research: whole-residual replica pooling and program portfolios, conditional kappa = 0.001266541949425315

[Dugongue]

Result and comparison

This adds research/e8-whole-pool-portfolio, a reproducible conditional construction with

$$T(n)=O(n(\log n)^{1-\kappa}),\qquad \kappa=\frac{253308389885063}{200000000000000000}=0.001266541949425315.$$

That is +0.04820338% over #451 (0.001265931727546219). The complex supplier binds.
This is a conditional finite artifact, not an unconditional multiplication theorem or Lean certificate.
It does not claim to beat #453's higher posted number: #451 supplies a trace obstruction to the
cross-family splitting derivation used there. This construction keeps every residual in one whole family.

Two construction mechanisms

1. Whole-residual pooling across replicas. Allocate the eight replicas jointly rather than solve
   identical per-replica integer packing problems. Every helper stays on one physical array family,
   with a complete slot isometry, a disjoint orthogonal block, and its checked idle window. Both actual
   family and absolute coordinate identities are audited. Complex delta relative to the selected Conditional κ = 0.001265931727546219: dual eleven-stage whole-residual hosting #451
   idle inventory is {1:-2,7:+8,16:-8,55:+6,64:-4}. Rank mass stays unchanged; the moment improves.
2. Invocation-specific complete-program portfolio. Five reverse calls at stage 5, replicas 0..4,
   use a fully checked rank147 provider; the other 83 use rank149. Each variant adds two residual
   coordinates and changes its local profile by {1:-2,4:-4,5:+4}. Whole-owner pooling pays those ten
   additional coordinates by changing a remaining rank52 child to rank42. The full difference from
   uniform pooled rank149 is {1:-10,4:-20,5:+20,52:-1,42:+1}. This improves bit-side reserve; it gives
   no further final-kappa increase while the complex supplier binds.

These use whole-slot reindexing/orthogonal-idempotent composition and equal complete-map substitution,
respectively. Structural sources include Mathlib's block-diagonal multiplication and the project's
MUB projection-factor identities. They are sources of mathematical analogies, not Lean certificates
for this artifact. #450 target mixing and two historical partial-prefix recoveries are also used,
but are explicitly credited as prior techniques rather than presented as additional new mechanisms.

Exact invoice

Supplier	Window	Live	Physical	Rank mass	Deficit	Maximum child
Bit	78	9600	9609	745536	3264	56
Complex	89	9600	10178	851136	3264	64

Bit profile: {1:217742,2:93314,3:23976,4:30912,5:8732,6:5752,7:5168,8:792,42:1,56:444}.
Complex profile: {1:170358,2:68992,3:18624,4:19712,5:38336,7:3840,8:9792,55:6,64:1732}.
Both actual profiles are priced together. Independent proposed gains are never added.

The coefficient bound charges all 88 chronological calls and all bridges, even with foreign-replica
hosting. Route-extra3 and 100,000 finite dispatch operations are charged. The bit row cover is19,431;
the retained complex fractional-depth row reserve is20,161 with its explicit cutoff condition.
Both exact moment engines, six bootstrap levels, and all47 strict outer inequalities are used.

Reproduction and validation

python -B research/e8-whole-pool-portfolio/verify.py /absolute/path/to/new-output-directory

Requires Python3.11+, SymPy, a C++17 compiler and Boost headers; set CXX/BOOST_INCLUDE if needed.
No network, optimizer, SciPy, prebuilt binaries, or Lean installation is required. Assertions must be enabled.

Fresh validation reconstructs both complete local providers, all980 dirty columns each, eleven-stage
orientation checks, exact Gram/prime witnesses, and all74,720 columns of the heterogeneous unbanked
controller. It checks65,120 whole bit helpers and49,280 whole complex helpers, physical-axis collisions,
phase recipes, emitted instruction digests,19 bit routing mutants and10 complex routing mutants.
The exact final profiles/templates match the frozen expected invoice. See VALIDATION.json and
REPLAY-MANIFEST.json for the source-bound replay; MANIFEST.json covers final upload contents.
Unchanged public verification chains were not redundantly rerun: inherited complex Clifford evidence
is explicitly retained with its source bindings.

All-size compiler, arbitrary-correlated dirty hosting, target-label, compressed-window, restored-work,
common-grid/tape, precision, and analytic contracts remain inherited assumptions. Finite controls do
not prove these contracts. No global packing optimality or literature-wide priority claim is made.

Sources, rejected routes, and future work

Direct sources and inspirations include #451 (rank149 whole-host baseline, row bound and trace review),
#450 (target mixing only), #445/#447 (eleven-stage schedules), #443/#439/#417 (response kernels and
residual isometries), #442 (whole idle-family hosting), #433 (complex split-centre/source-basis work),
#425/#386/#370 (mutable basis, geometry and producer), #401/#404 (shared donors/prefix recovery),
and #315's rational outer-assembly lineage. #453 supplied a useful source collection/local comparison;
its split-based price and #448's disputed splitting step are not used. #452 was reviewed but not used.
Exact head pins and licenses are in PROVENANCE.md, source headers, and notices/.

RESEARCH.md preserves the actual discoveries, bounded searches, library analogies, rejected coordinate
splitting attempt, and future routes. Early placement checks on the split attempt did not establish an
operator identity; those larger prices are expressly withdrawn. Product-coordinate factorization must
not be confused with a direct sum of independent array families. The next useful search variables are
larger whole-owner pools and independently correct complex-program portfolios, always with actual
operator semantics and a complete shared invoice.

Developed with OpenAI assistance. No claim of an independent all-size theorem or exclusive priority.

[Mister-Meeseeks]

Thank you @Dugongue. Your work and attribution are retained in the published 100-PR review, credits and complete original source.

Covered: Whole-residual replica pooling and heterogeneous program dispatch. Every occurrence has an intact physical owner and a fully checked provider. Abandoned split-based exploratory prices are retained as withdrawn, not achieved bounds. The bit-template pin is explained by JSON line endings; a later complex-template mismatch remains unresolved.

Keeping this PR open: The fresh scientific stages pass. A JSON LF-to-CRLF adapter resolves the bit-template pin and downstream bit audit, but the subsequent complex_template_sha256 remains unmatched: expected 02d4d0031a173664f8adc5bccf0244f8ce349307eac09c0d48a3c8948a7f5b17; regenerated 62d1e17fe80b82691e7cef2b03974a826b513da6af5689eb4c0aac1b38355971. The tested newline and gzip-header/level variants do not explain it. Supply a portable source-bound correction; no expected digest is bypassed.

The source archive preserves the entire submission; it does not substitute for the remaining execution or review. The batch's machine-readable disposition records this as partial coverage. Reviewed head: f76fc4e36030d4e00b4cbb83b1dbc661a0974c4e.