fix(distillation): publish consistent Naphtali-Sandholm state

[EvenSol]

Synchronize accepted tray inlets and terminal duties, preserve stream identity, and qualify energy diagnostics against the final public material state.

Add balance, warm-state, fail-closed, and sequential-reference regressions.

Refs #3698

AI-assisted implementation and validation.

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[EvenSol]

Exact-head repair and qualification evidence

Head: 99f479b981ef7dad8d0db14d313ac7b1947b89f4

• Previous head 11ee742bc22be3579a04b5cf4c78f531cbfbe2a2 failed two branch-attributable slow tests because sequential solvers evaluated reconciled product streams against stale terminal duties.
• The one permitted repair updates only DistillationColumn.finalizeSolve to refresh calculated reboiler and condenser duties before evaluating the published-state energy balance. Solver algorithms, tolerances, public APIs, and frozen feature scope are unchanged.
• The repair clears ColumnSpecificationTest.multicomponentProductFlowSpecificationHonorsMassUnit; slow shard 2 passes.
• Slow shard 1 still fails deterministically at DistillationColumnTest.adaptiveSolverRecordsSolveMetrics:471: getLastEnergyResidual() remains non-finite for the compact metrics column.
• Java 8 and Java 21 fast tests on Ubuntu and Windows, slow shards 2–4, Javadocs, agent checks, benchmark, documentation, formatting, PaperLab, CodeQL, and pre-commit pass.
• Frozen nine-file scope remains intact with no Huldra overlap.
• Open, non-draft, and mergeable with no reviews or unresolved threads.
• The repair allowance is consumed; no second source mutation or rerun was performed.

Autonomous portfolio occupancy is 5/10, below the ten-capability ceiling.

No new PR, merge, rebase, master synchronization, Huldra change, or scope expansion was performed.

VALIDATION BLOCKED — NON-FINITE PUBLISHED ENERGY METRIC REMAINS.