Screens Reject, Only Mechanism Confirms: Recovering Emergent Gamma in a Reduced Hippocampal CA1 Microcircuit

Version 5. This version corrects a misquotation and several citations carried in Versions 2 through 4. No result changed, no simulation was re-run, and the accompanying code release is unchanged (v4.0). A reader comparing this version with Version 4 will find identical results and a corrected reference apparatus. Accompanying code: 10.5281/zenodo.21444272 (release v4.0). All versions of the code: 10.5281/zenodo.21265445. WHAT VERSION 5 CORRECTS1. A sentence in the Introduction presented a quotation as verbatim from Cho et al. (2024). That quotation does not appear in that paper. It has been removed and replaced with an accurate description of what Cho et al. did: an autocorrelation-based method to distinguish fundamental frequencies from their harmonics. The point the paragraph makes is unchanged; the false quotation is gone.2. The Lozano-Soldevilla et al. (2016) citation was placed on the wrong side of the argument. The claim that it demonstrated a genuine rhythm surviving alongside harmonics is removed; that paper's actual finding is spurious cross-frequency coupling arising from non-sinusoidal waveform shape. The related-work case for genuine-rhythm-and-harmonic coexistence now rests on Fransen et al. (2016).3. Bezaire et al. (2016) and Romani et al. (2024) are now cited in the Introduction as the full-scale reconstructions of the rat CA1 circuit against which reduced models are benchmarked.4. A numbering error in the "three errors found by the archive" paragraph of the Methods is corrected: three claims are listed, and each is matched to the check that caught it.5. The source of the two corrections made in Version 4 is now named: Professor Christoph Börgers (personal communication), with his permission. Version 4 deferred the attribution pending that permission; it is made here. No simulation was re-run for Version 5 and no figure was redrawn. The changes are confined to citations, wording, and the presentation of the supplementary tables; every result reported in Version 4 is unchanged here. WHAT THE PAPER FINDSReduced spiking-network models of hippocampal CA1 are validated by asking whether they preserve theta and gamma, using spectral peak prominence as the criterion. Where theta is imposed as a drive rather than emergent, that criterion becomes unusable, and the failure is worse than a false positive.On synthetic spike trains whose gamma content is zero by construction, a population locked tightly enough to a 6 Hz drive produces 12 to 37 dB of "gamma", which a surrogate null calls significant in 100% of datasets. Worse, when a genuine 40, 55 or 68 Hz rhythm IS present, the raw statistic still reports its peak at 30.0 Hz, which is the drive's fifth harmonic, in every case. The statistic's output is nearly uncorrelated with the quantity it names.No screen repairs this. The raw statistic followed by every check in the paper rejects a genuine 40 Hz rhythm, and each screen is correct in doing so: the peak it was handed really is significant, really is at a band edge, and really is the fifth harmonic. All three verdicts are true, and none of them is about the rhythm, because the rhythm was never the peak. A screen can only reject a peak the statistic has already found.Excise the comb before taking the maximum and the false-positive rate is 5.0% against a nominal 5%, with 100% power. Applied to a corrected CA1 microcircuit, a gamma peak then survives every analysis-side check in two of five conditions, and no analysis can say what it is. It is resolved by a model manipulation with a prediction attached: PING requires the cycle period to be affine in tau_GABA. Under a criterion fixed in advance, on seeds never previously used: T_cycle = 16.8 + 0.760 * tau_GABA (ms) 320 + 80 neurons: slope +0.760 +/- 0.113, R^2 = 0.884, p = 0.0005 PING 80 + 20 neurons: slope -0.041 +/- 0.123, R^2 = 0.018, p = 0.748 not PINGVersion 1 of this work concluded that emergent gamma is absent from reduced CA1 models. That conclusion is wrong and is corrected here. WHAT VERSION 4 WITHDREW, AND THIS VERSION RETAINS1. THE INTERCEPT WAS NEVER A LOOP DELAY.Versions 2 and 3 reported, in the abstract, twice in section 3.8, in a figure annotation, and in the test script's own printed output, that the 16.8 ms intercept is the fixed part of the loop delay, attributable to AMPA kinetics, the membrane time constant and the refractory period.At tau_GABA = 0 there is no PING at all. The affine form is a local approximation over the range actually swept, 2 to 24 ms, so the intercept is where a fitted line crosses an axis in a regime the model does not describe. Reading a mechanism out of it was reading a mechanism out of an extrapolation. The word "fixed" was also never measured: in a two-cell PING, a 1% reduction in the drive to the E-cell lengthens the period by 0.66%, against 0.14% for a 1% increase in the inhibitory decay constant and 0.10% for a 1% increase in the inhibitory-to-excitatory conductance (Börgers, 2017, Table 30.1). The drive was held constant here, so anything the fit calls constant is constant only in that sense.The intercept is now a fit parameter and is not interpreted. The pre-registered criterion is on the slope, and on nothing else.It is worth recording what caught this, because it is the paper's own thesis landing on the paper. Not the surrogate null, not the four screens, not the manuscript audit that checks every number in the paper against the archived logs, and not two machines reproducing the fit to the last digit. The intercept is a CORRECT NUMBER, COMPUTED CORRECTLY. Every check in this archive tests whether a number is real. None of them tests whether the meaning attached to it was earned.2. "NETWORK SIZE IS THE SWITCH."The 80 + 20 and 320 + 80 conditions differ in cell count and in in-degree at the same time, so that comparison could never have isolated size. The weight normalisation holds the MEAN synaptic drive per cell constant, but for N inputs of weight w the mean goes as Nw while the variance goes as Nw^2, so it does not hold the FLUCTUATIONS constant. Brunel and Wang (2003), which this paper already cited, states the correct protocol verbatim: vary network size "keeping the number of connections and the synaptic conductance fixed so as to keep unchanged the temporal average and fluctuations of the synaptic currents as network size was varied". WHAT VERSION 4 ADDED: THE SWITCH IS THE INPUT FLUCTUATION, NOT THE CELL COUNTThe coefficient of variation of the total conductance onto a cell is sqrt((1 - p)/(p * N_pre)) (Börgers, 2017, section 30.3). Raising the 80 + 20 network's connection probabilities so that each pathway's coefficient of variation matches the 320 + 80 network's holds the fluctuations fixed while the cell count stays at 80 + 20. Under that manipulation the small network passes the same pre-registered test: 320 + 80 control slope +0.760 +/- 0.113 | R^2 0.884 | p 0.0005 PASSES 80 + 20, base p slope -0.041 +/- 0.123 | R^2 0.018 | p 0.75 fails 80 + 20, CV-matched slope +0.609 +/- 0.118 | R^2 0.815 | p 0.0021 PASSESThe same 80 + 20 cells give a null result and a PING result depending only on the input fluctuations. The cell count was never the switch. The unchanged 320 + 80 control reproduces the gated code's fit to the last digit, which is what licenses trusting the number beside it.CAVEAT, STATED IN THE PAPER. Raising the probabilities lowered the coefficient of variation as intended, but it also brought the firing rates into line with the larger network. Fluctuation and the operating point it disturbs are entangled in this manipulation, and this study separates them no further than to say the count alone does not decide the outcome. The experiment that isolates the fluctuation from the operating point, holding both firing rates fixed while varying only the coefficient of variation, has not been run. WHAT DID NOT CHANGENo result in Versions 2, 3, or 4 was found to be numerically wrong, and Version 5 changes no result. Three of the five gated simulation scripts are byte-identical to release v2.2, and the other two differ only in comments and printed prose, with an identical abstract syntax tree and every number and verdict certified identical by compare_runs.py. The affected script was re-run for Version 4 and the new log is archived, because the previously archived log printed a claim the paper has now retracted, and an archive that contradicts the paper is the failure this paper is about. ATTRIBUTIONBoth Version 4 withdrawals came from Professor Christoph Börgers, who works on PING, by email after Version 3 was published. He is named here with his permission. Version 4 deferred the personal attribution because permission had not been obtained when it was archived; only the personal attribution was deferred, as his published work has been cited throughout section 3.8 and in the reference list since Version 3. VERSION NUMBERINGThe paper is numbered in whole integers: Version 1, 2, 3, 4, 5. The code is versioned separately as software releases, v1.0 through v4.0, and is unchanged in this paper version. A code release number is not a paper number: there is no paper v3.1, and counting the code releases does not count the papers. Version 3's record has a third component (3.0, 3.0.1, 3.0.2) because two uploads had to be redone without the paper changing; those are superseded records, not earlier papers, and they remain visible and say so.