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1988 bytes, as of the version from 2026-10-27 01:07 (current). Recorded here, not run.
# Balanced reference selection for T193
Run `python generate.py` for complete offline reproduction or `python generate.py --independent` for the independent checks. Install `numberdb`, `python-flint`, and `mpmath`. Neither command writes to the website.
it holds the twenty extremal heights at $x=(2n-1)\pi/2$, $1\leq n\leq20$; the selection is not exhaustive over the real domain. In addition, it includes $x=1/4,1/2,1,2,4,8$ and the complementary phase arguments $n\pi$ for $1\leq n\leq4$. The exploratory families are identification references with practical finite bounds, not claims of documented applications for every input. All prior entries are retained.
The exploratory reference set $x=1/4,1/2,1,2,4,8$ provides sparse positive inputs near the origin and into the oscillatory regime. It complements the extrema without claiming a special use for every input. The cosine integral uses its real branch on $x>0$ CITE{BalancedIntegralDefinitions}.
The additional arguments $n\pi$, $1\leq n\leq4$, sample the complementary phase positions between successive stationary points. They are selected from the phase of the defining sine or cosine integrand, with a short noncanonical cutoff, rather than from a decimal mesh CITE{BalancedIntegralDefinitions}.
## Normalization formulas
## Primary references
- [DLMF 6.2(ii): sine and cosine integrals](https://dlmf.nist.gov/6.2#ii)
## Provenance
The current generate.py reproduces the complete attached selection, including the retained entries. Their original written values and entry comments are preserved rather than reassigned to a new source. The selection manifest records the predecessor revision and source hashes; earlier generators and checks remain historical provenance, not the enumeration of this extension.
The source manifest identifies the predecessor revision and records whether the preparation used a fresh export or a stale cached repaired readback. It is not authorization to overwrite a later revision.