feat: Add Research Lab pack with paralleled math modules

Create comprehensive research-lab pack structure with mathematical
and quantum computing modules from blackroad-prism-console:

Math Modules:
- hilbert_core.py: Hilbert space symbolic reasoning
- collatz/: Distributed Collatz conjecture verification
- linmath/: Linear mathematics C library
- lucidia_math_forge/: Symbolic proof engine
- lucidia_math_lab/: Experimental mathematics

Quantum Modules:
- lucidia_quantum/: Quantum core
- quantum_engine/: Circuit simulation

Experiments:
- br_math/: Gödel gap, quantum experiments

Includes pack.yaml manifest and comprehensive README.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

packs/research-lab/pack.yaml

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+# BlackRoad OS Research Lab Pack
+# Mathematical and Quantum Research Infrastructure
+
+id: pack.research-lab
+name: "Research Lab"
+version: "1.0.0"
+description: "Mathematical research, quantum computing experiments, and computational proofs"
+owning_team: blackroad-research
+repo: blackroad-os-pack-research-lab
+status: active
+risk_level: medium
+
+# Domain areas
+domains:
+  - mathematics
+  - quantum_computing
+  - proof_systems
+  - number_theory
+  - computational_research
+
+# Associated agents
+agents:
+  - agent.lucidia.core
+  - agent.lucidia.math
+  - agent.research.assistant
+
+# Module registry
+modules:
+  # Core Mathematics
+  math:
+    - id: hilbert_core
+      name: "Hilbert Space Symbolic Reasoning"
+      path: math/hilbert_core.py
+      description: "Quantum-inspired symbolic reasoning with density matrices and truth degrees"
+      capabilities:
+        - projector_construction
+        - density_matrices
+        - truth_degree_computation
+        - luders_measurement
+        - tensor_products
+      dependencies: [numpy]
+
+    - id: collatz
+      name: "Collatz Conjecture Verification"
+      path: math/collatz/
+      description: "Distributed Collatz counterexample search with LLM-assisted verification"
+      capabilities:
+        - chunk_orchestration
+        - worker_distribution
+        - verification_pipeline
+      components:
+        - orchestrator.py
+        - worker.py
+        - verifier.py
+        - db.py
+
+    - id: linmath
+      name: "Linear Mathematics Library"
+      path: math/linmath/
+      description: "C header library for vectors, matrices, and transformations"
+      capabilities:
+        - vector_operations
+        - matrix_operations
+        - quaternions
+        - transformations
+      language: c
+
+    - id: lucidia_math_forge
+      name: "Lucidia Math Forge"
+      path: math/lucidia_math_forge/
+      description: "Symbolic proof engine with contradiction tracking"
+      capabilities:
+        - symbolic_proofs
+        - operator_definitions
+        - number_theory
+        - dimensional_analysis
+        - fractal_generation
+      components:
+        - proofs.py
+        - operators.py
+        - numbers.py
+        - dimensions.py
+        - fractals.py
+        - sinewave.py
+
+    - id: lucidia_math_lab
+      name: "Lucidia Math Lab"
+      path: math/lucidia_math_lab/
+      description: "Experimental mathematics with interactive exploration"
+      capabilities:
+        - prime_exploration
+        - trinary_logic
+        - quantum_finance
+        - recursion_experiments
+        - iterative_construction
+      components:
+        - prime_explorer.py
+        - trinary_logic.py
+        - quantum_finance.py
+        - recursion_sandbox.py
+        - iterative_math_build.py
+
+  # Quantum Computing
+  quantum:
+    - id: lucidia_quantum
+      name: "Lucidia Quantum Core"
+      path: quantum/lucidia_quantum/
+      description: "Quantum simulation and computation"
+
+    - id: quantum_engine
+      name: "Quantum Engine"
+      path: quantum/quantum_engine/
+      description: "Quantum circuit simulation and execution"
+
+  # Experiments
+  experiments:
+    - id: br_math
+      name: "BlackRoad Math Experiments"
+      path: experiments/br_math/
+      description: "Experimental mathematical concepts and gap analysis"
+      components:
+        - godel_gap.py    # Gödel incompleteness gap scoring
+        - qt3.py          # Quantum computation experiments
+        - abacus_gate.py  # Gate operations
+        - noether_care.py # Noether's theorem applications
+
+# Research Areas
+research_areas:
+  number_theory:
+    description: "Prime numbers, Collatz conjecture, Riemann hypothesis"
+    modules: [collatz, lucidia_math_lab]
+
+  proof_systems:
+    description: "Symbolic proofs, contradiction detection, formal methods"
+    modules: [lucidia_math_forge, hilbert_core]
+
+  quantum_computing:
+    description: "Quantum circuits, simulation, quantum-classical hybrid"
+    modules: [lucidia_quantum, quantum_engine]
+
+  computational_geometry:
+    description: "Linear algebra, transformations, spatial computing"
+    modules: [linmath, hilbert_core]
+
+  logic_systems:
+    description: "Trinary logic, non-classical reasoning, fuzzy logic"
+    modules: [lucidia_math_lab]
+
+# Integration points
+integrations:
+  - qlm_lab:
+      description: "Integration with Quantum Logic Math Lab in BlackRoad-Operating-System"
+      path: /qlm_lab
+      sync: bidirectional
+
+  - agents_registry:
+      description: "Agent personality integration for research assistants"
+      path: /blackroad-os-agents-work
+      sync: outbound
+
+# Scheduled tasks
+schedules:
+  daily_verification:
+    cron: "0 2 * * *"
+    task: "Run Collatz verification status check"
+    module: collatz
+
+  weekly_analysis:
+    cron: "0 3 * * 0"
+    task: "Generate research progress report"
+    module: all
+
+# Documentation
+docs:
+  - README.md
+  - RESEARCH_AREAS.md
+  - API_REFERENCE.md
+  - EXPERIMENT_LOG.md