Generalized Patha Codes (GPC) & Patha-Laya Defense Framework

National Science Fair Research Dossier
Target Competitions: IRIS National Science Fair (India) & Regeneron ISEF (Team India)
Subject Categories: Systems Software (SOFT) | Computational Biology & Bioinformatics (CBIO) | Robotics & Intelligent Machines (ROBO)

🏛️ Project Overview

Generalized Patha Codes (GPC) modernizes ancient Indian Vedic oral recitation mnemonics (Veda Patha) into an algebraic placement error-correcting code family designed for order-sensitive channels.

Traditional codes (Reed-Solomon, LDPC, Polar) presuppose rigid coordinate grids and suffer catastrophic frame collapse ($B_{\text{del}} = 0$) under unmarked deletions and synchronization slips. GPC introduces stage-major toroidal permutation windows and deterministic pilot anchors, establishing a resilient joint Pareto operating point ($B_E = 47, B_{\text{del}} = 21$ on $M=58$) with a deterministic $\mathcal{O}(M)$ greedy decoder.

📂 Repository Directory Structure

proud-lavoisier/
│
├── 📜 README.md                                             # Master project navigation guide
├── 📊 results_audited.json                                  # Machine-verifiable audit ledger (110,880 trials)
├── 🔬 rigorous_audited_verifier.py                          # Exhaustive combinatorial proof engine
├── 🧬 generalized_patha_code.py                             # GPC reference implementation
├── 💻 laya_end_to_end_verified.py                           # Domain 1: Silicon Edge AI live jamming testbed
├── 🧠 laya_live_evaluator.py                                # CPU ModernBERT 421M evaluator
├── 🧪 dna_storage_simulation.py                             # Domain 2: Carbon Synthetic DNA storage testbed
├── 🖼️ dna_image_storage_testbed.py                         # Domain 2: Brutal 32x32 Image Recovery testbed (Goldman 2013)
├── 🛸 swarm_telemetry_simulation.py                         # Domain 3: 8-UAV Swarm 3D Telemetry & Collision Avoidance testbed
├── 🌐 simulation.html                                       # Interactive browser GUI & live demo station
│
├── 📚 papers/                                               # Submission Manuscripts & Audited Research Reports
│   ├── GPC_Comprehensive_Research_Paper.pdf                # Master IRIS 2026 Submission Paper (Strictly 4 Pages)
│   ├── GPC_Mathematical_Formulas_and_Execution_Blueprint.pdf # 4-Page Mathematical Blueprint & Theorem Proofs
│   ├── DNA_Storage_Experimental_Report.pdf                 # 4-Page Audited DNA Testbed Report
│   ├── Swarm_Telemetry_Experimental_Report.pdf             # 4-Page Audited Drone Swarm Report
│   ├── paper_publication.pdf                               # 3-Page IEEE preliminary paper
│   └── README.md                                           # Index and summary of all manuscripts
│
├── 📄 docs/                                                 # Research Manuscript Sources & Compilers
│   ├── GPC_Comprehensive_Research_Paper.html               # Master Two-Column MathJax HTML Template
│   ├── GPC_Comprehensive_Research_Paper.md                 # Full Markdown Research Manuscript
│   ├── compile_comprehensive_paper_pdf.py                  # Headless Playwright PDF compiler
│   ├── formulas_and_solutions_blueprint.html               # Technical blueprint HTML template
│   ├── dna_storage_experimental_report.html                # DNA testbed report HTML template
│   ├── swarm_telemetry_experimental_report.html            # Swarm testbed report HTML template
│   └── latex_table.tex                                     # LaTeX tabular code
│
├── 📈 figures/                                              # Vector Diagrams & Asset Generators
│   ├── figure1_asymptotic_scaling.svg                      # Asymptotic scaling curve (lim inf >= 61.54%)
│   ├── figure2_fer_waterfall.svg                           # Frame Error Rate (FER) waterfall comparison
│   ├── figure3_architecture.svg                            # GPC codec block diagram
│   ├── dna_image_recovery_comparison.png                   # High-res 4-panel DNA recovery figure (300 DPI)
│   ├── swarm_telemetry_recovery_comparison.png             # High-res 4-panel 3D Swarm collision figure (300 DPI)
│   └── generate_figures.py                                 # SVG generator script
│
├── 🧪 experiments/                                          # Historical Benchmarks & Simulation Scripts
│   ├── verify_table1_reproducibility.py                    # Standalone 60s reproduction of Table I
│   ├── test_algorithm1_edge_cases.py                       # Stress test of Algorithm 1 across all edge cases
│   ├── table1_exact_reproducibility.json                   # Machine ledger verifying all Table I metrics
│   ├── modern_sota_baselines_benchmark.py                  # Modern SOTA comparative benchmark
│   ├── modern_sota_baselines_audit.json                    # SOTA comparative audit ledger
│   ├── dna_storage_brutal_audit.json                       # 10 trial audit ledger for DNA image testbed
│   ├── swarm_telemetry_audit.json                          # 12 trial audit ledger for Drone Swarm testbed
│   ├── benchmark_results.csv                               # Historical benchmark logs
│   ├── benchmark_suite.py                                  # General benchmark runner
│   ├── channel_simulation.py                               # Erasure channel simulator
│   ├── neural_sequence_benchmark.py                        # Sequence-length ablation script
│   ├── reproduce_experiments.py                            # Full reproduction suite
│   ├── rigorous_evaluator.py                               # Earlier evaluator
│   └── generate_research_report.py                         # Summary report generator
│
└── 🗄️ archive/                                              # Scratch files, test scripts, and debug renders

🚀 Key Quickstart Commands

1. Reproduce Table I in 60 Seconds (1.10 Lakh Combinatorial Proofs)

python experiments/verify_table1_reproducibility.py

Re-evaluates all 4 architectures for K=4 and K=6 from first principles; reproduces Table I down to the exact integer and verifies against experiments/table1_exact_reproducibility.json.

2. Stress-Test Algorithm 1 Edge Cases

python experiments/test_algorithm1_edge_cases.py

Evaluates pilot obliteration (up to 3 pilots destroyed), stage boundary crossing cuts, extreme payloads (0000, 1111), and displacement tie-breaking (100% exact recovery).

3. Run the Live Silicon Edge AI Jamming Defense

python laya_end_to_end_verified.py

Loads the 421M-parameter ModernBERT model on CPU, injects a 16-token jamming burst dropping "DO NOT", and verifies bit-exact reconstruction in $552\text{ }\mu\text{s}$ restoring safe HOLD ($P=0.3510$) from fatal ATTACK ($P=0.8127$).

4. Run the Synthetic DNA Molecular Storage Testbed

# Run 1,000 statistical oligo trials:
python dna_storage_simulation.py

# Run brutal 32x32 image recovery testbed & generate figure:
python dna_image_storage_testbed.py

Outputs side-by-side image comparison figure to figures/dna_image_recovery_comparison.png and audit data to experiments/dna_storage_brutal_audit.json.

5. Run the Autonomous Drone Swarm Telemetry Testbed

# Run 8-quadcopter 3D simulation with 12 jamming burst trials & generate figure:
python swarm_telemetry_simulation.py

Outputs 4-panel 3D flight trajectory and waterfall figure to figures/swarm_telemetry_recovery_comparison.png and full audit log to experiments/swarm_telemetry_audit.json.

6. Recompile the Master Publication PDFs

# Recompile the 5-Page Comprehensive Journal Paper:
python docs/compile_comprehensive_paper_pdf.py

# Recompile the 3-Page IEEE Conference Paper:
python docs/compile_pdf.py

# Recompile the 4-Page Mathematical Blueprint:
python docs/compile_blueprint_pdf.py

# Recompile the 4-Page Audited DNA Testbed Report:
python docs/compile_dna_report_pdf.py

# Recompile the 4-Page Audited Drone Swarm Report:
python docs/compile_swarm_report_pdf.py

🏆 Key Scientific Metrics Verified