Uniform (kappa) calibration of the field interval — fs_mr_field

Computes, at analysis time and from the trial's own influence structure, the smallest widening factor kappa on kappa_grid such that the two-sided field interval c + kappa * (q - c) attains 1 - alpha coverage uniformly over a winner-profile protection family: hypothetical true fields equal to the gate's shrunk field w with the winner's entry set to max_{g != winner} w_g + delta * sigma_sel, for delta on delta_grid (in SE units of the winner). Nothing is tuned to any simulation design.

Usage

fs_mr_field_uniform(
  B = NULL,
  Sigma = NULL,
  w,
  sel,
  sigma_sel,
  p_hat,
  t_g = NULL,
  reselection = "maxeff",
  sz = NULL,
  effect_neighborhood = 0.1,
  selection_rule = "neighborhood",
  log_scale = TRUE,
  sdv = NULL,
  zcons_c = NULL,
  delta_grid = seq(0, 4, by = 0.5),
  mass = 0.99,
  M_cap = 40L,
  R_rep = 300L,
  R_out = 300L,
  R_in = 150L,
  alpha = 0.05,
  kappa_grid = seq(1, 3, by = 0.01),
  seed = NULL
)

Arguments

B: Optional n x K influence matrix (the gate's asm$B); multiplier perturbations are crossprod(B, rnorm(n)), covariance t(B) %*% B.
Sigma: Optional K x K covariance, used when B is NULL (the reference checks); perturbations via its Cholesky root.
w: Numeric K: the gate's shrunk field (beta_hat with the winner's entry replaced by the de-biased estimate), working scale.
sel: Integer: the winner's index in w.
sigma_sel: The winner's SE on the working scale (sdv[sel]).
p_hat: Numeric K: re-selection frequencies from the gate's multiplier pass (tabulate(winner)/draws).
t_g: Numeric K admission floors, or NULL for no admission filter (the gate's resolved t_g, restricted with the candidate set).
reselection, sz, effect_neighborhood, selection_rule, log_scale: The gate's selection-map configuration; zcons_c, when non-NULL, is the consistency centre c_cons and sdv the per-candidate SEs so the maxcons score can be reconstructed on the restricted family.
sdv: Numeric K per-candidate SEs (needed only for maxcons).
zcons_c: Consistency centre c_cons, or NULL.
delta_grid: Winner-separation grid in SE units (H2 default 0-4 by 0.5).
mass, M_cap: Mass-carrying reduction controls (H3 as adjusted at the Gate 1 adjudication, 2026-09-05: cap 40, so the >= 0.99 mass target is reachable on enumerated forestsearch families; original default was 12).
R_rep, R_out, R_in: Monte Carlo sizes per delta (H4 defaults 300/300/150).
alpha: Two-sided miscoverage target (0.05).
kappa_grid: Candidate widening factors (default 1 to 3 by 0.01; the grid was extended past 2 at the Gate 1 adjudication after ceiling hits).
seed: Optional integer; drawn once at entry.

Value

List: kappa (kappa*), kappa_mcse (Monte Carlo SE of kappa* from the binding profile's binomial error and the local slope of min-delta C2 in kappa), M, mass_covered, keep (indices), minC1, C1 (profile over delta_grid), C2_k1 (profile at kappa = 1), C2_kstar (profile at kappa*), kappa_grid, C2_min (min-over-delta profile over kappa_grid), n_kept (trials with a winner per delta), delta_grid, timing_seconds.

Details

The computation restricts to a mass-carrying candidate set (the smallest M <= M_cap candidates by re-selection frequency whose cumulative share of the re-selection mass is at least mass, the winner always included), then per delta replays R_rep hypothetical trials with Gaussian multipliers of covariance exactly Sigma_hat (via crossprod(B, xi), or a Cholesky root of a supplied Sigma), applies the gate's own selection map (thresholded argmax under reselection = "maxeff", vectorized; any other rule via the per-draw .fs_mr_select path), drops trials with no winner (conditioning on detection, as in the real analysis), and runs the field procedure on each hypothetical trial to obtain the coverage profiles C1(delta) (one-sided) and C2(delta; kappa) (two-sided, widened).

The guarantee, as documented for the gate: the one-sided bound is uniformly valid; the two-sided interval widened by the returned kappa is uniformly valid over the winner-profile family; the plain quantile interval is approximate.