# Choose the Next Pop An interactive companion to *An Introduction to SpherePOP: Nested Circles, Typed Operators, and Reduction*, chapters 1–7. Open [`index.html`](index.html) through a static HTTP server. No package install, external assets, build step, or service is needed. From the repository root: ```sh python3 -m http.server 8000 ``` Visit . Select an eligible circle and pop it, reduce a simultaneous frontier, undo an action, substitute an integer for a free symbol, or compare leftmost, rightmost and parallel strategies. The JSON editor accepts typed terms, never executable Python or JavaScript. Export preserves exact input and output terms for every action. The presets cover explicit grouping, disjoint redexes, balanced parallel reduction, partial evaluation, inert terms, power towers, immutable images, recolouring, clockwise rotation, composition and domain restrictions. J/K selects ready circles, Enter pops, P performs one simultaneous round, U undoes, and R resets. Buttons and circle selection also support keyboard focus. Editing fields do not trigger these shortcuts. The layout supports small screens and uses no animation or audio. ## What the experiment establishes `engine.mjs` implements pure value-returning operators using exact BigInt arithmetic. A normal form may still be an inert circle: unknown operators, wrong arities, unsupplied symbols, sort mismatches and inadmissible operand tuples do not become successful values. The resource budget is reported separately; an admissible operation can exceed browser limits. Each ordinary pop removes exactly one circle. The simultaneous operation captures all ready positions before modifying the term, so newly enabled parents wait until the next round. Left/right/parallel comparisons start from the current expression. Bounded exploration deduplicates identical terms, counts distinct states and transitions, and explicitly reports when its state budget prevents exhaustive exploration. It does not count all paths and is not a proof of general confluence. Parallel rounds measure logical dependency depth, not actual parallel execution or wall-clock time. Input is limited to 255 terms, depth 24, 100 KB of JSON, and rectangular images up to 16 × 16. Arithmetic has a 20,000-decimal-digit result limit and a conservative exponent budget. The book's five-two tower, 2**65536, fits. Display abbreviates large numbers while exported traces retain them. The total-pops metric includes every recorded pop, including ones taken before a substitution. The parallel-rounds metric counts only explicitly requested simultaneous rounds, not mixed sequential actions. This core experiment does not implement the symbolic rewriting extension of chapter 8, lambda binding, mutable instruction bubbles, or the canonical event-history kernel in `experiments/flat`. In particular, an inert circle is not a REFUSE event and a pop here is not a historical commitment event. The existing `reduction-engine/` remains a separate teaching model. ## Verification With Node.js 20+ and Python 3.10+ available, run from the repository root: ```sh node experiments/circles/test.mjs ``` The runner uses `python3` by default. Set `PYTHON` to another executable name or path when needed, for example `PYTHON=python node experiments/circles/test.mjs` on a POSIX shell, or `$env:PYTHON = "python"` before running the command in PowerShell. `PYTHON=py` also works with the Windows Python launcher; the setting names one executable, not a shell command. Optional browser regressions use Playwright and Chromium. After installing those development tools, run `node experiments/circles/test-browser.mjs`. The script starts its own temporary local server and checks letter shortcuts with button focus, native Enter activation, substitution draft preservation, editing, images, export and mobile containment. `PLAYWRIGHT_MODULE` can name an alternate module location, and `CHROMIUM_PATH` an existing browser binary. These browser checks are separate from the dependency-free reference CI job. `oracle.py` explicitly loads `spherepop-book-source/spherepop.py` by path, avoiding collisions with older packages named `spherepop`. Presets, deterministically generated arithmetic and symbolic terms, substitutions, invalid operator applications, images and a large integer are compared against the book for their first reduction, normal form, size and pop count. Independent checks exercise disjoint-pop diamonds, size decrease, strategy agreement, parallel-frontier timing, image orientation and persistence, exploration cutoffs and resource/input limits. The dedicated `circle-laboratory.yml` workflow checks changes to this experiment, the book interpreter, or its own definition. It uses sparse checkout and read-only permissions. The existing C/cross-language workflow and its conformance report are unaffected.