fix 1

openspec/specs/client-authoritative-player-state/spec.md

@@ -13,11 +13,12 @@ The client SHALL keep one explicit owned authoritative `PlayerState` snapshot fo
 - **THEN** presentation and diagnostics read authoritative `position`, `rotation`, `hp`, and optional `velocity` from that owned snapshot
 
 ### Requirement: Local player reconciliation applies the full authoritative state by tick
-The controlled client SHALL continue reconciling local prediction from authoritative `PlayerState` snapshots while keeping authoritative HP and optional velocity synchronized with the owned player-state snapshot. Reconciliation MUST use the acknowledged movement-input tick defined by the sync strategy, and the visible controlled-player transform MUST keep authoritative gameplay truth separate from short-lived visual correction state. Small divergence after replay MUST converge through explicit bounded correction state, while large divergence or failed convergence MUST still snap immediately to authoritative `position` and `rotation`.
+The controlled client SHALL continue reconciling local prediction from authoritative `PlayerState` snapshots while keeping authoritative HP and optional velocity synchronized with the owned player-state snapshot. Reconciliation MUST use the acknowledged movement-input tick defined by the sync strategy, and the visible controlled-player transform MUST keep authoritative gameplay truth separate from short-lived visual correction state. **Replay of pending inputs during reconciliation MUST use fixed-step substeps matching the server authoritative movement cadence, producing identical trajectory to live prediction for the same input sequence.** Small divergence after replay MUST converge through explicit bounded correction state, while large divergence or failed convergence MUST still snap immediately to authoritative `position` and `rotation`.
 
 #### Scenario: Local authoritative state corrects predicted presentation
 - **WHEN** the controlled player accepts an authoritative `PlayerState` whose acknowledged movement-input tick is `N`
 - **THEN** local reconciliation prunes or replays predicted movement using tick `N` according to the sync strategy
+- **THEN** the replay uses fixed-step substeps matching the server authoritative movement cadence
 - **THEN** the controlled player's authoritative gameplay state updates immediately to the accepted `position`, `rotation`, HP, and optional velocity
 - **THEN** the local player's visible transform may temporarily differ only through bounded visual correction state that converges back to the authoritative baseline
 
@@ -31,6 +32,12 @@ The controlled client SHALL continue reconciling local prediction from authorita
 - **THEN** the controlled player's visible transform snaps immediately to authoritative `position` and `rotation`
 - **THEN** any temporary visual correction state is cleared before later local prediction resumes from that authoritative baseline
 
+#### Scenario: Replay produces identical trajectory to live prediction
+- **WHEN** the controlled player replays pending inputs after accepting authoritative `PlayerState`
+- **THEN** the replay applies inputs in fixed-duration substeps equal to the server authoritative movement cadence
+- **THEN** the final predicted pose equals what live `FixedUpdate` prediction would produce for the same input sequence
+- **THEN** the result is stable across multiple replays of the same input sequence
+
 ### Requirement: Remote players apply authoritative state without inventing gameplay truth
 Remote player presentation SHALL consume the accepted authoritative player-state snapshot owned by the client and MUST NOT invent HP or final gameplay state locally. Remote movement presentation MUST smooth authoritative position and rotation through a small buffered snapshot interpolation path instead of applying only the latest snapshot directly. Stale remote `PlayerState` packets that are older than the latest accepted authoritative tick for that player MUST NOT overwrite the owned snapshot or enter the interpolation buffer.