Docs: Sync capability-syntax + capability-matrix rows post-#764 (execute ✅)

[PurHur]

Problem

North Star 1 AOT execute is green on master (#764 ✅, #1529 ✅). Contributor-facing generated capability docs still describe execute as blocked:

Source	Stale claim
script/capability-syntax-lib.php	MiniWebApp rows note execute #764; footer cites #676 as active execute gate
script/capability-matrix.php	Intro line: execute #764 for user-class link
test/unit/CapabilitySyntaxTest.php	Asserts #764 appears in generated body (intentional until this lands)

#1525 covers root README + docs/pages/development-status.md; #1531 covers examples/README.md. This issue is the generator / matrix slice so php script/capability-matrix.php --check and CAPABILITY_SYNTAX_CHECK=1 ./script/ci-fast.sh reflect reality.

Goal

Update generators + committed output so web north-star rows show AOT execute ✅ (with remaining polish tracked in #1760 / #1044 gate-flip bundle, not found via issue links — not “blocked on #764”).

Implementation hints

File	Change
script/capability-syntax-lib.php	Flip 003-MiniWebApp / PATH_INFO / deploy / CGI rows from execute #764 → execute ✅ (#764 closed); point default-off shell gates to #1760
script/capability-matrix.php	User-class intro: link closed #568; execute #764 closed
docs/capabilities.md, docs/capabilities-syntax.md	Regenerate via scripts (do not hand-edit)
test/unit/CapabilitySyntaxTest.php	Replace #764 blocker assert with #1760 or #1044 gate-flip reference

Acceptance criteria

• php script/capability-matrix.php --check exits 0 on master after regen
• CAPABILITY_SYNTAX_CHECK=1 ./script/ci-fast.sh passes (default in script/ci-defaults.env, CI: CAPABILITY_SYNTAX_CHECK=1 in ci-fast (enforce #744 regenerate) #803)
• Generated docs no longer imply 003 native execute is empty/broken

Verification (local / Docker only)

php script/capability-matrix.php --write
php script/capability-syntax.php --write
./script/ci-fast.sh --filter CapabilitySyntaxTest
docker run --rm -v "$(pwd):/compiler" -w /compiler php-compiler:22.04-dev \
  ./script/ci-fast.sh --filter CapabilitySyntaxTest

No GitHub Actions required.

Dependencies

• AOT: MiniWebApp native binary CLI execute emits empty stdout (post-link) #764 ✅ (execute landed)
• Docs: Sync North Star 1 status — README, #1044, development-status.md (#764 closed) #1525 — README / public status (parallel)
• Examples: Sync examples/README.md run matrix after #764 close #1531 — examples/README.md matrix (parallel)
• CI: North Star 1 gate-flip bundle — #1530 done; #1523 + #1752 remain before #1044 close #1760 — last default-off CI gates before 🌐 North Star 1: Web-capable PHP application (living tracker) #1044 close

Links

• ROADMAP 🗺️ ROADMAP: Self-host + web-capable PHP subset (living) #78 Phase 4 Polish
• Parent doc sync umbrella: Docs: Sync North Star 1 status — README, #1044, development-status.md (#764 closed) #1525
• CI gate: CI: CAPABILITY_SYNTAX_CHECK=1 in ci-fast (enforce #744 regenerate) #803 ✅

[PurHur]

Minor doc fix on master: docs/roadmap-wave3.md language open count 4→3 to match #1380 / batch 66 sync. Capability-matrix generator refresh still pending (execute ✅ post-#764).