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Subset sum reconciliation backend
Edition: 8 October 2026. Initial decision: Conditional research. The product interpretation and pricing are hypotheses; independent proof and buyer validation remain open.
Research finding
The subset-sum paper claims worst-case O(2^(0.49n)) randomized word time on polynomial-bit positive-integer inputs, compared with the familiar half-exponent scale. The running-time constants and crossover remain to be established; no family scope document is listed.
Problem and buyer
A reconciliation system may need to find which bounded set of integer-valued items adds to a known total. Large ambiguous groups can make exact search expensive.
What the finding could enable
A backend could improve worst-case search for a carefully filtered candidate group if the exponent saving appears at realistic sizes. It enables a potentially stronger exact-search component; full accounting reconciliation needs additional evidence and business rules.
Technical and commercial limits
The problem remains exponential. Currency must be represented as exact scaled integers. Tolerances, negative adjustments, dates, duplicate identities and explanatory priorities change the practical problem. A decision algorithm may require self-reduction to return a witness.
Minimal architecture
Candidate filter -> exact-integer normalization -> search backend -> independently verified witness -> explanation record. Never change ledger data or approve transactions automatically as part of the research prototype.
Existing alternatives and differentiation
Existing exact search, meet-in-the-middle and integer-programming methods are the baseline. A usable improvement must include memory and preprocessing, not only an exponent comparison.
Monetization hypothesis
Hypothesis: AUD 4,000-15,000 for an offline reconciliation benchmark or integration. Price depends on handling a demonstrated unresolved workload; no financial return is established.
Validation experiment
Benchmark n, input bit length, repeated values and adversarial distributions against exact references. Verify every returned subset sum and measure correct negative decisions with known fixtures.
Conditions to reject or defer
Reject if candidate filtering already reduces n enough for current methods, or research overhead eliminates the modest exponent benefit.
Next concrete action
Read the witness-recovery and low-space companion constructions; quantify the ideal exponent saving separately from any implementation result.
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 138
Subject: Subset Sum in $O(2^{0.49n})$ time.
Current alternative sources
Primary documentation reviewed on 8 October 2026. Product availability demonstrates alternatives, not demand or willingness to pay for this proposal.