IndisputableMonolith.Ethics.SigmaExternalizationAudit
SigmaExternalizationAudit module supplies the core definitions for auditing sigma externalization in the Ethics domain of Recognition Science. It introduces sigmaImpact to quantify output effects, isSafeOutput and safe_when_small to certify safety, plus auditCost and audit_is_O1 to bound verification effort. The module shows zero output implies zero impact and establishes constant-time audits. It rests on Mathlib alone with no internal theorem dependencies.
claimIntroduces the map $I: xmapsto sigmaImpact(x)$, the predicate isSafeOutput, the implication zero_output_zero_impact, the bound safe_when_small, the cost function auditCost, and the claim audit_is_O1 that verification runs in $O(1)$ time.
background
The module sits in the Ethics subdomain and treats sigma externalization as an operation whose outputs must be measured for impact and certified safe before release. It defines sigmaImpact as the quantitative effect of an output, zero_output_zero_impact as the statement that the zero output produces zero measured effect, isSafeOutput as the safety predicate, safe_when_small as the sufficient condition on output magnitude, auditCost as the resource measure of verification, and audit_is_O1 as the assertion that this cost is bounded by a constant. The setting assumes only the ordered field structure of the reals supplied by Mathlib.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the ethical audit primitives required by any larger Recognition Science construction that externalizes sigma values. It directly supports downstream claims on safe output release and constant-cost verification, closing the interface between the mathematical sigma ladder and ethical constraints. No parent theorems are listed in the current dependency graph, yet the definitions are positioned to feed ethical validation layers.
scope and limits
- Does not supply numerical evaluation procedures or simulation code.
- Does not treat multi-agent or distributed externalization scenarios.
- Does not derive bounds from the phi-ladder or J-cost structure.
- Does not address quantum or relativistic corrections to impact.