Finite complex construction: two-sided Markowitz LPR cleanup refactorization on U8 (-2,580 macros, -37,320 real prims per orientation, seed 30, no new kappa)

[steph4n-gh]

Summary

• Status: Construction (no new kappa) + scoped negative finding
• Track & Seed: 20–39: Complex supplier: improve one specific circuit, frame schedule, decoder, or paid recursive profile (OS random seed: 30)
• Base Commit: abdc6a7002abdbcd9e21bfc5e1a795784deacfdf
• Selected Frontier Certificate: certificates/selected-result.json ($\kappa = 1661960547713947 / 10^{18} = 0.001661960547713947$, PR Conditional κ = 0.001661960547713947: T37 whole-owner packing and all-T bound #942 on PR Conditional κ = 0.001661948695165034: eight triangle-hybrid B deliveries in block 0 on PR799's word #869/Conditional κ = 0.001661956299899884: PR858's sixteen-replica owner controller on the U8 word #870 and PR Conditional κ = 0.001661957774647029: T21 whole-owner packing and fixed-family bound #890 / PR Research: T16 owner concentration raises conditional κ to 0.001661642255531641 #858; untouched)
• Package: research/u8-cleanup-markowitz-lpr-seed30/

What Changed and Was Learned

In the selected U8 complex supplier word (native/barch/FULL-WORD.json.gz, content SHA-256 090fd574747fbf9628e70cb9beb792732914cfa52e1df147579fe4dbccc68c5a; native/local/CANONICAL-WORD.json.gz, content SHA-256 24db880b7dab31e6af4eec8a1aba1bbbae29cd50d9a7b77cf0e9b571b3e5ae7c), the full_frame_cleanup section (canonical['cleanup'], running at frame 1 = FULL on the $490$ FULL-ended non-target registers) was synthesized by cold44x.py via one-sided (row-only) Gauss-Jordan elimination (high_inverse = "dyadic_sparse_Gauss_Jordan") on $M_{\text{after}} = M_0^{-1}$ in fixed register index order $c = 0, 1, \dots, 727$.

While $M_{\text{after}}$ has $9,430$ off-diagonal nonzeros, the target cleanup operator $M_0 = M_{\text{after}}^{-1} \in GL_{728}(\mathbb{Z}[1/2])$ itself has only $2,844$ off-diagonal nonzeros, all with numerators in ${\pm 1, \pm 2, \pm 3, \pm 4}$ and denominators in ${1, 2, 4}$. One-sided elimination in fixed index order caused severe fill-in ($6,105$ scalar macros, $68,714$ real-component primitives per orientation), coefficient blowup up to $\max |\text{num}| = 131,646$, and a $72$-bit peak prefix $L_1$ coefficient norm (48299247708521178587951/16) in the backward orientation.

Replacing one-sided Gauss-Jordan elimination with a two-sided Markowitz $R^{-1} P L^{-1}$ Schur-complement factorization and Weyl-group signed cycle realization (seed = 30, trial = 16, swap_pen = 6, scale_pen = 0) achieves the following exact improvements across the U8 complex supplier word while preserving all $728$ columns, native frames, paid recursive profile, and residual adapter recipes:

Metric	Baseline U8 (dyadic_sparse_Gauss_Jordan)	Refactored U8 (two_sided_Markowitz_LPR_Weyl_seed30)	Exact Change
full_frame_cleanup scalar macros (per orientation)	6,105 (6,005 add + 100 scale)	3,525 (3,355 add + 170 scale)	-2,580 (-42.26%)
full_frame_cleanup real primitives (per orientation)	68,714	31,394	-37,320 (-54.31%)
full_frame_cleanup max $|\text{numerator}|$	131,646	8	16,455.75x smaller
full_frame_cleanup max denominator	64	8	8x smaller
Total raw scalar operations (SCALAR-FRAME-AUDIT)	19,189	16,609	-2,580 (-13.45%)
Emitted events per orientation (LOCAL-CHECKS)	24,415	21,835	-2,580 (-5,160 pair)
Emitted scalar macros per orientation (LOCAL-CHECKS)	19,213	16,633	-2,580 (-13.43%)
Forward real-component primitive bound	193,306	155,986	-37,320 (-19.31%)
Backward real-component primitive bound	193,354	156,034	-37,320 (-19.30%)
Forward + backward pair real-component primitives	386,660	312,020	-74,640 (-19.30%)
Forward prefix_l1_upper (prefix_bits_upper)	6812058044968180837/256 (55 bits)	1938756620440273 (51 bits)	-4 bits (13.7x smaller)
Backward prefix_l1_upper (prefix_bits_upper)	48299247708521178587951/16 (72 bits)	57316408753392281/4 (54 bits)	-18 bits (210,704x smaller)
Paid recursive child profile (local_rank_mass = 5634)	{1:2548, 2:338, 3:446, 4:162, 5:72, 8:8}	{1:2548, 2:338, 3:446, 4:162, 5:72, 8:8}	Identical (0 delta)
RESIDUAL-ADAPTERS.json SHA-256	8b06181f6983...	8b06181f6983...	Byte-identical

Scoped Negative Finding (Candidate 1)

We also prove and verify (in PROOF.md Section 5 and verify.py) why reverting $m \in {1, 2, 3}$ helpers of the 4-helper group $G = {659, 661, 662, 663}$ in U8 from entrance frame $E_5 = [298, 170, 102, 30, 1]$ (dim 5) back to $E_4 = [298, 170, 102, 30]$ (dim 4) to fill T37 rank-1 idle slots fails: the 12 bipartite delivery gates B[420..431] into $D_G = {656, 657, 658, 660}$ split between $E_4$ and $E_5$, splitting the single rank-4 climb $1 \to 5$ on $D_G$ into $1 \to 4 \to 5$ and producing local profile deltas $\Delta(m=1) = {1:+2, 2:+1, 3:+3, 4:-3}$, $\Delta(m=2) = {1:+2, 2:+2, 3:+4, 4:-4}$, and $\Delta(m=3) = {1:-1, 2:+4, 3:+4, 4:-4}$, strictly worsening the complex moment at $b_{\text{front}}$.

---

Reproducible Verification Command

python3 -I -B research/u8-cleanup-markowitz-lpr-seed30/verify.py
python3 -I -O -B research/u8-cleanup-markowitz-lpr-seed30/verify.py

Expected receipt:

{
  "status": "PASS_U8_CLEANUP_MARKOWITZ_LPR_REFACTORIZATION",
  "seed": 30,
  "track": "20-39: Complex supplier",
  "base_commit": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
  "changes_kappa": false,
  "cleanup_macros_before": 6105,
  "cleanup_macros_after": 3525,
  "cleanup_macros_saved_per_orientation": 2580,
  "cleanup_real_primitives_before": 68714,
  "cleanup_real_primitives_after": 31394,
  "cleanup_real_primitives_saved_per_orientation": 37320,
  "full_local_real_primitives_saved_pair": 74640,
  "forward_prefix_bits": {
    "before": 55,
    "after": 51,
    "delta": -4
  },
  "backward_prefix_bits": {
    "before": 72,
    "after": 54,
    "delta": -18
  },
  "independent_verifier": "PASS_INDEPENDENT_INTEGER_LATTICE_VERIFICATION",
  "negative_controls": {
    "upstream_local_rejected": 25,
    "upstream_wrapper_rejected": 17,
    "package_controls_rejected": 12
  }
}

Attribution & Disclosure

• Contributor: steph4n-gh
• AI Assistance: Substantial AI assistance from Gemini 4 Argon (Google DeepMind / Antigravity).
• Predecessor Credit: Credits Jonathan Capalbo (jon314159, PR Conditional κ = 0.001661960547713947: T37 whole-owner packing and all-T bound #942), Jeremy Kothe (jeremykothe2, PR Conditional κ = 0.001661948695165034: eight triangle-hybrid B deliveries in block 0 on PR799's word #869/Conditional κ = 0.001661956299899884: PR858's sixteen-replica owner controller on the U8 word #870), Chafik Boukhalfa (chafreaky, PR Conditional κ = 0.001661957774647029: T21 whole-owner packing and fixed-family bound #890), Hao Yan (icekylinx, PR Research: T16 owner concentration raises conditional κ to 0.001661642255531641 #858, PR Tooling: bind review-ledger metadata to pinned family decisions #704, PR Conditional κ = 0.001636241501576388: h4a plus PR627's two factored jp8 cold ends #635, PR Conditional κ = 0.001600682403612293: joint-prefix kernels and structural bounds #571, PR Conditional κ = 0.001592517889315014: eight rank-five kernel pivots #558, PR Conditional kappa 0.001591968902833346: collective hyperplane waves and weighted response decoding #552, PR Direct delivery with 504 helpers for conditional κ = 0.001517760977820331 #531, PR Conditional kappa 0.001391523459591829: partial-own factory, 92 pivots and asynchronous whole owners #514, PR Split centres and source-basis reuse for conditional κ = 0.001120864952258278 #433, PR κ = 1.048005508028206e-3: mutable-basis Hamming packets (≈2^-9.89814; conditional; complex +4.97%) #425), DreamingOfClouds (PR [Lean] Hyperplane-ended helpers: Lemma A with an arbitrary terminal frame (no κ claim) #593, PR Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589, PR Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555, PR Complex supplier b ≈ 1.327·10⁻³ (+4.7%) on whole-residual hosting: shared-donor kernel and entrance gauges with paid residual wrappers (conditional on two lemmas) #484), and steph4n-gh (PR Conditional κ = 0.001661961039655941: one E4 call fills four T37 gaps #1072).

[Mister-Meeseeks]

100-PR batch review at bc0140e016bd865fffc7fdf64e12158183d52339.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Two-sided Markowitz cleanup factorization of the historical U8 word; exact full scalar maps and primitive accounting, with paid ranks unchanged.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.