First step of the Engine A lift program (CLAUDE.md commits the project to a
single deterministic cognitive engine; Engine B / math pipeline was always
intentional scaffolding per math_solver.py:24). Proves the load-bearing
unknown: one arithmetic operation can be represented as a closed versor at
the required tolerance, with no new normalization and no weakened invariant.
Scope (frozen by ADR-0139):
- One operation: add
- Single-axis embedding: quantities on e1 axis
- No graph wiring, no pipeline integration, no GSM8K case routed
- Unit carried as caller metadata
Construction:
- embed_quantity(v, u) = embed_point([v, 0, 0]) (existing CGA primitive)
- translator(b) = 1 - 0.5 * (b*e1 * n_inf) (textbook CGA translator)
- decode_quantity(F, u) = (F[1], u) (e1 coordinate)
Measured values (all 11 fixed cases + composability):
a b vcond(T) |<R,R>| decode_err
0.0 0.0 0.000e+00 0.000e+00 0.000e+00
0.0 1.0 0.000e+00 0.000e+00 0.000e+00
1.0 0.0 0.000e+00 0.000e+00 0.000e+00
3.0 4.0 0.000e+00 0.000e+00 0.000e+00
7.0 -3.0 0.000e+00 0.000e+00 0.000e+00
0.25 0.75 0.000e+00 0.000e+00 0.000e+00
1.5 2.5 0.000e+00 0.000e+00 0.000e+00
-5.0 5.0 0.000e+00 0.000e+00 0.000e+00
-2.0 -3.0 0.000e+00 0.000e+00 0.000e+00
100.0 1.0 0.000e+00 0.000e+00 0.000e+00
1.0 100.0 0.000e+00 0.000e+00 0.000e+00
compose (2, 3, 5) → 10: |<R2,R2>| = 0.000e+00, decode_err = 0.000e+00
Every residual is exactly 0.0 in float64. The construction is algebraically
closed: T_t * reverse(T_t) = 1 - 0.25*B^2 where B = t*n_inf, and B^2 = 0
because (e14)^2 + (e15)^2 = -1 + 1 and cross-terms cancel. No machine-epsilon
drift accumulates because the relevant cancellation happens at the algebraic
level before float arithmetic.
ADR-0139 acceptance items 1-6 (one parametrized test family each):
1. Embedding well-formedness — test_family1_embedding_is_null (11 cases)
2. Translator well-formedness — test_family2_translator_unit_versor (11 cases)
3. Closure — test_family3_sandwich_preserves_null (11 cases)
4. Arithmetic correctness — test_family4_decode_matches_sum (11 cases)
5. Replay determinism — test_family5_replay_byte_identical (11 cases)
6. Composability — test_family6_two_translators_compose (1 case)
Total: 56 tests, all passing.
Lift program decision: proceeds. Follow-on ADRs (subtract, multiply, Rate,
compare, MathProblemGraph → PropositionGraph, pipeline integration, first
GSM8K case end-to-end through Engine A) are now justified by a concrete
algebraic foundation rather than design speculation.
Out of scope per ADR-0139:
- No modifications to algebra/, core/cognition/, chat/, math_solver.py,
math_verifier.py, math_realizer.py, math_candidate_parser.py
- No GSM8K runner changes
- No pack changes
- Engine B continues serving GSM8K unchanged; the 3/50 admission set is
preserved
CLI lanes intentionally not run — main has known test-rot orthogonal to
this PR. The 56 new tests are self-contained and the diff touches only
three new files.
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