[sf624]

Step 3.2 of docs/design/refactor.md, layer 3 of 3 (stack: #240 → #241 → #242). Also updates the traceability rows S2, S5, S7.

Addresses: S2 (the leftovers of 2.6 given to 3.2)

• Integers at start: OPTIND, RANDOM, SRANDOM and HISTCMD have the integer attribute in the start state (INTEGERS_AT_START, vars.ts; also the baseline of test/state-probes.test.ts), and text given to an integer runs through the walk's arithmetic with what it assigns (WalkArith.integer): OPTIND='x=5' and declare -i n; n='x=5' set x in the state, as bash does (before, x kept its value). test/state.test.ts "runs the text given to an integer as arithmetic…" (bash rows, including unset OPTIND, local OPTIND, 64-bit wrap and an error). OPTIND=1 keeps status 0.
• =~: its right side is read with expansions (wordIn(…, 'regex'), quoted characters escaped as bash does) and decided when it matches plain text (plainRegex): p=b; [[ abc =~ $p ]], "$p", ^a$p, a\.c. test/conditions.test.ts rows against bash.
• $(( )) in conditions: run with the walk's arithmetic (ValueSource.arith), not the constant evaluator: false; [[ $(( $? + 1 )) == 2 ]] is decided. (A name arithmetic reads stays untrusted by the scan, so n=2; [[ $(( n + 1 )) == 3 ]] is not.)
• Cost per read: a plain word is its own value at once, commandName is kept per node, the walk reads a tree's definitions in one pass. esbuild bundle, main → this stack (medians): a 1,801-line script of conditions 145 → 112 ms, bash_completion 95 → 84 ms, the fixtures 15 → 11 ms.

Not reproduced: the chain of functions where f_i calls f_{i-1} in $( ) and f_{i-2} outside (with and without set -e, several body shapes) stays at 2–20 ms for 40 functions, before and after; no timing test added.

Probe tests and test/decisions.test.ts unchanged (only the probe baseline now comes from vars.ts); fixture dumps unchanged. Node 24 coverage 100%, snippets check clean. CHANGELOG: New (=~, $(( ))) and Fixed (integers).

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[github-actions]

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