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.
# External verification: 02-clock - **Subproject:** 04-ilang-time - **Package:** 02-clock - **Verified version:** v2 - **External round:** 1 of 2 - **Date:** 2026-10-10T06:50:21+02:00 - **Focus points:** none --- VERDICT: minor issues ## Summary The spectral calculations, classification of ring-clock generators, two-reading criterion—including the N = 3 example—and resolution bound are correct. Two qualifications remain: the general clock-reading claims need admissibility and label-independence conditions, and the Result section omits the stationary exception when summarizing indexing intervals. Neither issue changes the calculations for admissible, label-independent clocks. ## Issues ### I1. General clock-reading claims need admissibility qualifications - **Location:** Steps 1–3, especially Eq. (2.6); Setup assumption S2; Open issues - **Severity:** minor - **Problem:** S2 correctly qualifies the sequential-reading results, but the earlier clock-reading claims remain unrestricted. A place partition does not necessarily define an admissibility-preserving reading when identical-type instances are involved. For example, for two identical invariant-family objects in the admissible state \(\lvert v\rangle\otimes\lvert v\rangle\), with both place amplitudes of \(v\) nonzero, reading one object's place and obtaining \(0\) produces \(\lvert0\rangle\otimes\lvert v\rangle\), which violates (1.11). Equality of the two singleton views, as noted after (2.3), establishes label-independent statistics but does not establish a permissible reading operation. Thus (2.4)–(2.6) remain valid as formal distribution formulas, but identifying every ticking place distribution with an available clock reading needs an additional qualification. - **Suggested fix:** Explicitly condition the clock/readability conclusions on a label-independent part and admissibility-preserving reading projectors. For ring clocks, propagate the sufficient restriction that no object of \(R\) has the clock's type beyond item 4. For more general parts, distinguish the formal place distribution from a reading compatible with A3, A6 and M6. ### I2. Result summary omits stationary views - **Location:** Result, bullet summarizing Eqs. (2.7)–(2.8) - **Severity:** minor - **Problem:** The statement “Otherwise the maximal indexing intervals are half-open of length \(\tau=2\pi/\omega_*\)” also includes the stationary case \([C_K,V_0]=0\). In that case \(\omega_*\) is undefined, the recurrence group is \(\mathbb R\), and no interval of positive length is indexed. Step 3 handles this correctly; the summary does not. - **Suggested fix:** Restrict the half-open-interval statement to nonstationary views with commensurate active gaps, and separately state the stationary exception. ## Focus points None given.