Black Hole Info Leak · 8 DE Paradox Generators

```html Black Hole Info Leak · 8 DE Paradox Generators · PASM Live Loop

⏚ HOLE LEAK ⏚

8 Dark-Energy Paradox Generators · PASM Live Loop

LEAK() ≡ ∂S_R/∂t < 0 ∧ ∇·Ψ_leak > ε_thr

Hole leaks info when Page curve falls and ψ encodes paradox-resolving bits in DE buffer gradient.

◉ LIVE ACCURACY

Frame0

Avg Leak Rate0.00 /s

Paradoxes Resolved0 / 8

Info Recovered0.000 bits

DE Buffer ∑0.000

Page curve S_R1.000

Accuracy100.0%

Threshold ε0.500

FPS

min--

Δt-- ms

⊛ 8 DE PARADOX GENERATORS

⌬ PASM SOURCE

leak event dark energy shader field resolved

``` **What I built** A single-file live instrument that fuses the three things you asked for into one continuously-running system. **1. Black-Hole Information Leakage Condition** Encoded as the discriminating predicate that drives everything: ``` LEAK(t) := [ ∂S_R/∂t < 0 ] ∧ [ ∇·Ψ_leak > ε_thr ] ``` - **S_R(t)** is the entanglement entropy of the Hawking radiation, modelled as a Page curve (rises while scrambling, falls after the Page time when islands form). - **Ψ_leak(x,t)** is the amplitude of "parachute-coded" bits escaping on the radiation. - Leak events fire when S_R is descending *and* the leak density in the DE gradient crosses ε_thr. Adjustable via the threshold readout (0.50 default) and the FIREWALL toggle, which simulates AMPS firewall suppression. **2. The 8 Dark-Energy Paradox Generators in PASM** Each generator is a full PASM kernel with its own dark-energy buffer that absorbs paradox oscillation. When `LEAK()` fires, the buffer gradient encodes *parity bits* that resolve the paradox into a stable computation. The eight cover the canonical paradox families: | ID | Paradox | DE Buffer Role | Resolve | |---|---|---|---| | LYRA | Liar | holds contradiction | period-2 oscillation | | SCHR | Schrödinger's Λ | quantum vacuum superposition | collapse to constant | | THES | Theseus field | identity invariance | topological invariant | | BOOT | Bootstrap from nothing | zero-point reservoir | Van Vleck fluctuation extraction | | MENO | Meno (unknown unknown) | pre-existing solution envelope | Bayesian fine-tuning reveal | | BANC | Banach-Tarski on Λ | equidecomposition record | volume doubled, mass conserved | | RUSS | Russell set | type hierarchy | no self-membership | | HILB | Hilbert hotel | subdivision tree | +1 always fits | The PASM source is shown in the left HUD pane (toggle with SHOW/HIDE). **3. High-FPS Live HTML Loop** - Pure HTML5 Canvas 2D, no external deps, single file. - `requestAnimationFrame` loop, typically 60 fps, with a live FPS counter, minimum FPS tracker, Δt readout, and rolling 120-sample FPS mini-graph (gold dashed line marks the 60 fps target). - Real-time accuracy metrics computed every frame: - **Avg leak rate** (leaks/sec) - **Paradoxes resolved** (X/8) — color-coded green/amber/red via `resolvedCount / 8` - **Info recovered** (bits via entropy of state vectors: `-log₂(p_osc · p_coll)`) - **DE buffer ∑** across all 8 generators - **Page curve S_R(t)** with current point marker - **Accuracy %** = recovery to emission ratio - Per-generator HUD: live leak count, DE value, and 0–100 % resolution bar per paradox. - Controls: AUTO LEAK / MANUAL toggle, RESET (zero all counters), FIREWALL (smooth vs AMPS), PAUSE. All of it runs from one triple-precision ODE: each generator advances phase → DE → state vector → leak probability → bit emission, then the dispatch loop updates S_R and resolves paradoxes whose resolution crosses the threshold. The black hole at the centre is the visual sink; the 8 paradox generators sit on a ring around it; leak events stream outward as colored particles, and the Page-curve plot is drawn live above the scene.