[sanskarIN]

Summary

Add sample_cumulative_area(x: vector, y: vector) -> vector, a pure, deterministic numerical kernel for trapezoidal prefix integrals over strictly increasing coordinates.

• Reuse the exact finite-interval arithmetic from sample_area (merged in feat(science): bounded sampled integration and interval derivatives #153), preserving representable subnormal products and avoiding unnecessary overflow.
• First output is 0.0; every subsequent entry is the compensated integral through that sample coordinate. The last entry agrees with sample_area for representable results.
• Validate matching vector shapes, minimum two measurements, monotonic finite widths, and every output as finite binary64.
• Prepay existing kernel work budget: 4 × (N - 1) steps. Allocate exactly N floats = 8 × N output payload bytes; respect visible immutable windows.
• Add independent Python Decimal prefix oracle, Rust host/compiler tests, a full runnable .srp stdout fixture, CPU benchmark workloads, and Windows/Linux check-script coverage.

Compatibility and release gates

• Development-only: no new prerelease published. This function is not in v0.0.6-alpha.3 artifacts.
• No parser or language syntax changes, external numerical libraries, native compiler, tensor ABI, SIMD/GPU or threading claims.
• Adds numeric::Builtin::SampleCumulativeArea; Rust hosts exhaustively matching the experimental enum need to update matches.
• Require full Linux/macOS/Windows checks, Rust 1.74, independent numerical oracle and three package builds before merge.

Status

• Rustfmt/Clippy + debug and release tests
• Independent Decimal numerical oracle
• Cross-platform Rust 1.74 and packages
• Regression benchmarks and example corpus

No issue comments should be posted on the user's behalf.