Caller-safe native queried thin products

Main definitions

• CallableProduct.program: fixed standard unsigned code on 163 registers, with a runtime source-memory base in register 160 and an absolute answer pointer returned in register zero.
• CallableProduct.entryProgram, CallableProduct.input: actual initialized client, with a protected caller prefix and original raw matrices/interleaved request coordinates.
• CallableProduct.windowSize: explicit polynomial virtual address-space reservation; this interval is not initialized or copied in bulk.

Main results

• CallableProduct.exec: actual caller-safe product execution from original zero/one matrices, arbitrary query occurrences and dirty scratch, with exact local-input restoration and full outside-window frame. A bounded caller state supplies physical word validity throughout.
• CallableProduct.runs_wide: actual State.init input fit, same-data prefix Runs and charged halt at every physical width at least 256*clog₂(base+N+Q+P+5), for caller-word bound P.
• CallableProduct.runs_caller, CallableProduct.caller_prefix_bounded: the corresponding callable flat run and every-prefix physical fit with P bounding all initial caller words, including dirty memory words loaded before the real remainder. In initialized clients, scratch is zero and P only needs to bound the protected caller prefix.
• CallableProduct.timeBound_le: at most three times the original charged product plus 2048*(N*D+Q+1) standalone adaptation work, including halt.
• CallableProduct.runs_thin: at L=19m, D=4^m, D^18≤N and Q*2^m≤N², the actual charge is at most 17301504*(19m+1)*N²/D^(1/18). Distinct-set sparsity instead retains an explicit additive charge for duplicate occurrences through CallableProduct.thin_timeBound.

The original product program is unchanged. MemoryWindow.compile translates each load into actual base addition, load and remainder, each store into addition and store, and preserves native branching/loop decisions. Computed logarithm/power setup and two linear normalization loops are charged. Raw zero/one input is doubled by the original actual matrix-input loop. No source-Light semantics, new ALU operation, assumed execution or fast solver is used.

The finite tensor, band and query mathematics and their source mapping remain those of QueriedProduct; the compiler and callable controller are original native work. Stage APIs are internal implementation interfaces. The concrete ET-record adapter, backend/witness composition, whole ordinary-3SUM solver and improved 1.9992 endpoint remain open under #1394.