War and Peace: A Source-Generated Terminal Theorem

This paper proves constructive completeness of peace for open social worlds, establishing impossibility theorems and exact characterisations across five institutional boundaries. In the responsibility-reattachment comparison, conflict destroys material. The initiator gains when the shifted liability exceeds the destruction they bear. Once spendable capacity falls below the least eliminating rate, no ex post liability rate deters war (judgment-proof obstruction), while under incomplete observation a single prior policy's optimal guarantee equals the infimum of local observation-fibre suprema and is attained iff every binding fibre attains it. Under the old single-signature compiler erasing cross-community consent, unilateral return credits nothing whereas a cross-community receipt opens an equal reverse debt at the position it clears, keeping total unpaid reparation non-decreasing; the damage guard forwards exactly the lawful zero-damage requests as the widest safe admission. Without priority scheduling, zero-material stop inputs stall a lodged withdrawal forever within bounded time; priority yields sharp completion and anti-filibuster hourly progress bounds, and crossing an emergency hard deadline bars grants across all suffixes. For arbitrary participants, goods, technologies, and admitted histories, sustainable joint settlement holds iff the viable clearing domain is nonempty, attaining minimum visits. Verified post-settlement stock directly opens open-syntax peaceful continuation: zero-debit policy proposals can strip personal exits under an unchanged old quote word and evade any given finite adaptive duration query tree via out-of-sample alteration—ruling out static and finite-sample classifiers; dynamic prepaid verification triggers minimal semantic extensions that strictly shrink unsealed vulnerabilities, preserve every native word, impose strict net losses on overreaching or proxy probes, and erase zero-fee probes. Pending signatures, shortages, and delayed evidence are handled by paid due continuation, width-complete recipe search, and receipt transport. At the execution layer, safe stock-identical permuted replays refute snapshot criteria, and each parent head uses 3f + 1 = 4 (f = 1) quorum intersection, certifying handovers by three outgoing votes and four incoming source replays. Role-seal fault budgets pre-check maximal obtainable evidence first, and before replay completes, three honest outgoing seals dispose of stalled attempts without deadlock even if 0/4 nominees respond. Under reliable exclusion and exclusion-gated vote changes, arbitrarily many handovers, withdrawals, and reassignments keep finite certified histories prefix-comparable and infinite continuations identical at every index across possibly disjoint rosters; the same six-unit ledger runs continuously through productive settlement, two language revisions, deployed staging, cold recovery, and four-host handovers from clock 12 to clock 28.