[Matarener]

Requested by Mark

Change and mathematical scope

Independent verification; no new κ. The selected κ is unchanged.

The conditional κ = 0.00296 – 0.00300123 claims (#4440, #4441, #4446, #4447) rest on two formal identities. The first is a controller word that diagonalises over commuting formal variables (Q, D₀ … D₂ₚ). The second is a native word checked in the free word algebra, where frame transports are bookkeeping only. This package executes both on concrete operators at column multiplicity f, with semantic controls:

• A. Conditional κ = 0.0023 (+5.690e-4, +32.87% over #4181): productive helper jobs compiled into a uniform supplier #4359 delayed BIT cover (PROOF-REVIEW §3). Q_S D_P Q_S⁻¹ = D_(SPS⁻¹) with Q_S = diag(S, CSC) holds exactly. The check is exhaustive over every S, idempotent P and involution C in GL₂(F₂), GL₂(Z/4) and GL₂(F₃), and over all P and C with 30 sampled S in GL₃(F₂), about 118,000 cases. Random cases add Z/2⁸, Z/2¹⁶, Z/2³⁰ and Z/3⁵ up to n = 12. Rank is preserved, and fibre routing g ↦ gS is a bijection. Two controls must fail and do: a lower block S instead of CSC, and C² ≠ I.
• B. Conditional κ = 0.00296 via query-thinned productive controllers (+10.18%) #4440 controllers on lifted operators. The emitted p17 complex word (19 full calls, 16 query shears) and p16 BIT word (18, 15) are replayed block-row by block-row, with every generator lifted to G^⊗f, f = 1, 2, 3. In both, L·A·R equals the advertised diagonal. Every query shear, executed literally through an owned stream, returns the stream to zero and matches S_y(Q⁻¹) / S_x(−Q). Controls rejected: Q in place of Q⁻¹, a deleted query shear, a non-commuting D_s, and a non-involutive Q (BIT).
• Finding: one load-bearing premise. With D₀ = F·q⁻¹ and [F, q] ≠ 0, the identity fails (off-diagonal error ≈ 72); with [F, q] = 0 it holds. The source states D₀ = F9·Q⁻¹ (kappa-rebuild/bit/complex_controller_factor.py). The premise holds when F9 is a product of one-axis gates that includes the central gate Q, as canonical_frame builds full frames. The Laurent factorisation cannot see this premise, because its variables commute by construction. We recommend stating it explicitly; we found no violation.
• C. Conditional kappa = 0.00300123 via a missing three-dimensional contact span #4447 native word on physical frames. The retimed THREE-base word (Conditional κ = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming #4441's 117 entrances, 42 exits and 395 retimings, plus frame 1159) is synthesised by this package's own code. It reproduces the L-role bill {1:2254, 2:514, 3:444, 4:103, 5:40}. All 1,160 frames are realised as random invertible matrices (climb C_b·C_a⁻¹, warp C_b·G·C_a⁻¹), and all 632 inputs are independent. Both orientations meet the endpoint at f = 1, 2, 3, and the centres are cleared. Controls rejected: a skipped climb into frame 1159, and the frame realised differently on one incident transport. The positive common-frame control passes: frame 1159 realised as old frame 732 everywhere.
• D. Conditional kappa = 0.00300123 via a missing three-dimensional contact span #4447's four new transports. Each is built as a dense 512 × 512 matrix from its gate list. Every column has 2^r nonzero entries of modulus 2^(−r/2), with r = 1, 1, 2, 4 as declared. The package lowering equals the transport exactly, absolute phase included, in both orientations. C(q, −1) = X^q·C(q, +1) and D⁻¹ = Z^α·D hold exactly (the "Gaussian followed by a Pauli translation" reading of Q⁻¹).
• E. Frame screen after Conditional kappa = 0.00300123 via a missing three-dimensional contact span #4447. Retiming a gate or a whole constant-frame component to any legal common frame changes the moment only through dim g, because the mass is fixed. On Conditional κ = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming #4441's state the screen finds exactly Conditional kappa = 0.00300123 via a missing three-dimensional contact span #4447's move (B/480, span ⟨45, 133, 336⟩). After Conditional kappa = 0.00300123 via a missing three-dimensional contact span #4447, none of the 17,253 gates or the 1,073 components improves at t = 0.997 or t = 0.9999.

Remaining obligations, not covered here: the invoices, moments, tensor completion, compiler and outer predicates; whether [D₀, Q] = 0 holds at every physical caller; the BIT charts and the common external weight (premises of #4440); and joint moves of several components.

Task and overlap

• Card. independent-moment, priority revision 7. Scope refined: operator semantics rather than the ledger.
• Base. 2a13eb1827784206202db90e5dc8327cf8a250db.
• Heads read. Conditional κ = 0.00296 via query-thinned productive controllers (+10.18%) #4440 40e22a83e, Conditional κ = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming #4441 5f9d871c6, Conditional kappa = 0.00300123 via a missing three-dimensional contact span #4447 322e0ec76. Their four inputs are vendored byte for byte, with blobs and SHA256 checked.
• Overlap. Independent retimed p17 certificate: conditional kappa = 0.003001053 #4446, Independently reconstruct PR4441 helper tariffs and complete p17 invoice #4448 and Audit THREE-base supplier billing from native events (no new kappa) #4450 independently reconstruct the changed invoices and the THREE-base billing. Independently check #4359's explicit-rank chain: H0/H1, superpotentials, the exit recurrence and 19,895 exact lockstep flows hold (no new κ) #4404 and Independently check #4405's refined #4359 ranks and endpoint family: all reproduce; z0 and the exit constant are not levers, the uniform saving is (no new κ) #4410 check the Conditional κ = 0.0023 (+5.690e-4, +32.87% over #4181): productive helper jobs compiled into a uniform supplier #4359 rank chain. None executes the controller or native identities on concrete lifted operators, builds the transports densely, or isolates the stage-zero commutation premise. The native word here is synthesised and executed without importing a predecessor interpreter.

Validation

python3.12 -B scripts/research_package.py --package research/productive-controller-lift-audit
python3.12 -B scripts/check_research_commit.py --package research/productive-controller-lift-audit --check-source-history
python3.12 -B research/productive-controller-lift-audit/verify.py

All three pass on CPython 3.12 (Windows) with numpy 2.2.6. verify.py takes about 2.5 minutes and regenerates RESULT.json byte for byte; RESULT.json stores only booleans and exact counts. These are finite checks with random realisations, not proofs. The cover algebra is exact; the operator replays are floating point, with endpoint errors of 1e-15 to 6e-9 against a 1e-6 tolerance. Every control error exceeds 1e-3.

Credit

The audited constructions are by 1337isnot1337 (#4440/#4441/#4447, with OpenAI Codex assistance), on zxv's #4359 native and controller work and Jacob Alan Sussman's #4268 compiler. clifford_exact.py defines the frame operators and is used only as the comparison object in D. Mark (Matarener), with substantial Claude Code (Claude) assistance. Apache-2.0.

Open next questions

1. Is every full call's stage-zero multiplier exactly F9 = Q ⊗ F8, so that [D₀, Q] = 0? First step: read the initial native call's nine-axis frame operator and check that it factors through the central-axis gate.
2. Do joint retimings of adjacent constant-frame components help after Conditional kappa = 0.00300123 via a missing three-dimensional contact span #4447? First step: screen nested frame pairs over adjacent components by dimension.

🤖 Generated with Claude Code