# Reports, routes and finite geometry

Run `python reproduce.py` with numpy and matplotlib. Original mathematical teaching assets; no physical experiment or performance prediction.

Report states are pairs (support for, support against): neither00, for_only10, against_only01, both11. NOT swaps components. Conjunction=(t1 AND t2,f1 OR f2); disjunction=(t1 OR t2,f1 AND f2); merging=(t1 OR t2,f1 OR f2). Four unary and16 binary rows enumerate this selected formalism. Recorded assertions are not probabilities or guaranteed truth. Merging retains contradiction rather than resolving it.

arc-chord.csv contains181 angles0–180 degrees. Unit radius gives arc=theta and chord=2sin(theta/2), theta in radians. Both vanish at zero; at180 degrees the values are pi and2. A shorter geometric path does not establish physical access or a transport mechanism.

finite-geometry.csv contains121 logarithmically spaced radii R from1 to1000. The dimensionless profile is y=exp(-1/r²), revolved around the vertical axis. Radius at height y is1/sqrt(-ln y). Stopping at height h=exp(-1/R²) gives volume pi E1(1/R²). R labels the radius at the top slice. Clipping the entire region below y=1 at cylindrical radius R is a different operation: it adds cap volume pi R²[1-exp(-1/R²)]. expm1 avoids cancellation in this cap calculation. Figures distinguish these regions explicitly.

The E1 evaluator is restricted to0<a<=1: E1(a)=-EulerGamma-ln(a)-sum_{k>=1}(-a)^k/(k*k!). It is not a general special-function library. Independent Simpson quadrature uses substitution t=a exp(s) in the defining integral and stops at t=50; the omitted tail is below exp(-50)/50. quadrature-check.csv has20 comparisons, five radii and250/500/1000/2000 panels. At2000 panels maximum volume difference is9.47e-14. reference-comparison.csv independently compares four existing finite-slice results at2/10/100/1000; maximum difference3.56e-15. Historical originals are never overwritten. The generator optionally reads a local reference result; standalone reproduction skips that comparison if the reference is absent and records null for its error.

All coordinates and volumes are dimensionless. Radial/vertical physical scales Lr,Lz would multiply volume by Lr² Lz. Bounded height does not ensure finite volume: as y approaches1, cross-sectional area pi/(-ln y) behaves as pi/(1-y), whose integral diverges. Equivalently the slice volume grows as2pi ln R minus pi*EulerGamma. A finite plot alone does not prove this limit. Revolving about another axis creates another solid and is not modeled as an interchangeable operation.

CSV counts:4 unary+16 binary+181 arc+121 geometry+20 quadrature+4 reference=346 rows. Runtime versions and baseline SHA256 hashes appear in study.json. Checks include exhaustive report tables, arc endpoints/inequality, increasing finite volume, independent integration and historical parity. No mass, dynamics, force, energy or propulsion model is supplied.

Sources: [NIST DLMF exponential integral](https://dlmf.nist.gov/6.2); [author survey of four-valued logic](https://arxiv.org/html/2503.20679v1); [NASA model verification/validation handbook](https://standards.nasa.gov/sites/default/files/standards/NASA/A/0/nasa-hdbk-7009a.pdf). These support mathematical/methodological context; numerical verification is not empirical validation.