# Practical feasibility: weighted facility review and retained research limits

9 October 2026. The first product remains facility-planning assurance. The [preceding feasibility record](FEASIBILITY-2026-10-09-v21.md) preserves source-parameter calculations, narrow-model distinctions and conventional-library comparisons across the other opportunities. No source backend was promoted or proof accepted in this edition.

## New ordinary assignment checker

The [weighted rectangular module](prototypes/facility-assignment-review-2026-10-09-v2/report.md) now checks exact submitted costs, whole-client assignments, mandatory openings and capacities. It accepts exactly-k or at-most-k selection with stable independent client/site namespaces. A capacity control shows why nearest-site reassignment cannot be accepted without checking loads. Required sites need not have positive load or be filled.

Input caps are 512 clients/128 sites, eight MiB/file, sixteen MiB combined and 128-bit rational input components. Optional conventional solver scales are exact and capped at one million, with conservative integer limits of 2^60, two seconds and one worker. These are explicit domain/solver bounds, not memory or total-runtime guarantees. Additional business constraints are refused rather than omitted. Geographic distances and physical measurements are not validated by arithmetic checks.

The exact relaxed lower bound drops opening, capacity and mandatory-site restrictions. Difference from a checked cost bounds suboptimality from above; it is not a measured actual optimum gap. A solver OPTIMAL/INFEASIBLE status remains a solver report. Only equality with the independent lower bound proves optimality in this module. The original strict-metric reference retains its own enumeration/dual contract, and no new source theorem is applied to weights/capacities.

## Evidence and remaining work

7,952 new controls include a complete 7,776-model grid containing 93,312 submitted plans, plus eleven recorded solver/export examples and intake/display boundaries. A self-authored 100-client/10-site case has checked cost 2373, bound 2260 and submitted cost 5472. The numbers are synthetic objective units. They do not establish speed superiority, actual savings, formal program correctness or a profitable market.

Local browser intake now runs. Stronger weighted/capacity certificates, standard-browser export verification and permissioned study evaluations remain useful next work. Production hosted jobs, accounts and data handling have not been deployed. Fixed costs, fairness, splitting, time windows, multiple demand types, utilization minima and uncertainty require new contracts before support can be claimed.

The [product plan](plans/optimization-assurance-first-product-2026-10-09-v5.md) retains an unvalidated AUD 5,000-10,000 assisted-review experiment. Buyer demand and delivery economics remain unknown. [Complete current utility list](PROTOTYPES-2026-10-09-v27.md): 41 utilities, 32,107 passed checks in 65 saved reports. [Reading ledger](MANUSCRIPT-REVIEW-2026-10-09-v18.md): 51 selected-section records and 147 source hashes, with full source/proof acceptance incomplete.

## Browser execution boundary

The [browser release](prototypes/facility-browser-2026-10-09-v1/report.md) adds 119 controls and actual six-file/fractional UI observations. Its worker has a 15-second limit, 131,072-bit rational-component cap and JSON depth limit of 32, with no accepted result on exhaustion. Asset/file loading and rendering are outside the worker limit. Native in-app save completion remains unverified; visible export text provides a fallback. No study-data upload or hosted solver exists. User provenance, physical measurements and business usefulness remain unvalidated.

## Finite-field backend eligibility

The [new selected review](prototypes/finite-field-factorization-2026-10-09-v1/report.md) computes a necessary 4,753,080-bit degree-two boundary for the source large-prime branch and records its uniform Hecke dependency. Extreme upper bounds do not prove all executions slow, but no practical new-backend advantage is shown. A separate classical audit checks multiplication and irreducibility within explicit finite limits; 456 controls include 401 exhaustive monic polynomials. Existing SymPy already factors the examples cheaply. Keep the integration low-confidence and defer a source port.

## Community model and algorithm boundaries

[The selected family-229 review](prototypes/community-recovery-2026-10-09-v2/report.md) distinguishes three-state asymptotic weak recovery, four-state ferromagnetic trees and a bounded-degree deterministic-tree capacity criterion. A declaration checker does not validate a real network. Across 54 graphs, a conventional spectral baseline materially changes results relative to forced-three modularity; finite chance correction and stripping planted metadata are essential. The 1,048 controls establish finite implementation behavior, not source-proof acceptance, real-model fit or market value.

## Random-SAT model and cost boundaries

[The selected family-235 review](prototypes/random-sat-stream-2026-10-09-v1/report.md) separates asymptotic limits from finite centering, proper clauses from a relaxed Poisson auxiliary model, and computability from efficiency. The displayed lower-certificate penalty alone needs n>=2^402 to fall to one; this is not a universal runtime lower bound. Exact coupon controls and 679 passing checks support a bounded benchmark audit, with unknowns and solver-only UNSAT evidence preserved. No new solver advantage, limiting digits or customer demand is established.