Function grouping - #551
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Several functions can now be proven by ONE circuit: the members are walked like branches of a single function - auxiliary columns and lookup slots are shared across members (the same save/restore sharing match arms already use), selector columns are laid out consecutively per member, and every member folds its selector-gated return message (carrying its own function index) into the shared lookup slot 0 against a single shared multiplicity column. One extra constraint enforces cross-member exclusivity: the sum of the members' top-block selectors must be boolean. Callers are untouched - calls still target function indices on the function channel - so grouping is invisible to execution, the query record, and the interpreter. Grouping is a CIRCUIT-level choice, not a property of the function library, so there is no source annotation: Source.Toplevel.compile builds the default singleton partition (Bytecode.Toplevel.circuits, one circuit per constrained function - behavior-identical to before), and CompiledToplevel.groupFunctions optionally regroups it by function NAME (validated: known, constrained, non-entry, no duplicates). The merged layout is max inputs, summed selectors, max auxiliaries, max lookups - so grouping fits rarely-called functions of similar shape: each (rare) row pays the group's selector count while the system sheds one circuit (vk entry, commitment matrix, verifier work) per absorbed member. Rust consumes the partition directly (bytecode Circuit via FFI; constraints/trace/synthesis iterate circuits, witness rows concatenate the members' queried rows in member order). The stage-2 lookup group size and the branchless raw-argument rule now key on the CIRCUIT layout: multi-member circuits are branching by construction, so their arguments are selector-superposed exactly like match arms. Tests: the aiur suite proves the same toplevel twice - ungrouped and with a 3-member test group (different arities, matches, cross-member call, recursion) - plus structural checks on the partition (members, merge-rule layout, every constrained function in exactly one circuit). All suites pass unchanged (ixvm FFT pins identical - the default partition is behavior-neutral); codegen is unaffected (execution ignores the partition).
…ions) Route every site that compiles the IxVM kernel or the recursive-verifier toplevel for proving/verifying through `compileWithGroups` with a per-toplevel grouping datum (`IxVM.coldGroups`, `MultiStark.verifierColdGroups`) - CLI check/prove/verify, the ixvm test runner, the recursive-verifier tests, and the benches. `groupFunctions` resolves members by STRING name (the exact `toString` of the Global, the inverse of what statistics print, so measured groupings feed back verbatim). Both partitions start EMPTY, i.e. singleton circuits - behavior-identical to before; the data files are the single knob later commits turn.
Add Sel/Aux/Lkp columns (the circuit layout's selectors, auxiliaries, lookups; zero for memory/gadget rows) to the per-circuit statistics table. Grouping instrumentation only: merging is cheapest between circuits whose auxiliaries and lookups are CLOSE (both merge by max, selectors sum), so these columns are what a partition builder needs next to the width. Meant to be reverted once the partitions are chosen - this commit is self-contained in Ix/Aiur/Statistics.lean.
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Rebuilt from fresh String.split / Array.extract_append kernel-check profiles on the post-xor-split circuits (the pre-rebase groupings were discarded as obsolete). Same conservative heuristic as before: cold = max FFT share < 0.5% across the workloads (668 of 709 function circuits), banded while aux stays within 1.6x, lookups within max(2x, +4), and summed selectors <= 40; verify_claim excluded. 85 bands over 630 circuits: 730 -> 185 circuits, total committed width 33,331 -> 15,763 (-53%), at +13.6% (String.split) / +8.8% (Array.extract_append) measured FFT cost. Kernel pins re-measured (median +10.4%, shard +9.1%). Profiles, band data, and methodology in cold-groups/.
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Circuit-level function grouping; grouped kernel and verifier partitions
Several rarely-used functions can now share ONE proving circuit instead of
each committing its own. Grouping is a circuit-level choice (no source
pragma): the bytecode, execution, and query record are untouched, and
callers still target function indices on the function channel, so claims
are partition-agnostic. A merged circuit branches on per-member function
selectors and takes the max of the members' auxiliary columns.