Add detailed phase plans for foundational macrosteps

- Macrostep 00: Model contract and retained historical options.
- Macrostep 01: Project foundation and configuration, including schema, presets, CLI, and CI setup.
- Macrostep 02: Mathematical core implementation and deterministic oracles.
- Macrostep 03: CPU-based planar simulation engine, FFT backend, and headless runner.

Provides exhaustive objectives, phase breakdowns, validation policies, and deliverables for each macrostep.

plans/09_delayed_time_backend.md

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+# 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.
+- Imported DT catalogue with named presets.
+- 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.