A small, deterministic research laboratory for 90° rotations, quadrature oscillators, state persistence, and interruption/recovery experiments. Inspired by a public question from Robert Dumont (@Voltardark), J90 tests operational, mathematical claims without presupposing life, agency, or consciousness.
Status: v0.3.3 nonlinear evidence consolidation / exploratory research. License: Apache-2.0.
For the counterclockwise quarter-turn operator
[ J=\begin{bmatrix}0 & -1\1 & 0\end{bmatrix},\qquad J^2=-I,\quad J^4=I ]
the model is the familiar linear dynamical system
[ \dot{s}=(\omega J-\gamma I)s,\qquad s(t+\Delta t)=e^{-\gamma\Delta t}R(\omega\Delta t)s(t). ]
The state is a two-component real vector. In the undamped case its squared norm is conserved up to floating-point rounding. With damping, squared norm decays exponentially.
The interruption experiment saves an exact model state, advances no logical time during a simulated gap, and restores it. The same-state/no-clock reference and resumed branches match exactly because they have the same inputs. An independently advancing clock or physical system can reveal a gap. This is a test of information available to an observer, not a test of whether anything is alive.
Requires Node.js 20+ and, for cross-runtime parity, Python 3.11+ (stdlib only). There are no runtime package dependencies, dependency downloads, or hidden randomness. Tests and experiments do not require network access; GitHub Actions runs the test suite before publishing the static site.
npm test
npm run experiment
npm run experiment -- --omega 1.57 --damping 0.1 --before 1 --gap 2 --after 1
npm run controls
npm run controls -- --case phase-alias
npm run parity
npm run parity -- --atol 1e-12 --rtol 1e-12
npm run evidence
npm run evidence -- --full
npm run nonlinear
npm run stability
npm run zoom
npm run consolidate
npm run consolidate -- --out evidence-v0.3.3The experiment, controls, parity and evidence commands produce machine-readable JSON with validated inputs and interpretation limits. The original experiment emits a canonical SHA-256 checkpoint; the adversarial controls command includes registry results, analytical comparisons, and replay receipts. All times are abstract nonnegative time units; omega is radians per unit time.
Serve the repository root over HTTP (for ES modules):
python3 -m http.server 8000Then visit http://localhost:8000/. The static interactive lab needs no backend. The browser includes a seven-case adversarial challenge panel and a Mandelbrot/Julia interactive escape-time portrait, a real-axis stability plot, and a precision-aware fractal zoom explorer using the same browser-safe analytical oracle and oscillator kernel. Checkpoint hashing and structured experiment receipts remain in the Node CLI.
The repository is configured for Settings → Pages → Build and deployment → Source: GitHub Actions. The deployment workflow automatically runs on pushes to main, including merges, and also supports Actions → Deploy J90 Laboratory → Run workflow for manual publication.
The workflow uses Node.js 22 and Python 3.12 and runs npm test, the original experiment smoke test, the v0.2 controls report, and the cross-runtime parity command, and the evidence/stress command, the nonlinear comparison CLI, the stability CLI, the zoom CLI and the nonlinear consolidation CLI. Pull requests run validation without publishing. Pushes to main and manual dispatches package a minimal _site containing the static browser files, shared adversarial oracle, nonlinear map and visualizer, and attribution page, then deploy only after validation passes. The deployment job alone receives Pages write / OIDC permissions. No npm dependencies or build tool are needed. The same workflow uploads a separate temporary, checksum-verifiable v0.3.3 evidence bundle; the public Pages artifact remains strictly static browser files. The published address is https://qsolkcb.github.io/J90/.
After any merge to main, review Actions → Deploy J90 Laboratory for test and deployment results. PRs run validation but do not deploy. The v0.2.2 evidence tools remain CLI-only; the v0.3.0 nonlinear comparison runs separately from the v0.1 linear oscillator, in its own browser module.
- Deterministic closed-form linear evolution, finite-number validation, pure functions.
- Tests for quarter-turn algebra, energy, damping, checkpoint reproducibility, tampering, interruption, and negative cases.
- A seven-case falsification registry and 24-point deterministic boundary sweep; a separate scalar analytical oracle checks numerical agreement within a declared absolute/relative tolerance.
- Explicit optional observation channels (clock, sensor, recorded interruption) that never read a hidden wall clock or infer awareness from a signal.
- See Adversarial Protocol v0.2 for formulas, known confounders, and evidence limitations.
- v0.2.1: Node.js issues 40 checkpoint receipts across eight fixed scenarios; Python verifies SHA-256 over each raw payload and independently replays 32 segments. Comparison checks both resumed snapshots and Python-only trajectories against bounded numerical tolerances. See cross-runtime protocol.
- v0.2.2: explicit 35-cell synthetic observer-access matrix with source-labelled, SHA-256 hash-chained events; 450-case deterministic IEEE-754 boundary sweep; six additional Node/Python edge cases with 30 checkpoints and 84 comparisons. See observation/provenance protocol.
- v0.3.0: a separate deterministic complex quadratic map, Mandelbrot and Julia escape-time probes, a sensitivity counterexample against 90° rotation, fixed image-grid receipts, and an interactive browser portrait. See nonlinear protocol.
- v0.3.1: deterministic real-axis sweep, finite-window period candidates, tangent-vs-finite-difference comparisons, Python differential reference and versioned receipts. See stability protocol.
- v0.3.2: bounded cursor-anchored zoom/pan/reset, Float64 adjacent pixel collision checks, adaptive iteration budgets, quarter-pixel sensitivity overlay, independent Python grid verification and deterministic SHA-256 receipts. See zoom protocol.
- v0.3.3: iteration-budget convergence, matched physical samples across three zoom scales, independently checked Python pixel grids, source-hash provenance and deterministic evidence bundles. GitHub Actions offers a temporary downloadable research artifact; see evidence consolidation protocol.
- No reliance on presumed "emergence"; no claim that a geometrical rotation proves consciousness, new physics, or equivalence of unrelated mathematical transforms.
- Checkpoints are integrity receipts, not cryptographic proof of physical truth.
- See experiment protocol, attribution, invariants, and roadmap.
Project and independent implementation: QSOL-IMC (Trent Slade).
Conceptual prompt and research inspiration: Robert Dumont (@Voltardark), particularly his public comment about a 90° geometrically inverse counterpart, maintained oscillation, and a system's inability to observe an interruption without an external signal, alongside his advertised The Law of Dimensional Transposition — The 90° Joints as a Universal Operator J(θ), Version 4.0 (October 2026; described as AMENRA S-DMT / USM Collective work).
This is an independent exploration, not a reproduction, endorsement, validation, or collaboration claimed on Robert's behalf. See ATTRIBUTION.md for source/verification limitations.
Correctness outranks a compelling story. If an experiment returns an ordinary trigonometric result, we report an ordinary trigonometric result.