GENERIC_PROCESSES_TO_UPDATE.md

Generic Processes Needing Real Content

These processes use the generic template ("This X process visualization demonstrates... The flowchart shows...") and need to be replaced. Use different approaches for different process types.

Strategy by Process Type

1. Algorithm flowcharts (like Binary Search)

Examples: Binary Search (done), Cryptographic Algorithms, Numerical Methods

Approach: Process-like flowcharts with:

• Inputs (sorted array, search key)
• Steps (initialize interval, compute middle, compare)
• Decision diamonds (interval empty? key == A[mid]? key < A[mid]?)
• Outputs (found index, not found)
• Chart title: "Algorithm Flowchart" (do not use "GLMP 6-Color Scheme" in the title)

Reference: Binary Search – O(log n) complexity

Candidates: Add specific algorithms – e.g. RSA, Newton-Raphson, Sieve of Eratosthenes, Dijkstra – each as its own process flowchart.

2. Axiom-theorem dependency graphs (like Euclid, Peano, Propositional Logic, Aristotle)

Examples: Euclid Book I (done), Peano Arithmetic (done), Propositional Logic (done), Aristotle Syllogistic (done)

Approach: Real mathematical development:

• Axioms / definitions at the base
• Theorems with explicit dependencies (arrows = "depends on")
• Split into subgraphs for clarity (like Euclid Book I's 5 views)

Reference: Euclid Book I

Candidates:

• Group Theory – done (43 nodes, 69 edges across 3 subcharts; Euclid-style layered dependencies)
• Ring Theory – ring axioms → integral domain, polynomial rings
• Field Theory – field axioms → extensions, algebraic closure
• Limit / Derivative / Integral – ε-δ, limit laws, FTC, etc.
• Modular Arithmetic – congruence, Fermat's little theorem, etc.
• Topology – open sets, continuity, compactness
• Differential Geometry – manifold, metric, curvature

3. Axiomatic combinatorics (like Euclid Book I for counting)

Example: Combinatorics (done)

Approach: Axiomatic theory of combinatorics – definitions (factorial, sum/product principles) and theorems (permutations, combinations, binomial, pigeonhole, inclusion-exclusion) with dependency graph. Can be expanded to be more comprehensive like Euclid Book I.

Reference: Combinatorics

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Updated (with real content)

• Combinatorics – Axiomatic counting theory (14 nodes, 15 edges)
• Binary Search – Algorithm flowchart (already had real content)
• Sieve of Eratosthenes – Prime Number Generation (10 nodes, 14 edges) ✓ Batch 1
• Newton-Raphson Method – Numerical Methods (9 nodes, 11 edges) ✓ Batch 1
• Bisection Method – Limit Calculation (8 nodes, 10 edges) ✓ Batch 2
• Extended Euclidean Algorithm – Modular Arithmetic (6 nodes, 6 edges) ✓ Batch 2
• Dijkstra's Algorithm – Graph Theory Algorithms (7 nodes, 8 edges) ✓ Batch 2
• RSA Algorithm – Cryptographic Algorithms (7 nodes, 7 edges) ✓ Batch 3
• Simpson's Rule – Integral Calculation (6 nodes, 5 edges) ✓ Batch 3
• Kruskal's Algorithm – new (9 nodes, 12 edges) ✓ Batch 3
• AES Algorithm – new (8 nodes, 8 edges) ✓ Batch 4
• Merge Sort – new (7 nodes, 7 edges) ✓ Batch 4
• Prim's Algorithm – new (9 nodes, 12 edges) ✓ Batch 4
• Quicksort – new (6 nodes, 6 edges) ✓ Batch 5
• Breadth-First Search – new (7 nodes, 8 edges) ✓ Batch 5
• Binary Search Tree Insert – new (8 nodes, 9 edges) ✓ Batch 5
• Group Theory – Axiom-theorem dependency graph (21 nodes, 29 edges across 3 subcharts) ✓

Need Updates (by type)

Algorithm flowcharts to create

• DFS, Heap sort, etc.
• Graph Theory Algorithms → Dijkstra, Kruskal, etc.

Axiom-theorem graphs to create (placeholders removed)

• Field Theory, Ring Theory
• Derivative, Integral, Limit Calculation
• Modular Arithmetic, Diophantine Equations
• Topology, Differential Geometry, Euclidean Geometry
• Logic & Set Theory (or point to Propositional Logic)
• Statistical Analysis (probability axioms → theorems)

Removed (generic placeholders deleted ✓)

• Field Theory, Ring Theory, Derivative Calculation, Statistical Analysis, Logic & Set Theory
• Differential Geometry, Euclidean Geometry, Topology, Diophantine Equations
• Integral Calculation, Limit Calculation, Modular Arithmetic, Cryptographic Algorithms, Graph Theory Algorithms
• Run delete-generic-charts-from-gcs.sh to remove from GCS; then upload-mathematics-database-to-gcs.sh for updated metadata

Duplicates (resolved ✓)

• statistics_probability-aristotles-syllogism → removed (canonical: discrete_mathematics-aristotle-syllogistic)
• statistics_probability-euclids-geometry → removed (canonical: geometry_topology-euclid-elements-*)