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\section*{Phase~2a Session Summary: Linear Decay and Freeze Flag (November 2025)}

Phase~2a of the StarForth physics engine implementation was completed in a
single session on 2025-11-07, delivering two production features under commit
\texttt{3e87fd4b}.

\textbf{Freeze Flag (\texttt{WORD\_FROZEN}).}
A new dictionary entry flag (bit~0x04) prevents execution heat from decaying,
enabling system-critical words (\texttt{DUP}, \texttt{DROP}, \texttt{SWAP},
and eighteen others frozen by \texttt{FREEZE-CRITICAL}) to remain in the
hotwords cache across OS context switches. The flag operates independently of
the existing \texttt{WORD\_PINNED} flag.

\textbf{Linear Decay Mechanism.}
The heat decay model $H(t) = \max(0, H_0 - d \cdot t)$ was selected over an
exponential half-life model on three grounds: integer-only arithmetic (no
floating-point overhead), deterministic bounded convergence, and compatibility
with Isabelle/HOL formal verification. Decay is applied lazily at word-lookup
time, adding fewer than 5~nanoseconds of overhead per execution.

\textbf{FORTH Interface.}
Nine control words were added: \texttt{FREEZE-WORD}, \texttt{UNFREEZE-WORD},
\texttt{FROZEN?}, \texttt{HEAT!}, \texttt{HEAT@}, \texttt{SHOW-HEAT},
\texttt{ALL-HEATS}, \texttt{DECAY-RATE@}, and \texttt{FREEZE-CRITICAL}.

The implementation modified eleven files and added 2{,}236 lines (less 23
deletions). All 782 tests passed; zero compiler warnings were produced.