proof/: add physics diagnostic/benchmark/pipelining coverage

StarForth_Physics_Diagnostic_Words.thy (physics_diagnostic_words.c):
3 of 4 words are pure-printf identity transitions; PHYSICS-BURN's guard
modelled, its arbitrary dynamically-selected func-pointer execution loop
is a new class of gap (not reducible to any prior one).

StarForth_Physics_Benchmark_Words.thy (physics_benchmark_words.c):
hot-words cache is a whole unmodelled subsystem. PHYSICS-RESET-STATS's
pipeline_metrics half (3 real vm_state fields) modelled; everything else
in the file deferred.

StarForth_Physics_Pipelining_Diagnostic_Words.thy
(physics_pipelining_diagnostic_words.c): root-cause finding --
`word_transition_metrics` has been a declared record type in
StarForth_Base.thy since early in the sweep but was never wired into
`dict_entry` as a field, so every word in this file touches state with
zero abstract representation. Three no-arg words modelled as identity
(with an explicit caveat that this reflects the model's blind spot, not
a no-op claim about the C); the three lookup words get only their
simplest empty-stack underflow case.

Suite now 43 theories, green.

proof/StarForth_Physics_Benchmark_Words.thy

@@ -0,0 +1,109 @@
+theory StarForth_Physics_Benchmark_Words
+  imports StarForth_Base
+begin
+
+(* =========================================================================
+   Mirrors: src/word_source/physics_benchmark_words.c
+   Registers: BENCH-DICT-LOOKUP PHYSICS-CACHE-STATS PHYSICS-TOGGLE-CACHE
+              PHYSICS-RESET-STATS PHYSICS-BUILD-INFO PHYSICS-BAYESIAN-REPORT
+
+   ── Hot-words cache -- a whole unmodelled subsystem ─────────────────────
+   Every word in this file reads or writes `vm->hotwords_cache` (a
+   `HotwordsCache*`) and/or its nested `HotwordsStats` -- neither has any
+   counterpart in vm_state. This is the same class of gap as the block-
+   window cache StarForth_Block_Words.thy/StarForth_Editor_Words.thy
+   already deferred (own subsystem-modelling project, not a one-word
+   extension), just for a different cache.
+
+   ── Scope ─────────────────────────────────────────────────────────────
+   PHYSICS-RESET-STATS is the one partial exception: alongside its
+   unmodelled `hotwords_stats_reset` call, it ALSO resets three
+   `pipeline_metrics` fields that ARE in vm_state
+   (`pm_prefetch_attempts`/`pm_prefetch_hits`/`pm_tuning_checks`). Modelled
+   assuming the (unmodelled) cache-initialized guard is reached -- i.e.
+   this states the word's effect on `pipeline_metrics` conditional on
+   control reaching that point, not the guard itself.
+
+   BENCH-DICT-LOOKUP's guard/pop shape is modelled (same pattern as
+   COMPARE-LOOKUPS/PHYSICS-BURN); its benchmark body is not (timed
+   `vm_find_word` loop, same FIND-family gap, PLUS the hot-words cache
+   gap above).
+
+   PHYSICS-CACHE-STATS, PHYSICS-TOGGLE-CACHE, PHYSICS-BUILD-INFO, and
+   PHYSICS-BAYESIAN-REPORT are entirely reads/writes of the unmodelled
+   cache subsystem (or pure stdout using only compile-time constants) --
+   not modelled at all.
+   ======================================================================== *)
+
+(* ── BENCH-DICT-LOOKUP ( iterations -- ) : guard/pop only ────────────────── *)
+
+definition forth_bench_dict_lookup_guard :: "vm_state \<Rightarrow> vm_state" where
+  "forth_bench_dict_lookup_guard vm =
+    (case data_stack vm of
+       []     \<Rightarrow> set_error vm
+     | n # xs \<Rightarrow> vm\<lparr>data_stack := xs\<rparr>)"
+
+lemma bench_dict_lookup_underflow:
+  assumes "data_stack vm = []"
+  shows "vm_error (forth_bench_dict_lookup_guard vm)"
+  by (simp add: forth_bench_dict_lookup_guard_def set_error_def assms)
+
+lemma bench_dict_lookup_pops_one:
+  assumes "data_stack vm = n # xs"
+  shows "data_stack (forth_bench_dict_lookup_guard vm) = xs"
+  by (simp add: forth_bench_dict_lookup_guard_def assms)
+
+lemma bench_dict_lookup_body_not_modelled: True
+  \<comment> \<open>iterations \<ge> 1: timed vm_find_word loop over the hot-words cache --
+     both the FIND-family gap and the cache-subsystem gap above.\<close>
+  by simp
+
+(* ── PHYSICS-RESET-STATS ( -- ) : pipeline_metrics half only ─────────────── *)
+(* C: guarded by `if (!vm->hotwords_cache) { ...; return; }` (unmodelled);
+   once past that guard: hotwords_stats_reset(...) (unmodelled, cache
+   subsystem) THEN three real vm_state field writes:
+     vm->pipeline_metrics.prefetch_hits = 0
+     vm->pipeline_metrics.prefetch_attempts = 0
+     vm->pipeline_metrics.window_tuning_checks = 0
+   Modelled as the pipeline_metrics update alone, conditional on the guard
+   having been reached (not itself expressed, since "cache initialized"
+   has no vm_state predicate). *)
+
+definition forth_physics_reset_stats_metrics :: "vm_state \<Rightarrow> vm_state" where
+  "forth_physics_reset_stats_metrics vm =
+     vm\<lparr>pipeline_metrics := (pipeline_metrics vm)
+          \<lparr>pm_prefetch_hits := 0, pm_prefetch_attempts := 0, pm_tuning_checks := 0\<rparr>\<rparr>"
+
+lemma physics_reset_stats_clears_pipeline_counters:
+  "pm_prefetch_hits     (pipeline_metrics (forth_physics_reset_stats_metrics vm)) = 0"
+  "pm_prefetch_attempts (pipeline_metrics (forth_physics_reset_stats_metrics vm)) = 0"
+  "pm_tuning_checks     (pipeline_metrics (forth_physics_reset_stats_metrics vm)) = 0"
+  by (simp_all add: forth_physics_reset_stats_metrics_def)
+
+lemma physics_reset_stats_preserves_other_pipeline_fields:
+  "pm_last_window_size    (pipeline_metrics (forth_physics_reset_stats_metrics vm))
+     = pm_last_window_size    (pipeline_metrics vm)"
+  "pm_last_accuracy_num   (pipeline_metrics (forth_physics_reset_stats_metrics vm))
+     = pm_last_accuracy_num   (pipeline_metrics vm)"
+  "pm_last_accuracy_den   (pipeline_metrics (forth_physics_reset_stats_metrics vm))
+     = pm_last_accuracy_den   (pipeline_metrics vm)"
+  "pm_suggested_next_size (pipeline_metrics (forth_physics_reset_stats_metrics vm))
+     = pm_suggested_next_size (pipeline_metrics vm)"
+  by (simp_all add: forth_physics_reset_stats_metrics_def)
+
+lemma physics_reset_stats_data_stack_unchanged:
+  "data_stack (forth_physics_reset_stats_metrics vm) = data_stack vm"
+  by (simp add: forth_physics_reset_stats_metrics_def)
+
+(* ── Everything else -- NOT MODELLED ──────────────────────────────────── *)
+
+lemma cache_stats_not_modelled: True       \<comment> \<open>PHYSICS-CACHE-STATS: reads hotwords_cache subsystem, stdout only.\<close>
+  by simp
+lemma toggle_cache_not_modelled: True      \<comment> \<open>PHYSICS-TOGGLE-CACHE: flips hotwords_cache->enabled -- outside vm_state.\<close>
+  by simp
+lemma build_info_not_modelled: True        \<comment> \<open>PHYSICS-BUILD-INFO: stdout of compile-time constants + hotwords_cache read.\<close>
+  by simp
+lemma bayesian_report_not_modelled: True   \<comment> \<open>PHYSICS-BAYESIAN-REPORT: reads/synthesizes HotwordsStats, stdout only.\<close>
+  by simp
+
+end