perf(exec): polish scale/performance for rank(by="harmonic_closeness") #508

Problem

rank(by="harmonic_closeness") is a shipped public analyst algorithm whose primary cost class is
BFS-heavy all-sources harmonic closeness. After M4's shared infrastructure (#337/#340/#341) and the first
compute-kernel batch (#342–#344), this algorithm still needs focused scale and
performance polish so large embedded workloads do not leave available CPU/memory
headroom unused—or so remaining serial costs are measured and dispositioned honestly.

Objective

Polish scale and performance for public rank(by="harmonic_closeness") (BFS-heavy all-sources harmonic closeness) while preserving deterministic ordering, fingerprints, cancellation, resource limits, and structured errors.

Debt / regime

• Debt type: development and test/proof
• Quality regime: A compute
• Family: rank

Requirements

1. Prefer feat(api): define a bounded embedded execution resource policy #337's instance-owned private ComputePool and automatic crossover when
   independent work units exist; keep a serial path for one thread and below a
   measured crossover. Never use Rayon's process-global pool.
2. Consume CSR-native adjacency (perf(exec): consume persisted CSR without edge-scale hash-map expansion #340) and bounded Arrow sinks (perf(exec): shape analyst outputs directly into bounded Arrow batches #341); do not
   introduce parallel-only graph copies or O(E) HashMap expansion on index hits.
3. Preserve deterministic public contracts: schemas, row order, ties, fingerprints,
   cancellation, work/output limits, and structured errors at 1/2/4/8/automatic
   configurations where parallelism is introduced.
4. If parallelism is unsafe for numeric/order semantics, keep the algorithm serial and
   instead polish representation, allocation, early-exit, and evidence—document the
   disposition rather than changing bits.
5. Record test(performance): establish the M4 embedded baseline and entry gate #334-style before/after structural evidence (work units, threads/path, peak
   RSS, fingerprint, hardware-specific timing). Timing is never a CI pass/fail gate.
6. Keep Rust authoritative; Python/Node remain thin bindings.

Acceptance Criteria

• Public rank(by="harmonic_closeness") has an evidence-backed performance disposition
  (parallel path with measured crossover or explicit serial polish with proof).
• Deterministic fingerprints / schemas / ordering match the accepted one-thread
  oracle at every supported thread configuration that executes.
• Cancellation, work/output limits, and worker failure return structured outcomes
  without partial public results.
• CSR-native / Arrow-shaping structural gates hold for the changed path.
• Docs name the crossover or serial disposition; no universal scale claim or GPU claim.
• Exact-head CI for the changed surface is green.

BDD Completion Scenarios

Scenario: Independent work uses the private pool when safe

Given a workload above the measured crossover and a multi-thread policy
When harmonic_closeness executes
Then eligible independent work runs on the instance-owned compute pool
And public results match the one-thread oracle.

Scenario: Small work avoids universal parallel tax

Given a small fixture or one-thread policy
When the same invocation runs
Then the serial path is retained
And no pool setup becomes a universal latency tax.

Scenario: Unsafe parallelism is dispositioned, not forced

Given an algorithm whose numeric/order semantics forbid parallel reduction
When this issue closes
Then the serial contract is preserved
And allocation/representation/evidence polish is documented instead.

Non-Goals

• Approximate algorithms that change public exactness contracts.
• GPU / distributed / foreign-engine fallbacks.
• Changing public schemas or tie-breaking rules.
• Re-doing perf(exec): parallelize exact cosine KNN by canonical source #342–perf(exec): parallelize Node2Vec walk generation deterministically #344 cosine / PageRank / Node2Vec walk work.

Related Issues

• epic(performance): polish scale and performance for remaining M4 analyst algorithms #498 — parent tracker; this issue blocks it.
• epic(performance): close M4 embedded performance and scale #335 — M4 close tracker; this issue blocks it.
• feat(api): define a bounded embedded execution resource policy #337 / perf(exec): consume persisted CSR without edge-scale hash-map expansion #340 / perf(exec): shape analyst outputs directly into bounded Arrow batches #341 — shared infrastructure prerequisites.
• test(performance): establish the M4 embedded baseline and entry gate #334 / test(performance): reconcile final M4 exit evidence and scale claims #345 — evidence methodology.