Percentile identification calculator

Companion application to the article What percentile sound levels identify: energy bounds, background recovery, and source combination (Omri Abas; DOI 10.5281/zenodo.23088962).

The page computes, from measurement records or from reported values, the identification sets the article proves: what percentile levels, equivalent levels, extrema, activity bounds and durations establish about a target quantity, with endpoint status and unbounded directions, in the reporting form of the article's Section 7.6. It is a static web page. Everything runs in the visitor's browser; no server is involved in the computation.

Using the page

Load a record. Choose a CSV, TXT, TSV, Excel or ODS file with one row per observation and a column of levels in dB. The page detects the delimiter, a decimal comma, the header row and the most plausible level column; correct them if needed. Optional columns: a time column (used only for the research contribution) and a duration column (observations are otherwise taken as equal durations). Levels are read as written and converted to energy at 40 decimal digits, so equal written levels give identical energies and every comparison in the core is exact.
Or enter a report by hand: percentile levels, optional lowest and highest level, optional equivalent level. Use it for values stated in a document.
Choose an operation and press Compute. Each result is a Section 7.6 report: target, observation basis, inputs, classification (exact, valid index, identified set, unidentified, model-based), the assumptions the calculation used, the identified result with endpoint status, and the representativeness entry, which is always "not established by this computation" because transfer beyond the measured window is the separate question of the article's Section 8. "Copy as text" copies the report.

Conventions: percentiles are lower quantiles, L_N = inf{L : F(L) >= 1 - N/100} (equation (1)); the record is read as the complete observation window (Section 2.4); levels are shown to 2 or 4 decimals; energies are exact rationals and can be displayed in full.

Operations and the results they implement

Operation	Article result
Descriptors of a record	Section 2.1, equations (1) and (2)
Equivalent level from percentiles and extrema	Theorem 3.1, equations (5) to (7); Proposition 3.3 without an upper support
Gaussian conversion of ISO 1996-2 Annex I.2.2	Section 3.5, equation (8), flagged as model-based
Background and source from the total record	Equation (9); Section 4.4 bracket; Section 4.5 and equation (13); Theorem 4.2 with a separation check on the record
Percentile report with a known total mean	Section 4.2; Theorem 4.1, equation (10)
Adding percentiles of several sources	Proposition 5.1, equation (14); equation (15); Theorem 5.2, equation (16); Proposition 5.3
Subtracting a background percentile from a total percentile	Section 5.3
Mixing descriptors	Proposition 5.4 and the mixed-addition bounds of Section 5.3
Activity defect and tail certificate	Theorem 5.5, equations (17) to (21): equation (19) for two sources, equation (20) for three equal bounds
Combined percentile range from equivalent levels and duty cycles	Theorem 5.6
Joint percentile-mean interval	Theorem 5.7, equation (22)
Two records combined	Independent product law (Kessler and Gottlieb's combination rule) and Theorem 5.9, equation (24)
Pooling percentile reports across windows	Proposition 5.10; exact pooled percentile and Leq when the complete records are loaded

Not in this version: the grid computation of Theorem 5.8 and equation (23) (Section 5.6), the exact transport optimisation of Supplement S.3, the interior-anchor bound of Supplement S.4, and the activity defect for three unequal bounds (Supplement S.1) or four or more sources, for which the article gives no closed form. The roots of Theorems 5.6 and 5.7 are irrational in general; they are bracketed by bisection to 2^-80 of the starting bracket and marked as approximate.

Self-tests

selftest.html runs 171 checks in the browser: the 67 checks of the verification function in the deposited figure program, ported one for one; 86 worked examples stated in the article text; 18 checks of the decibel conversion and input parsing. Under Node: node run_tests.js.

Research contribution

With contribution.enabled = true in config.js, each time-history record gets a "contribute to research" button. The panel asks for the metadata needed by the companion study on measurement duration and representativeness, shows what the page derived from the file, and sends the file (compressed) and the answers only when the contributor ticks the consent boxes and presses Send. See notice.html (the contributor notice, to be reviewed before switching on), supabase/schema.sql and DEPLOY.md.

Files

index.html, app.js, styles.css: the interface.
core/rational.js: exact rational arithmetic (BigInt) and the 40-digit decibel conversion.
core/identify.js: the identification results, one function per result of the article.
core/tests.js, selftest.html, run_tests.js: self-tests.
contribute.js, notice.html, supabase/schema.sql: research contribution.
config.js: title, DOI, contact, version, contribution settings.
vendor/xlsx.full.min.js: SheetJS Community Edition 0.18.5 (Apache-2.0) for spreadsheet reading.
download/: this source as a zip and the figure-code package of the article.

Licence

Application code: MIT (see LICENSE). SheetJS: Apache-2.0 (vendor/LICENSE-sheetjs.txt). The article and its figure code are cited by their DOI.