04-ilang-time / 02-clock
02clockverified
Determines when a part of a system can serve as a clock, how its readings change with λ, how reading it affects it, and what limits its resolution.
# Review: 02-clock v1 - **Subproject:** 04-ilang-time - **Package:** 02-clock - **Reviewed version:** v1 - **Date:** 2026-10-09 --- VERDICT: minor issues ## Issues ### I1. Item 4(a) is answered completely only for the minimal member - **Location:** Step 6, Eq. (2.17), and the second item of "Open issues" - **Severity:** minor - **Problem:** Item 4 concerns every self-driven uniform ring clock with $\theta_m=0$, i.e. every admissible choice of the $\ell_k$ in (2.9). It asks to determine whether the first reading changes the distribution of the second outcome, and when. - v1 gives a sufficient condition for "no change" that holds for every member: $\lambda_1\in\lambda_0\mathbb Z$ or $\lambda_2-\lambda_1\in\lambda_0\mathbb Z$. - It proves the exact condition only for the minimal member. - For the other members, "Open issues" records further no-change values, with an example, but no condition. A requested item is thus left partly unanswered. Every step that v1 does derive is correct; I checked them, including the computation of $\hat D$ in (2.17). - **Fix:** Determine a necessary and sufficient condition, valid for every member with $\theta_m=0$, under which the first reading leaves the distribution of the second outcome unchanged. Derive it, for example from all discrete Fourier components of $D(m)$, as Step 6 does for one component in the minimal case. Keep the minimal-member result (2.17) as a special case of the general condition. Remove the corresponding open issue. ### I2. The extra assumption S2 is not stated in the results that use it - **Location:** Result, items (2.14)–(2.18); Setup, S2 - **Severity:** minor - **Problem:** Item 4 rests on S2: the state after a reading is admissible, which holds when no object of $R$ has the type of $k$. The Setup and "Open issues" state this, but the Result lines (2.14)–(2.18) do not. A later package that quotes these results would lose the condition. - **Fix:** State the condition S2 in the Result lines of (2.14)–(2.18), or once in the Result for item 4. Keep the tags and their meanings.