This table follows the original specification’s numbered headings, retained verbatim in ORIGINAL_SPECIFICATION.md. It is not a claim that the 87-section project is complete.
Implemented means working application code is present with relevant recorded checks; it does not mean exhaustive verification of every possible input. Partial means a useful subset exists with limits identified. Adapter only means real-engine integration code is present but was not executed in the packaging environment. Deferred / Design only means no delivered working feature. The final acceptance and final-standard rows remain not complete.
Physical-drop rendering and engine tests must be executed after installing the dependencies before those rows can be promoted. Canvas previews are not physical validation or proof of photorealism.
| Section | Original heading | Status | Delivered scope / remaining gap |
|---|---|---|---|
| 1 | Core Mathematical Experiment | Implemented | Short- and long-needle at-least-one-crossing mathematics; long-needle aggregate has an explicit 1e9 precision limit. |
| 2 | Separate Three Different Simulation Concepts | Partial | Ideal and aggregate work. Physical adapter is included but untested; Hybrid switches statistical backends, not empirical physical extrapolation. |
| 3 | Scale Presets | Implemented | Exact quantities, configurable packaging, broad presets and hypothetical all-matches scenario; supported counts stop at 1e48. |
| 4 | Real Match Geometry | Partial | Centerline mathematics and cuboid-shaft/spherical-head geometry with densities; no full menu of scanned or faceted match profiles. |
| 5 | Crossing Definition | Implemented | Centerline, physical-plane and painted-region projected crossing rules; finite-shape transforms are labeled descriptive. |
| 6 | Randomness | Partial | Versioned seeded generator and isolated display domains; one compute worker, no arbitrary multi-worker stream partitioning. |
| 7 | Correct Random Orientation | Implemented | Uniform ideal line orientations; separately tested uniform SO(3) construction for the physical adapter. |
| 8 | Correct Random Position | Implemented | Uniform center phase, nearest-line distances and verified crossing geometry. |
| 9 | Board | Partial | Paper/cardboard, wood and lab appearances; dimensions, spacing, stripe width, tilt in physics. No arbitrary line rotation or custom material importer. |
| 10 | Boundary Effects | Partial | Infinite ideal and finite policies; ideal retry supported, physical retry rejected; physical edge paths remain engine-untested. |
| 11 | Physical Throw Generator | Adapter only | Gentle, handful, scatter, pour and rain source paths; no validated throws or animated hand/container model. |
| 12 | Match-to-Match Interaction | Adapter only | Rapier interactions, independent removal, collider-start counts and approximate pile metric; no empirical contact validation. |
| 13 | Camera and Presentation | Partial | Four camera modes and tested Canvas presentation; optional PBR renderer. No validated photorealism, depth of field or motion blur. |
| 14 | Massive-Scale Rendering | Implemented | Experimental population, recorded/displayed specimens and independent aggregate illustrations are distinguished. |
| 15 | Progressive Simulation | Partial | Progressive statistics, elapsed/work time, rate and worker metadata. No fabricated CPU/GPU utilization readings. |
| 16 | Confidence Intervals | Implemented | Wilson default, numerical Clopper-Pearson to 1e6 with named fallback, optional normal intervals, error and delta-method SE. |
| 17 | Convergence Graph | Implemented | Live SVG convergence, interval shading, logarithmic axis and overlays of recent completed runs. |
| 18 | Error Scaling | Implemented | Observed error scaling, theoretical reference and repeated-study moments, histograms and interval inclusion. |
| 19 | Experiment Presets | Partial | Demonstration, box/classroom, large-scale, warehouse and hypothetical presets; not every optional named experiment. |
| 20 | Performance Architecture | Partial | Bounded scalar reference, one worker/cooperative channel, aggregate and optional physics adapter. No SIMD, GPU computation or worker pool. |
| 21 | Aggregate Statistical Backend | Implemented | Binomial order-statistic splitting and disclosed high-precision rounded-normal increments; no small-sample multiplication. |
| 22 | Chunked Monte Carlo | Implemented | Bounded batches with limited recorded specimens, histogram accumulation and decimated checkpoints. |
| 23 | Precision | Implemented | BigInt counts, 90-decimal statistical arithmetic, string exports and a hard supported limit at 1e48. |
| 24 | Reference π | Implemented | Reference probability/error is separate from the count-based estimate; aggregate circularity is explicitly disclosed. |
| 25 | Physics Calibration | Partial | Every physical constant is configurable and labeled assumed. No measured calibration system or validated material profiles. |
| 26 | Statistical Bias Analysis | Partial | Orientation/phase histograms and descriptive chi-square warnings; no calibrated sequential test or comprehensive joint clustering analysis. |
| 27 | Heatmaps | Partial | Canvas center-density and parameter-space overlays; no impact, contact-force or collision-density heatmaps. |
| 28 | Individual Match Inspection | Partial | Actual geometric inspection and physical metadata source. Force vectors and some advanced geometric fields are absent. |
| 29 | Educational Math Overlay | Partial | Mathematical explanation, equations, and live parameter-space view; no animated integration tutorial. |
| 30 | Visual Parameter-Space Mode | Implemented | Threshold region and actual recorded or explicitly illustrative theta/distance dots. |
| 31 | Multiple Experiments | Partial | Session notebook and overlaid completed runs; no multiple independent 3D boards side by side. |
| 32 | Speed Controls | Partial | Run, pause, resume, cancel, replay and physical speed controls. No fake instant-settle operation. |
| 33 | Experiment Replay | Partial | Seed/configuration re-execution and provenance; no stored frame-by-frame physical playback. |
| 34 | Export | Partial | Actual JSON, CSV, PNG, SVG and HTML reports. No Parquet or generated PDF export. |
| 35 | Research-Grade Run Manifest | Partial | Rich exportable run metadata and SHA-256; not automatic durable archival of every run, nor full hardware/GPU provenance. |
| 36 | Verification Suite | Implemented | Deterministic and statistical tests, independent checks and browser recomputation; coverage limited to recorded cases. |
| 37 | Analytical Sanity Checks | Implemented | Theoretical probabilities and manually entered 163/52 remain distinct from randomized outcomes. |
| 38 | Convergence Challenge | Implemented | Conservative anytime Hoeffding alpha-spending stopping rule; ideal explicit mode only, no lucky-point stopping. |
| 39 | Simulation Race | Deferred | No dedicated simulation race; session comparisons and repeated studies are available. |
| 40 | Historical Experiments | Deferred | No externally verified historical gallery or additional historical claims. |
| 41 | UI Layout | Implemented | Polished control/board/statistics/chart layout with real screenshots and accessibility-oriented labels. |
| 42 | Visual Quality Modes | Partial | Quality presets change preview limits or WebGL pixel/shadow quality; no cinematic optical post-processing. |
| 43 | Accessibility | Partial | Keyboard controls, focus states, readable data alternatives and Canvas cross markers; no formal accessibility certification. |
| 44 | Responsive Design | Partial | Responsive layouts and a tested 390px mobile view; no comprehensive tablet/device/browser certification. |
| 45 | Performance Benchmark | Partial | CPU benchmark adjusts the numerical auto cutoff; no measured GPU or real-physics benchmarks. |
| 46 | No Fake Scale | Implemented | No multiplied-up small realization; explicit, aggregate, approximate and illustrative representations are labeled. |
| 47 | Extreme Number Handling | Partial | Counts through 1e48 are supported and tested; larger inputs and unreliable long-needle extreme configurations are rejected. |
| 48 | Physical Reality vs Mathematical Reality | Implemented | Physical and ideal interpretations, finite geometry, selection bias and aggregate assumptions are made explicit. |
| 49 | Bias Experiment Mode | Partial | Physical parameters can define bias scenarios, but there is no dedicated validated physical causal-comparison workflow. |
| 50 | Example Head-Heavy Match Experiment | Deferred | Head density is configurable; a measured head-heavy comparison preset/study is not supplied. |
| 51 | Scientific Dashboard | Partial | Core dashboard and numerical analytics work; optional physical metrics remain unvalidated and utilization metrics are absent. |
| 52 | Event Timeline | Adapter only | Physical event timeline is recorded in source snapshots/exports; no complete live timeline UI or actual validated event traces. |
| 53 | Slow-Motion Inspection | Deferred | No selected-throw frame playback with velocity, force, friction or collision-normal vectors. |
| 54 | Units | Partial | Physics uses SI and UI lengths use millimeters. No imperial or configurable display-unit selector. |
| 55 | Precision Comparison | Partial | Reference, estimate, high-precision exports and meaningful uncertainty; no matching-prefix digit visualization. |
| 56 | Rare Lucky Runs | Implemented | Lucky or unlucky small runs are allowed naturally; observed error and uncertainty are separate. |
| 57 | Batch Study Mode | Implemented | Up to 1,000 repeated numerical runs with conditional moments, quantiles, RMSE, histograms and interval inclusion. |
| 58 | Experiment Builder | Implemented | Named local configurations, complete JSON editor, import and export. |
| 59 | URL / Shareable State | Partial | Hosted URL settings and portable config JSON; standalone shares JSON rather than a nonexistent hosted page. |
| 60 | Suggested Technical Architecture | Implemented | Separated numerical core, scheduling, physics, rendering, charts, UI, data and verification modules. |
| 61 | Physics Engine Requirement | Adapter only | Mature Rapier engine selected and isolated; dependency integration and release evaluation remain outstanding. |
| 62 | Statistical Engine Tests | Implemented | Actual 10-million-trial reference run, replicated statistical tests and justified tolerances; no forced exact random counts. |
| 63 | Property-Based Testing | Implemented | Tested scaling, visual-setting invariance, chunk/replay invariance and deterministic geometry properties. |
| 64 | Numerical Verification | Implemented | Geometric and aggregate distributions cross-checked, with independent NumPy/SciPy/mpmath verification. |
| 65 | Benchmark Against Analytic Result | Implemented | Observed/expected probabilities, error and reference comparisons in data and UI; actual verification outputs retained. |
| 66 | Reproducibility | Implemented | Seed/configuration export, hash-checked import and replay; compatibility limits documented. |
| 67 | Cinematic Intro | Deferred | No cinematic intro or scripted scale-transition animation. |
| 68 | Quantity Visualization | Implemented | Scale comparisons derive from the configurable packaging factors, not universal capacity claims. |
| 69 | "Throw Them All" Button | Partial | Prominent run control dispatches the selected actual backend; physical operation requires the unvalidated optional dependency path. |
| 70 | Absurd Scale Presets | Partial | Pocketful, boxes, pallets, fleets, warehouse and hypothetical extremes; not every humorous label from the examples. |
| 71 | Real-Time Results Overlay | Adapter only | Provisional/timeout physical result source and settled/resolved reporting; no verified live physical run yet. |
| 72 | Settling Detection | Adapter only | Continuous linear/angular quiet thresholds and reset on waking; escaped bodies are resolved, not falsely called settled. |
| 73 | Collision Scalability | Adapter only | Rapier-native collision handling and total work timing; no separately measured collision-cost benchmark. |
| 74 | Rendering Scalability | Partial | Instanced Three.js source and draw statistics; tested bounded Canvas preview. Advanced LOD and real WebGL profiling remain. |
| 75 | CPU/GPU Separation | Adapter only | Fixed-step physics separated from rendering; source design is not a substitute for a real cross-frame-rate validation. |
| 76 | Deterministic Mathematical Mode | Implemented | Count reproducibility independent of render settings and cooperative scheduling verified; universal runtime identity not promised. |
| 77 | Data Integrity | Implemented | Canonical SHA-256 manifests, native/portable hash checks and actual tamper-rejection tests. |
| 78 | Comparison Panel | Partial | Theory, simulations, session comparisons and separate manual calculator; manually entered results are not full notebook run objects. |
| 79 | Manual Experiment Calculator | Implemented | Manual calculator uses the correct count-based formula, keeps precision, and handles invalid/zero-crossing inputs. |
| 80 | Advanced Mathematical Extensions | Design only | Core boundaries allow extensions, but noodles, grids, random lengths, Bayesian models and related variants are not implemented. |
| 81 | Variance-Reduction Research Mode | Deferred | No antithetic, stratified or quasi-Monte Carlo experiment backend. Default sampling remains ordinary pseudorandom Monte Carlo. |
| 82 | Accuracy Target Projection | Implemented | Delta-method fixed-sample precision projection, explicitly a planning estimate rather than a stopping guarantee. |
| 83 | Simulation Summary | Partial | Result dashboard, notebook and exportable report; not an automatically persisted report for every session run. |
| 84 | Scientific Caveats | Implemented | Statistical, physical, small-sample, finite-edge and aggregation caveats are present in UI, exports and documentation. |
| 85 | Acceptance Criteria | Not complete | Numerical acceptance has substantial recorded evidence; real physics, production visuals and other listed requirements remain open. |
| 86 | Development Order | Partial | Core, interface, analytics and scale work is supplied; later physical realism and production release phases remain open. |
| 87 | Final Standard | Not complete | This is a functional development deliverable with an explicit scope map, not the full final standard of the supplied specification. |