matched bits instrument
| Definition | The rule that two codes are compared only at the same bit count. At matched bits two codes with equal reconstruction error can still differ for a reader, which is the flip. Chapter 4 section 4.3. Also bit-matched, matched reconstruction. |
|---|---|
| Example | Two 4-bit codes of the same vector are compared; a 4-bit code against a 6-bit code is not a comparison. |
| Book | Data Mining as Observation, draft 0.2, commit f3914f0; entry id matched-bits, kind instrument. |
| Status | measures [demonstrated]. Corrections: none recorded. |
| Defining equation | none |
| Assumptions and scope |
|
| Prior art | none recorded |
| Evidence | geometric-observation/claims/LEDGER.md:63, lean/DataMiningAsObservation/Bit.lean, lean/DataMiningAsObservation/Isotropy.lean |
| Reviewed | not yet reviewed; generated 2026-09-10 from records at the commits on the provenance page. |
Equation
none
Conditions
- The rule that two codes are compared only at the same bit count, since each added bit halves the step and quarters the squared error. At matched bits two codes with equal reconstruction error can still differ for a reader, and the flip is that difference.
- A comparison that was not bit-matched was refuted by the twenty-five percent codebook confound, and the redesign matched bits before any verdict was read.
Conditions are curated in entries.toml rather than read
from a record.
Ledger
- measures. GO-2 (neg. half: not reconstruction)
[demonstrated]. At matched bits, downstream preservation is not controlled by reconstruction error.geometric-observation/claims/LEDGER.md:63.
First stated
Chapter 4 section 4.3 of Data Mining as Observation, with
the bit-matched redesign in
geometric-observation/chapters/ch08_value.md:1-30.
Measurements
none
Failures and corrections
none
Invariance envelope
none declared
Machine checked
lean/DataMiningAsObservation/Bit.lean,
theorems levels_succ, levels_add,
step_succ, sqError_succ,
sqError_antitone, levels_zero, at
observation-data-mining f3914f0; what the check covers is stated in the
book’s appendix
C.
lean/DataMiningAsObservation/Isotropy.lean,
theorems isotropic_reads_same,
isotropic_no_flip, anisotropic_readers_differ,
flip_iff_anisotropic, at observation-data-mining f3914f0;
what the check covers is stated in the book’s appendix
C.
Used in
Data Mining as Observation chapters 4, 6, 12.
Related
bit; budget; quantization; control.
See also
Book equations stated beside the entry’s terms, not defining it: 4.2, 4.6, 0.15.
Ledger rows that cite the entry’s records without naming it: GO-2 (pos. half: consumer-projected covariance controls), NEG-4.
Sources-table rows that share a record with the entry without naming it: chapter 1 section 1.4, chapter 3 section 3.3, chapter 4 section 4.3, chapter 4 section 4.6, chapter 6 section 6.2, chapter 8 section 8.2.
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.