# LFR Trace Field Process Receipt v0.1

## Purpose

Expose the frozen canonical generative state as a replayable, deterministic process record. The receipt lets an observer see the shared field recur while the cumulative relation ledgers do not reset.

It is not a marketing animation, an empirical trace, an application Logo, or a new generative kernel.

## Contract

- **Identity:** the frozen canonical three-response state for `LFR TRACE FIELD|CANONICAL|V0.1`.
- **Time spine:** the native 1080-interval-per-period theta grid from `0` through `2.50*pi`, inclusive.
- **Sign convention:** theta advances counter-clockwise in mathematical coordinates; the recorder inverts canvas y.
- **Channels:** `u`, `m_i`, `d_i`, `H_i`, model radius `r_i`, and recorded position `p_i` for three histories.
- **Normalisation:** no per-channel, per-trace, per-period, or viewport-dependent data normalisation. Plot panels may use declared local display ranges only.
- **Missingness:** none; the deterministic native grid contains 1351 complete rows.
- **Claim boundary:** this is a declared mathematical process and its recording. It is not measured physical history, evidence of natural memory, or application fitness.

## Formula disclosure

The live instrument shows the smallest formula chain needed to read the panels:

```text
u(theta) = sum_k A_k cos(k theta + phi_k)
dm_i/dtheta = lambda_i (u - m_i)
e_i = u - m_i
d_i = abs(e_i - mean_j(e_j))
H_i(theta) = integral_0^theta d_i(s) ds
r_i = R_i + alpha_i m_i + beta H_i
p_i = c_i + r_i [cos(theta + delta_i), sin(theta + delta_i)]
```

The expandable Method and lineage section must keep three things separate:

1. the mathematical definitions above;
2. the interpretation used by this project: shared field, unequal response histories, accumulated non-return;
3. the evidence boundary: a modeled construct, not telemetry or a fitted natural law.

## Observation commitment

All histories share one end coordinate, `2.50*pi`. This records one complete field recurrence and one quarter of the next. It does not claim that the modeled process stops there.

> Common horizon, unequal histories.

The receipt must show a same-phase comparison after `2*pi`, using `theta - 2*pi`. Markers and comparison connectors are observation overlays and are not part of canonical mark geometry.

## Recorder

- source canvas: 512 by 512;
- visible body: 4.2 source pixels;
- endpoint taper: 28 degrees, smoothstep profile;
- receipt ink: `#66BC92`;
- no gradient, glow, blur, filter, opacity encoding, or responsive repair;
- stable trace identity: T1 circle/solid, T2 square/dashed, T3 diamond/dotted in analytical panels.

At the terminal frame, the filled recorder paths must equal the three path-data strings in `canonical_generative_state_v0.1.svg` byte for byte. Colour is a downstream receipt projection; geometry is unchanged.

## Interaction and accessibility

- playback starts only after a user action and does not loop;
- the range control exposes every native grid row;
- reduced-motion preference is respected;
- the final state remains available without JavaScript through the canonical green SVG fallback;
- desktop and narrow layouts may rearrange panels but may not change data or geometry.

## Verification gates

- all declared source hashes match;
- 1351 complete native-grid rows are emitted;
- all three histories share end interval 1350;
- terminal generated outlines equal canonical SVG paths byte for byte;
- `u`, `m_i`, and `d_i` repeat at the same phase within numerical tolerance;
- `H_i` and `r_i` do not reset;
- the same-phase radial displacement equals `beta` times the first-period ledger increment within tolerance;
- the HTML contains the formula chain, modeled-not-empirical boundary, and observation-continuation statement;
- the HTML has no remote resources;
- a deterministic rerun produces unchanged outputs.

## Allowed sentence

> The mark was not drawn. It is a recorded state of a relational process.

This sentence is qualified only together with the modeled-process boundary and frozen lineage.