Planck Aperture

1. Short Summary

Planck Aperture is a Rust/WASM particle workbench built to test whether a simple boundary rule can produce persistent caustic structure without manually drawing that structure. The simulation uses many particles, a central attraction term, a spin torque term, a boundary parameter called A_ab, and a 3D view that projects the particle sheet into a visible fold surface.

The hypothesis says that a boundary can be more than a passive edge. It can be an active aperture: a rule that both identifies a state and performs work on the state. In this project, the special identity being tested is the 1/2 spinor boundary. The practical marker for that test is A_ab = 0.50.

2. The Hypothesis

The Planck Aperture hypothesis starts from one idea: when a boundary has a spinor character, crossing or coupling to that boundary may not behave like ordinary scalar interpolation. A scalar boundary can often be moved from 0 to 1 and treated as a simple strength control. A spinor boundary is different. It can require a half-turn before the state has completed one identity cycle.

In plain language: the boundary is not only a wall. It is a rule. If the rule has half-spin behavior, the halfway condition is not just "half as much." It can be the point where orientation, handedness, and return-path identity matter.

The working statement is:

Planck Aperture = an active boundary operator whose half-state behaves like a 1/2 spinor aperture.

The simulation names this boundary control A_ab. The project treats A_ab = 0.50 as the half-boundary marker. The visual question is whether this marker produces repeatable geometry that is not simply painted into the renderer.

Identity and Function

The phrase "identity and function in one" means that the aperture does two jobs at once:

• It identifies the type of boundary being tested: half-spinor, full aperture, or overdriven aperture.
• It changes the update rule: attraction strength and spin torque are both tied to the same control.

This is important because a boundary that only labels a state cannot generate dynamics. A boundary that only changes dynamics has no identity. The hypothesis requires both. The name Planck Aperture is therefore used as the canonical project name because the object of study is an aperture-scale rule, not just a particle cloud.

3. Current Model

The simulator is intentionally small. That is a strength. If structure appears from a small rule set, it is easier to audit than a large model with many hidden knobs. The present physics update is a 2D particle state with velocity, central attraction, spin torque, and drag. The 3D view is a separate projection used to inspect the field shape.

State Variables

Update Rule

The core update can be summarized as:

dx = -x
dy = -y
r2 = x*x + y*y + softening
force_base = 0.0001 * A_ab
torque_amplitude = (1.0 - A_ab) * 0.08

ax = dx * (force_base / r2) - y * torque_amplitude
ay = dy * (force_base / r2) + x * torque_amplitude

vx = (vx + ax) * drag
vy = (vy + ay) * drag
x = x + vx * dt
y = y + vy * dt

Driver buttons modify this rule. B.H. Catalyst strengthens attraction. Hyperdrive changes drag into drive. Cosmic Rip amplifies torque. Detonation applies a burst impulse outward.

Render-Space Sheet

The 3D view currently uses a render-space height:

z_view = sin((x + y) * 8 + phase * 0.025) * 0.16 + (x*x - y*y) * 0.22

This is not claimed to be a full physical third dimension. It is a viewing surface that lets the particle sheet reveal folds, lobes, caustics, and collapse paths. The important audit point is that the old direct A_ab = 0.50 visual lock was removed. The current sheet no longer says "if half, flatten."

4. Why 1/2 Matters

A half-spinor is not special because the number 0.5 is pretty. It is special because half-turn identity is different from scalar halfway. In spinor language, a state can require a larger return path before it is equivalent to itself. In the workbench, the half marker is used as a practical way to ask:

The formula shown in the simulator is a ledger for the same idea:

eta_B = ln(2) / (N_Sigma * m * G * 4*pi)

This should be read as a hypothesis ledger, not as a completed derivation from accepted particle physics. The terms have local meaning:

The defense of this formula is structural. It compresses a boundary-choice idea into a normalized aperture ledger. It is not yet a final physical derivation. That is acceptable at this stage because the project is still testing whether the geometry is even worth formalizing.

5. Observed Behavior

The strongest visual observation so far is that after reset, around the half-boundary setting, the particle field can pass through a narrow hourglass or line-like caustic before settling. The user-visible behavior is not merely random scatter. It has repeatable organization: folded sheets, concentrated paths, driver-sensitive curvature, and a center that can act like an attractor when the catalyst is held.

The black-hole catalyst is particularly useful because it tests whether the structure responds to the same curvature rule or merely sits on the screen. The observed "B.H. follows curvature" behavior supports the idea that the visible path is coupled to the update rule, not just a static drawing.

The Hard Result From Sweeps

A blind parameter sweep was run after removing the direct half-lock from the renderer. That sweep did not say that A_ab = 0.50 is the strongest global anomaly. It found stronger broad scalar anomalies near A_ab = 1.00, which makes sense because the torque term changes sign around 1.00.

That distinction matters. A boundary event can be short-lived and still meaningful. If a system passes through a narrow constraint window and then relaxes, endpoint metrics can miss it. The next tests therefore need to measure the first few seconds after reset, frame by frame.

6. Defense of the Hypothesis

Defense 1: The rule is compact

A weak hypothesis needs many knobs. The Planck Aperture workbench has few knobs. Attraction, torque, drag, and a boundary value are enough to create folded geometry. This does not prove the model is real physics, but it does make the visual behavior harder to dismiss as decoration. When simple rules generate organized paths, the correct response is to measure those paths, not ignore them.

Defense 2: The half marker has a reason

The half marker is not arbitrary in the story being tested. It is tied to a half-spinor boundary idea. The number 0.50 represents a half condition, and the hypothesis specifically expects half-boundary behavior to differ from ordinary scalar interpolation. This gives the test a target before looking at the output.

Defense 3: The old hardcoded half-lock was removed

Earlier versions visually favored 0.50. That was not acceptable evidence. The project corrected it by removing the direct half-lock. This matters because the current defense is not allowed to depend on a renderer branch that says half equals flat. The remaining observations must come from the state update, the sheet projection, and the viewing controls.

Defense 4: A negative sweep result sharpens the claim

The sweep result near 1.00 is not embarrassing. It is useful. It says the simulator is sensitive to the obvious torque sign change. That confirms the metrics can detect some real rule changes. It also says the half claim cannot be defended by pretending every metric points at half. The better claim is more precise: half may be a transient caustic condition, not the largest endpoint anomaly.

Defense 5: The hypothesis is falsifiable

A strong hypothesis can lose. Planck Aperture can lose if blind tests show that half-boundary caustics are no more stable, no more repeatable, and no more structurally constrained than neighboring values. It can lose if the effect disappears under small initial-condition changes. It can lose if the same hourglass appears equally everywhere once camera and color biases are removed.

That is good. A claim that cannot lose is not a research program. This one can lose, which means it can also earn confidence if it survives.

7. Objections

Objection: The simulation is not physics

Correct. The current workbench is not a finished physical theory. It is a model-building instrument. Its job is to expose whether a boundary rule can generate the kind of geometry the hypothesis expects. A simulator does not become cosmology just because it looks cosmic.

Answer

Many serious physical ideas start as toy models. The standard is not whether the first simulator contains everything. The standard is whether it isolates a rule, produces measurable behavior, and suggests stricter tests. Planck Aperture meets that lower but meaningful standard.

Objection: The visuals could be camera or color artifacts

Yes. That is why the project now separates camera behavior, makes the space tether optional, preserves a hideable UI, and keeps a written audit trail. Color and view can help a human see structure, but they cannot be the proof. The next tests must save numeric state and score geometry directly.

Objection: The strongest sweep feature is near 1.00, not 0.50

Correct. The current global metrics favor 1.00 because the torque term changes sign there. The half hypothesis must therefore predict a different kind of signature: a short-time collapse path, a caustic angle, or a topology change that endpoint metrics miss.

8. Tests That Would Increase Confidence

1. Frame-by-frame half-window test. Reset the wave state at A_ab values from 0.40 to 0.60 in small steps. Score the first five seconds for line collapse, hourglass angle, peak density, and time-to-settle.
2. Blind neighboring-value comparison. Hide the parameter labels and ask whether a script can identify 0.50 from geometry alone better than chance.
3. Renderer removal test. Measure the raw 2D state without the 3D sheet projection. If the caustic only exists in the renderer, it is not enough.
4. Initial-condition perturbation test. Add small random offsets to starting positions. A real boundary signature should weaken gracefully, not vanish instantly.
5. Null torque test. Replace the torque law with a shuffled or constant law. The half signature should degrade if the spin rule matters.
6. Jacobian or local-flow test. Estimate local contraction and shear near the observed caustic. A true aperture constraint should show a measurable compression direction.

These tests are the path from "this looks meaningful" to "this has earned confidence." They also protect the project from wishful thinking. If the half marker is real in the model, it should survive hostile tests.

9. Conclusion

The Planck Aperture hypothesis is worth defending because it is specific, visual, mathematical enough to test, and vulnerable to being wrong. It says a half-boundary spinor condition can act as an active aperture: identity and function together. The current simulator gives that idea a concrete workbench.

The honest status is this: the project has not proven the universe. It has produced a small rule system where boundary value, torque, attraction, and projection can form surprisingly organized structures. The half-spinor claim remains alive if it can be shown to produce repeatable transient caustics after the old visual bias has been removed.