Native ordinary 3SUM host with a concrete finite Exact Triangle callee

Decision.runs_input starts with actual signed-encoded State.init input, executes complete Chan–He preprocessing, reads its raw output table/count/common length, and invokes a caller-safe native Convolution host for every actual payload. It returns the existing integer 3SUM verdict: three distinct input positions summing to zero, with equal values permitted.

For each fixed magnitude exponent and concrete certified finite Exact Triangle block, there is one finite standard-basis program with a fixed register count independent of input length and physical width. The actual callee code must meet Host.Callee's explicit matrix/width/frame/time contract on arbitrary old scratch memory. Host.Slow.callee proves that this contract is inhabited by a finite exhaustive native program, without a solver oracle.

The positive threshold Decision.width is logarithmic in the original input length; it derives all intermediate and address fits. Every prefix at every wider admitted width has polynomial word magnitudes and memory support. Decision.cost charges preprocessing, every catalogue and loop operation, every matrix builder and every callee instruction at the actual packed size.

This conditional host is not a fast Exact Triangle solver. The unconditional truly subquadratic native 3SUM algorithm, its final asymptotic composition and published exponent 1.9992 remain open. No curated headline changes here.

Main definitions

This import-only module re-exports these definitions:

• Decision.flatProgram: one actual finite ordinary 3SUM host per exponent and callee.
• Host.Callee: explicit actual finite-code protocol and certification requirements.
• Host.Slow.callee: fully proved finite exhaustive native Exact Triangle instance.
• Decision.cost, Decision.width: compositional charged time and global physical width.

Main results

It also re-exports these results:

• Decision.exec_input, Decision.runs_input: exact initialized native verdict and real run.
• Decision.intermediates_polynomial, Decision.space_polynomial: every-wide-prefix bounds.

The finite mathematical reduction and underlying Convolution builder retain their existing Anthropic source credit. The caller-owned layout, ordinary native composition and exhaustive callee are original.