[Matarener]

Requested by Mark

Before: the selected chain (#5383 eight-relation body on Cao Yifan's #4610 word, through #5392, #5398 and #5413) keeps precision_tape as a retained premise. For this word the repository only checks that formal prefix l1 norms and denominators stay below a 2^192 envelope (research/eight-owned-relations/native.py).

After: the exact uniform grid is certified, and it is attained. With public physical inputs (dirty helpers and owned entries included) on 2^-f Z[i], every atomic cut is exact with ceil(9 lambda/2) + 6 extra fractional bits backward (11, 15, 20, 24 at lambda = 1..4) and ceil(9 lambda/2) + 5 forward. Stored magnitudes stay below H · 457 · 2^(9 lambda/2). The #4610 source word gives the same numbers. For comparison, the P104 words have the sharp guard ceil(9 lambda/2) + 2. No new κ; this is step 1 of target 7 in #5428.

How. The model is PR2772/PR2813/p104-joint-prefix-grid: a field in frame F holds Σ c_s U_s^(⊗λ) V_s(0).

• Dyadic coefficients. verify.py replays both programs exactly over Q. Every coefficient is dyadic; there is no odd division.
• Fourier ranks. For each term it computes the Fourier rank r of Delta_F Delta_{I_s}^-1 with the repository's Clifford compiler. That rank equals the paid rank on every climb. By Ross Richardson's lemma a rank-r Clifford column has denominator exactly 2^ceil(r/2).
• Pareto front. The front of (v2(den c_s), r) is {(6,9)} backward and {(5,9)} forward.
• Attainment. Backward event 19537: input L470 occurs once, with coefficient −1/64 and rank 9. Forward event 19466: coefficient −1/32, rank 9. Inputs are independent, so nothing cancels these terms.

test_verify.py rejects a drifted input, an odd division, a corrupted climb rank, a smaller guard claim and a tampered RESULT.json.

Part 2 (complete #5413 body and controller). caller.py executes the literal #5413 backward body, the only runtime local direction (18 calls). Inside it, the #5402 provider is expanded per its schedule: wrappers, mode scalars, the basis programs, the 21,473-event provider word, and the cache SWAP/CLEAR. Monomials, Gaussians and warps stay symbols.

• Body. There are no odd denominators, including in the ZW = 14 I provider, and all 17 owned fields are zero at exit. The maximum 2-adic exponent is 6, attained by the same single-occurrence rank-9 witness, so the body guard stays ceil(9 lambda/2) + 6. Main-data terms have v2 <= 4.
• Controller. Its bank coefficients are all integers (ADD ±1, SCALE −1, SWAP, 0/1 boundaries), and each call has fresh helper fields. One 145-axis controller level therefore needs between 73 and 77 extra bits. The lower bound comes from the 224 rank-145 targets. For comparison, Complete coupled-output caller: conditional κ = 0.003027288235 (+5e-12 over #5400) #5413's FRESH-PRECISION.json records heights of about 19,452 (local) and 377,688 (global) bits. The exact value inside the bracket is left open; it needs the global 145-axis charts.
• Controls. Three more mutations are rejected.

python3.12 -B scripts/research_package.py --package research/selected-word-exact-grid

PASS locally on CPython 3.12 (Windows), about 2 min for both parts, standard library plus the pinned repository Clifford compiler; check_research_commit.py passes. Scope: native correctness and the tensor-lift convention stay inherited. The second commit is the unchanged docs/ci-verification.md repair from #5420, needed while main's CI section is stale.

Task card formal-interface-lemma, scope changed (see TASK.json). Credit: Cao Yifan (#4610), Ali Romman (#5377, #5383), Ross Richardson (Clifford denominator lemma), the P104 grid packages (PR2674, PR2772, PR2813), zxv (#5428).

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