# Subset-sum decisions: resource, identity and assurance boundary

Family 138. Edition: 9 October 2026. [Source metadata](source.json). Revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.

## Problem and possible application

Two positive-integer randomized decision results suggest separate time and writable-space research improvements. A practical bounded module can preserve original item IDs, check exact witnesses and label ambiguity, unsupported solver range and unknown negatives. Source decision output is not an exact solution count or intended accounting match.

## Source review and boundary

Fast introduction/setup/implementation were read in full, plus numerical lines 1–65. Low-space introduction/implementation/resources were read in full, plus preliminaries lines 1–70. Full proof/certificate closure, source execution and independent acceptance remain open; no family formal-scope document is listed. The known 64-bit main guards require at least 600,000 and 36 billion items respectively; further fixed cutoffs are unselected. Failed guards use exact fallback methods. Fast two-sided and low-space one-sided guarantees cannot be combined without a separate result.

## Business decision

Prototype an identity/count/witness assurance module within the shared platform; defer literal source backends and production speedup claims. Dynamics 365/NetSuite already provide matching and ambiguity controls. No recurring buyer value, novel conventional compression algorithm or profitability is established. [Updated dossier](../../../../opportunities/017-subset-sum-reconciliation/2026-10-09-v2.md).

## Concrete validation

2,294 finite reference/planner controls include 28,404 queries on all 1,089 value words through six items. 150 live solver controls include 1,080 tiny queries and ten generated cases. The 64-equal-value fixture retains exact binomial multiplicity with 98 peak sum records; that support-heavy control is not a general memory claim. Existing CP-SAT supplies checked positive witnesses even when bounded exact count is unknown.

## Next verification action

Test read-only workflow value against incumbent review, then inspect remaining numerical/filtering/alias and low-space representation/survival proof arguments separately. Preserve original identity, exact arithmetic, source word/memory models and error assumptions.