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Correct format ceiling displays and stage endpoint checks - #602
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Mister-Meeseeks merged 1 commit intoOct 12, 2026
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Mister-Meeseeks merged 1 commit into
Mister-Meeseeks merged 1 commit into
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Summary
Follow-up to #595 by @DreamingOfClouds. The published headline
κ ≤ 0.0051595remains valid. Two finer inequalities rounded their upper bounds downward; this changes them to outward upper displays0.0051594939for the complex side and0.005964704for the bit-only corollary.The A2 stage comparison now places competing certified upper bounds below the lower endpoint of
X(5), which proves that stage 5 is the maximum. A1 now checks the displayed ceilings as exact rational inequalities and reports the certified bounds. The package checksum manifest is updated for the three edited files.Scope
These are conditional S2 accounting ceilings for the realized units and retained balanced outer assembly described in #595. They are not a global lower bound, an achieved rate, or a provider certificate. The unit floors and imported structural lemmas remain premises of that result.
Verification
python3 -B scripts/a1_ceiling_roots.py— all checks passed, including exact rational upper inequalities.python3 -B scripts/a2_ceiling_sup.py— all checks passed for both units, finite stages, and tail checks.git diff --checkpassed.0.005159493816457...and0.005964703560823..., both below the new outward displays, and independently verified the strict lower-endpoint stage comparison.The full package verifier was not run in this sparse checkout because its vendored inputs and other package files were not checked out.