[JingsongLi]

Summary

• Dispatch the existing public hybrid route_builders() and rank() operations to Native execution. Rust captures one authorized snapshot for the routes and performs score fusion.
• Keep ordinary, configurable public vector/full-text builders in route.search_builder, including their scan/read methods, metadata transport, and empty or retained read views.
• Specify and verify that editing a route's retained search builder changes subsequent route execution while retaining the captured snapshot. Cover query, limit and filter changes through the SDK and both public backends.
• Keep to_route_result() as shared public result validation, preserving scored result identity and normalizing empty unscored selections.
• Preserve pure in-memory ranking without REST/table access, authorization, or validation of unused queries. Supplied results can be empty, reordered, repeated, or externally evaluated; use the current final limit/ranker.
• Align Python scores, weights, intermediate arithmetic and accumulation with current Java float32 semantics. Add finite weight boundary and exact Java score fixtures.
• Preserve custom abstract builder implementations and backend isolation. Native phase failures propagate without Python replay.
• Update hybrid search documentation. No public PyPaimon API or dependency changes.

Review follow-up

• Preserve public route/conversion/rank hooks for custom abstract hybrid builders that store a native-enabled table. Only the default implementation enters the Native configuration protocol. The added cases reproduce the original AttributeError before the fix.
• Independently verify custom scheduled execution with concurrency 1 and 2, both with and without stored table state. A second complete review found no additional actionable issue.

Verification

• 170 focused Python phase, ranker, execution, search filter, authorization and Ray coordinator tests passed.
• Arrow 16 focused checks from the initial PR: 23 passed.
• 90 real Native joint cases passed against the companion Rust implementation, exercising 62 Native plans. The actual SDK was registered inside a Cargo test executable; no Native extension was installed or rebuilt into a Python environment, and the temporary runner is not committed.
• Companion Rust: 112 Core search-builder tests and eight embedded SDK tests passed. Rust 1.98.0 all-targets Clippy for Core, DataFusion and bindings with warnings denied passed.
• Scoped flake8 and diff checks passed. Independent review found no remaining actionable issue.

Dependency

Depends on apache/paimon-rust#1206, which unifies execute() -> GlobalIndexResult, removes execute_scored and retains live route builder state. Keep this PR draft until the new APIs reach Rust main. Native CI continues to build Rust main; no SDK version probes, old-API compatibility or CI pins are introduced.

[leaves12138]

LGTM