The composition frontier: multi-step arithmetic compiled from a MathProblemGraph
into an ordered turn program (one affine relation-well per step) and executed as
a chain of certified relaxation turns. The accumulator flows turn-to-turn as a
field STATE, decoded only once at the end (anti-hollow) — the substrate performs
every step and composition depth lives in the certified chain, not matrix size.
Verified: ((5+3)*2)-4=12, (10/2+7)*3=36, (100-40)/4=15, all turns
ground_state_certified.
Ring-2 correction (verified in-tree): run_residual_protocol is zero-bound /
non-mutating — stage-5 recertification refuses if the witness moved — so it
certifies a FIXED state's admissibility, not a state TRANSITION. Arithmetic turns
mutate. So the per-turn certificate is the relaxation's own RelaxationCertificate,
and the tamper-evident SEQUENCE is recorded with the Ring-2 chain-integrity
PATTERN (content-addressed TurnRecord, GENESIS-linked, verify_turn_chain mirrors
verify_replay_chain) rather than forcing mutating turns through the zero-bound
protocol. Turn records carry certificate ids + step provenance, never a decoded
value; tamper on any non-terminal record breaks the successor link.
Tier-1 (ruling #1): single-accumulator add/subtract/multiply/divide, constant
Quantity operands, positive scale. Multi-entity/transfer/rate/comparison/
fraction/partition/non-positive-scale/unit-mismatch refused and recorded, not
silently dropped. Off-serving (A-04).
15/15 pins green.
[Verification]: uv run python -m pytest tests/test_adr_0249_turn_program.py -q
