Daily oxygen summaries bound the mean share below 5 mg/L to 5.26–12.36% at 244 US stream sites under common weights, June–August 2010–2025

We tested what daily dissolved oxygen summaries can show about the share of low readings. We rebuilt a fixed panel of 296,741 valid days at 244 US stream sites in June-August 2010-2025. We used the reported minimum and maximum as support limits and the reported mean as a mean under common reading weights. Elementary mean inequalities give sharp closed bounds within this model. After equal summer and site weights, the mean daily share below 5 mg/L lies between 5.26% and 12.36%. An allowance of plus or minus 0.1 mg/L for each value expands the interval to 4.82-13.42%. On 56.74% of weighted days with a reported minimum below 5 mg/L, the bounds do not resolve whether more than one quarter of readings were low. These are model bounds, not confidence limits or measured event lengths. An elapsed-time interpretation needs time-based weights and full-day coverage, which the summaries do not prove. The package has source extracts, provenance, the proof, code, figures and all results. Independent source, exact-arithmetic and optimization checks passed. A clean repeat matched 26 generated files. We claim a reproducible application and tool, not a new probability theorem or national prevalence.

dissolved oxygen · daily summaries · partial identification · exposure · stream monitoring · moment bounds · open data