DANDI:000939

The probe was implanted either vertically ( n = 931 units from 14 mice, range ... or parallel to PoSub cell layers ( n = 1,999 units from 18 mice ... PoSub units were subdivided into putative excitatory cells ( n = 1,835) and putative PoSub-FS cells ( n = 427) based on mean firing rate and waveform shape ... were classified as PoSub-HD cells (>0.2 bits per spike, n = 1602, 87% of excitatory cells

Results, High-density recordings in the PoSub of freely moving mice, paragraph 1; Methods, Spike sorting and unit classification, and HD tuning curves and tuning metrics

Under the Methods' classes there are 1,661 excitatory cells, 430 FS cells and 1,512 HD cells (fraction 0.910), all within tolerance; the code's 0.35 ms cut gives 1,699, 415, 1,532 and 0.902, and the HD threshold as the 99th percentile of the time-reversed information (0.272 bits per spike) 1,481 and 1,501. The 14 vertical sessions hold 931 units, the paper's number. The 17 parallel sessions hold 1,760 units, below the tolerance of 1,999 - 200. The code's list of the paper's 32 PoSub sessions (dataset_All.list) has one session the dandiset lacks, A8603-210602, the Neuropixel recording of figshare Dataset_4, with 239 units; 1,760 + 239 = 1,999, the paper's count. The shortfall is that one session's units, the case the criterion foresees, so the counts reproduce. The dandiset's labels agree with the code's classes for 99.9% of units (excitatory and FS) and 99.7% (HD).

How the test differed from the paper’s method

• A negative waveform is read as a finite trough-to-peak in the units table; the code marks positive spikes with NaN, and 177 units have none.
• Speed is computed from the position (Gaussian smoothing of 0.1 s s.d.), as the files hold no speed series; the agreement of the recomputed classes with the dandiset's labels (99.9%) supports it.
• Viable units are those at or above 0.5 Hz (Methods, at least 0.5 Hz; the code's gd uses > 0.5).
• The time-reversed control reverses the HD series over the used span (the tracked epoch, or its half) before the speed mask, as the claims file says; round 1 reversed only the used samples.

Distribution of HD information carried by tuning curves of putative excitatory cells in PoSub ( n = 1835; Wilcoxon signed rank test vs time-reversed control, z = 37.1

Extended Data Fig. 2b,c

Median log10 HD information 0.10 against -1.41 for the time-reversed controls, |z| = 35.3, p = 7e-273, n = 1,661 (paper z = 37.1, n = 1,835); 97 to 100% of excitatory cells per session are above their control. The histogram over viable units has maxima near log10 = -1.67 and 0.19, shown and not judged.

at the population level, the quantity of HD information conveyed by PoSub-FS cells was significantly higher than that of the time-reversed control

Results, Tuning of PoSub-FS cells is stable and anchored to landmarks, paragraph 1; Figure 2a

Median log10 HD information -1.70 against -2.63, |z| = 17.86, p = 2e-71, n = 430 (paper z = 17.9, n = 427); 419 of 430 FS cells exceed their control. Median HD information of HD cells 1.35 bits per spike, of FS cells 0.02.

The information contained in PoSub-FS cell tuning curves was sufficient to accurately decode the animal's HD from PoSub-FS cell spiking activity

Results, Tuning of PoSub-FS cells is stable and anchored to landmarks, paragraph 1; Figure 2b; Extended Data Fig. 2e

Mean over 31 sessions of the FS decoder's median error 36.0 degrees, chance 92.8, both scored against the real HD (signed-rank over sessions p = 1.3e-6); Pearson r between FS cell number and error -0.449, p = 0.011, n = 31. HD-cell decoder 9.9 degrees.

How the test differed from the paper’s method

• 31 sessions where the paper has 32.

the tuning of PoSub-FS cells was stable within a single exploration epoch (Extended Data Fig. 2h ) and independent of the enclosure geometry (Fig. 2c ), reflecting the properties of canonical PoSub-HD cells

Results, Tuning of PoSub-FS cells is stable and anchored to landmarks, paragraph 2; Figure 2c; Extended Data Fig. 2j

20 sessions with a triangle. FS median r 0.80 against -0.01, |z| = 14.2, p = 1e-45, n = 273 (paper 264, z = 14.0); HD 0.96 against -0.01, |z| = 28.9, p = 4e-184, n = 1,118 (paper 1,013, z = 27.6). The 2 degree smoothing of the code gives the same.

How the test differed from the paper’s method

• The control correlates the time-reversed square curve with the time-reversed triangle curve shifted by the same session rotation; the criterion says "the same for time-reversed curves" without saying which curves are paired.

PoSub-FS cell tuning curve correlation across two halves of the square arena epoch

Extended Data Fig. 2h,i

FS median r 0.83 against -0.011, |z| = 17.91, p = 1e-71, n = 430; HD 0.97 against -0.011, |z| = 33.7, p = 1e-248, n = 1,512; the same at 2 degree smoothing.

How the test differed from the paper’s method

• The halves are halves of the time above 2 cm/s, taken in order; the code's regIntervals(ep, 2) is not described further.

PoSub-FS cell tuning curves followed the rotated distal landmark in concert with PoSub-HD cells

Results, Tuning of PoSub-FS cells is stable and anchored to landmarks, paragraph 2; Figure 2d-f

Six figshare sessions, 99 FS cells, the paper's number. Under the main exclusion reading 89 of 96 rotations are kept; the median absolute difference between FS and mean HD realignment is 36.2 degrees against 91.8 for the control, |z| = 8.57, p = 1e-17 (paper z = 8.25). The second reading (95 kept), the change condition alone (93) and the code's rule (91) give |z| 8.58 to 8.59.

How the test differed from the paper’s method

• Condition (1) of the Methods ("less than 45 degrees of mean decoder error in the following 200 s epoch") is read as the change of circular mean error from the 200 s before the rotation to the 200 s after it, as the code computes it; read literally it would exclude every rotation back to the first wall.
• The sigmoid is fitted to the decoder error re-centred on the preceding epoch's mean, from 50 s before to 200 s after each rotation (the code's window), with scipy's curve_fit; the code's second, fine sigmoid fit is not run.
• The control is the FS cells' realignment from curves with the HD time-reversed within each epoch segment, against the real HD cells' mean; the paper does not say what the control reverses.
• Cell classes are the figshare files' own CellTypes.
• The code's angular head velocity is computed here from the head direction in the 50 s before each rotation, as Ahv.mat is not read.

In mice, ADN-HD cells tend to have broader HD tuning curves than PoSub-HD cells

Results, Equivalence of PoSub-HD and FS cell tuning in Fourier space, paragraph 1; Figure 3c

97 ADN-HD cells recomputed from the figshare spike times (the files' CellTypes also give 97, agreement 100%). Median width 62 against 42 degrees for 1,512 PoSub-HD cells, z = 11.58, p = 4e-31 (paper z = 11.4). The figshare data give ADN-HD cells only, so the claim's notes on the dataset side are the PoSub-HD widths of the dandiset.

the similarity between PoSub-HD and PoSub-FS cell Fourier signatures on a population level was preserved when the analysis was limited to HD cells with a single receptive field. Additionally, it was preserved when a threshold was applied to keep only the best isolated unit clusters or when a higher velocity threshold was used to compute tuning curves

Results, Equivalence of PoSub-HD and FS cell tuning in Fourier space, paragraph 3; Extended Data Fig. 3j,k

The Fig. 3f test holds under every control and reading, PoSub-HD closer than ADN-HD with p from 0.019 to 5e-22 (multipeak below 0.05, 762 and 69 cells, paper 789 and 69; contamination at most 0.2, 1,399 and 81, paper 1,472 and 83; 10 cm/s, 1,512 and 97). The multipeak scores differ (z = 4.18, p = 3e-5; paper z = 4.25), ADN-HD cells scoring lower (median 0.022 against 0.049), as the paper's counts below 0.05 (69 of 97 ADN-HD, 789 of 1,602 PoSub-HD) imply. The answer to the question in questions/000939.yaml changed the outcome. The statement had ADN-HD scores higher, the reverse of what was found, and the outcome was partially_reproduced; the reader found that the paper gives no direction for this test and amended the claim to say only that the scores differ, with the multipeak test accepted in either direction. The analysis is unchanged; all four tests now meet the criterion.

How the test differed from the paper’s method

• The contamination score takes the autocorrelogram bin next to zero (0.5 to 1.5 ms), as the code does (it zeroes the zero bin); the Methods say "the value at 0.1 ms".
• The contamination and speed controls are applied to FS cells too when computing the FS mean, as the code's onlyGoodClusters filters FS cells; the 10 cm/s control recomputes all curves.

while the shape of Fourier signatures was largely uniform among HD cells from the same brain region, it was highly variable among PoSub-FS cells

Results, Equivalence of PoSub-HD and FS cell tuning in Fourier space, paragraph 5; Extended Data Fig. 3g

What the paper reports

• cell type effect on distance from own population mean: one-way ANOVA, F (2,2123) = 169, p = 5 × 10⁻⁶⁹ (n = 427 PoSub-FS, 1,602 PoSub-HD and 97 ADN-HD cells)

FS distances from their own population mean exceed PoSub-HD distances under all four readings (z/3 5.78 to 5.97, p x 3 below 1e-66; paper z = 5.71). With the figshare ADN-HD cells, reported and not judged, the one-way ANOVA gives F(2,2036) = 184.3, p = 3e-74 (Euclidean, squared modulus; paper F(2,2123) = 169), FS against ADN z/3 = 3.42 and PoSub-HD against ADN z/3 = 0.48 (paper 3.40 and 0.45).

In contrast, the Fourier components of individual PoSub-FS cells had random phases relative to each other

Results, Equivalence of PoSub-HD and FS cell tuning in Fourier space, paragraph 5; Extended Data Fig. 3l

PoSub-HD rho = 0.322 (p below 1e-15) and 0.087 (p = 1e-4); FS rho = 0.014 (p = 0.77) and 0.005 (p = 0.91); with the code's classes FS p = 0.90 and 0.74.

Auto-correlograms of tuning curves for cells with maximum power for the second component showed a second maximum at 180°, reflecting their twofold radial symmetry. For cells with maximum power in the third component, auto-correlograms peaked at 120° and 240°

Results, Equivalence of PoSub-HD and FS cell tuning in Fourier space, paragraph 6; Extended Data Fig. 4a

Twofold FS cells (146) at 180 degrees, median 0.19 against 0.02, signed-rank p = 3e-13, rank-sum p = 2e-13; threefold cells (47) at 120 degrees, 0.17 against -0.002, p = 2e-4 and 6e-5; at 240 degrees, shown only, 0.18 against -0.02, p = 3e-6.

The distribution of PoSub-HD cells occupied the center of the PoSub-FS cell distribution while that of ADN-HD cells was closer to the periphery

Results, Equivalence of PoSub-HD and FS cell tuning in Fourier space, paragraph 6; Extended Data Fig. 4c,d

Median distance to the FS centre 2.34 for PoSub-HD against 3.39 for ADN-HD, z = 2.93, p = 0.0034, n = 1,512 and 97 (paper z = 4.26).

How the test differed from the paper’s method

• Isomap from scikit-learn, not the MATLAB Dimensionality Reduction Toolbox.

The distribution was heavy-tailed (Fig. 4f ), with the ratio of s.d. and mean input weight (i.e. coefficient of variation), in the range where in silico simulation predicted the emergence of radial symmetries

Results, PoSub-FS cell tuning reveals key circuit properties, paragraph 2; Figure 4e,f; Extended Data Fig. 2f,g

1,176 connections among 24,498 HD-FS pairs (4.8%), in every session. strZ mean 8.58, s.d. 16.32, CV 1.90, skewness 9.34, median 4.60. Spans of 50 and 25 ms give identical results because the test window (0 to 2 ms) and the baseline kernel never reach either edge, so the span variant tests nothing. strR, a variant, has CV 0.71.

How the test differed from the paper’s method

• In cch_conv the window of 41 bins has an odd width, so its centre index is fractional; the two central samples are hollowed here (an assumption that only shifts the baseline slightly).

Targeted illumination of ADN (inactivating the inhibitory presynaptic terminals of the TRN neurons) resulted in a net increase of the firing rates of ADN-HD cells but not of untuned neurons (non-HD cells) recorded in the same sessions

Results, PoSub-FS cells receive directionally uniform thalamic input, paragraph 2; Extended Data Fig. 7b-d

What the paper reports

• width of ADN-HD tuning curves, baseline against high gain: Wilcoxon signed rank test, z = 0.67, p = 0.5 (n = 52 ADN-HD cells)

Figshare Dataset_6, 10 ADN sessions from 3 mice, 127 cells kept (paper 127), 53 ADN-HD (paper 52) and 74 non-HD (paper 75). ON/OFF ratio 1.54 against 1.06, z = 6.85, p = 8e-12 (paper z = 6.57); non-HD rates do not change (p = 0.13). ADN-HD width 62 against 58 degrees, signed-rank p = 0.61, rank-sum p = 0.80 (paper p = 0.5). The ratio is near 1.5 in each mouse.

Similarly to the upstream ADN-HD cells, PoSub-HD and PoSub-FS cells increased their firing rates

Results, PoSub-FS cells receive directionally uniform thalamic input, paragraph 3; Figure 5b; Extended Data Fig. 7e,f

Two ArchT mice (A1813, A1815) and three control mice. FS ON/OFF ratio 1.33 against 1.04, z = 5.41, p = 6e-8, n = 33 and 43 (paper z = 4.99, n = 47 and 38); HD 1.46 against 1.00. Both ArchT medians exceed 1 and the control medians, in each ArchT mouse. The HD comparison with control is significant here (z = 7.77, n = 62 and 92), where the paper's is not (z = 1.69, 83 and 89); the criterion does not judge it. With every window moved 2.5 s from the pulses the ArchT ratio is 0.91, and the decoded pulses match the figshare pulse table within 0.1 ms, so the pulse times share the spike clock. Variant with the three figshare ArchT mice added (102 HD, 50 FS ArchT cells, 5 mice), deciding nothing. FS z = 5.60, p = 2e-8, ArchT medians 1.29 (FS) and 1.32 (HD); one figshare mouse (A1804) has medians below 1.

How the test differed from the paper’s method

• The dandiset holds 2 of the paper's 5 ArchT mice; the other three are in figshare Dataset_6. The claim is judged on the dandiset, as the claims file gives it data dataset; the five-mouse result is a variant (notebook, after ed8e).
• Light pulses are read from the optogenetic series as four interleaved channels (see findings); they match the figshare Opto_TS.csv tables.

increased their firing rates (Fig. 5b and Extended Data Fig. 7e,f ) while preserving their HD tuning

Results, PoSub-FS cells receive directionally uniform thalamic input, paragraph 3; Extended Data Fig. 7g-j

PoSub-HD width OFF against ON 44 and 46 degrees, signed-rank p = 0.53, n = 62 (paper z = 0.30); rank-sum p = 1.0. FS ON-OFF tuning correlation, ArchT 0.72 against control 0.69, p = 0.68, n = 33 and 43 (paper z = 1.14). These are claims of absence on smaller samples than the paper's (83 and 47); with the three figshare ArchT mice added, a variant, n = 102 and 50, p = 0.24 and 0.95.

How the test differed from the paper’s method

• Two of five ArchT mice (see fig5b-posub-rates-increase); the five-mouse result is a variant.

These simulations allowed us to establish that multiplicative gain is indeed detectable in tuning curves with correlation values similar to those observed experimentally in PoSub-FS cells and that our experimental results in PoSub-FS cells are best explained by significant additive gain

Results, PoSub-FS cells receive directionally uniform thalamic input, paragraph 4; Methods, Gain modulation analysis, simulations; Extended Data Fig. 8c,d

With the noise titrated to the observed correlations (4.25 Hz; no-gain median r 0.731 against the observed 0.730) and the simulated control, the multiplicative simulation gives multiplicative factors above control (p = 0.022) and the additive simulation reproduces the data's pattern (additive p = 8e-5, multiplicative p = 0.13; data p = 3e-4 and 0.27); over 50 seeds all three hold in 80% of runs. Against the recorded control factors the titrated additive simulation also changes the multiplicative factor (p = 0.0008), but the titrated no-gain simulation already differs from the recorded control (multiplicative p = 0.0026, additive p = 0.039), so that comparison cannot tell gain types apart. Variant with the code's fixed noise of 1.8 x 1.8 Hz (simulated r 0.82, above the observed 0.73), which the criterion does not call for, as it titrates the noise. The additive simulation changes the multiplicative factor against the simulated control (p = 0.008), and against the recorded control the multiplicative simulation is not detected (p = 0.80). The outcome was partially_reproduced until round 3, as it counted the fixed-noise readings; round 2 found that they are not readings of the criterion, and round 3 agreed with reproduced. With the three figshare ArchT mice, a variant, the same split (titrated noise 4.00 Hz; simulated control p = 0.019, 3e-7 and 0.38; recorded control, additive simulation multiplicative p = 7e-5).

How the test differed from the paper’s method

• The noise is titrated as the Methods and the criterion describe (simulated high-gain curves "until we obtained a similar distribution of tuning curve correlations to the one observed experimentally"), on a grid of s.d. matched by the median correlation; the code's fixed s.d. of 1.8 x 1.8 Hz is a variant. The match by median is a choice.
• Simulated factors are compared with the simulated control group (control cells with ON = OFF plus noise, as Figure_GainSimulation.m builds it) and with the recorded control factors, two readings of the criterion's control group.

this high degree of multiplicative modulation largely reflected the modulation of the upstream ADN-HD cells

Results, PoSub-FS cells receive directionally uniform thalamic input, paragraph 4; Extended Data Fig. 8e,f

Figshare ADN-HD (53) against the dandiset's ArchT PoSub-HD cells (62). Multiplicative 1.26 against 1.30, p = 0.47; additive 0.032 against 0.009, p = 7e-6 (paper z = 0.55 and 5.07). Under reading (b), p = 0.62 and 0.002. The PoSub-HD side holds 2 of 5 ArchT mice.

Similarly, PoSub-FS cell pairs also preserved their coupling across WAKE and REM, albeit to a smaller degree than PoSub-HD cell pairs (Fig. 6a-c , middle). Notably, the coupling of the two cell populations to each other was also preserved across WAKE and REM

Results, PoSub-FS cells are coupled to the PoSub-HD ring manifold, paragraph 2; Figure 6a-c

27 sessions with at least 100 s of REM inside the home-cage epochs (paper 26). With the code's cell selection (HD and FS cells, no rate condition) and pairs with a glmfit warning removed, WAKE against REM coupling gives HD-HD r = 0.641 (34,611 pairs), FS-FS r = 0.364 (2,683, p = 1e-84), HD-FS r = 0.359 (19,602), all positive with p below 1e-80, FS-FS below HD-HD; the pair counts are close to the paper's (34,270, 2,492, 18,992). Spearman 0.762, 0.417 and 0.514. The glmfit mirror flags 1,795 HD-HD pairs (4.9%), 24 HD-FS and no FS-FS; the round-1 rule flags the same pairs. The flagged fits diverge (median |coupling| 2.77 in WAKE, up to 3e73, against 0.28 in kept pairs; the lower REM rate of the pair is below 1 Hz in 32% of them). Keeping them gives a pooled HD-HD Pearson r of 0.000 and a Spearman r of 0.759. The round-1 selection of cells above 1 Hz in both states gives 0.698, 0.380 and 0.425. Fitted at four more lags (-10, -1, 1 and 10 s) in 9 of the 27 sessions, warnings flag 60 more HD-HD pairs of 10,507 (0.6%; 417 at lag 0) and no more FS-FS or HD-FS pairs; removing them moves the HD-HD r of those sessions from 0.638 to 0.647, with FS-FS (0.282) and HD-FS (0.479) unchanged.

How the test differed from the paper’s method

• Only lag 0 is fitted for the result, so a pair is removed for warnings at lag 0 (WAKE or REM, either order); the code removes a pair with a warning at any of 201 lags. A check at four more lags in every third session, chosen for time, removes 0.6% more HD-HD pairs and changes their r by 0.009.
• The fits mirror glmfit's iteratively reweighted least squares in Python (start at y + 0.25, weights sqrt(mu), bad-scaling warning when a weight falls below eps^(2/3) of the largest at any iteration, iteration limit 100, convergence at 1e-6 relative change). That this flags the pairs MATLAB's glmfit would is an assumption, and the outcome rests on it for HD-HD pairs.
• Cells as Figure_GLMRemWake.m selects them (ixHd = isHd & isGd, ixFs = isFs & isGd). Round 1 required rates above 1 Hz in WAKE and REM, taken from a sanity-check block of GetGLM_Forward.m after its return statement; it is now a variant.
• REM is the scored REM inside the home-cage epochs; the files' sleep states run past the recording in three sessions and put REM inside an exploration epoch in two (see findings).
• Pairs counted once, unordered; the coupling is the mean of the two ordered fits, as the Methods say.

Predictably, the polarity of the cross-coupling coefficient depended on the HD tuning relationship within each cell pair during both WAKE and REM

Results, PoSub-FS cells are coupled to the PoSub-HD ring manifold, paragraph 2; Extended Data Fig. 9d

HD-FS r = 0.758 (WAKE) and 0.281 (REM), n = 19,602; FS-FS r = 0.451 and 0.123, n = 2,683; all p below 1e-9. Pairs as in fig6c-coupling-preserved-wake-rem (code's selection, glmfit warnings removed).

How the test differed from the paper’s method

• REM inside the home-cage epochs, and the pair selection of fig6c-coupling-preserved-wake-rem.

The HD tuning curves of both PoSub-HD and PoSub-FS cells computed using virtual HD values during WAKE were equivalent to those computed using real HD values

Results, PoSub-FS cells are coupled to the PoSub-HD ring manifold, paragraph 3; Figure 7a,b; Extended Data Fig. 10e

HD median r 0.94 against -0.002, |z| = 33.7, p = 1e-248, n = 1,512 (paper z = 34.7); FS 0.84 against 0.02, |z| = 17.95, p = 4e-72, n = 430 (paper z = 17.9). Per-session medians 0.77 to 0.98 (HD) and 0.62 to 0.95 (FS).

How the test differed from the paper’s method

• Isomap from scikit-learn, fitted on at most 4,000 population vectors per session drawn at random (seeded), with the others placed by its out-of-sample transform; an assumption for time.

Distance of population vectors to the center of the manifold ( d ) is the same during WAKE and REM

Extended Data Fig. 10b,d; Figure 7c legend

Shuffled mean distance 0.33 to 0.65 of the real in every session, signed-rank p = 1.2e-6, n = 31 (paper z = 4.79). REM against WAKE in the joint embedding, median 0.98 against 1, p = 0.46, n = 27 (paper z = 0.17).

How the test differed from the paper’s method

• The manifold centre is the mean of the first two Isomap dimensions.
• REM inside the home-cage epochs (see findings).

Notably, HD tuning of PoSub-FS cells could also be accurately estimated during REM based solely on the virtual HD obtained from the HD ring attractor manifold

Results, PoSub-FS cells are coupled to the PoSub-HD ring manifold, paragraph 4; Figure 7c,d; Extended Data Fig. 10f

27 sessions. Reading (i), HD median r 0.86, |z| = 30.4, n = 1,259; FS 0.43, |z| = 11.4, n = 336. Reading (ii), 0.82 and 0.36, |z| = 30.3 and 11.5. All p below 1e-29 (paper z = 29.2 and 10.4, n = 1,148 and 317).

How the test differed from the paper’s method

• The control reverses the virtual HD in time within REM.
• REM inside the home-cage epochs (see findings).

We first established the functional border between PoSub and posterior retrosplenial cortex (pRSC) using a Neuropixel linear electrode array

Results, High-density recordings in the PoSub of freely moving mice, paragraph 1; Figure 1a-c

Qualitative, as the criterion says. 134 excitatory cells (the file's own count 137). The running mean HD information is 0.008 to 0.240 bits per spike over the top 1.4 mm and 0.777 to 1.192 from 1.8 mm down, with one crossing of its half-range level, at -1.675 mm; a smaller local maximum of 0.191 at -0.625 mm, and two more of 0.107 and 0.240 at -0.925 and -1.375 mm. The crossing lies at cellDep = -35 um in the file's units. GetCellTypes_PoSub.m carries, commented out, a line that drops units above cellDep = 0 from the PoSub cells for this recording, so the low end is the pRSC side (71 excitatory cells, mean 0.145 bits per spike) and the high end the PoSub side (63 cells, mean 0.905). The files hold no probe geometry; which end is shallower rests on the code's depth - max(depth).

How the test differed from the paper’s method

• Depth from CellDepth.mat set to 0 at the largest value, as Figure_SingleRec_NPX.m does with its depth variable (depth - max(depth)); the files hold no probe geometry to confirm the sign.

Across the cell population, the Fourier power decayed rapidly as a function of frequency. Hence, for clarity, we focused our analysis on the relative power of the first ten Fourier components that contained, on average, 98% of the total power

Results, Equivalence of PoSub-HD and FS cell tuning in Fourier space, paragraph 2

Squared-modulus power gives a mean fraction of 0.989 in harmonics 1 to 10 for FS and HD cells pooled, 0.969 for FS and 0.994 for HD, all within 0.98 +- 0.02; mean power falls to 0.10 of the first harmonic's at the fifth. Root-mean-square power gives 0.872, 0.778 and 0.898, none within tolerance. The criterion asks for a population within tolerance under each power reading, so it holds under one of the two. Only the squared modulus satisfies the Parseval check that the Methods report (ratio 1.0000 here).

How the test differed from the paper’s method

• The Methods' "root mean square of the projection values onto the sine and cosine basis" is read as sqrt((re^2 + im^2) / 2) of the complex coefficient.

the Fourier signature of ADN-HD cells was different from both PoSub-HD and PoSub-FS cells, with higher power at low frequencies and lower power at higher frequencies

Results, Equivalence of PoSub-HD and FS cell tuning in Fourier space, paragraph 3; Figure 3e; Extended Data Fig. 3f

What the paper reports

• two-way ANOVA, Fourier component by cell type interaction, F (9,19116) = 2.76, p = 0.003 (n = 427 PoSub-FS, 1,602 PoSub-HD and 97 ADN-HD cells)

The direction holds under both readings and both powers (ADN-HD mean at component 1 0.509 against 0.398 and 0.358; ADN cumulative signature above both at components 1 to 9). With squared-modulus power and cell type as a numeric covariate (the code), the component by cell type interaction gives F(9,18333) = 1.09, p = 0.365 (paper F(9,19116) = 2.76, p = 0.003). Root-mean-square power gives F = 10.68, p = 1e-16, and a categorical cell type gives F(18,18324) = 24.7, p = 5e-82 (squared modulus) and 44.6, p = 2e-155. The test holds under some readings and not under the one that follows the code, so the claim holds in part. A numeric code for three cell types tests a linear trend from FS through PoSub-HD to ADN-HD; FS and ADN-HD both depart from PoSub-HD at component 1 in the same direction, which such a trend does not capture. The PoSub-only ANOVA, a variant, gives F(9,17460) = 11.4, p = 6e-18.

How the test differed from the paper’s method

• The repeated-measures interaction is computed as the univariate test of ranova, with the within-subject deviations regressed on the between-subjects term, not with MATLAB.
• 1,942 PoSub cells from 31 sessions where the paper has 2,029 from 32.

we found that the average Fourier signature of the PoSub-FS cell population was often indistinguishable from the Fourier signatures of individual PoSub-HD cells

Results, Equivalence of PoSub-HD and FS cell tuning in Fourier space, paragraph 3; Figure 3f

What the paper reports

• Mann-Whitney U test, p < 10⁻⁹ (n = 1,602 PoSub-HD and 97 ADN-HD cells)

PoSub-HD spectra are closer to the mean FS spectrum under all four readings. Squared modulus, D_KL(cell||FS) (the Methods' direction), median 0.082 against 0.133, p = 0.008; squared modulus, D_KL(FS||cell) (the code's), p = 1e-7; root mean square, p = 1.8e-9 and 3e-12. p is below 1e-9 under one reading only, which is the criterion's partial outcome.

Compared to controls, the spectrum of PoSub-FS cells showed higher power for the first three Fourier components only

Results, Equivalence of PoSub-HD and FS cell tuning in Fourier space, paragraph 4; Figure 3g

What the paper reports

• component by condition interaction, FS against time-reversed control: two-way ANOVA, Fourier component by cell type interaction, F (9,3834) = 64.1, p = 4 × 10⁻¹¹⁰ (n = 427 PoSub-FS cells)
• first component, FS against control: Wilcoxon signed-rank test, z = 0.65, p = 8 × 10⁻¹⁰, Bonferroni-corrected (n = 427 PoSub-FS cells)
• second component, FS against control: Wilcoxon signed-rank test, z = 0.85, p = 3 × 10⁻¹⁶, Bonferroni-corrected (n = 427 PoSub-FS cells)
• third component, FS against control: Wilcoxon signed-rank test, z = 0.46, p = 4 × 10⁻⁵, Bonferroni-corrected (n = 427 PoSub-FS cells)

Interaction significant under both powers (squared modulus F(9,3861) = 122.9, p = 1e-203; root mean square F = 227.2; paper F(9,3834) = 64.1, p = 4e-110). After Bonferroni correction, squared modulus, components 1 and 2 are above control (p = 4e-28, 8e-20) and component 3 is higher in median (0.114 against 0.093) but p = 0.064; root mean square, components 1 to 4 are above control (component 4, p = 0.003). The set 1, 2 and 3 and no other holds under neither power. Round 1 had component 3 significant (p = 0.028) with squared-modulus power; the change comes from the corrected time-reversed control (the HD series reversed before the speed mask, as the claims file says).

How the test differed from the paper’s method

• The time-reversed control reverses the HD series over the tracked epoch before the speed mask (claims file).

The modulation of PoSub-HD cells was purely multiplicative ... In contrast, modulation of PoSub-FS cell tuning was exclusively additive

Results, PoSub-FS cells receive directionally uniform thalamic input, paragraph 4; Figure 5c-e; Extended Data Fig. 8a,b

Under readings (a), (b) and (c), HD multiplicative above FS (p 1e-5 to 2e-8), FS additive above HD (5e-7 to 3e-10), HD multiplicative above control (below 3e-7), FS additive above control (below 4e-4), FS multiplicative not different from control (p 0.21 to 0.40). HD additive against control is not different under (a) and (c) (p = 0.19) but is under (b) (p = 0.015), which excludes 31 of 62 HD cells. The criterion asks for every reading. Readings (a) and (c) exclude 0 HD and 0 or 1 FS cells, as the Methods report (1 of 47 FS cells and no other cells); whether reading (b) belongs in the criterion is asked of a reader (questions/000939.yaml). With the three figshare ArchT mice, a variant, the same pattern; all conditions hold under (a) and (c), and HD additive against control gives p = 0.016 under (b).

How the test differed from the paper’s method

• Two of five ArchT mice (see fig5b-posub-rates-increase); the five-mouse result is a variant.

The proportions of recorded PoSub-FS cells with the highest relative power in each of the first three Fourier components were similar to the relative mean power for the population

Results, Equivalence of PoSub-HD and FS cell tuning in Fourier space, paragraph 4; Figure 3h; Extended Data Fig. 4a legend

237 and 146 FS cells peak in components 1 and 2, within tolerance; 47 peak in component 3, below 55 - 6. The criterion's reproduced and partial outcomes both need every count within tolerance, so with one count outside it the claim is not reproduced. The proportions (0.551, 0.340, 0.109) are in the order of the renormalized mean powers (0.486, 0.326, 0.187), reading (a), but differ from them by 13%, 4% and 42%, so reading (b) fails, under both power readings. The dandiset has 430 FS cells where the paper has 427.