two-paths-structure-lethal-weapon Lethal Weapon (1987)
Quadrant. Better tools, sufficient — classical comedy / redemption arc inside a buddy-cop surface.
Initial approach. Police work as suicide-deferred. Riggs uses lethality as the tool that delays the hollow-point bullet he keeps in his trailer for himself; the job is the reason he hasn't pulled the trigger yet.
Post-midpoint approach. Lethality re-grounded in someone-to-live-for. The same skill set, now aimed at protecting Murtaugh's family instead of at auditioning for his own death.
Equilibrium. Roger Murtaugh's fiftieth-birthday family breakfast in the Murtaugh kitchen. Trish, Rianne, the two younger kids — cake, candles, presents, "Make a wish." The film's home base, the unit Riggs's arc will eventually move toward.
Inciting Incident. Michael Hunsaker phones Murtaugh at the precinct about his daughter Amanda. The call is the polite request a Vietnam buddy makes that the partner-cop can't refuse — and that Hunsaker is calling at all is the disruption.
Resistance / Debate. Murtaugh told he's being assigned a new partner from narcotics — Riggs — and reacting to the dossier (suicidal, ex-Special-Forces, "lethal weapon"). The trailer-introduction sequence, the squad-room first meeting, and the rooftop jumper stunt where Riggs handcuffs himself to a man on the ledge and steps off. Murtaugh tries to keep the partnership at arm's length while the case opens.
Commitment. The trailer confrontation. Riggs has eaten his own gun barrel and Murtaugh has come to talk to him; Riggs pulls out the hollow-point bullet he's saved for the job, hands Murtaugh his service weapon, dares him to do it. Murtaugh refuses. The two men go get something to eat. The partnership is now mutual.
Rising Action. The Beverly Hills meal-ticket address, the dealer trail, the pool-house raid where Riggs takes a hostage at gunpoint, the Dixie identification and the booby-trapped house. Procedural lethality at full output, the case treated as a homicide investigation. Adrian-style parallel: Riggs starts being invited to the Murtaugh house, eats Trish's cooking, meets Rianne.
Escalation 1. Joshua introduces himself at the General's pool by holding his bare forearm into a butane flame at the General's request. The antagonist is established as Riggs's mirror — lethality calibrated by self-mortification. The Dixie-house bomb that follows (mercury switches, professional ordnance) accelerates the case toward the conspiracy reveal.
Midpoint. Outside the memorial service at Hunsaker's hilltop home. Hunsaker tells Murtaugh the case is Shadow Company, Air America, a heroin operation that ran out of Laos and reactivated stateside. He names the unit, names the players, says he's ready to talk — and a Shadow Company helicopter (Delta One) crests the bluff as Joshua kills Hunsaker before the operational details land. The case re-specifies in one bounded scene: not a homicide, a war. Riggs's lethality finds a target it was trained for.
Falling Action / new approach. Riggs and Murtaugh treat the case as the war it is. Riggs gathers the bomb-fragment evidence at Dixie's, identifies the mercury-switch CIA signature, recognizes Joshua's Special Forces tattoo. The new approach is named when Riggs explains to Murtaugh what they're up against: "These are real pros. Same setup as the war." From here the case is fought as a Shadow-Company op rather than a homicide.
Escalation 2. The kidnapping. Joshua takes Rianne off the street; Riggs and Murtaugh walk into a sunrise handoff at the Victorville dry lake and are taken alive (Riggs shot and presumed dead). Murtaugh and Rianne are brought to a Hollywood Boulevard nightclub basement (a Shadow Company front); Riggs (the dry-lake "kill" was incomplete) is hung in chains under Endo's electric-shock rig in one room while Murtaugh is worked over in another. Riggs dislocates his shoulder to slip the wrist chains, kills Endo, frees Murtaugh and Rianne. The new approach is staged in miniature — Riggs's lethality used to protect Murtaugh's family — and the cost is shown.
Climax. The front-lawn hand-to-hand fight at the Murtaugh house. Joshua has come to finish the job at home; Riggs meets him on the grass while Murtaugh and the LAPD ring the perimeter. Riggs gets Joshua in a chokehold and the cops chant break his neck — Riggs releases. The arresting officers move in and Joshua breaks the hold, snatches an LAPD officer's revolver. Riggs and Murtaugh shoot him together. The post-midpoint approach is tested at maximum stakes (kill-because-you-want-to vs. kill-because-the-family-is-in-the-line) and holds. The lethality is re-grounded in the partnership.
Wind-Down. Christmas Eve at the Murtaugh house. Riggs hands Trish the hollow-point bullet on the doorstep — "Tell him I won't be needing it anymore" — turns to leave. Murtaugh calls him back: "If you think I'm gonna eat the world's lousiest Christmas turkey by myself, you're crazy." Riggs steps inside. The new equilibrium is the Murtaugh family unit with Riggs in it. The bullet that was for the job of killing himself has been handed away.