# Stage 137: 8-Space LSH & Procrustes (aq137_align_multispace_procrustes_and_lsh / DB-UNIT-04)

Computes exact distances across 8 provably matched LSH geometries and aligns old-to-new embedding spaces via Orthogonal Procrustes without corpus re-embedding.

- Atomic micro-queue: `aq137_align_multispace_procrustes_and_lsh` (visibility: `public_commons`)
- Backing database unit: `DB-UNIT-04` (`48-Cell Hybrid Search, LSH & Retrieval Core`)
- Database cell: `lsh-db.teleon.dev` (`teleon_core.teleon_lsh_signatures_256`, `teleon_core.bm25f_seven_field_postings`, `teleon_core.roaring_trigram_inverted_index`, `teleon_core.markov_l0_prefetch_transitions`)
- Claim row hydration: `single_self_contained_flat_task_row` (100% context inline, normalized writeback)
- Track 2 Sister queue (`SISTER-04`): `sq04-improve-search-queue.teleon.dev` (Tune BM25F field weights, MMR diversity, synonym rings, multilingual stemmers, and 0..N retrieval steps.)
- Lanes: 8 Matched Distance/LSH, Orthonormal Procrustes, MRL int8 Prefixes

## Execution engines & AI Agent freedom contract

- **Deterministic (0 model calls)**: `bm25f_roaring_lsh_zero_model_v1` (8-geometry distance/LSH engine & Gram-Schmidt Procrustes solver (0 calls))
- **Hybrid (<=1 model call)**: `query_intent_expansion_hybrid_v1`
- **AI Agent & Bot Fleet (1..6 calls)**: `multi_hop_federated_scout_v1` (Cross-model anchor curator & hyperbolic/subsumption space tuner)
  - Contract: **Instructions + Resources + Freedom to search for new resources and new ways not bound by instructions**

## Database invariants

- Retrieval stays deterministic at 0 model calls when optimize_mode=zero_model_deterministic.
- Return compact contract cards first; defer source bytes until inspect_or_stream.

## External & internal bot fleet actions

- Pair heavy-tailed L1 counts with Cauchy LSH, trees with Poincare shells, and IOPE ports with box orthants
- Upgrade embedding models at zero downtime by fitting orthonormal Procrustes bridges on anchor pairs
- Filter coarse candidates with Matryoshka int8 prefixes before full-precision reranking

## Sister self-tuning areas

- Tune 7-field BM25F weights and MMR diversity_floor on frozen retrieval benchmarks
- Expand multilingual query synonym tables and domain aspect boosters
- Add pre-retrieval / post-retrieval deterministic reranking steps and code_blocks