Add adaptive TCI interpolation for partitioned tensor trains

[SamuelBadr]

Summary

• add tensor4all_partitionedtt::adaptiveinterpolate and AdaptiveInterpolateOptions
• run TCI2 independently per patch, splitting nonconverged patches in an explicit full-index order
• support exact 0/1-active-site leaves, scalar and optional batch callbacks, sampled-zero patches, and opt-in pivot recycling
• replenish children that receive no compatible recycled pivots instead of incorrectly treating them as zero
• embed fixed middle sites with compact structured copy/one-hot storage
• fix TCI2 convergence to compare normalized error history with the configured relative tolerance
• record TCIAlgorithms.jl MIT provenance and license notice

Validation

• cargo fmt --all -- --check
• cargo clippy --workspace --all-targets -- -D warnings
• cargo test --release --workspace
• cargo test --doc --release --workspace
• cargo doc --workspace --no-deps (passes; pre-existing rustdoc warnings remain)
• cargo run -p api-dump --release -- . -o docs/api

cargo nextest and mdbook are not installed in the local environment, so cargo nextest run --release --workspace and ./scripts/test-mdbook.sh could not run locally. The full release cargo test --workspace fallback passed.

Provenance

The patch queue and pivot-recycling structure are derived from TCIAlgorithms.jl commit e501032278c9dd41b46c5851d8238169c8d178c5 under MIT. The upstream notice is retained in crates/tensor4all-partitionedtt/LICENSE-TCIALGORITHMS-MIT.

[shinaoka]

I found a few blocking issues before this should merge. The main correctness problem is that adaptive patch acceptance currently ignores TCI2's full convergence criterion, and there are also repository-rule gaps around checked arithmetic and structured-copy testing. I did not complete local test execution because it was interrupted, so these comments are based on static review of the PR diff and repository rules.