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shard instrument

DefinitionOne partition of an index that is searched separately, with the results merged. The global top k lies inside the union of the shards' top k. Chapter 13.
ExampleEight shards each returning their top 10 hand the merger 80 candidates, among which the global top 10 lies.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id shard, kind instrument.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scope
  • One partition of an index that is searched separately, with the results merged. If each shard returns its own top k and the global top k is strict, the global top k lies inside the union of the shards’ answers, so the merge loses nothing and reads at most the number of shards times k candidates.
  • A placement study over 64 shards reported search times taken with the file cache already holding the shards, and a speedup of 63.7 times was fragmentation, so a sharded number names whether it is warm and what the shards were.
Prior artnone recorded
Evidenceturboquant-pro/docs/RESEARCH_ROADMAP.md:133-160, lean/DataMiningAsObservation/Shard.lean
Reviewednot yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.
each shard returns its top k, and the global top k lies in the union
A partition searched separately, with the answers merged.

Equation

none

Conditions

Conditions are curated in entries.toml rather than read from a record.

Ledger

none

First stated

Chapter 13 section 13.1 of Data Mining as Observation, with the placement study in turboquant-pro/docs/RESEARCH_ROADMAP.md:133-160 and the fleet run in openvector-bench/README.md:250-263.

Measurements

Where the book states it Numbers, as the book’s sources table records them Source
chapter 13 section 13.1 22.30 s cold vs 0.835 s warm at eight probes, every prior number warm, fragmentation 63.7 bracketing 42 to 47, 64 shards, routing sparsity computed and discarded turboquant-pro/docs/RESEARCH_ROADMAP.md:133-160

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/Shard.lean, theorems global_in_local, global_in_union, merge_cost, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation chapters 11, 13.

Related

inverted file; recall at k; cold, warm; cache; budget.

See also

Book equations stated beside the entry’s terms, not defining it: 11.3, 11.4, 13.2.

Ledger rows that cite the entry’s records without naming it: GO-12.

Sources-table rows that share a record with the entry without naming it: chapter 8 section 8.4, chapter 11 section 11.4, chapter 13 section 13.1.

Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.

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