[aliromman]

This construction gives an actual 38-port selected set for the historical response J=I-KR whose ordinary block and corrected original-X response are both dyadic units. A union of the specified complete eight-port minors first has both properties at 40 ports. The construction therefore permits a smaller selected set than that restricted class. It does not prove that 38 is the global minimum or reduce every native cost below S40.

The proof, source pins, decisive replay receipt, and independent publication review give the exact scope. This does not improve the complete kappa calculation. Routed access, caller exterior phases, owner histories, child hosting, final decoding, recursive precision, and complete supplier pricing remain open.

The general criterion separates two unit conditions. For RK=14I, the ordinary block is a dyadic unit exactly when T=R_S K_S-13I is. Given that condition, the corrected original-X response is a dyadic unit exactly when W=I-R_S K_S is. The actual S38 witness has det(T)=2^24, det(W)=2^12, and det(A)=2^-12. Its balanced backward, diagonal-borrowed backward, and balanced forward words cost 170,446, 171,662, and 171,290 real dyadic scalar primitives. The diagonal-borrowed backward word followed by A^-1 costs 179,074. Both response inverse orders are checked on all 112 data coordinates. The separate fixed-A,T paired class has extra restrictions and is not a lower bound for arbitrary selected sets.

The package also proves a general short normalization. For a selected principal unit L, first apply -L^-1 to selected X, then use the changed selected values in the lower shear. It needs neither an ordinary-block inverse nor a full-response inverse. On the retained changed responses, the complete prices are:

Changed response	Long normalized backward	Short normalized backward	Saving
Signed S8	99,472	89,200	10,272
Structured S24	96,012	89,592	6,420

These complete local words retain 2433 H1 + 724 H2 + 228 H3 + 102 H4 + 20 H5: 3,507 native children and rank mass 5,073. Prices include the scalar core, physical exchanges, boundary factors, and owned operations. The signed S8 suffix uses no owned field. The S24 suffix uses the existing C0 and restores its query to zero before every reuse and final reset. The full borrowed-Y response and ordered port operators remain explicit.

The old raw S8 backward words are different: they need 16 real division-by-three scans with a separate price and common-grid contract, and their original-X response has nullity eight even after exact division. Their full two-bank word remains invertible. The changed signed S8 words in the table are dyadic and use no odd division. The odd-grid review retains the rational-grid obligations.

The fixed-baseline spectral annex adds a reviewed lower bound for a different, explicit class: S contains the fixed disjoint A,T minors and retains the selected source baselines. Complete split-sign pairs are not required. Every admissible S has at least 27 ports, and sizes 28 through 31 are also excluded. Size 27 remains open and requires det(-4D)=2^42; this is not an existence or optimum claim. The original spectral proof, selected-baseline necessity lemma, and independent source review bind the actual 112 columns. This bound does not apply to the unrestricted S38 class or adopt the separate lower-twelve claim. It changes no complete kappa calculation.

The annex uses the historical source archive at bce54fb3f895cbe5cd4c0eb477c3afeed100190f. Its source manifest and notice retain the exact archive members, source credit, and licenses. The schur-selection lane supplied the proof, temporal-reuse supplied the separate proof and interval check, and cover-algebra supplied the necessity lemma, with substantial OpenAI Codex assistance. The earlier accepted package bytes and manifests remain unchanged; the annex has its own manifest.

With Python 3.10 or later, the standard library, one process, and at least 3 GiB free, run from the repository root:

python3 -I -B research/raw-selected-centre-units/annex/fixed-baseline-spectral-gap/replay.py --out /tmp/fixed-baseline-spectral-gap

The output directory must be new. The final line is:

PASS_FIXED_BASELINE_SPECTRAL_GAP

The fresh normal and optimized runs both passed; both producer and independent receipts matched the historical bytes exactly. The independent publication review gives separate source, algebra, and replay checks. The producer retained assertions in both modes. The independent checker reconstructs eight forms across the 12,550-event prefix, checks all 112 source columns and 6,216 root pairs, and verifies all 16 size intervals with exact rational arithmetic. No split-pair enumeration, native word replay, routed caller, current selected-supplier replay, or complete kappa calculation ran for the annex.

The publication base is b58ad9ef4d4e861b0eaa5dba41742bdc072dca51. Its selected record names PR #4470, with conditional kappa 60403/20000000=0.00302015. This package uses different historical inputs and proves no transfer to that selected construction.

The consumed core comes from PR #3133, pinned at 51eb9c4ee9e4722010d308aa3309e039d3940cc2; its source credit identifies @dcharb78 for the coupled folds and helper endpoints. Jeremy Diviney (@jeremydiviney) supplied the exchange, integration, and verification in PR #3148, pinned at f2927a4b8afcf0701a6b945e14f30de1d94f5176; its base and extra payloads match the consumed core. The retained phase sources come from PR #2588, pinned at 8cd9dc88e24f062e2ca2fa7f4844a3d3319381fb. Its notice credits Rohan Arun (@rohanarun) for native lowering and owner construction and Cinna Davis (@1337isnot1337) for PR #2226 borrowing and warp machinery. The package notice retains the full predecessor credit, exact source notices, and Apache-2.0 licenses. All five phase-source files match primary GitHub readbacks. Substantial OpenAI Codex assistance was used; the separate agent reviews are not human peer review or formal-kernel proofs.

Use Python 3.10 or later on macOS or Linux, the standard library, one process at a time, and at least 3 GiB free space. From the repository root:

python3 -I -B research/raw-selected-centre-units/reproduce.py --out /tmp/raw-selected-centre-units-normal
python3 -I -B research/raw-selected-centre-units/reproduce.py --optimized --out /tmp/raw-selected-centre-units-optimized

Each output directory must be new. Both commands end with:

PASS_RAW_SELECTED_CENTRE_UNITS

The normal and optimized runs passed all eight stages; their mathematical receipts agree. The assertion-based witness producer remains assertion-enabled in both modes. A separate reviewer repeated all eight stages from a relocated copy and independently checked the source bytes, S38 Gram identity, unit classification, scalar prices, and suffix order. The native checks cover both providers, 3,036 child classes per provider, 12 serial words, six S38 words and both response inverses, and 18 changed-response words on all 640 input columns plus 91 private zero outputs. Controls reject wrong global phase, helper endpoints, physical factors, Q order, suffix order, and nonzero C0 at reuse. Owned admission permits CLEAR; arbitrary helper restoration is checked separately.

The old complete-minor check uses its own 480-helper core; its prices are not combined with the later 408-helper core. The producer lower-twelve claim and later separator claims are not adopted. No large fixed-pair enumeration, complete historical compiler regeneration, current selected-supplier replay, or complete kappa calculation ran. Python 3.14.7 on macOS was tested; Linux and other Python versions were not. The open next questions state the remaining mathematical and caller obligations.

The selected-interface family annex adopts five additional reviewed families. The complete-minor theorem gives the exact dyadic criterion for unions of square minors. The actual six-minor response has all 64 unions checked and all 20 balanced 24/24 splits verified. Its V2 common-frame data gauges cost 2,368 real primitives each; ordinary gauges cost 1,172 each, with one serial zero field. The separate positive-diagonal-metric obstruction is sharp at rank 64 only in the stated 42-dimensional symmetric family.

The signed-pivot theorem gives a six-step ordinary factor using existing arbitrary data fields and 960 algebraic selections in the fixed-sign cycle-cover construction. Only the displayed selection has emitted and priced gauges: 1,648 each for H,H^-1 and 4,720 each for A,A^-1. Its sharp selection-size bound of eight is not a native capture-rank bound. These results do not classify all eight-port subsets or all native responses.

The annex also adopts all five raw variants and all five signed or oblique forms on both historical providers. Their full local bills and distinct owned-output contracts are retained. For example, raw B0 costs 168,896 primitives at rank mass 5,073 with no added native child; F8 costs 169,152 at mass 5,081. Plain signed, coded signed, and oblique forms cost 164,626, 171,938, and 172,050, respectively. These words retain the 164,514-primitive clean core. The separate live-eight suffix uses the changed signed core. Its four complete forward words work for arbitrary current selected Y. Raw and balanced versions cost 89,088 and 92,784, with 3,515 children and rank mass 5,081. The eight added H1 calls and sixteen permutation wrappers are explicit; wrapper access and descriptor costs are outside the scalar subtotal.

The fresh receipt records six original independent checks in normal and optimized Python. All twelve results match frozen receipt bytes. Negative controls reject omitted exchanges, wrong line signs, wrong oblique returns, borrowed-helper clears, and a missing live-field subtraction. They cover 36 complete words per mode on all 640 arbitrary live and owned input columns, exact geometry and metric identities, new signed-line kernels, all 4,096 live-eight kernel columns, and all 4,096 FULL-commutation columns. The source manifest binds 133 unchanged files, including compressed and decompressed input hashes. A separate Codex agent repeated all twelve checks from a cold copy and checked the proof scope. This was not human review. No import adaptation is used. The retained core-phase suite, parent suite, and producer emission were not rerun.

With Python 3.11+, the standard library, one process, at least 3 GiB free, and a new output directory outside the annex:

python3 -I -B research/raw-selected-centre-units/annexes/selected-interface-families/replay.py --out /tmp/selected-interface-families-annex

Expected final line:

PASS_SELECTED_INTERFACE_FAMILIES_ANNEX

All accepted core and spectral files and their historical manifests stay unchanged. The notice retains the construction, independent-review, and inherited provider/phase credits. The parent source commits and publication base remain fixed. No complete kappa improvement follows. Routed access, inter-call codes, exterior phases, decoding, owner histories, child hosting, full pricing, and precision remain open. These local words are not an admission to the current selected supplier. Apache-2.0; substantial OpenAI Codex assistance was used.