# Macrostep 09 — Delayed-time backend

## Objective

Implement the distance-dependent delayed-time experiment as a deterministic, configurable 2-D backend with explicit history indexing, CPU oracle, accelerated GPU path, history diagnostics, and decoupled simulation/window resolution.

## Dependencies

Macrosteps 00–06 complete; follow the roadmap order after Macrostep 08.

## Phase 9.1 — Explicit history model

### Substep 9.1.1 — Storage and indexing

Represent history as `depth × height × width` with default depth 16 and a circular `head` denoting the next layer to overwrite. Define helpers:

```text
latest = wrap(head-1, depth)
sample(distance) = wrap(latest-floor(distance+0.5), depth)
```

Tests, UI, and shader must use the same integer helpers. Spatial x/y addressing is periodic. Window resize never changes simulation resolution by default.

### Substep 9.1.2 — Causal policy

Use one policy only: delay zero reads `latest`, and increasing rounded distance walks backward from it. Smooth dynamics also use `latest` as their base. The historical next-overwrite-head anomaly is discarded and is not configurable.

Use explicit integer layer selection; do not blur time through normalized 3-D texture interpolation.

## Phase 9.2 — Delayed neighborhood oracle

### Substep 9.2.1 — Stencil

Implement:

```text
ri = ra/3
inner width = outer width = 1
search radius = ceil(ra+0.5)
```

For each spatial offset, precompute:

- `(dx,dy)`;
- Euclidean distance;
- integer delay layer offset;
- disk and ring weights.

Normalize by numerically summing this exact discrete stencil, not analytic area.

### Substep 9.2.2 — CPU evaluation

For each output point, wrap x/y, choose the causal history layer, accumulate `M/N`, evaluate the shared rule, then:

```text
discrete: next = clamp(S)
smooth:   next = clamp(history[latest] + 0.1*(2S-1))
```

Commit next into `history[head]`, then advance `head`. Separate `preview()` from `commit()` so pause semantics are explicit.

### Substep 9.2.3 — Pause and reset

Pause freezes output and head. Reset initializes every layer; recompute-without-commit and stale/undefined storage are not supported.

## Phase 9.3 — Initialization and interaction

Provide deterministic modes:

- all layers zero;
- one seeded frame replicated to all layers;
- independently seeded layers;
- populate one layer as an explicit analysis operation;
- source-inspired seeded boxes applied through a documented all-layer policy;
- import a restart state under an explicit layer-fill policy;
- import/export an exact checkpoint containing all history layers, `head`, generation, run descriptor, and RNG state.

The seeded box initializer uses width/height in `10..19` and one documented boundary policy, then initializes all layers explicitly. Keep reset and later overlay actions distinct; do not retain gradual history filling.

## Phase 9.4 — GPU history representation

### Substep 9.4.1 — Choose after capability spike

Preferred portable path is a tiled 2-D history atlas (default `4×4`) plus separate output/current targets. A texture array is an optional optimized path behind the same tested index abstraction.

Atlas requirements:

- integer tile/texel fetch;
- no interpolation bleed;
- dimensions preflighted against maximum texture size;
- clear ownership of padding;
- distinct read and write targets.

### Substep 9.4.2 — Rule pass and commit

Run the direct stencil pass using precomputed offsets/weights/delays (uniform buffer, lookup texture, or generated shader according to measured limits). Copy/blit output into the `head` tile only after all reads complete, then rotate the logical head. Never sample the atlas tile while writing it.

### Substep 9.4.3 — CPU/GPU parity

Read back `M`, `N`, output, and selected history tiles for small tests. Initial one-step max-error target: `≤1e-3`.

## Phase 9.5 — Workbench integration

Add:

- current committed state and computed preview;
- history timeline with selectable layer, age, and physical tile;
- radial delay map showing which distance uses which age;
- `M/N/S/increment` inspection;
- head/latest indicators;
- history initialization controls;
- direct/smooth mode selector;
- DT preset browser and model-resolution controls independent of window size.

Parameter edits state whether they preserve or reinitialize history. Rule-only edits may preserve state but must produce a reproducible run descriptor; radius or depth changes are cold rebuilds.

## Phase 9.6 — Verification

### History tests

1. Fill each layer with its index and verify every radial delay.
2. Test boundaries around `distance=n±0.5`.
3. Test head wrap `15→0`.
4. Verify smooth base is `head-1`.
5. Place one layer impulse and observe only the expected radial shell.
6. Verify x/y wrapping at all edges/corners.
7. Verify pause leaves head/state unchanged.
8. Verify every reset initializes all layers.
9. Verify atlas and CPU layouts select identical values.

### Performance target

At 512² and `ra≈12`, target p95 GPU step below 33 ms on the designated machine after offset/weight/delay precomputation. Keep CPU for correctness and reduced-resolution fallback. High-resolution cost limits must be visible before allocation.

## Deliverables

- CPU delayed-history oracle and GPU backend.
- One explicit causal indexing policy.
- Newly authored deterministic DT presets with stable names and identities.
- History/radial-delay workbench views, restart-state export, and exact continuation checkpoints.

## Exit gate

- All layer, radial shell, wrap, pause, and reset tests pass.
- CPU/GPU one-step tolerance passes.
- Window resize does not reset history.
- No atlas bleed, uninitialized layer, or read/write alias exists.
- Every DT preset uses the causal latest-relative delay policy and is reproducible.