Graph robustness and repeated-scan boundaries

Use an iterative component search for NNL graphs, avoiding recursion-stack exhaustion on long components.
Exclude used MST edges with infinity instead of a fixed finite distance; reject disconnected residual graphs explicitly. Normal-scale tie ordering is retained.
Align repeated-observation OET/WET nonpositive-threshold analytic output with ordinary scans, returning the conservative value 1 independently for average and union components.

Numerical stability fixes

Evaluate the skewness-correction root with its continuous zero-skewness limit, avoiding cancellation near zero.
Combine MET tails without subtracting from one, preserving very small positive p-values.
Apply both fixes to ordinary and repeated-observation single-change and interval scans. Defaults, graphs, scan statistics, permutations and extrapolation domains are unchanged.

Integrated performance implementation

Preserve default methods and outputs with native MST/distance and exact graph-count kernels; batch single-change adjacency assembly.
Keep scalar accumulation for x3 when an exact-in-double bound cannot be established.

gSeg 1.2

Fixed the documented statistics = "max" alias in analytic scan calls.
Reject dist objects in x instead of silently recomputing distances between distance-matrix rows; use dissimilarity = ....
Reject non-converged analytic quadrature and invalid analytic probability outputs explicitly. Existing skew-correction fallbacks remain available.
Repeated-observation interval MET no longer silently substitutes zero for an undefined weighted component.
Validate that requested k-MST layers produce exactly k*(N-1) distinct edges; fail explicitly if the underlying constructor reuses exhausted edges.
Fixed changed-interval maximizer indexing and restricted all tied maximizers to the requested interval-length range, including repeated-observation scans.
Corrected returned GET permutation paths and tied permutation tail curves.
Reject undefined candidate scan locations instead of silently dropping non-finite permutation maxima, which could yield spuriously small p-values.
Reject zero-width ranges for analytic scan approximations; permutation calibration remains available for those restricted ranges.
NNL construction excludes self-links under zero-distance ties, validates inputs/layer counts, and detects exhausted layers.
Fixed mixed named/positional legacy graph calls, including gseg1(n, E=E) and gseg1(n=n, E) (and the corresponding gseg2 calls).
Supplying k with an explicit graph now raises an error rather than silently ignoring it. Set k only when constructing a graph from data/dissimilarities.
Reworked package documentation and examples around the main data-level calls, with explicit graph entry points and a migration guide.
gseg1() and gseg2() now accept observations or dissimilarities directly.
Added explicit gseg1_graph() and gseg2_graph() functions for supplied similarity graphs.
Calls using the earlier gseg1(n, E, ...) and gseg2(n, E, ...) forms remain supported.
gseg1_data() and gseg2_data() remain available as aliases.
The main data-level calls construct a k-MST with k = floor(sqrt(N)) by default and report MET.

gSeg 1.1

Added data-level gseg1_data() and gseg2_data() interfaces.
The data-level interfaces use a k-MST with k = floor(sqrt(N)) by default.
Default calls report MET. GET, OET, and WET remain available through the explicit statistics = "g", "o", or "w" options, or together through statistics = "all".
Existing graph-level interfaces remain available.
Monte Carlo permutation p-values use the standard plus-one correction.
Corrected changed-interval permutation output so that it retains one scan maximum per permutation and uses all B maxima to compute the p-value.
Added explicit checks for analytic small-sample limits, degenerate graphs, duplicate edges, and malformed inputs.