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Research algorithm feasibility and semantic workbench
Edition 9 October 2026. Current decision: Prototype now. Prices and product uses remain hypotheses. No independent source-proof verification or buyer validation has been completed.
Research finding
Existing dossiers document extreme finite constants behind headline complexity improvements. New reviews add delayed k-server activation at 2^T_P-1 and the exact logspace derandomization compiler's explicit resource-bound construction. A language-class equality is not automatically a usable compiler or speed improvement. 41 declared definitions across three computational interfaces have now received selected source-level semantic comparison.
Problem and buyer
Research commercialization teams need to distinguish a novel theorem, a computable construction, a practical implementation and a useful customer workflow. A formal result can match its intended model while still leaving a costly operational bridge.
What the finding could enable
The workbench can produce source-pinned implementation gates with exact quantifiers, numerical parameter derivations, semantic definition records and finite controls. Use it as part of the shared evidence/model-assurance product to support an investment decision.
Technical and commercial limits
No intended-model mismatch was detected in the selected 41 definition comparisons; this is not trusted kernel or whole-proof verification. LogspaceEquality selects equality of binary language classes, not the paper compiler or numerical resource bounds. The compiler assumes supplied all-input/all-coin polynomial-time and logarithmic-workspace promises; it does not discover them. It preserves decisions under an error gap, not a random output distribution.
Minimal architecture
Pinned source and declaration references -> manual semantic observations -> source-vs-application contract -> exact parameter worksheet -> bounded reference/benchmark evidence -> reviewed build/defer decision. Thirteen curated documentary contracts exist. A complete manifest does not authenticate the supplied evidence or prove applicability.
Existing alternatives and differentiation
Internal technical review, expert consulting and existing benchmark tools are substitutes. Value requires a material missed assumption, changed engineering decision or reduced preparation time. Lexical equality of displayed definitions is only a useful control, not an automated semantic proof.
Monetization hypothesis
Hypothesis: AUD 3,000-12,000 per assessment and a subscription only after reuse is demonstrated. An illustrative AUD 8,000 project at 40 assumed hours and AUD 180/hour leaves AUD 800 before overhead; 45 hours exceed the fee. Overlapping evidence, semantic and parameter modules do not represent separate paying accounts.
Validation experiment
The compiler uses P=1000(d_code+2)^4(a+b+2), rho=100(P+2), S=1+(t+1)(2rho+1)(g+2), K=4S, c=2S+1, H=2^((u+100)^2)*(q_D+1). Even the conservative minimal-parameter envelope gives c>=2,592,016,043 and H>=2^10202 for the declared upper bounds. These are not runtime lower bounds. No compiler/library transition list was executed. Have a qualified reviewer compare ten operational claims selected from thirteen contracts and measure material gaps, false alarms and preparation time.
Conditions to reject or defer
Defer compiler speedup claims until a concrete implementation and useful resource measurements exist. Reject a subscription if the workflow remains bespoke or reports cannot improve an engineering decision. Never turn a loose upper bound into a claim of algorithmic impossibility.
Next concrete action
Review the remaining seven semantic interfaces/24 declared entries, enrich exact source locations for older contracts, and prepare the ten-claim expert comparison. Keep finite reference validation separate from the unrestricted source algorithms.
Source evidence
Repository sources are pinned to revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. Selected scope notes and manuscript statements have been reviewed to the extent described above; these links do not represent successful kernel checks.
Family 109
Subject: Integer multiplication below $n\log n$.
Family 111
Subject: One-sample matroid prophet inequalities against an almighty adversary.
- One Sample Suffices for Matroid Prophet Inequalities against an Almighty Adversary
- Formal scope notes
Family 124
Subject: Polynomial-time scheduling on three identical machines.
Family 130
Subject: Exact Fourier transforms below $n\log n$.
- An explicit power saving for the exact discrete Fourier transform
- Finite tensor savings and exact Fourier circuits
- Formal scope notes
Family 139
Subject: Subpolynomial query complexity for log-concave sampling.
Family 107
Subject: Matrix multiplication with exponent at most 9/4.
- An Upper Bound of 9/4 for the Matrix Multiplication Exponent
- Complex Matrix Multiplication Below 2.258 and Rectangular Bounds
- Staggered extraction for exact matrix multiplication over every field
- Formal scope notes
New local evidence
Computational feasibility, semantic comparison, eighteen utilities. All sources remain pinned to the cited revision.
Additional pinned sources: logspace scope, k-server scope, transport scope.