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Signed Analytic error plus documentation - #172

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Signed Analytic error plus documentation#172
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Description
This PR adds:

  • some documentation on integrals (I had intended to work out error models there, but then got distracted; I'll return to the documentation in a future PR).
  • Changes how the analytic error model works so that it predicts a signed error.
  • Creates a TaylorFactory (I will generalize tomorrow) to create a single source of truth for the process of propagating UQ settings (such as TaylorModel's truncation order, and eventually TAffine's threshold) and the UQ type to use.

TODOs

  • Generalize TaylorFactory to UQFactory

@ryanmrichard ryanmrichard self-assigned this Aug 13, 2026
ryanmrichard and others added 2 commits August 17, 2026 09:24
Adds the docs/source/background tree covering overlap, kinetic,
nuclear attraction, and electron repulsion integrals, including the
density-fitting derivation. Wires up sphinxcontrib-bibtex with a
references.bib, and excludes that file from the license header check.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Adds two background pages under docs/source/background/eris/:

- screening.rst documents the primitive screening models the package
  already implements (coarse K_ij, libint's fine metric, Cauchy-Schwarz)
  and records which are actually rigorous bounds. The coarse and fine
  metrics derive from the s-type closed form and retain no angular
  prefactor, so they do not bound l > 0 contributions; Cauchy-Schwarz
  does, at every angular momentum.

- error_bounds.rst derives a rigorous two-sided bracket on the error
  from neglecting primitive contributions. A Cauchy-Schwarz magnitude
  bound brackets each discarded quartet symmetrically; a three-valued
  sign oracle collapses that to a half-interval where the sign can be
  established a priori. The bound is valid with no sign information and
  tightens monotonically as coverage grows.

Scopes the existing bibliography directives per-document and gives each
a label prefix so the three pages cite disjoint key sets without
duplicate-label warnings under -W.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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