Sarga 14–15: the first challenge-duel — Rāma cannot loose: the brothers, identical in the melee, cannot be told apart (so he says; the tradition adds that he would not risk the error). Sugrīva, mauled, flees and reproaches him; a garland of gajapuṣpī marks him for the second bout. Sarga 16: Tārā's counsel to Vāli — do not go; Sugrīva returning so soon means backing, and the backing is Rāma, of whom the reports are terrible; make Sugrīva yuvarāja instead. Vāli's reply is his epitaph: he cannot refuse a challenge, and Rāma, being dharma itself, will do him no wrong. He goes. The arrow takes him in the chest mid-grapple.
The indictment and the defense
Sarga 17, Vāli dying: a prosecution in full form — I was in combat with another; you struck unseen, unprovoked, unannounced; kings hunt with proclamation, kṣatriyas duel face to face; you wear dharma as a grass-covered well. Sarga 18, Rāma's answer: this land is Ikṣvāku jurisdiction under Bharata, and we execute its law; your crime — living in your brother's wife Rumā as in a daughter-in-law — is capital under that law (aurasīṁ bhaginīṁ vāpi…); judgment is not a duel, and the executioner owes the condemned no face; further, you are a branch-ranging creature whom kings take by snare and concealment without adharma — and I had given Sugrīva my word. Sarga 19–26: Vāli accepts the verdict wholly, asks protection for Aṅgada and pardon for Tārā, and dies at peace; Tārā's lament (sargas 19–24 passim) is among Vālmīki's greatest women's speeches; Sugrīva is crowned, Aṅgada made yuvarāja, and Rāma — keeping his own exile's maryādā — will not enter the city, wintering instead on Prasravaṇa.
Maryādā Puruṣottama — read both briefs, then note the frame
Vālmīki refuses to make this easy: Vāli's speech is written at full strength and never rebutted line-by-line. Rāma's position reduces to rājadharma (magistrate, not duellist — the condemned has no claim on the executioner's frontality) plus satya (the vow to Sugrīva). The deliberate mirror is the study-key: Rāma punishes in Vāli exactly the offence — a brother's wife appropriated — that Rāvaṇa is committing against him; Kiṣkindhā is Laṅkā's dress rehearsal, and the sentence passed here is the sentence coming there. Whether the concealment was maryādā or its breach is the argument Vālmīki bequeaths, unresolved, to every generation of readers — perhaps deliberately: a tradition that must keep arguing about dharma is a tradition in which dharma stays alive.
Kamba Rāmāyaṇam differs
Kambar cannot leave the wound open. His Vāli-vadhaip paṭalam expands the debate and resolves it devotionally: Vāli comes to recognize the archer as the Lord, and the arrow in his chest as grace — death at that hand being liberation. Tamil tradition reads Vāli's end as a mokṣa-scene; Vālmīki's Vāli dies a satisfied litigant, Kambar's a realized devotee. Same arrow, two theologies.