Repository navigation
Contextual rank-5 provider selection and finite pooling: conditional kappa 0.001592576636390595 - #563
Conversation
|
Thank you @Dugongue. This contribution at Context-sensitive provider selection and clone pooling compose through an actual dispatch. Local nonlinear cost is retained. Fresh replay passed; its numerical gain is not added to the alternative #560 witness. Preserved implementation and research: The family review and individual disposition record the scope, evidence and attribution. Parallel and intermediate contributions remain credited even where a later composition has a stronger bound. The published multiplication bound remains conditional on the documented compiler, realization, hosting and analytic assumptions; these finite checks are not a full Lean multiplication proof. |
2 participants
This adds
research/contextual-provider-pooling, with conditional kappa = 0.001592576636390595 and complex saving b = 0.0015951169824291220178. The public comparison snapshot is frozen through #559. The selected #555 bit endpoint remains nonbinding.The checked gain is 0.00368877094% over #559 and 0.0377757067% over the previous finite-copy delivery. The full clean replay completed in 201.0 seconds; all 47 outer constraints passed.
The new numerical contribution is contextual selection of a complete local supplier at each invocation, followed by a finite five-copy pooling construction. It combines #558's rank-five kernel promotions with the inherited complex circuit; it does not add their reported gains. The previous epoch rewrite removes 28 scalar instructions per call without changing its paid child profile and is retained as an inherited simplification.
Why choosing a provider by its resource context helps
Every provider has 504 helpers and the same required normalized data endpoint. Before promotion its residual widths are 56 of width 5,156 of width 8,292 of width 9. Each selected rank-five entrance changes one width 5 residual into width 4, but also changes the actual local child profile. Promoting all possible pivots is not the objective: each residual must fit an actual idle owner for the whole invocation, and every leftover owner coordinate is paid.
A capacity screen examined all 545 patterns over the available ranks and widths. Its preferred fractional profile used32 calls with four promotions and 40 with eight. That screen alone is not a timed physical construction. The literal realization instead uses the following source-bound registry in the72-call asynchronous controller:
This produces448 width 4 occurrences per controller, suitable for the available rank 16 contexts, while retaining enough width 5 occurrences for rank 32 patterns
(5,9,9,9). Complete calls select one independently admitted provider; their internals are not spliced together across incompatible normalizations.Partial groups are charged exactly. The local histogram of n6+n2 exceeds that of n8+n0 by
The complete timed mixture remains profitable after this penalty. Treating partial promotion as a linear fraction of a full group would overstate the gain.
Five finite copies of that controller are then interleaved at complete-call boundaries. Five width 9 occurrences share disjoint coordinate ranges of one rank 48 pending owner, replacing five rank 39 remainders by four rank 48 remainders and one rank 3 remainder. This is the already established finite-copy pooling method applied to the new mixed registry. The local ambient dimension stays73; the larger finite controller is fully charged.
The final literal plan has360 complete calls,181440 whole helper roles,35840 live families and deficit12800. Its complete child histogram is
The exact moment, finite invoice and all 47 outer inequalities were recomputed from this profile. No scalar-only simplification or floating capacity result is counted as an additional kappa improvement.
Sufficient mathematical construction
The promoted prefix consists of additions from pivots to donors, with source and destination sets disjoint. Their elementary matrices have zero pairwise cross products, so these additions commute on arbitrary inputs, including dirty helpers. A selected pivot's entrance is enlarged from its rank 4 frame to the specified rank 5 frame, every correction using that pivot is moved to the new frame, and correction gates are reordered along legal containment chains. All resulting frame costs are reconstructed; inverse background cleanup is regenerated literally.
For heterogeneous composition, each provider independently implements the same required normalized data operation in both orientations, restores private work and spectators, and realizes the stated residual on its borrowed owner subspace. The owner table binds the selected provider to the actual width, chart and complete idle interval of every role. Each pending owner is partitioned into disjoint hosted subspaces and an explicit remainder. Induction over the actual call order gives the global data action; disjoint owner factors compose to the required pending operator. This is stronger than dimension matching or clean-input agreement and does not assume a free basis change.
The local registry reconstruction is pinned by canonical JSON hashes. Fresh exact scalar replay has passed all 728 columns in both orientations for n0,n2,n6,n8 and the auxiliary complete-group n4 provider. All20 promoted-pivot omission controls across these four changed providers reject. These are local results; complete phase, adapter, owner and finite-invoice admission is separately required.
Reproduction and verification scope
Run from the repository root, keeping assertions enabled and choosing a new work directory outside the package:
The final package reconstructs the selected local providers, verify exact arbitrary-dirt identities and physical charts, build the literal mixed/cloned controller, audit owner chronology and paid remainders, and derive fresh rational moments and the outer assembly. Final full-replay status: PASS: all four offline stages, including a complete Windows CRLF source replay. GitHub's remote CI status is separate from local evidence.
Canonical content pins avoid treating incidental CRLF or gzip serialization differences as mathematical changes. New provider gzip output fixes compression level 9, mtime 0 and the OS header byte. Original upstream source notices, licenses and assistance disclosures remain with vendored dependencies.
Attribution and relationship to recent PRs
Research retained for future workers
The notes include the exact selected-promotion proof, the full bounded entrance-extension census, the distinction between fractional pattern discovery and literal timed ownership, and the partial-group penalty. For the fixed prefix/downstream geometry, twelve of fourteen four-pivot groups admit rank 5 extensions and none admits rank 6. This is a scoped census, not an obstruction to a different response basis or circuit.
OpenAI proof sources were used as explicit structural guides.
UniformKServer/RealFlowMixture.lean(mixture_valid,mixture_cost) provides finite-mixture conservation and affine cost identities;PeriodicTiling/StackingContributions.lean(IsColorPartition.eq_of_mem,card_stack,IsColorPartition.sum_card) provides disjoint product and multiplicity accounting. Their adaptation motivates support-preserving provider selection and exact finite clone counts; the present operator and chronology conditions are proved and checked independently. Additional inspected constructive projection/injection identities emphasize actual reconstructing charts; block-operator adjoints and flattening emphasize orientation and copy bookkeeping; direct-sum norm bounds motivate a possible prefix estimate only after exact block-boundary invariants are established. Tensor restriction composition and separated-fiber decomposition suggested a further multi-carrier factorization route, but that paid search was not completed and contributes no numerical gain. The inspected source paths, theorem names and hashes are recorded. Source inspection is not a fresh Lean certification, and the package does not pretend that every cross-field connection is an independent improvement.Future work can change the local residual alphabet or search time-dependent provider mixtures, but must price shared donor/frame costs and supply actual whole-owner chronology. Repeating fixed-word frame searches or unrestricted identical cloning does not by itself escape the already examined models.
The numerical result remains conditional on the inherited all-size compiler, common-label/mutable-source, whole-call hosting, precision/tape and analytic-transfer interfaces, including the selected bit premises. It is not an unconditional integer-multiplication theorem, a complete Lean formalization or a measured practical speedup.