…ema (#3420)

## Summary:
PR series to add logarithm graph support to the Interactive Graph widget:
1.  ▶️ [Add logarithm graph type definitions and data](#3420)
2. [Add logarithm math utilities to kmath](#3421)
3. [Add logarithm graph state management and reducer](#3422)
4. [Add logarithm graph rendering, SR strings, and equation string](#3423)
5. [Add logarithm graph scoring](#3424)
6. [Add logarithm graph option in the Interactive Graph Editor](#3425)

Add logarithm type definitions, this is the initial implementation for supporting Logarithm graph in Interactive Graph widget.

- Add `PerseusGraphTypeLogarithm` and `LogarithmGraphCorrect` types to the data schema, following the exponential pattern (coords + asymptote)
- Add JSON parser for the new `"logarithm"` graph type
- Add `generateIGLogarithmGraph()` test data generator
- Add placeholder cases in all exhaustiveness switches so the build stays green

## Details

This is the first PR in the logarithm interactive graph series (LEMS-3950). It adds the type definitions with zero runtime behavior change — no graph renders, no scoring, no editor UI.

**Data shape:** Logarithm follows the exponential pattern — two curve points plus an asymptote value. For logarithm the asymptote is the x-value of a vertical line (vs. exponential's y-value for a horizontal line).

**Placeholder cases** were added to satisfy `UnreachableCaseError` exhaustiveness in:
- `interactive-graph-editor.tsx` — graph merging switch
- `start-coords/util.ts` — `shouldShowStartCoordsUI` (returns `false`), `getDefaultGraphStartCoords` (returns `undefined`)
- `interactive-graph.tsx` — `getEquationString` (returns `""` — safe no-op since this is called unconditionally in the editor render path)
- `initialize-graph-state.ts` — `initializeGraphState` (returns `type: "none"`)
- `interactive-graph-ai-utils.ts` — `getGraphOptionsForProps` and `getUserInput`

These placeholders will be replaced with real implementations in subsequent PRs.

**Why `getEquationString` returns `""` instead of throwing:** `getEquationString` is called unconditionally in the editor's `render()` method (`interactive-graph-editor.tsx`). Since this PR adds the parser that accepts `type: "logarithm"`, any content with `correct.type === "logarithm"` (e.g. created via API) would reach the editor and crash the React render if the placeholder threw. All other placeholders in this PR are safe (return no-op values), but `getEquationString` is uniquely on the render path, so it must return a safe value. Future graph types should follow the same pattern: return `""` here, not throw.

Issue: LEMS-3953

Co-Authored by Claude Code (Opus)

## Test plan
- [ ] `pnpm tsc` passes
- [ ] `pnpm knip` passes
- [ ] `pnpm lint` passes
- [ ] `pnpm prettier . --check` passes
- [ ] Generator tests pass (2 new tests: default graph, graph with all props)
- [ ] Parser regression tests pass (170 snapshots unchanged)
- [ ] Interactive graph tests pass (199 tests)
- [ ] Verify no runtime behavior change in Storybook (existing graph types still work)

Author: ivyolamit

Reviewers: claude[bot], ivyolamit, SonicScrewdriver, handeyeco

Required Reviewers:

Approved By: SonicScrewdriver

Checks: ⏭️  1 check has been skipped, ✅ 10 checks were successful

Pull Request URL: #3420

## Summary:
PR series to add logarithm graph support to the Interactive Graph widget:
1.  [Add logarithm graph type definitions and data](#3420)
2. ▶️ [Add logarithm math utilities to kmath](#3421)
3. [Add logarithm graph state management and reducer](#3422)
4. [Add logarithm graph rendering, SR strings, and equation string](#3423)
5. [Add logarithm graph scoring](#3424)
6. [Add logarithm graph option in the Interactive Graph Editor](#3425)

Add the logarithm math utilities to kmath for supporting Logarithm graph in Interactive Graph

- Add `LogarithmCoefficient` type and `getLogarithmCoefficients()` to kmath, following the exponential pattern
- Compute coefficients `{a, b, c}` for `f(x) = a·ln(b·x + c)` using the inverse exponential approach
- No canonical normalization needed (logarithm has no periodic equivalences, same as exponential)

## Details

This adds the shared math utility for logarithm coefficient computation to `@khanacademy/kmath`, following the same pattern as `getExponentialCoefficients()`. Both the rendering component (PR 4) and scoring (PR 5) will consume this function.

**Mathematical approach (inverse exponential):**
1. Flip each coordinate `(x, y) → (y, x)` — treating the logarithm as the inverse of an exponential
2. Use the asymptote x-value as the flipped exponential's `c` coefficient
4. Compute exponential coefficients `aExp`, `bExp` from the flipped points
5. Invert to get logarithm coefficients: `a = 1/bExp`, `b = 1/aExp`, `c = -cExp/aExp`

**Validation guards** (returns `undefined` for invalid inputs):
- Same y-coordinate on both points (makes `bExp` undefined)
- A point lying on the asymptote
- Points on opposite sides of the asymptote
- Non-finite or zero intermediate results

This matches the reference implementation in `packages/perseus-core/src/utils/grapher-util.ts` (the Grapher widget's `Logarithm` object, lines 449–558).

Co-Authored by Claude Code (Opus)

Issue: LEMS-3953

## Test plan
 - [ ] `pnpm tsc` passes
 - [ ] `pnpm knip` passes
 - [ ] `pnpm lint` passes
 - [ ] `pnpm prettier . --check` passes
 - [ ] Coefficient tests pass (6 new tests, 17 total in coefficients.test.ts)
 - Grapher test data: `[-4,-3]`, `[-5,-7]`, asymptote `-6` reproduces correct y-values
 - Natural log: `[1,0]`, `[e,1]`, asymptote `0` → `a≈1, b≈1, c≈0`
 - Negative b: points left of asymptote (`y = ln(-x)`) → `b≈-1`
 - Same-y → `undefined`
 - Point on asymptote → `undefined`
 - Opposite sides → `undefined`

Author: ivyolamit

Reviewers: claude[bot], SonicScrewdriver, handeyeco

Required Reviewers:

Approved By: SonicScrewdriver

Checks: ⏭️  1 check has been skipped, ✅ 10 checks were successful, ⚪️ 1 check is neutral

Pull Request URL: #3421

…3422)

## Summary:
PR series to add logarithm graph support to the Interactive Graph widget:
1.  [Add logarithm graph type definitions and data](#3420)
2. [Add logarithm math utilities to kmath](#3421)
3. ▶️ [Add logarithm graph state management and reducer](#3422)
4. [Add logarithm graph rendering, SR strings, and equation string](#3423)
5. [Add logarithm graph scoring](#3424)
6. [Add logarithm graph option in the Interactive Graph Editor](#3425)

Add logarithm graph state management and reducer for supporting Logarithm graph in Interactive Graph

- Add `LogarithmGraphState` to the internal state type system
- Wire up reducer actions (`movePoint` + `moveCenter`) with logarithm-specific constraints
- Add graph state initialization with sensible defaults
- Add test data fixtures and question builder support

## Details

This PR adds the state management layer for logarithm graphs, following the exponential pattern throughout. Logarithm is the vertical-asymptote mirror of exponential's horizontal-asymptote design.

**Action registration:** Reuses existing `movePoint` and `moveCenter` action creators (no new action types). The `actions` export object gets `logarithm: { movePoint, moveCenter }`, identical to exponential.

**Reducer — `doMovePoint`:**
- Point cannot land on the asymptote's x-coordinate
- Both points must have different y-values (prevents degenerate coefficient computation)
- Cross-asymptote reflection: when a point is dragged past the asymptote, the other point is reflected (`reflectedX = 2 * asymptoteX - otherX`) so both points end up on the same side — matches Grapher widget behavior

**Reducer — `doMoveCenter`:**
- Asymptote moves horizontally only (X component extracted, Y ignored)
- Snap-through logic: when the new position would land between or on the curve points, snaps past all points using the midpoint heuristic for direction detection (prevents oscillation/flicker)
- Final safety check: asymptote cannot land exactly on either point's x-coordinate

**Initialization:** `getLogarithmCoords()` follows `getExponentialCoords()` pattern — returns `{coords, asymptote}`. Default coords use normalized fractions `[0.55, 0.55]` and `[0.75, 0.75]` to ensure both points are to the right of the default asymptote at x=0 after normalization (x=0.5 would land exactly on the asymptote).

**Placeholders:** `mafs-graph.tsx` returns `{graph: null, interactiveElementsDescription: null}` for logarithm (replaced in PR 4). `mafs-state-to-interactive-graph.ts` has the real serialization (not a placeholder).

Co-Authored by Claude Code (Opus)

Issue: LEMS-3953

## Test plan:
- [ ] `pnpm tsc` passes
- [ ] `pnpm knip` passes
- [ ] `pnpm lint` passes
- [ ] `pnpm prettier . --check` passes
- [ ] Reducer tests pass (147 total, 14 new logarithm tests):
  - `movePoint`: same-y rejection, bounding-to-same-y rejection, valid move, on-asymptote rejection, cross-asymptote reflection
  - `moveCenter`: valid move, snap-through between points, Y-component ignored, final safety rejection
  - Initialization: given coords, startCoords, defaults
  - Gradable graph: logarithm state conversion
  - Serialization: logarithm state to interactive graph
- [ ] Interactive graph tests pass (206 total, logarithm added to parameterized test maps)
- [ ] Serialization tests pass (14 total)

Author: ivyolamit

Reviewers: claude[bot], ivyolamit, SonicScrewdriver

Required Reviewers:

Approved By: SonicScrewdriver

Checks: ⏭️  1 check has been skipped, ✅ 10 checks were successful, ⚪️ 1 check is neutral

Pull Request URL: #3422

…uation string (#3423)

## Summary:
PR series to add logarithm graph support to the Interactive Graph widget:
1.  [Add logarithm graph type definitions and data](#3420)
2. [Add logarithm math utilities to kmath](#3421)
3. [Add logarithm graph state management and reducer](#3422)
4. ▶️ [Add logarithm graph rendering, SR strings, and equation string](#3423)
5. [Add logarithm graph scoring](#3424)
6. [Add logarithm graph option in the Interactive Graph Editor](#3425)

Create the logarithm graph visual component, add Storybook coverage, SR strings, and equation string for supporting Logarithm graph in Interactive Graph

- Create the logarithm graph visual component (`logarithm.tsx`) with curve rendering, draggable asymptote, and movable points
- Add 6 screen reader strings for accessibility
- Add equation string display for the editor
- Add Storybook story

## Details

This is the largest PR in the series. It creates the visual rendering of the logarithm graph, following the exponential component pattern with the axis swapped (vertical asymptote instead of horizontal).

**Curve rendering:**
- Single `<Plot.OfX>` with domain restricted to one side of the asymptote (`[asymptoteX + 0.001, xMax]` or `[xMin, asymptoteX - 0.001]`)
- Plot function computes `a * ln(b*x + c)`, returning NaN when outside domain or when y-value exceeds visible range + padding (prevents curve visually touching the asymptote)
- `coeffRef` caches last valid coefficients as fallback during transient invalid states

**Asymptote rendering:**
- Uses existing `MovableAsymptote` component with `orientation="vertical"`
- Dispatches `actions.logarithm.moveCenter()` on drag
- `constrainAsymptoteKeyboard()` implements snap-through logic for keyboard navigation (mirrors exponential's vertical version but on X-axis)

**Keyboard constraints:**
- `getLogarithmKeyboardConstraint()` prevents points from landing on the asymptote's x-coordinate or sharing y-value with the other point
- Uses bounded retry (max 3 steps) to skip past invalid positions

**Equation string:**
- `getLogarithmEquationString()` displays `y = a*ln(b*x + c)` with computed coefficient values
- `defaultLogarithmCoords()` provides fallback coords (normalized fractions `[0.55, 0.55]`, `[0.75, 0.75]`)

**Screen reader strings (6):**
- `srLogarithmGraph` — graph container label
- `srLogarithmPoint1` / `srLogarithmPoint2` — point position labels
- `srLogarithmAsymptote` — asymptote label with keyboard instructions
- `srLogarithmDescription` — graph state description
- `srLogarithmInteractiveElements` — interactive elements summary

Co-Authored by Claude Code (Opus)

Issue: LEMS-3953

## Test plan:

- [ ] `pnpm tsc` passes
- [ ] `pnpm knip` passes
- [ ] `pnpm lint` passes
- [ ] `pnpm prettier . --check` passes
- [ ] Logarithm component tests pass (15 new tests):
  - 9 screen reader tests (aria-labels, descriptions, interactive elements, updates on state change)
  - 3 keyboard constraint tests for points (valid move, skip asymptote, skip same-y)
  - 3 keyboard constraint tests for asymptote (free move, snap-through, skip point x-value)
- [ ] Interactive graph tests pass (178 passed, 28 skipped)
- [ ] Verify rendering in Storybook (logarithm story renders correctly, curve matches expected shape)

Author: ivyolamit

Reviewers: claude[bot], ivyolamit, SonicScrewdriver

Required Reviewers:

Approved By: SonicScrewdriver

Checks: ⏭️  1 check has been skipped, ✅ 10 checks were successful

Pull Request URL: #3423

…ph Editor (#3425)

## Summary:
PR series to add logarithm graph support to the Interactive Graph widget:
1.  [Add logarithm graph type definitions and data](#3420)
2. [Add logarithm math utilities to kmath](#3421)
3. [Add logarithm graph state management and reducer](#3422)
4. [Add logarithm graph rendering, SR strings, and equation string](#3423)
5. [Add logarithm graph scoring](#3424)
6. ▶️ [Add logarithm graph option in the Interactive Graph Editor](#3425)

Add logarithm graph option in the Interactive Graph Editor

- Add `StartCoordsLogarithm` component for configuring logarithm start coordinates in the editor
- Gate the "Logarithm function" option behind the `interactive-graph-logarithm` feature flag
- Export `getLogarithmCoords` for use by the editor
- Add start asymptote validation

## Details

This PR enables content creators to configure logarithm exercises in the Interactive Graph editor, following the exponential editor pattern.

**StartCoordsLogarithm component:**
- Two coordinate pair inputs (Point 1 and Point 2)
- A single number input for the asymptote x-position (labeled "Asymptote x =")
- Equation display showing `y = a * ln(b*x + c)` with computed coefficient values
- CSS module styling (not Aphrodite), following `start-coords-exponential.module.css`

**Feature flag:** "Logarithm function" appears in the graph type selector only when `interactive-graph-logarithm` is enabled, preventing content creators from selecting it until it's ready for launch.

**Editor validation:** The start asymptote x-value is validated — it cannot fall between or on the x-coordinates of the curve's start points (mirrors exponential's y-axis validation but for x-axis).

**Exports:** `getLogarithmCoords()` is now exported from `initialize-graph-state.ts` and re-exported from `@khanacademy/perseus` for use by the editor's start-coords UI.

Co-Authored by Claude Code (Opus)

Issue: LEMS-3969

## Test plan:

- [ ] `pnpm tsc` passes
- [ ] `pnpm knip` passes
- [ ] `pnpm lint` passes
- [ ] `pnpm prettier . --check` passes
- [ ] Editor tests pass (422 total across 15 suites)
- [ ] Verify in Storybook: "Logarithm function" appears in graph type selector when feature flag is on
- [ ] Verify start coords UI renders correctly with asymptote input and equation display

Author: ivyolamit

Reviewers: claude[bot], SonicScrewdriver, ivyolamit

Required Reviewers:

Approved By: SonicScrewdriver

Checks: ⏭️  1 check has been skipped, ✅ 10 checks were successful

Pull Request URL: #3425

This PR was opened by the [Changesets
release](https://github.com/changesets/action) GitHub action. When
you're ready to do a release, you can merge this and the packages will
be published to npm automatically. If you're not ready to do a release
yet, that's fine, whenever you add more changesets to main, this PR will
be updated.


# Releases
## @khanacademy/[email protected]

### Minor Changes

- [#3421](#3421)
[`9099a40a4e`](9099a40)
Thanks [@ivyolamit](https://github.com/ivyolamit)! - Add the logarithm
math utilities to kmath for supporting Logarithm graph in Interactive
Graph

### Patch Changes

- Updated dependencies
\[[`a72f7db4a3`](a72f7db)]:
    -   @khanacademy/[email protected]

## @khanacademy/[email protected]

### Minor Changes

- [#3422](#3422)
[`a4eaa5a1f8`](a4eaa5a)
Thanks [@ivyolamit](https://github.com/ivyolamit)! - Add logarithm graph
state management and reducer for supporting Logarithm graph in
Interactive Graph


- [#3425](#3425)
[`2c36b8a4c3`](2c36b8a)
Thanks [@ivyolamit](https://github.com/ivyolamit)! - Add logarithm graph
option in the Interactive Graph Editor


- [#3423](#3423)
[`3cc56f60dd`](3cc56f6)
Thanks [@ivyolamit](https://github.com/ivyolamit)! - Create the
logarithm graph visual component, add Storybook coverage, SR strings,
and equation string for supporting Logarithm graph in Interactive Graph


- [#3420](#3420)
[`a72f7db4a3`](a72f7db)
Thanks [@ivyolamit](https://github.com/ivyolamit)! - Add logarithm type
definitions, this is the initial implementation for supporting Logarithm
graph in Interactive Graph widget.

### Patch Changes

- [#3461](#3461)
[`0481b4238d`](0481b42)
Thanks [@nishasy](https://github.com/nishasy)! - [Image] | (DX) | Update
CSS modules to kabab case


- [#3455](#3455)
[`0d6cf3c3ce`](0d6cf3c)
Thanks [@nishasy](https://github.com/nishasy)! - [Image] | (UX) | Fix
messed up Graphie labels behind scale feature flag

- Updated dependencies
\[[`08b1218b62`](08b1218),
[`a72f7db4a3`](a72f7db),
[`9099a40a4e`](9099a40)]:
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]

## @khanacademy/[email protected]

### Minor Changes

- [#3420](#3420)
[`a72f7db4a3`](a72f7db)
Thanks [@ivyolamit](https://github.com/ivyolamit)! - Add logarithm type
definitions, this is the initial implementation for supporting Logarithm
graph in Interactive Graph widget.

## @khanacademy/[email protected]

### Minor Changes

- [#3425](#3425)
[`2c36b8a4c3`](2c36b8a)
Thanks [@ivyolamit](https://github.com/ivyolamit)! - Add logarithm graph
option in the Interactive Graph Editor


- [#3420](#3420)
[`a72f7db4a3`](a72f7db)
Thanks [@ivyolamit](https://github.com/ivyolamit)! - Add logarithm type
definitions, this is the initial implementation for supporting Logarithm
graph in Interactive Graph widget.

### Patch Changes

- [#3461](#3461)
[`0481b4238d`](0481b42)
Thanks [@nishasy](https://github.com/nishasy)! - [Image] | (DX) | Update
CSS modules to kabab case

- Updated dependencies
\[[`a4eaa5a1f8`](a4eaa5a),
[`2c36b8a4c3`](2c36b8a),
[`3cc56f60dd`](3cc56f6),
[`08b1218b62`](08b1218),
[`a72f7db4a3`](a72f7db),
[`9099a40a4e`](9099a40),
[`0481b4238d`](0481b42),
[`0d6cf3c3ce`](0d6cf3c)]:
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]

## @khanacademy/[email protected]

### Minor Changes

- [#3424](#3424)
[`08b1218b62`](08b1218)
Thanks [@ivyolamit](https://github.com/ivyolamit)! - Add logarithm graph
scoring to support the Logarithm graph in Interactive Graph

### Patch Changes

- Updated dependencies
\[[`a72f7db4a3`](a72f7db),
[`9099a40a4e`](9099a40)]:
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]

## @khanacademy/[email protected]

### Patch Changes

- Updated dependencies
\[[`a72f7db4a3`](a72f7db)]:
    -   @khanacademy/[email protected]

## @khanacademy/[email protected]

### Patch Changes

- Updated dependencies
\[[`a72f7db4a3`](a72f7db)]:
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]

## @khanacademy/[email protected]

### Patch Changes

- Updated dependencies
\[[`a72f7db4a3`](a72f7db),
[`9099a40a4e`](9099a40)]:
    -   @khanacademy/[email protected]
    -   @khanacademy/[email protected]