Observation of a Discrete Time Crystal

• p. 5 Reference [36]

  Nature Communications 6, 7341 (2016)

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: that Nature Communications volume 6 is the 2015 volume. The page 5 image prints '6, 7341 (2016)' as quoted. Nothing in the files gives the true year, so this is a query for the authors.

Second check: another model agreed

• p. 6 Methods, Experimental time sequence, H3 paragraph

  (“Strong random disorder” in Fig. 5)

• p. 8 Fig. 5, U3 block

  Programmable random disorder

Judge's note: Compared the page 6 text with the Fig. 5 image on page 8. The U3 block reads 'Programmable random disorder'. The other quoted labels (Initialization, Spin-spin interactions, Compensation, Prepare for measurement) match the figure. It is plainly the same block, so the mismatch is minor.

Second check: another model agreed

• p. 8 Fig. 5, label under the pulse train

  101 Floquet periods

• p. 1 Fig. 1 caption

  The system evolves for 100 Floquet periods

• p. 6 Methods, Experimental time sequence

  After up-to 100 applica-

• p. 3 main text

  up to N = 100 Floquet periods

Only the authors can say what is right here.

Judge's note: The "101 Floquet periods" label is visible on the page 8 image of Fig. 5. The 100-period statements were found in the text for pages 1, 3 and 6. The caption of Fig. 5 only says "See text for detailed explanations", and nothing in the text explains a 101st period. The 101 may count sampled time points (t = 0 to 100), but the label says periods; only the authors can say which is meant.

Second check: another model agreed

• p. 3 Left column, paragraph 'The global π-pulse…'

  splitting in the Fourier spectrum by

• p. 2 Fig. 2(a) FFT spectrum, ε = 0.03

  ε = 0.03, W t3 = 0

• p. 3 Main text, paragraph on the global π-pulse

  a splitting in the Fourier spectrum by 2ε (Fig. 2(a))

Only the authors can say what is right here.

Judge's note: Reworked: a rotation of π(1−ε) per period gives magnetization (−1)^n cos(nπε), so the peaks sit at 0.5 ± ε/2 in units of 1/T, a separation of ε = 0.03. In the Fig. 2(a) crop the peaks sit at about 0.48 and 0.52 with points spaced 0.01, consistent with 0.03 and not with 0.06. The 2ε would be right in another convention (for example angular frequency in units of π/T), and the text gives no unit, so this is a query about the convention, not a definite error.

Second check: another model agreed

• p. 4 Main text, first paragraph

  the expected DTC to time crystal “melting” boundary

• p. 3 Fig. 3 caption

  the DTC to symmetry unbroken phase boundary

Judge's note: Seen on the page 4 image and in the Fig. 3 caption on page 3. The phrase can be read as 'the DTC-to-(time-crystal-melting) boundary', which is redundant but not wrong, so this is a wording point only.

Second check: another model agreed

• p. 7 Methods, 'Emergence of time crystal…', third paragraph

  This damping can be due to two possible sources: one

Only the authors can say what is right here.

Judge's note: Read the paragraph on the page 7 image. After 'one is…' there is no 'the other'. The next sentence says this residual effect 'can behave like residual σx and σy terms, or coupling between the clock spin states and the Zeeman states', which may be the intended pair, but it is written as two forms of the one effect. Only the authors can say what the second source is.

Second check: another model agreed

• p. 3 Fig. 3 caption (a)

  long-range interation term

• p. 3 Fig. 3 caption

  long-range interation term J0

Judge's note: Seen on the page 3 image in the Fig. 3 caption; it is in the PDF, not an extraction artefact.

Second check: none (judge only)

• p. 7 Methods, Data analysis and fitting procedure, last paragraph

  deviation (67%) confidence interval

• p. 3 Fig. 3 caption

  Grey shaded region indicates 90% confidence level

• p. 7 Methods, data analysis

  one standard deviation (67%) confidence interval

Judge's note: Read on the page 7 image: the text prints "(67%)" just after stating that the sampled peak centres follow a Gaussian distribution. The Gaussian ±1σ coverage is 0.6827, so 68% is the conventional figure; 67% is a loose rounding and the meaning is unchanged. The second point raised (90% in the Fig. 3 caption against 67% here) is not a defect: the caption's 90% refers to the grey shaded region around the numerically determined phase boundary, whereas the 67% refers to the error bars on the fitted points in Fig. 3(b). These are different quantities.

Second check: none (judge only)

• p. 4 Left column, paragraph after Fig. 4

  auxilary probe

• p. 4 Left column, paragraph after Fig. 4

  entanglement that underly the DTC phase

Judge's note: Both spellings seen on the page 4 image in the paragraph after Fig. 4.

Second check: none (judge only)

• p. 5 Reference [30]

  Kanp, M.

• p. 5 Ref. [30]

  & Kanp, M.

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: that the co-author of arXiv:1607.07868 is M. Knap. The page 5 image prints 'Kanp, M.' as quoted; the files do not give the correct spelling.

Second check: none (judge only)

• p. 6 Methods Summary, Generating the effective Ising Hamiltonian, last sentence

  Raman beatnode detuning to be 155 kHz

• p. 6 Generating the effective Ising Hamiltonian

  Raman beatnode detuning

Judge's note: Seen on the page 6 image. The same page uses 'beatnote' three times ('pair of beatnote frequencies', 'beatnote frequencies detuned 4.8 MHz', 'closest beatnote').

Second check: none (judge only)

• p. 6 Methods, Pulse shaping, first paragraph

  is applied as a square pulse will

• p. 6 Pulse shaping

  is applied as a square pulse will be significantly broadened

Judge's note: Seen on the page 6 image in the pulse-shaping section; a word is missing.

Second check: none (judge only)

• p. 7 Methods, Data analysis and fitting procedure, before Eq. 5

  nomenologial lineshape

• p. 7 Methods, Data analysis and fitting procedure

  nomenologial lineshape, a Lorentzian of the log10(ϵ)

• p. 7 Methods, Data analysis and fitting procedure

  extracted peak centers ϵp

• p. 7 Data analysis

  phenomenologial lineshape

Judge's note: Seen on the page 7 image, hyphenated across the line as "phe-nomenologial"; the letter c is missing. The ε/ϵ glyph switch raised in one reviewer note is handled under C018.

Second check: none (judge only)

• p. 7 Methods, Data analysis and fitting procedure

  a Lorentzian of the log10(ϵ)

• p. 7 Methods, Data analysis, last paragraph

  extracted peak centers ϵp

Judge's note: On the page 7 image the two glyphs are visibly different: ϵ appears in "log10(ϵ)" and "ϵp", while ε appears in Eq. 5 and in the rest of the section. The same quantity is clearly meant, so this is cosmetic.

Second check: none (judge only)

• p. 7 Methods, Data analysis and fitting procedure, second paragraph

  the same 10 instance of disorder

Judge's note: Seen on the page 7 image. The very next sentence uses the plural correctly ("These 10 instances are averaged").

Second check: none (judge only)

• p. 9 Fig. 7 caption (b)

  experimnetal result

• p. 9 Fig. 7 caption

  experimnetal result for one single instance

Judge's note: Clearly legible in the enlarged crop of the Fig. 7 caption and on the page 9 image.

Second check: none (judge only)