garywelz/programming_framework

1# Generic Processes Needing Real Content2 3These 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.**4 5## Strategy by Process Type6 7### 1. Algorithm flowcharts (like Binary Search)8**Examples:** Binary Search (done), Cryptographic Algorithms, Numerical Methods9 10**Approach:** Process-like flowcharts with:11- Inputs (sorted array, search key)12- Steps (initialize interval, compute middle, compare)13- Decision diamonds (interval empty? key == A[mid]? key < A[mid]?)14- Outputs (found index, not found)15- Chart title: **"Algorithm Flowchart"** (do not use "GLMP 6-Color Scheme" in the title)16 17**Reference:** [Binary Search](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/processes/discrete_mathematics/discrete_mathematics-binary-search.html) – O(log n) complexity18 19**Candidates:** Add specific algorithms – e.g. RSA, Newton-Raphson, Sieve of Eratosthenes, Dijkstra – each as its own process flowchart.20 21### 2. Axiom-theorem dependency graphs (like Euclid, Peano, Propositional Logic, Aristotle)22**Examples:** Euclid Book I (done), Peano Arithmetic (done), Propositional Logic (done), Aristotle Syllogistic (done)23 24**Approach:** Real mathematical development:25- Axioms / definitions at the base26- Theorems with explicit dependencies (arrows = "depends on")27- Split into subgraphs for clarity (like Euclid Book I's 5 views)28 29**Reference:** [Euclid Book I](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/processes/geometry_topology/geometry_topology-euclid-elements-book-i.html)30 31**Candidates:**32- **Group Theory** – done (43 nodes, 69 edges across 3 subcharts; Euclid-style layered dependencies)33- **Ring Theory** – ring axioms → integral domain, polynomial rings34- **Field Theory** – field axioms → extensions, algebraic closure35- **Limit / Derivative / Integral** – ε-δ, limit laws, FTC, etc.36- **Modular Arithmetic** – congruence, Fermat's little theorem, etc.37- **Topology** – open sets, continuity, compactness38- **Differential Geometry** – manifold, metric, curvature39 40### 3. Axiomatic combinatorics (like Euclid Book I for counting)41**Example:** Combinatorics (done)42 43**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.44 45**Reference:** [Combinatorics](https://storage.googleapis.com/regal-scholar-453620-r7-podcast-storage/mathematics-processes-database/processes/geometry_topology/geometry_topology-combinatorics.html)46 47---48 49## Updated (with real content)50- **Combinatorics** – Axiomatic counting theory (14 nodes, 15 edges)51- **Binary Search** – Algorithm flowchart (already had real content)52- **Sieve of Eratosthenes** – Prime Number Generation (10 nodes, 14 edges) ✓ Batch 153- **Newton-Raphson Method** – Numerical Methods (9 nodes, 11 edges) ✓ Batch 154- **Bisection Method** – Limit Calculation (8 nodes, 10 edges) ✓ Batch 255- **Extended Euclidean Algorithm** – Modular Arithmetic (6 nodes, 6 edges) ✓ Batch 256- **Dijkstra's Algorithm** – Graph Theory Algorithms (7 nodes, 8 edges) ✓ Batch 257- **RSA Algorithm** – Cryptographic Algorithms (7 nodes, 7 edges) ✓ Batch 358- **Simpson's Rule** – Integral Calculation (6 nodes, 5 edges) ✓ Batch 359- **Kruskal's Algorithm** – new (9 nodes, 12 edges) ✓ Batch 360- **AES Algorithm** – new (8 nodes, 8 edges) ✓ Batch 461- **Merge Sort** – new (7 nodes, 7 edges) ✓ Batch 462- **Prim's Algorithm** – new (9 nodes, 12 edges) ✓ Batch 463- **Quicksort** – new (6 nodes, 6 edges) ✓ Batch 564- **Breadth-First Search** – new (7 nodes, 8 edges) ✓ Batch 565- **Binary Search Tree Insert** – new (8 nodes, 9 edges) ✓ Batch 566- **Group Theory** – Axiom-theorem dependency graph (21 nodes, 29 edges across 3 subcharts) ✓67 68## Need Updates (by type)69 70### Algorithm flowcharts to create71- DFS, Heap sort, etc.72- Graph Theory Algorithms → Dijkstra, Kruskal, etc.73 74### Axiom-theorem graphs to create (placeholders removed)75- Field Theory, Ring Theory76- Derivative, Integral, Limit Calculation77- Modular Arithmetic, Diophantine Equations78- Topology, Differential Geometry, Euclidean Geometry79- Logic & Set Theory (or point to Propositional Logic)80- Statistical Analysis (probability axioms → theorems)81 82### Removed (generic placeholders deleted ✓)83- Field Theory, Ring Theory, Derivative Calculation, Statistical Analysis, Logic & Set Theory84- Differential Geometry, Euclidean Geometry, Topology, Diophantine Equations85- Integral Calculation, Limit Calculation, Modular Arithmetic, Cryptographic Algorithms, Graph Theory Algorithms86- Run `delete-generic-charts-from-gcs.sh` to remove from GCS; then `upload-mathematics-database-to-gcs.sh` for updated metadata87 88### Duplicates (resolved ✓)89- statistics_probability-aristotles-syllogism → removed (canonical: discrete_mathematics-aristotle-syllogistic)90- statistics_probability-euclids-geometry → removed (canonical: geometry_topology-euclid-elements-*)91