feat(interval): add certified determinant sign enclosures

[acgetchell]

• Add outward-rounded interval arithmetic with typed range and input errors.
• Certify determinant signs through D=7 with explicit inconclusive results.
• Provide runtime dimension dispatch, documentation, and benchmark coverage.
• Refresh pinned Python development tools and transitive dependencies.

Closes #218

Summary by CodeRabbit

• New Features

  • Added validated, outward-rounded Interval arithmetic and IntervalMatrix support.
  • Added determinant evaluation and sign classification—positive, negative, zero, or inconclusive—for matrices up to dimension 7.
  • Added runtime dispatch for supported interval-matrix dimensions.
  • Added clear handling for invalid bounds, non-finite values, unsupported dimensions, and exhausted ranges.

• Documentation

  • Expanded guidance on interval arithmetic, determinant certification, limitations, errors, and usage.

• Benchmarks & Tests

  • Added interval benchmark workflows and comprehensive arithmetic and determinant validation coverage.

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📒 Files selected for processing (3)

• docs/mathematical_basis.md
• src/error.rs
• src/interval.rs

🚧 Files skipped from review as they are similar to previous changes (1)

• docs/mathematical_basis.md

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📝 Walkthrough

Walkthrough

The crate adds outward-rounded Interval arithmetic and fixed-size IntervalMatrix determinant-sign evaluation through dimension 7. It also adds structured errors, runtime dispatch, property tests, documentation, and interval benchmarks.

Changes

Interval determinant feature

Layer / File(s)	Summary
Interval arithmetic and error contracts src/error.rs, src/interval.rs, tests/proptest_interval.rs	Adds validated finite intervals, outward-rounded operations, range-exhaustion handling, and structured interval errors.
Interval matrices and runtime dispatch src/interval.rs, src/lib.rs, tests/prelude_exports.rs	Adds fixed-size matrix construction, division-free determinant signs, try_with_interval_matrix!, public exports, and dispatch tests.
Independent interval validation tests/proptest_interval.rs	Compares interval containment and determinant classifications with independent BigRational calculations through dimension 7.
Interval API documentation README.md, REFERENCES.md, docs/mathematical_basis.md	Documents interval semantics, determinant classifications, storage, supported dimensions, range failures, limitations, and IEEE 1788 context.
Interval benchmark workflow Cargo.toml, benches/interval.rs, docs/BENCHMARKING.md, justfile, pyproject.toml	Adds the interval Criterion suite and command, validates benchmark fixtures, updates benchmark documentation, and refreshes development tool pins.

Estimated code review effort: 4 (Complex) | ~60 minutes

Merge Risk: ⚪ Minimal · up to c2437

This change adds validated outward-rounded interval arithmetic and interval determinant-sign classification. The reviewed range, rounding, and matrix-access paths show no remaining concrete merge-blocking risk.

Sequence Diagram(s)

sequenceDiagram
  participant Caller
  participant try_with_interval_matrix
  participant IntervalMatrix
  participant determinant_DP
  Caller->>try_with_interval_matrix: provide runtime dimension
  try_with_interval_matrix->>IntervalMatrix: dispatch typed matrix for dimensions 0–7
  Caller->>IntervalMatrix: construct interval matrix
  IntervalMatrix->>determinant_DP: evaluate determinant sign
  determinant_DP-->>Caller: return determinant classification

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🚥 Pre-merge checks | ✅ 3 | ❌ 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Out of Scope Changes check	⚠️ Warning	Most changes support issue #218, but the pinned tool updates for dprint, rumdl, ruff, and ty are unrelated to the interval determinant feature.	Remove the unrelated development-tool version updates or move them to a separate pull request. Keep the interval implementation, tests, documentation, and benchmark changes.

✅ Passed checks (3 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly identifies the main change: adding certified determinant sign enclosures using interval arithmetic.
Linked Issues check	✅ Passed	The pull request addresses the requirements in issue #218. It adds outward-rounded fixed-size interval arithmetic, explicit range and input errors, division-free determinant sign classification throug…

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• Commit unit tests in branch feat/218-interval-determinant-signs

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[codecov]

Codecov Report

❌ Patch coverage is 98.22161% with 13 lines in your changes missing coverage. Please review.
✅ Project coverage is 97.87%. Comparing base (7bb3776) to head (c2437b8).
✅ All tests successful. No failed tests found.

Files with missing lines	Patch %	Lines
src/interval.rs	98.05%	13 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #231      +/-   ##
==========================================
+ Coverage   97.82%   97.87%   +0.04%     
==========================================
  Files           9       10       +1     
  Lines        5338     6069     +731     
==========================================
+ Hits         5222     5940     +718     
- Misses        116      129      +13     

Flag	Coverage Δ
unittests	97.87% <98.22%> (+0.04%)	⬆️

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Actionable comments posted: 1

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Inline comments:
In `@docs/mathematical_basis.md`:
- Around line 4-7: Update the introductory guarantee for Interval and
IntervalMatrix<D> to state that enclosure applies when interval operations are
used throughout expression assembly, or explicitly note the limitation of
IntervalMatrix::from_matrix for already-rounded Matrix values. Keep the binary64
approximation description for Matrix<D> and Vector<D> unchanged.

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📥 Commits

Reviewing files that changed from the base of the PR and between 7bb3776 and cd94ebb.

⛔ Files ignored due to path filters (1)

• uv.lock is excluded by !**/*.lock

📒 Files selected for processing (13)

• Cargo.toml
• README.md
• REFERENCES.md
• benches/interval.rs
• docs/BENCHMARKING.md
• docs/mathematical_basis.md
• justfile
• pyproject.toml
• src/error.rs
• src/interval.rs
• src/lib.rs
• tests/prelude_exports.rs
• tests/proptest_interval.rs

Included review availability: 2 reviews are currently available. Your included PR review attempts over the past 7 days set your current allowance at 4 reviews per hour.