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

Version 3. Relative to Version 2 this version adds a related work section and narrows what the paper claims. No result, figure, number or verdict changed, and nothing was re-run. WHAT THE PAPER FINDS Reduced 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 neurons: slope +0.760 +/- 0.113, R^2 = 0.884, p = 0.0005 PING 80 neurons: slope -0.041 +/- 0.123, R^2 = 0.018, p = 0.748 not PING Network size, not reduction, is the switch. Version 1 of this work concluded that emergent gamma is absent from reduced CA1 models; that conclusion is wrong and is corrected here. WHAT CHANGED IN VERSION 3 Version 2 used the word "harmonic" twenty-three times and cited none of the literature on theta harmonics contaminating hippocampal gamma. That literature is a live dispute and this paper sits inside it. * A related work section has been added to section 1. It states both sides of the dispute over whether hippocampal slow gamma is a rhythm or the harmonics of theta, and says plainly that this study does not adjudicate it and cannot: its data are simulated, and no construction of a model network is evidence about what a hippocampus contains. * "as it is in a large fraction of this literature" is gone from section 1, and "theta is almost always imposed" is gone from the abstract. Both were unquantified magnitude claims, and the paper's own Limitations section says the opposite: "They do not establish how often they do arise in published work." The paper contradicted itself. * The artifact is conceded. That a sharp drive puts harmonics into the bands above it, and that they are read as activity there, is established (Kramer et al., 2008; Cole & Voytek, 2017; Donoghue et al., 2022). It was not discovered here. That the comb could mask a genuine rhythm has also been stated in print (Schaworonkow, 2023), twice, in prose, untested. * What remains is narrower, and is the actual contribution: on data where the gamma content is known because it was placed there, and where the comb falls inside the analysis band, the full pipeline of statistic plus screens rejects a genuine rhythm and no screen is at fault. Cho et al. (2024) name the reason nobody had done this: "the general absence of a defined ground truth, i.e., data for which we know the harmonic structure." * Section 4 now says why bicoherence is absent from its list of checks: it identifies harmonics, and identifying the harmonic correctly is what the screens already do. References went from 16 entries to 32, every field verified against Crossref. VERIFICATION Every number in this paper is printed by a script in the archived code, or is arithmetic from numbers that are with the derivation recorded, or is quoted from a cited paper with the source recorded. audit_manuscript.py enforces this and exits non-zero otherwise: 275 claims, 254 in a log, 20 derived, 1 cited, 0 unsupported. The five gated simulation scripts are byte-identical to those archived with Version 2, so the run logs behind Version 2 are the run logs behind this version. They were reproduced to the last digit on two machines with different Python (3.13 / 3.12), numpy (2.5 / 2.2) and hardware. LINKS Code, run logs, figures (v3.1) https://doi.org/10.5281/zenodo.21392319 All versions of the code https://doi.org/10.5281/zenodo.21265445 Repository https://github.com/Larryzpl123/CA1-simplification Version 1 preprint https://doi.org/10.5281/zenodo.21272959 Version 1 code https://doi.org/10.5281/zenodo.21273211 Version 1 is preserved unmodified on purpose: the corrigendum in this paper cannot be independently checked without it. Its record carries a notice that its conclusion is wrong.