build(deps): bump actions/checkout from 4 to 6

.github/CODEOWNERS

@@ -0,0 +1,15 @@
+# Default owner for everything
+* @djdarcy
+
+# Python source
+*.py @djdarcy
+
+# Lean proofs
+proofs/ @djdarcy
+
+# Documentation
+docs/ @djdarcy
+*.md @djdarcy
+
+# GitHub configuration
+/.github/ @djdarcy

.github/FUNDING.yml

@@ -0,0 +1,15 @@
+# These are supported funding model platforms
+
+github: djdarcy # Replace with up to 4 GitHub Sponsors-enabled usernames e.g., [user1, user2]
+ko_fi: djdarcy # Replace with a single Ko-fi username
+buy_me_a_coffee: djdarcy
+#patreon: dustinjd # Replace with a single Patreon username
+
+open_collective: # Replace with a single Open Collective username
+tidelift: # Replace with a single Tidelift platform-name/package-name e.g., npm/babel
+community_bridge: # Replace with a single Community Bridge project-name e.g., cloud-foundry
+liberapay: # Replace with a single Liberapay username
+issuehunt: # Replace with a single IssueHunt username
+otechie: # Replace with a single Otechie username
+lfx_crowdfunding: # Replace with a single LFX Crowdfunding project-name e.g., cloud-foundry
+#custom: ['https://buymeacoffee.com/djdarcy'] # Replace with up to 4 custom sponsorship URLs e.g., ['link1', 'link2']

.github/ISSUE_TEMPLATE/bug-report.md

@@ -0,0 +1,30 @@
+---
+name: Bug report
+about: Create a report to help improve Prime-Square-Sum
+title: "[BUG] "
+labels: bug
+assignees: ''
+---
+
+**Describe the bug**
+A clear and concise description of what the bug is.
+
+**Command used**
+```bash
+python prime-square-sum.py --expr "..."
+```
+
+**Expected behavior**
+A clear and concise description of what you expected to happen.
+
+**Actual behavior**
+What actually happened, including any error messages.
+
+**Environment:**
+- OS: [e.g., Windows 11, Ubuntu 22.04]
+- Python version: [e.g., 3.12]
+- Prime-Square-Sum version: [e.g., 0.8.2]
+- Installation method: [conda / pip / manual]
+
+**Additional context**
+Add any other context about the problem here.

.github/ISSUE_TEMPLATE/config.yml

@@ -0,0 +1,5 @@
+blank_issues_enabled: true
+contact_links:
+  - name: Documentation
+    url: https://github.com/djdarcy/Prime-Square-Sum/tree/main/docs
+    about: Browse the expression syntax, equations, and function reference docs

.github/ISSUE_TEMPLATE/feature-request.md

@@ -0,0 +1,19 @@
+---
+name: Feature request
+about: Suggest an idea for Prime-Square-Sum
+title: ''
+labels: enhancement
+assignees: ''
+---
+
+**Is your feature request related to a problem?**
+A clear and concise description of what the problem is. E.g., "I'm frustrated when..."
+
+**Describe the solution you'd like**
+A clear and concise description of what you want to happen.
+
+**Describe alternatives you've considered**
+A clear and concise description of any alternative solutions or features you've considered.
+
+**Additional context**
+Add any other context about the feature request here.

.github/dependabot.yml

@@ -0,0 +1,21 @@
+version: 2
+updates:
+  # Python dependencies (requirements.txt)
+  - package-ecosystem: "pip"
+    directory: "/"
+    schedule:
+      interval: "weekly"
+    open-pull-requests-limit: 10
+    labels:
+      - "dependencies"
+    versioning-strategy: increase-if-necessary
+
+  # GitHub Actions
+  - package-ecosystem: "github-actions"
+    directory: "/"
+    schedule:
+      interval: "monthly"
+    open-pull-requests-limit: 5
+    labels:
+      - "dependencies"
+      - "github-actions"

.github/pull_request_template.md

@@ -0,0 +1,31 @@
+## Description
+<!-- Provide a brief summary of the changes in this PR -->
+
+## Type of change
+- [ ] Bug fix (non-breaking change which fixes an issue)
+- [ ] New feature (non-breaking change which adds functionality)
+- [ ] Breaking change (fix or feature that would cause existing functionality to not work as expected)
+- [ ] Documentation update
+- [ ] Code refactoring (no functional changes)
+- [ ] Performance improvement
+- [ ] Lean proof addition/modification
+
+## Components affected
+- [ ] CLI / Expression engine
+- [ ] Number theory utilities
+- [ ] Lean 4 proofs
+- [ ] Documentation
+- [ ] Tests
+- [ ] Infrastructure (scripts, CI, etc.)
+
+## How Has This Been Tested?
+<!-- Describe the tests you ran to verify your changes -->
+<!-- e.g., python -m pytest tests/ -v -->
+
+## Checklist:
+- [ ] My code follows the style guidelines of this project
+- [ ] I have performed a self-review of my own code
+- [ ] I have made corresponding changes to the documentation
+- [ ] My changes generate no new warnings
+- [ ] New and existing tests pass (`python -m pytest tests/ -v`)
+- [ ] I have updated the CHANGELOG (for user-facing changes)

.github/release-template.md

@@ -0,0 +1,34 @@
+# Release v$NEXT_VERSION
+
+## What's Changed
+
+### New Features
+-
+
+### Bug Fixes
+-
+
+### Lean Proofs
+-
+
+### Documentation
+-
+
+### Maintenance
+-
+
+### Breaking Changes
+-
+
+## Installation
+
+```bash
+git clone https://github.com/djdarcy/Prime-Square-Sum.git
+cd Prime-Square-Sum
+conda create -n prime-square-sum python=3.12
+conda activate prime-square-sum
+conda install -c conda-forge numpy primesieve
+```
+
+## Full Changelog
+$CHANGES

.github/stale.yml

@@ -0,0 +1,37 @@
+# Configuration for probot-stale - https://github.com/probot/stale
+
+# Number of days of inactivity before an Issue or Pull Request becomes stale
+daysUntilStale: 90
+
+# Number of days of inactivity before a stale Issue or Pull Request is closed
+daysUntilClose: 14
+
+# Issues or Pull Requests with these labels will never be considered stale
+exemptLabels:
+  - pinned
+  - security
+  - enhancement
+  - bug
+  - "in progress"
+  - "help wanted"
+  - "lean-proofs"
+
+# Label to use when marking as stale
+staleLabel: stale
+
+# Comment to post when marking as stale
+markComment: >
+  This issue/PR has been automatically marked as stale because it has not had
+  recent activity. It will be closed if no further activity occurs within 14 days.
+  Thank you for your contributions.
+
+# Comment to post when closing a stale Issue or Pull Request
+closeComment: >
+  This issue/PR has been automatically closed due to inactivity.
+  Please feel free to reopen if this is still relevant.
+
+# Limit the number of actions per hour, from 1-30. Default is 30
+limitPerRun: 30
+
+# Set to true to ignore issues with an assignee
+exemptAssignees: true

.github/workflows/ci.yml

@@ -0,0 +1,65 @@
+name: CI
+
+on:
+  push:
+    branches: [main, master]
+  pull_request:
+    branches: [main, master]
+
+jobs:
+  # Primary test: conda with primesieve (the recommended install path)
+  test-conda:
+    name: conda (Python 3.10, ${{ matrix.os }})
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        os: [ubuntu-latest, windows-latest]
+    defaults:
+      run:
+        shell: bash -el {0}
+
+    steps:
+    - uses: actions/checkout@v6
+
+    - name: Set up Miniconda
+      uses: conda-incubator/setup-miniconda@v3
+      with:
+        activate-environment: prime-square-sum
+        environment-file: environment.yml
+        auto-activate-base: false
+
+    - name: Verify primesieve available
+      run: |
+        python -c "import primesieve; print(f'primesieve {primesieve.primesieve_version()} available')"
+
+    - name: Run tests
+      run: |
+        python -m pytest tests/ -v --tb=short
+
+  # Compatibility test: pip-only, newer Python (no primesieve, tests fallback sieve)
+  test-pip:
+    name: pip (Python ${{ matrix.python-version }}, ${{ matrix.os }})
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        os: [ubuntu-latest, windows-latest]
+        python-version: ['3.12']
+
+    steps:
+    - uses: actions/checkout@v6
+
+    - name: Set up Python ${{ matrix.python-version }}
+      uses: actions/setup-python@v5
+      with:
+        python-version: ${{ matrix.python-version }}
+
+    - name: Install dependencies
+      run: |
+        python -m pip install --upgrade pip
+        pip install numpy pytest lark
+
+    - name: Run tests
+      run: |
+        python -m pytest tests/ -v --tb=short

README.md

@@ -6,7 +6,7 @@
 
 📓 **[View the Mathematica Notebook](https://github.com/djdarcy/Prime-Square-Sum/blob/main/paper%20and%20notes/2010%20-%20Recurrence%20relation%20between%20triangular%20numbers%20and%20squared%20primes%20-%20D.%20Darcy.nb)** *(Requires [Mathematica](https://www.wolfram.com/mathematica/) or [Wolfram Player](https://www.wolfram.com/player/))*
 
-The python program is a computational platform for validating mathematical relationships. It checks LHS expressions against RHS targets and stores sequences for future analysis. The main focus of `prime-square-sum` is on summing triangular row values together (where `stf()` is an acronym for sum triangular factors) to determine if:
+The python program is a computational platform for validating mathematical relationships. It checks LHS expressions against RHS targets and stores sequences for future analysis. The main focus of `prime-square-sum` is on summing triangular row values together (where `stf()` below is an acronym for "sum triangular factors") to determine if:
 
 ![stf(b) = sum_(z=1)^qg(b) tf(b,z);](<paper and notes/function-stf-defined.png> "stf defined")
 
@@ -18,7 +18,7 @@ r = qg(b) = size of the base row of the triangular number; //qg(b) = 1/2(-1+sqrt
 z = row in the triangular number;  //ex. tf(10,4)=0123; tf(10,3)=456; tf(10,2)=78, etc.)
 ```
 
-Where `tf()`, the individual triangular row factors, are defined to be:
+Where `tf()`, the individual "triangular row factors", are defined to be:
 
 ![tf(b,z) = (-2 + 2b - 2b^2 + z - bz - z^2 + bz^2 + b^z(2 + 2b^2 + z + z^2 - b(2 + z + z^2))) / (2(-1 + b)^2)](<paper and notes/function-tf-defined.png> "tf defined")
 
@@ -41,19 +41,43 @@ Due to the huge size of the 98-digits I've further adapted `prime-square-sum` to
 ## Usage
 
 ```bash
-# Find n where sum of first n squared primes equals 666
+# Find n where sum of first n squared primes equals 666 (this is the known result: stf(10))
 python prime-square-sum.py --expr "does_exist primesum(n,2) == 666"
 # Output: Found: n=7  (because 2² + 3² + 5² + 7² + 11² + 13² + 17² = 666)
 
 # Shorthand using default expression
 python prime-square-sum.py --target 666
 ```
 
+### The Open Question
+
+The core investigation: does the sum of triangular row factors as `stf(666)`, the 98-digit number, equal a sum of squared, cubed, or some p-th power primes?
+
+```bash
+# The main search — does stf(666) = primesum(n, 2) for some n?
+python prime-square-sum.py --expr "does_exist primesum(n,2) == trisum(666)" \
+    --algorithm sieve:primesieve --max n:1000000000
+
+# The pattern may continue at a higher power — search p = 3, 4, 5
+python prime-square-sum.py --expr "does_exist primesum(n,3) == trisum(666)" \
+    --algorithm sieve:primesieve --max n:50000000
+python prime-square-sum.py --expr "does_exist primesum(n,4) == trisum(666)" \
+    --algorithm sieve:primesieve --max n:10000000
+python prime-square-sum.py --expr "does_exist primesum(n,5) == trisum(666)" \
+    --algorithm sieve:primesieve --max n:5000000
+
+# Skip early values that are too small to match a 98-digit target
+python prime-square-sum.py --expr "does_exist primesum(n,p) == trisum(666)" \
+    --algorithm sieve:primesieve -min n:50000000 -max n:1000000000 --max p:5
+```
+
+This search requires billions of prime sums and benefits from `--algorithm sieve:primesieve` (C++ [primesieve](https://github.com/kimwalisch/primesieve) library via conda). See [Installation](#recommended-conda) for setup. The answer to this question would establish whether the chain `primesum(3,1) → stf(10) → primesum(7,2) → stf(666) → primesum(?,?)` continues — and whether it may continues indefinitely. The formal [proofs](proofs/README.md) provide the algebraic framework (closed-form `stf(b)`, verified in Lean 4), while the numerical search here would supply the concrete witness needed for induction.
+
 The `--target` flag searches against the **default expression** `primesum(n,2)` (sum of squared primes). This default is defined in `equations.json` and can be customized via `config.json`. See [docs/equations.md](docs/equations.md) for details.
 
 ```bash
 # Find matches between prime sums and triangular numbers
-python prime-square-sum.py --expr "for_any primesum(n,2) == tri(m)" --max-n 100 --max-m 50
+python prime-square-sum.py --expr "for_any primesum(n,2) == tri(m)" --max n:100 --max m:50
 
 # List available functions
 python prime-square-sum.py --list functions
@@ -66,7 +90,7 @@ Use standard arithmetic operators directly in expressions:
 ```bash
 # Arithmetic in expressions
 python prime-square-sum.py --expr "does_exist n**2 == 25"                     # n=5
-python prime-square-sum.py --expr "does_exist tri(n) + 1 == 11" --max-n 10    # n=4
+python prime-square-sum.py --expr "does_exist tri(n) + 1 == 11" --max n:10    # n=4
 python prime-square-sum.py --expr "verify (2 + 3) * 4 == 20"                  # true
 
 # Operators: +  -  *  /  //  %  **  ^  (unary: -x, +x)
@@ -77,14 +101,14 @@ python prime-square-sum.py --expr "verify (2 + 3) * 4 == 20"                  #
 
 ```bash
 # Boolean logic with short-circuit evaluation
-python prime-square-sum.py --expr "does_exist n > 0 and n < 10 and tri(n) == 28" --max-n 20
+python prime-square-sum.py --expr "does_exist n > 0 and n < 10 and tri(n) == 28" --max n:20
 
 # Bitwise operations via keyword operators
 python prime-square-sum.py --expr "verify 5 xor 3 == 6"
 python prime-square-sum.py --expr "verify 5 band 3 == 1"
 
 # Chained comparisons
-python prime-square-sum.py --expr "does_exist 1 < n < 10 and tri(n) == 28" --max-n 20
+python prime-square-sum.py --expr "does_exist 1 < n < 10 and tri(n) == 28" --max n:20
 
 # Context blocks for operator disambiguation
 python prime-square-sum.py --expr "verify bit[2^3] == 1"    # ^ is XOR in bit context
@@ -103,8 +127,8 @@ python prime-square-sum.py --expr "solve tri(36)"                    # 666
 python prime-square-sum.py --expr "tri(36)"                          # 666 (implicit)
 
 # Enumerate sequence values
-python prime-square-sum.py --expr "solve tri(n)" --max-n 10          # n=1: 1, n=2: 3, ...
-python prime-square-sum.py --expr "for_any primesum(n,2)" --max-n 7  # tabulate squared prime sums
+python prime-square-sum.py --expr "solve tri(n)" --max n:10          # n=1: 1, n=2: 3, ...
+python prime-square-sum.py --expr "for_any primesum(n,2)" --max n:7  # tabulate squared prime sums
 ```
 
 ### Verify Mode (v0.7.6+)

VERSION

@@ -1 +1 @@
-0.8.1
+0.8.2

docs/equations.md

@@ -152,7 +152,7 @@ Set default variable bounds in the equation:
 
 CLI flags override equation bounds:
 ```bash
-python prime-square-sum.py --equation tri-match --max-n 500
+python prime-square-sum.py --equation tri-match --max n:500
 ```
 
 ## Built-in Equations