Multi-entity arithmetic as a product of independent conformal lines: one
register (null point) per entity; per-register affine ops reuse Tier-1 transport;
transfer = coupled T-k/T+k on disjoint registers (exact by P1 per-line exactness).
Transactional atomicity: immutable register mapping, prepare->validate->commit —
both candidate states relaxed into locals, validated (both converged AND
conservation), then a NEW mapping only on full success. Failure anywhere = new
mapping never built, original untouched (no partial mutation, no rollback); abort
raises typed MultiRegisterError and aborts the whole program (fail-closed).
Conservation pin = hard-reject, RELATIVE (|after-before| <= rtol*max(1,|before|)):
decoded-quantity error scales with magnitude (found via gma-050 chaining to 222),
so absolute tol is wrong; relative still catches real violations (off by whole k).
Content-addressed MultiRegisterRecord chain carries entity + certificate id +
step, never a decoded value; GENESIS-linked; verify_multi_register_chain mirrors
verify_replay_chain. Tier-2a fail-closed taxonomy: total-unknown (needs summation
= 2b), derived operand, non-affine kind, non-positive scale, unit mismatch,
unknown endpoints. Off-serving (A-04).
REAL GSM8K single-entity refused holdout: 18/18 solved wrong=0 (26/50 -> 44/50).
11/11 pins green.
[Verification]: uv run python -m pytest tests/test_adr_0250_multi_register.py -q
