

SAQ: 5-10 citations (1 per major claim)
VIVA: 15-25 citations (comprehensive)
Academic: 30-50 citations (scholarly)

Φ10: Validation & QA

def validate_grounded_response(response, theses, synthesis):
    checks = {
        # Coverage checks
        "citation_coverage": all_claims_cited(response),
        "synthesis_reflected": synthesis_in_response(response, synthesis),
        "thesis_coverage": all_theses_subsumed(theses, synthesis),

        # Format checks
        "word_count": word_count_in_range(response, mode),
        "cascade_preserved": no_decomposed_cascades(response),
        "values_contextualized": all_values_have_context(response),

        # Quality checks
        "tensions_acknowledged": variations_noted(response),
        "deontic_compliance": deontic_constraints_met(response),
        "examiner_optimized": meets_examiner_expectations(response),

        # Parsimony checks
        "synthesis_minimal": len(synthesis) <= len(theses) / 2,
        "confidence_floor": all(s.confidence >= 0.60 for s in synthesis)
    }
    return ValidationResult(
        valid=all(checks.values()),
        issues=[k for k, v in checks.items() if not v],
        score=sum(checks.values()) / len(checks)
    )

Output Structures

SAQ Mode Output

---
topic: "{topic}"
type: saq-model-response
textbooks-analyzed: {n}
theses-extracted: {m}
antitheses-identified: {k}
citations: {c}
confidence: {0.85}
---

# {Topic}

> [!abstract] Definition
> {Core definition with citation}[^1]

## {Domain Heading 1}
- {Cascade with context}[^2]
- {Value with clinical relevance}[^3]

## {Domain Heading 2}
...

## Syntopical Analysis

> [!warning] Key Variation
> {Identified discrepancy with resolution}[^4][^5]

## References

[^1]: {Full citation with page}

VIVA Mode Output

Extends SAQ mode with:

• Examiner Anticipation: Likely follow-up questions with prepared responses
• Deep Dive: Extended mechanistic detail on key points
• Edge Cases: Acknowledged limitations and exceptions
• Clinical Vignettes: Application scenarios
• Recovery Strategies: If caught off-guard

Academic Mode Output

Full scholarly structure:

• Abstract: Synthesis summary
• Introduction: Context and scope
• Literature Review: Organized theses with critical analysis
• Methodology: Syntopical approach description
• Results: Synthesis with tension resolution
• Discussion: Implications and limitations
• Conclusion: Universal principles
• References: Complete bibliography

Integration Points

With /m Universal Meta-Router

tensor_activation:
  on_prompt: "Generate SAQ on propofol pharmacology with citations"

  decomposition:
    C: sc:document (0.70)
    A: researcher (0.75)
    S: textbook-grounding (0.95)
    T: pdf-search (0.90)
    L: pdf-brain (0.90)

  synergies_activated:
    S×T×L: 0.95 → parallel_search_mode
    S×S×S: 0.90 → skill_chain_mode

  execution_plan:
    mode: sequential
    steps:
      1: T×L → parallel search (pdf-brain + pdf-search + perplexity)
      2: S → textbook-grounding (thesis extraction + antithesis detection)
      3: S×S → dialectical → critique (synthesis + validation)
      4: S → saq (template + formatting)

With pdf-search / pdf-brain (Primary T×L)

# Parallel search execution
pdf-search "{query}" --limit 15 &
pdf-brain search "{query}" --semantic --top-k 10 &
wait

# Merge and deduplicate results
# Weight by source quality

With SAQ Skill (S Synergy)

handoff:
  from: textbook-grounding
  to: saq
  data:
    synthesis: universal_principles
    citations: formatted_footnotes
    constraints: word_count, symbol_lexicon

With Critique Skill (S Synergy)

invocation:
  purpose: "Multi-lens thesis evaluation"
  lenses: [STRUCTURAL, EVIDENTIAL, SCOPE, ADVERSARIAL, PRAGMATIC]
  output: per_thesis_scores, aggregate_confidence

With Dialectical Skill (S Synergy)

structure:
  α_AGONAL: consensus_with_paradox
  β_MAIEUTIC: mechanism_through_questioning
  γ_APOPHATIC: limitations_with_humility

With Constraints Skill (S Synergy)

deontic_framework:
  O: [cite, page, synthesis]
  P: [multi_cite, quote]
  F: [uncited, single_source_consensus]

With knowledge-orchestrator (Meta-S)

delegation:
  IF task.requires_multi_skill:
    delegate_to: knowledge-orchestrator
    skills: [textbook-grounding, dialectical, critique, saq]
    coordination: confidence-weighted

Extended Examples

Example 1: Reynolds Number SAQ

Input: "Describe the Reynolds number and factors affecting flow type"

Φ2 Search Results:

• Physics in Anaesthesia (Middleton) p.115
• Ganong's Review of Medical Physiology p.567
• West's Respiratory Physiology p.112
• Nunn's Applied Respiratory Physiology p.89
• Power & Kam Physiology p.203

Φ3 Theses Extracted: 25 from 12 sources

Φ4 Antitheses Identified: 5 (threshold variations, equation forms)

Φ7 Synthesis: 6 universal principles + 2 resolved tensions

Φ8 Response (198 words):

## Definition
- Dimensionless ratio of inertial/viscous forces[^1]
- Re = ρvd/μ = vd/ν (kinematic form)[^2]

## Factors
- ↑ρ (density) → ↑Re → ↑turbulence[^3]
- ↑v (velocity) → ↑Re → most significant clinically[^4]
- ↑d (diameter) → ↑Re → larger airways turbulent[^5]
- ↓μ (viscosity) → ↑Re → ↑turbulence[^6]

## Critical Values
- Re < 2000 → laminar (generally)[^7]
- 2000 < Re < 4000 → transitional[^8]
- Re > 4000 → turbulent[^9]

> [!warning] Variation
> Some sources cite Re < 1000 for laminar (conservative)[^10]

## Clinical Integration
- Heliox: ↓density → ↓Re → ↓turbulence → ↓WOB in UAO[^11]
- ETT: ↓diameter → ↓Re → more laminar despite ↑velocity[^12]
- Blood: non-Newtonian → Re applicability limited[^13]

## References
[^1]: Middleton B. *Physics in Anaesthesia*. 3e. Scion; 2021. p.115.
[^2]: Ganong WF. *Review of Medical Physiology*. 26e. McGraw-Hill; 2019. p.567.
...

Example 2: VIVA Depth Response

Input: "VIVA preparation on propofol including pharmacokinetics and clinical applications"

Execution: Full Φ0-Φ10 with VIVA mode

Output includes:

• Extended mechanistic cascades (800 words)
• Anticipated examiner questions with prepared answers
• Edge cases (propofol infusion syndrome, allergies)
• Clinical vignettes (TCI, sedation, induction)
• 25 citations with page references

Anti-Patterns

File Reference

Quality Metrics

grounding_quality:
  citation_density: citations_per_claim >= 1.0
  source_diversity: unique_sources >= 5
  synthesis_ratio: |synthesis| / |theses| <= 0.5
  confidence_floor: all_confidence >= 0.60
  tension_coverage: all_antitheses_resolved
  examiner_alignment: meets_expectations >= 0.85

Core Insight: Orthogonal tensor integration transforms textbook grounding from isolated skill to synergistic capability. Cross-dimensional activation (S×T×L) enables parallel search, skill chaining, and optimal composition. The Hegelian dialectic ensures tensions are not hidden but resolved through evidence-weighted abduction, producing responses that withstand examiner scrutiny.

Research Sources:

• Self-reflecting LLMs: A Hegelian Dialectical Approach
• Model of Dialectical Learning
• Hegel's Dialectics (Stanford Encyclopedia)