eq-d858d8d35cc9aemathematical expression
Read the equation
Taking the reciprocal of δ makes the score grow as positive discrepancy shrinks, but the expression is undefined at δ=0 and unbounded near zero. It differs from the bounded 1/(1+δ) score used elsewhere. A numerical implementation needs an explicit zero case, positive regularizer, or a restricted domain.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| Phi | Inverse-discrepancy score |
| delta | Positive discrepancy |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
This expression cannot directly assign a finite value to perfect agreement.
Original context
Read the surrounding source passage
8.2 A singularity can be intentional without proving its interpretation The discussed inverse-discrepancy form is Φδ=1δ. For positive δ→0, Φ→+∞; at exactly zero the ordinary real-valued expression is undefined. Treating the singularity as intentional is mathematically permissible if the domain and limiting interpretation are specified. It does not derive a biological birth/death event or a consciousness transition merely by naming the singularity that way. The bounded alternative 1/1+δ approaches one and is a different function. This audit does not replace the original expression with it. It records the different consequences so a future implementation does not silently substitute one model for another. Likewise, ΦΦ is not fully specified if the inner Φ is a scalar while the outer operation originally expects two states. The input and output types of the outer map, its reference, and its prediction rule must be supplied before numerical evaluation.
Exact original notation
\Phi \left(\delta \right)=\frac{1}{\delta }.Sources & provenance
01
Machine_Consciousness_Mathematical_Audit.docx
paragraph 230, math 1 · Sep 17, 2026
\Phi \left(\delta \right)=\frac{1}{\delta }.
02
Machine_Consciousness_Mathematical_Audit.docx
paragraph 230, math 1 · Sep 17, 2026
\Phi \left(\delta \right)=\frac{1}{\delta }.