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allocation instrument

DefinitionThe assignment of a bit budget across directions. Water-filling gives directions below the water no bits, and the allocation report warns below effective rank two. Chapter 4 section 4.2. Also allocat.
ExampleWith directions of variance 4, 1, and 0.1 and a water level of 0.5, the first two directions get bits and the third gets none.
BookData Mining as Observation, draft 0.2, commit f3914f0; entry id allocation, kind instrument.
Statusno ledger row names this entry. Corrections: none recorded.
Defining equationnone
Assumptions and scope
  • The assignment of a bit budget across directions. Water-filling gives directions below the water no bits, the allocation report states its gain over uniform and warns below effective rank two, and a spectrum with half its mass in one direction has effective rank at most four.
  • The fragile-first allocation read 0.7118 against 0.7251 and was redesigned, and the budget inversion of GO-4 shows an allocation at fixed m rising while the matched-m allocation collapses.
Prior artnone recorded
Evidenceturboquant-pro/turboquant_pro/read_allocation.py:244-307, turboquant-pro/docs/RESULTS_strata_phase23_gates.md:110-125, lean/DataMiningAsObservation/WaterFilling.lean, lean/DataMiningAsObservation/EffectiveRank.lean
Reviewednot yet reviewed; generated 2026-09-10 from records at the commits on the provenance page.
directioneigenvaluewater level
Bits go to the directions above the water level and none to those below it.

Equation

none

Conditions

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

Ledger

none

First stated

Chapter 4 section 4.2 of Data Mining as Observation, with the allocation report in turboquant-pro/turboquant_pro/read_allocation.py:244-307.

Measurements

Where the book states it Numbers, as the book’s sources table records them Source
chapter 4 section 4.2 allocation report, gain over uniform, concentration caution below effective rank 2 turboquant-pro/turboquant_pro/read_allocation.py:244-307
chapter 10 section 10.5 fragile-first allocation 0.7118 vs 0.7251, targets up 0.004 to 0.034, redesigned allocator passed turboquant-pro/docs/RESULTS_strata_phase23_gates.md:110-125

Failures and corrections

none

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/WaterFilling.lean, theorems contribution_eq_water, terms_mul, two_sqrt_le, distortion2_ge, distortion2_eq_of_equal, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

lean/DataMiningAsObservation/EffectiveRank.lean, theorems sq_sum_le, effRank_le, sum_sq_le_sq_sum, one_le_effRank, effRank_const, effRank_single, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation chapters 0, 1, 2, 4, 10, 11.

Related

water-filling; budget; effective rank; concentrated; bit.

See also

Book equations stated beside the entry’s terms, not defining it: 4.2, 0.7, 4.6.

Ledger rows that cite the entry’s records without naming it: GO-4, GO-6.

Sources-table rows that share a record with the entry without naming it: chapter 4 section 4.2.

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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