Physics starter - Resolve a localized integral

MODEL "Physics starter - Resolve a localized integral"
DESCRIPTION "A deliberately narrow Gaussian illustrates why adaptive samples can miss known structure."
VERSION "1.0.0"
AUTHOR "Grid Team"
TAGS "physics", "starter", "quadrature"

# A peak well inside [0,1]; the restricted interval covers ten widths either side.
input PeakWidth = 0.0001
  VALIDATE BETWEEN 0.00001 AND 0.001 MESSAGE "Use width from 0.00001 to 0.001."
input PeakCenter = 0.12345
  VALIDATE BETWEEN 0.1 AND 0.9 MESSAGE "Keep the peak away from interval boundaries: center 0.1 to 0.9."
output Unsplit = INTEGRATE((x) => EXP(-(((x - PeakCenter) / PeakWidth)^2)), 0, 1, 1e-12)
output Restricted = INTEGRATE((x) => EXP(-(((x - PeakCenter) / PeakWidth)^2)), PeakCenter - 10 * PeakWidth, PeakCenter + 10 * PeakWidth, 1e-12)
output Reference = PeakWidth * SQRT(PI())
output UnsplitError = ABS(Unsplit - Reference)
output RestrictedError = ABS(Restricted - Reference)
output Interpretation = "The infinite-domain reference differs by negligible Gaussian tails in this admitted range. An unsplit zero is not physical validation. Supplying the known peak neighborhood recovers the area; estimated quadrature error cannot certify unseen structure."
output PeakProfile = MAKEARRAY(101, 2, (row, col) => col = 1 THEN PeakCenter + (row - 51) * PeakWidth / 10 ELSE EXP(-(((row - 51) / 10)^2)))
output ScenarioGuide = "Save Baseline, double PeakWidth, compare recovered area with Reference, then restore. Plot PeakProfile using column 1 for position and column 2 for height, with unsmoothed segments. Save and reopen .gridoc."

Charts_1!type = "charts"
Charts_1!config = <toml>
  version = 1
  kind = "charts"
  title = "Known localized peak"
  [layout]
  x_axis = "Position"
  y_axis = "Integrand"
  [[charts]]
  type = "line"
  smooth = false
  bind = "PeakProfile"
  x = "0"
  y = "1"
  label = "Known Gaussian structure"
</toml>

END MODEL