Theorem. Independent discovery probability [ftip-00I7]
✍️source

For \(B\in \mathbb N\) independent discovery events with the probabilities declared in Convention [ftip-0077], the identity in Theorem [ftip-0078] gives \(\Pr (D_B)=1-\prod _{i=1}^{B}(1-p_i)\).

Theorem. Independent discovery probability [ftip-00I7]
✍️source

Finite probability and execution results [ftip-00I2]

Convention. Domains of the finite results [ftip-00I5]

Theorem. Independent discovery probability [ftip-00I7]
✍️source

Theorem. Discovery budget for a failure threshold [ftip-00I8]

Theorem. Support under finite exponential tilting [ftip-00I9]

Theorem. Uniform proxy error and objective regret [ftip-00IA]

Theorem. Utility under a change of evaluation law [ftip-00IB]

Theorem. Response classes under feedback refinement [ftip-00IC]

Theorem. Equal execution inputs give equal replay traces [ftip-00IJ]

Theorem. Observational equivalence under a common update kernel [ftip-00IK]

Theorem. Conditions for an admissible commit decision [ftip-00IL]

Theorem. Admission of a finite audit plan [ftip-00IM]

Theorem. Discovery under independent attempts [ftip-0078]

Proof.

Convention. Repeated attempts and the discovery event [ftip-0077]