* feat(ADR-0141): multiply as CGA dilator versor (positive non-zero)
Adds `multiply(scale)` to `generate/math_versor_arithmetic.py` as the
standard CGA dilator for multiplicative scaling along e1, restricted to
`scale > 0`. All ten ADR-0141 assertion families pass.
Preliminary measurement confirmed:
N = n_o ∧ n_inf: component -1 at index 15 (blade (3,4) = e4∧e5)
N² = +1.0 (pure scalar) → closed-form D_s = cosh(α/2) + sinh(α/2)·N
n_o · n_inf = -1; n_o² = n_inf² = 0
Because N² = +1, the cosh/sinh expansion is exact in float64 and
D_s · ~D_s = cosh² − sinh² = 1 holds to machine epsilon.
The sandwich D_s·X·~D_s produces a null point with n_inf normalization
1/s. `decode_quantity` is updated to divide by that factor, recovering
value · s. For translator outputs (normalization = 1) the result is
identical to the previous direct e1 read; all 152 prior add/subtract
tests pass unchanged.
`embed_quantity` is updated to embed directly in float64, eliminating
float32 quantization error for values like 0.01 (float32(0.01) ≠ 0.01);
all prior test-case values were exactly representable in float32.
* docs(ADR-0141): add decision document for multiply-as-dilator spike
The ADR doc was drafted in a separate branch and not present when the
implementation worktree was created from origin/main. Adding it now so
the decision record lands on main with the implementation it specifies.
Content unchanged from the draft — same spec the implementation already
satisfies (10 assertion families, fixed test cases, falsification
discipline, deferred scope for negative / zero / divide / Rate).
No code or test changes in this commit.
Extends generate/math_versor_arithmetic.py with one new function:
def subtract(addend: float) -> np.ndarray:
return translator(-float(addend))
Single-line delegate to translator(); no new algebra.
Adds tests/test_arithmetic_subtract_and_group.py covering all nine
ADR-0140 acceptance families:
Families 1-6 (ADR-0139 families applied to subtract):
1. Embedding well-formedness — null cone preserved for subtract cases
2. Translator-of-negative well-formedness — versor_condition < 1e-6
3. Closure — sandwich result stays on null cone
4. Arithmetic correctness — decoded value == a − b within 1e-9
5. Replay determinism — byte-identical across runs
6. Composability — subtract(c) ∘ subtract(b) decodes to a − b − c
New group-property families (structural verification of ADR-0139 claim):
7. Inverse composition — T_{-b} * T_b = identity (max residual: 0.000e+00)
8. Round-trip closure — versor_apply(T_{-b}, versor_apply(T_b, X)) → (a, u)
9a. Sum composition — T_a * T_b = T_{a+b} (max residual: 0.000e+00)
9b. Commutativity — T_a * T_b byte-equals T_b * T_a (all 10 cases)
All 96 tests pass. Group residuals are exactly 0.0 in float64.
The additive subgroup of Cl(4,1) translators along e1 is abelian and
closed; ADR-0139's algebraic claim holds at the group level.
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.
