{"id":"7e7a5b05-68f3-428a-93f4-302ab16fd119","arxiv_id":"hep-ph/0304285","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Lattice simulation of tachyonic preheating after hybrid inflation finds Chern-Simons number generated at a rate of order 10^-5 m^4 in localized lumps of size about 1/m_W, with results stable under changes of lattice spacing and box size.","lead":"A 3+1 dimensional lattice simulation of the symmetry-breaking transition that ends hybrid inflation, tracking how SU(2) gauge fields generate Chern-Simons number. It matters because Chern-Simons number is what the electroweak anomaly converts into baryon number, so this is a prerequisite test of whether preheating could explain why the universe is made of matter.","discovery_kind":"new_application","skeptic_critique":{"model":"selfhosted/deepseek-v4.1-flash","headline":"The cutoff-independence evidence and the quoted 10^-5 m^4 rate are established for model A1 (mH/mW = 4.65), not for the physical ratio (model A4, mH/mW ≈ 1.55), where the paper itself reports the worst cutoff sensitivity and mW a ≈ 0.79 exceeds its own stated safe range.","rationale":"The reader's weakest_assumption correctly locates the soft spot, but frames it as 'the rate depends only on mW a and not on mH a.' The paper does not quite claim that; it claims cutoff independence at fixed model and separately notes the rate depends on mH/mW. The sharper statement is that the cutoff-independence demonstration is confined to model A1 (mH/mW = 4.65), while the physically relevant ratio (A4, mH/mW ≈ 1.55) is the one the paper flags as most cutoff-sensitive and where mW a ≈ 0.79 at Ns = 48 exceeds the paper's own imported safe range. So the concern is real and load-bearing for the abstract's unqualified claim and for the 10^-5 m^4 number that feeds Sec. V. It does not overturn the central lattice result — CS number is generated, locally, with a Gaussian distribution, and A1's cutoff scan is genuine — so the verdict stays CONDITIONAL. The sphaleron-identification concern (Sec. IV D, Δmt = 2-3 offset, no comparison to the static solution) is secondary and the paper hedges with 'sphaleron-like'; the CP-violation gap in Sec. V is acknowledged by the authors. Neither displaces the cutoff concern as the most load-bearing. I therefore agree partially with the reader: same target, sharper framing, same verdict.","tokens_in":34041,"tokens_out":7171,"duration_ms":131752,"concrete_test":"Run model A4 (gW = 0.15, λ = 0.00675, mH/mW = 1.55) at Ns = 96 with pmin = 0.15m (ma ≈ 0.436, mW a ≈ 0.40, at the edge of the paper's stated safe range) and accumulate ~150 configurations, matching the statistics of the Ns = 48 run. Compare I(45) with the tabulated Ns = 48 value of 16.10 ± 1.74 × 10^-5. If the two agree within errors, the physical-ratio rate is cutoff-controlled and the concern does not land; if I(45) shifts by more than the quoted error (as the Ns = 48 vs Ns = 32 discrepancy of ~12% hints), the abstract's unqualified cutoff-insensitivity claim and the 10^-5 m^4 rate are not established at the physical mass ratio. A cheaper intermediate check is Ns = 64 at pmin = 0.20m (ma ≈ 0.49, mW a ≈ 0.45), which should show the trend.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline rate (abstract:s6) and the unqualified cutoff-insensitivity claim (abstract:s3) rest on Fig. 7 and Table II, which are dominated by model A1 (gW = 0.05, mH/mW = 4.65). The paper's own Sec. IV C states that 'as we decrease the ratio our results, in particular those concerning the Chern-Simons number, become increasingly sensitive to the cutoffs,' and that the controlling scale is mW a. For model A1 at ma = 0.65-1.30, mW a = 0.19-0.40, inside the safe range the paper imports from Ref. [45] (mW a ≤ 0.40-0.60). For model A4 (mH/mW = 1.55, the closest to the physical 125/80 ≈ 1.56), mW = 0.91 m, so at Ns = 48, pmin = 0.15m (ma = 0.87) one has mW a ≈ 0.79 — outside the paper's own stated criterion. Table II shows A4's I(45) differing by ~12% between Ns = 48 (16.10 ± 1.74) and Ns = 32 (14.17 ± 1.44), a larger discrepancy than A1's. The paper never demonstrates convergence of I(mt) for A4 as mW a is reduced below 0.4. Consequently the abstract's 'insensitive to the various cut-offs' and the quoted 10^-5 m^4 are not established at the physical mass ratio; they are established at a ratio where the Higgs is 4.65 times the W, which is not the Standard Model. This is the load-bearing gap: the rate that would feed Sec. V's baryogenesis estimate is the one least controlled by the cutoff scan.","agreement_with_reader":"partial"},"referee_report":{"model":"selfhosted/deepseek-v4.1-flash","summary":"The manuscript reports a (3+1)-dimensional lattice study of the SU(2) gauge-Higgs sector of the Standard Model coupled to a singlet inflaton, evolved classically from stochastic initial conditions set at the end of hybrid inflation. The authors follow the tachyonic preheating stage through symmetry breaking and into the approach to thermalization, tracking gauge field energy fractions, gauge-invariant spectra, and — the central observable — the time-integrated Chern-Simons number dispersion I(mt) = m ∫ dt Γ(t). They report that Chern-Simons number is generated starting around mt ≈ 15, that the production is localized in structures of spatial extent ~1/m_W correlated with regions where the Higgs field lingers near the false vacuum, and that I(mt) is stable against changes of lattice spacing and box volume over the range studied. A final section converts the measured rate, of order 10^{-5} m^4, into an order-of-magnitude estimate of n_B/s in the presence of a dimension-6 CP-violating operator, concluding that δ_CP ~ 10^{-3} suffices. The paper is explicitly framed as a pilot study and as a response to the criticism of Ref. [43].","tokens_in":34454,"tokens_out":6965,"duration_ms":116558,"significance":"If the results hold, this is a substantive contribution: it is one of the first fully nonperturbative (3+1)-dimensional treatments of Chern-Simons production during tachyonic preheating with non-Abelian gauge fields, and it supplies the raw ingredient that the electroweak preheating baryogenesis scenario of Ref. [9] requires. The paper earns credit on several counts. The lattice action, equations of motion, gauge fixing, and the Gauss-constraint initialization are written out in Appendices A and B, so the numerical scheme is reproducible in principle. The statistical effort is real: 128 to 210 configurations per parameter point, with quoted errors, and Gaussian fits to the ΔN_CS distribution with χ² per degree of freedom of order unity. The direct rebuttal of Ref. [43] in Sec. IV B, via spectra at three lattice spacings and three times, is exactly the right kind of evidence to bring to that dispute. The localization analysis in Sec. IV D — the fraction of charge-squared inside 1/m_W spheres, the minimum-distance histograms of Fig. 12 — is a genuine, checkable structural claim. And Sec. V is honestly labelled an order-of-magnitude estimate rather than a prediction. The weaknesses I.","major_comments":[{"comment":"The abstract states without qualification that 'Our results are shown to be insensitive to the various cut-offs introduced in our numerical approach,' but the body establishes this only for model A1. The authors themselves write in Sec. IV C that 'as we decrease the ratio our results, in particular those concerning the Chern-Simons number, become increasingly sensitive to the cutoffs,' and identify m_W a as the controlling scale. Table II bears this out: model A3 gives I(45) = 38.00(5.62) at Ns = 48 versus 24.58(2.42) at Ns = 32, a 55% difference; model A4 gives 16.10(1.74) versus 14.17(1.44); model B rises monotonically from 14.89(1.65) at Ns = 32 to 19.89(1.74) at Ns = 64. Only model A1, at m_H/m_W = 4.65, shows the flat behaviour of Fig. 7. The abstract's unqualified claim should either be restricted to the parameter window where it is demonstrated, or supported by an A4 run at reduced m_W a. As written, a reader of the abstract alone would conclude that cutoff independence has been shown for the Standard Model mass ratio, which is not the case.","section":"Abstract [abstract:s3]; Sec. IV C; Table II; Fig. 7","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The statement that model B, after a time shift of 3.3/m and a 20% rescaling, 'match[es] perfectly' with model A1 is made at a single lattice size (Ns = 48, pmin = 0.15m). Model B is simultaneously the entry with the largest cutoff dependence in Table II, rising by roughly 34% between Ns = 32 and Ns = 64. The agreement with A1 is therefore asserted at precisely the point where B's own systematic uncertainty is least controlled, and the 20% rescaling is of the same order as that uncertainty. Either the comparison should be repeated at Ns = 64, or the text should state that the A1-B agreement is established only at one lattice spacing and is subject to B's own cutoff systematics.","section":"Sec. IV C, paragraph on model B; Table II","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The abstract states 'We establish that the Chern-Simons production mechanism is associated with local sphaleron-like structures,' but Sec. IV D reports 'a relative time shift Δmt = 2 − 3 between the presence of zeroes in the Higgs field and that of maxima in the charge density.' For a static sphaleron the magnetic energy maximum sits at the Higgs zero by construction, so a shift of two to three inverse inflaton masses indicates that the observed objects are dynamical transients rather than sphaleron configurations. The body is appropriately hedged ('one might be tempted to identify'), but the abstract's 'establish' is stronger than the evidence supports. I would ask the authors to either soften the abstract wording to match the body, or to quantify the offset — for instance, by showing the distribution of |φ| at the charge-density peak positions rather than only the contour overlays.","section":"Sec. IV D, Figs. 13-14; Abstract [abstract:s5]","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The baryon-asymmetry estimate uses Γ_sph ~ 2 × 10^{-5} m^4, a value read from Table II at m_H/m_W = 4.65 (model A1) and 2.82 (model A2). Fig. 9 shows that I(mt) varies by factors of two to three across the model set and depends sensitively on m_H/m_W, and the paper's own Sec. IV C identifies the physical ratio as the case least controlled by the cutoff scan. The derived δ_CP ~ 10^{-3} therefore inherits a factor-of-few uncertainty that is not propagated. Since the conclusion is explicitly order-of-magnitude, this is not fatal, but Eq. (18) should carry an explicit statement of the range of δ_CP implied by the spread in Table II, rather than a single number. Relatedly, the criterion m_W a ≤ 0.40-0.60 used to justify the parameter choices is imported from the vacuum sphaleron study of Ref. [45]; applying it to a far-from-equilibrium dynamical process is an extrapolation beyond the source's stated hypotheses and should be flagged as an assumption in the text rather than presented as an established bound.","section":"Sec. V, Eqs. (16)-(18)","authors_acknowledge":null,"authors_acknowledge_p":null}],"minor_comments":[{"comment":"Grammatical: 'The spectra preserves a large hierarchy' should read 'The spectra preserve a large hierarchy.'","section":"Abstract","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The inflaton bare mass is listed as μ = 10^{-5} gv ≈ 0. Please state explicitly in the caption or the surrounding text that μ is set to zero in the evolution, since the equations of motion in Appendix A retain μ_L.","section":"Table I","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The caption says errors are 'computed in the standard fashion from the dispersion within the various configurations.' Please give the formula (standard error of the mean over configurations, or the dispersion of the estimator from a jackknife) so that the reader can judge whether the quoted errors on I(mt) are correlated across times.","section":"Table II","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The caption should state that the pmin = 0.12m data are rescaled by the square root of the volume because ΔN_CS² scales linearly with volume, and should give the number of configurations entering each histogram.","section":"Fig. 8","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"It would help the reader considerably if the values of m_W a for each model and each lattice size were tabulated alongside Table II, so that the comparison with the Ref. [45] criterion can be made without recomputation. At present the reader must reconstruct m_W = m g_W/(2√λ) and ma for each row.","section":"Sec. IV C, paragraph on cutoff independence","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The residual Gauss-constraint violation is quoted as 'smaller than 10^{-11}.' Please state whether this is an absolute or a relative measure, and over what time interval it holds.","section":"Appendix B","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The axis labels and legends in these figures are difficult to read in the current version; the panel structure (six stacked panels per side) also makes it hard to identify which curve corresponds to which cutoff. Consider consolidating or enlarging.","section":"Figs. 3 and 4","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The conclusions would be strengthened by an explicit statement of which of the specific objections raised in Ref. [43] are addressed by the present data and which remain open. The rebuttal in Sec. IV B is effective but is not carried through to the concluding summary.","section":"Sec. VI, Conclusions","authors_acknowledge":null,"authors_acknowledge_p":null},{"comment":"The choice to set all propagating gauge modes to zero initially is defended by the argument that there are no tachyonic gauge modes. A short quantitative remark on how large a nonzero initial gauge fluctuation would have to be before I(mt) changes appreciably would make this defence more convincing, since this choice is precisely the point on which Ref. [43]'s criticism turns.","section":"Sec. III B 1 and Appendix B","authors_acknowledge":null,"authors_acknowledge_p":null}],"recommendation":"major_revision"},"author_rebuttal":null,"desk_editor":{"model":"selfhosted/deepseek-v4.1-flash","letter":"This is the paper that puts non-Abelian gauge fields into the tachyonic preheating story and actually measures Chern-Simons number on the lattice. That is the contribution, and it is worth your time. The setup is careful: quantum-matched initial conditions from the linear evolution, a proper lattice action with the Gauss constraint imposed at t_i, and Appendices A and B spell out the discretization and the constraint implementation so someone could redo it. The cutoff scan is genuine — Fig. 7 shows I(mt) collapsing across ma = 0.65, 0.87, 1.30 for model A1 — and the statistics (130-210 configurations per point, Gaussian fits with chi-squared near 1) are adequate for a fluctuating quantity like this. The direct answer to Moore's Ref. [43] criticism holds within the parameter range studied, and the localization analysis in Sec. IV D (a few percent of the volume carrying 80-90% of the charge squared, structures of size ~1/mW) is a nice piece of work. The paper is also honest that the lumps are only 'sphaleron-like': it reports the Delta mt = 2-3 offset between Higgs zeros and charge maxima and never compares to the static sphaleron solution, so the identification stays correlational. That is a fair limitation, not a flaw in the lattice result itself. The stress-test concern lands, though. The abstract's 'insensitive to the various cut-offs' and the 10^-5 m^4 rate are established for model A1, where mH/mW = 4.65 and mW a sits inside the safe range imported from Ref. [45]. The paper's own Sec. IV C says sensitivity grows as the ratio decreases, and model A4 — the closest to physical at mH/mW = 1.55 — has mW a ~ 0.79 at Ns = 48, outside the paper's own stated criterion, with a ~12% discrepancy between Ns = 48 and Ns = 32 in Table II. Convergence of I(mt) for A4 as mW a drops below 0.4 is never shown. So the rate that feeds Sec. V is the one least controlled by the cutoff scan. Sec. V itself is an order-of-magnitude estimate with delta_CP, M_new and T_eff chosen to land on the observed asymmetry; the authors acknowledge this, so it is not a new finding, but the abstract should not read as if the rate were a Standard Model number. For readers working on electroweak baryogenesis or on lattice real-time dynamics this is a must-read and a solid reference. Send it to referees; the revision should either demonstrate A4 convergence or soften the abstract's cutoff claim and the rate's framing.","headline":"A real first 3+1D lattice measurement of Chern-Simons production during tachyonic preheating, but the headline rate and the cutoff-independence claim are established at mH/mW = 4.65, not at the physical mass ratio.","tokens_in":35161,"tokens_out":1034,"duration_ms":17426},"pith_extraction":{"msc":[],"pacs":["98.80.Cq"],"model":"selfhosted/deepseek-v4.1-flash","headline":"Hybrid inflation ends with the Higgs field going unstable, and the authors ask whether the resulting burst of symmetry breaking generates Chern-Simons number at a rate large enough to matter for baryogenesis.","keywords":["hybrid inflation","tachyonic preheating","Chern-Simons number","sphaleron transitions","electroweak baryogenesis","classical lattice field theory","SU(2) gauge-Higgs model","non-equilibrium dynamics"],"falsifier":"Repeat the measurement for a model with $m_H/m_W approx 1$, which the authors estimate needs $m_H a approx 0.4$ and $N_s gtrsim 148$, and check whether $I(mt)$ per unit volume stays at the quoted $10^{-5}m^4$; a rate that moves with the Higgs mass ratio would show the quoted number is an artifact of the $m_H/m_W = 4.65$ choice rather than a property of the transition.","tokens_in":35298,"feed_emoji":"🌌","tokens_out":3873,"duration_ms":72298,"temperature":0.7,"pith_summary":"Hybrid inflation ends when the inflaton rolls past a critical value and the Higgs field, held at zero until then, suddenly finds itself with a negative mass squared. The paper asks whether the resulting collapse into the true vacuum also shakes loose Chern-Simons number, the quantity that anomalous electroweak processes convert into baryon number. The authors simulate the $SU(2)$ gauge-Higgs sector plus a singlet inflaton on a $(3+1)$-dimensional lattice, evolving the long-wavelength modes classically and seeding them with the stochastic distribution that linear quantum evolution predicts at the moment those modes become classical. They report that Chern-Simons number does diffuse, at a rate of order $10^{-5}m^4$, that the production sits in compact lumps of size about $1/m_W$ located where the Higgs field lingers near zero, and that the answer barely moves when the lattice spacing or box size is changed. If that holds, the interval right after hybrid inflation supplies the out-of-equilibrium ingredient baryogenesis needs, and the classical lattice treatment survives the objection that its spectra are swamped by short-wavelength artifacts.","feed_headline":"Symmetry breaking after inflation churns Chern-Simons number","feed_subtitle":"A lattice run puts the sphaleron rate near 10^-5 m^4, enough to seed the observed baryon asymmetry.","key_machinery":"The load-bearing object is the lattice topological charge density, built from $1times1$, $1times2$ and $2times2$ plaquettes combined to cancel the leading $O(a^2)$ error, so that $Q(vec{x},t)$ is measured without adding discretization artifacts of its own. Around it sit three supporting devices: gauge-invariant lattice equations of motion in which Gauss's law, once imposed initially, is shown to propagate (Appendix A); an initialization scheme that leaves the Higgs distribution untouched and puts all the necessary charge into the longitudinal electric field, with the transverse part set to zero (Appendix B); and a cutoff-independence test in which the box size $p_{min}$ and the lattice spacing $ma$ are varied separately, since volume should scale the dispersion $langle Delta N_{CS}^2 rangle$ while the spacing should not.","core_discovery":"The central claim is that the symmetry-breaking transition after hybrid inflation is itself a Chern-Simons source. Working in the $A_0=0$ gauge with the Gauss constraint imposed on the initial data, the authors measure $I(mt) = m^{-3}V^{-1}m^2 dlangle Delta N_{CS}^2 rangle/dt$ and find it rising from zero around $mt approx 15$, steeply at first with oscillations up to $mt approx 25$, then more gently, reaching values of order $10^{-5}$ in the units shown in their Table II. The distribution of $Delta N_{CS}$ across configurations is Gaussian to within a $chi^2$ of about 1 per degree of freedom, consistent with production in many independent local events of random sign. Those events are resolved: peaks of the topological charge density $Q = 4,mathrm{Tr}(vec{E}cdotvec{B})$ above $7m_W^4$ occupy a few percent of the lattice volume while containing 60 to 90 percent of the charge squared, sit inside spheres of radius $1/m_W$, and appear at the points where the Higgs field stays longest in the false vacuum, with a lag of $Delta mt = 2$ to $3$ between the Higgs zeros and the charge maxima. The authors also argue that the long-wavelength modes stay dominant throughout, so the classical approximation is not undone by the ultraviolet cascade that Ref. [43] warned about.","pith_inferences":["The $Delta mt = 2$ to $3$ lag between a Higgs zero and the charge-density maximum suggests the lumps are not passing through the sphaleron saddle quasistatically; tracking the field trajectory through one lump would show whether it actually crosses the barrier or merely oscillates near it.","Because $Q$ flips sign at a fixed point as $vec{E}$ and $vec{B}$ oscillate out of phase, the net Chern-Simons number accumulated by a single lump nearly cancels; the efficiency of any CP-biased baryogenesis therefore depends on how the bias period compares with the oscillation period, a timing question the paper raises but does not resolve.","The oscillatory dependence of the gauge energy fraction on $g_W$, with a maximum near $g_W = 0.0825$ and a minimum near $0.147$, hints at a resonance between the Higgs oscillation frequency and the gauge field mass, which would be worth mapping before any extrapolation to physical couplings.","A run at $m_H/m_W approx 1$ with $m_H a approx 0.4$ and $N_s gtrsim 148$, which the authors say is beyond their present resources, is the natural next step and would decide whether the quoted rate is a property of the dynamics or of the parameter choice."],"forward_implications":["With a dimension-six CP-odd operator of the form $delta_{CP}(Phi^daggerPhi/M_{new}^2)(3g_W^2/32pi^2)Ftilde{F}$, the rate quoted here gives $n_B/s approx 1.1times10^{-8}delta_{CP}$ for $M_{new} approx 3$ TeV, so $delta_{CP} approx 10^{-3}$ would match the observed asymmetry.","The classical-statistical lattice method, with stochastic initial conditions taken at $mt_i = 5$ rather than at the bifurcation point, is argued to be a valid tool for this problem up to the cutoffs used, answering the spectral-cascade criticism directly.","The Chern-Simons yield depends on the Higgs-to-W mass ratio: the four A-models share $lambda$ and differ only in $g_W$, and their $I(mt)$ curves differ by factors of two or more, so no single number can be read off as the Standard Model value.","The production is spatially clustered and time-lagged relative to the Higgs zeros, which means the mechanism is not a gas of static sphalerons but a set of driven, oscillating configurations whose charge density even flips sign at fixed location.","Model B, with a gauge coupling closer to the Standard Model value, matches model A1 after a time shift of $3.3/m$ and a 20 percent rescaling, suggesting the result tracks $m_H/m_W$ rather than the absolute coupling."],"supporting_citations":[{"why":"Supplies the entire baryogenesis scenario being tested: the CP-odd operator, the effective chemical potential, and the estimate this paper is trying to substantiate numerically.","marker":"[9]"},{"why":"Paper I of this series, which establishes the scalar-sector dynamics, the lump-to-bubble picture, and the justification for turning on classical evolution at $mt_i = 5$.","marker":"[26]"},{"why":"Establishes that preheating after hybrid inflation proceeds by spinodal instability rather than parametric resonance, which is the premise for the tachyonic growth of long-wavelength Higgs modes.","marker":"[17]"},{"why":"States the objection the paper is written against, namely that coupled gauge fields drive an ultraviolet cascade that would make the classical lattice description cutoff-dependent.","marker":"[43]"},{"why":"Supplies the window of $m_W L$ and $m_W a$ values, and the claim that sphalerons survive as $m_H to infty$, which licenses running at $m_H/m_W = 4.65$.","marker":"[45]"},{"why":"Provides the Abelian $(1+1)$-dimensional precedent for the Chern-Simons measurement and the procedure for imposing the Gauss constraint on initial data used in Appendix B.","marker":"[22]"},{"why":"Supplies the gauge-invariant lattice discretization of the classical equations of motion on which the whole simulation rests.","marker":"[42]"},{"why":"Source of the dimension-six CP-violating operator and the Boltzmann-like treatment used in Section V to convert the Chern-Simons rate into a baryon asymmetry.","marker":"[51]"}],"fun_headline_variants":["Post-inflation symmetry breaking generates Chern-Simons number","Lattice run ties Chern-Simons yield to local sphaleron-like peaks","Sphaleron rate near 10^-5 m^4 in post-inflation symmetry breaking","Baryon link is conditional: Chern-Simons yield needs extra CP source","Classical lattice sees Chern-Simons production in hybrid inflation"],"cache_read_input_tokens":0,"weakest_assumption_plain":"The rate is assumed to depend only on the combination $m_W a$ and not on $m_H a$, a scaling imported from lattice studies of static vacuum sphalerons and applied here to a violently non-equilibrium process; if it fails, the demonstrated cutoff independence does not carry over to physical Higgs-to-W mass ratios.","fun_headline_variants_meta":{"raw":{"variants":["Post-inflation symmetry breaking generates Chern-Simons number","Lattice run ties Chern-Simons yield to local sphaleron-like peaks","Sphaleron rate near 10^-5 m^4 in post-inflation symmetry breaking","Baryon link is conditional: Chern-Simons yield needs extra CP source","Classical lattice sees Chern-Simons production in hybrid inflation"]},"model":"selfhosted/deepseek-v4.1-flash","effort":"low","attempts":1,"cost_usd":0.0,"raw_usage":{"total_tokens":2211,"prompt_tokens":1044,"completion_tokens":1167,"prompt_tokens_details":null,"completion_tokens_details":{"reasoning_tokens":1080}},"tokens_in":1044,"tokens_out":1167,"duration_ms":20190,"image_pages":[],"temperature":1.0,"reasoning_budget":50,"reasoning_tokens":1080,"transport_provider":"selfhosted","cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-11-13T09:16:05.361701+00:00","model_set":{"reader":"selfhosted/deepseek-v4.1-flash"},"pipeline_version":"pith-pipeline@v1.5.0-archive-selfhost","input_kind":null,"input_chars":null,"input_total_chars":null,"passes_missing":null,"published_standing":null,"published_confidence":null,"objection_audit":null,"run_record":null,"basis":{"kind":"not_recorded","source":null,"chars_given":null,"chars_total":null},"receipt":null,"falsifier":"Repeat the measurement for a model with $m_H/m_W approx 1$, which the authors estimate needs $m_H a approx 0.4$ and $N_s gtrsim 148$, and check whether $I(mt)$ per unit volume stays at the quoted $10^{-5}m^4$; a rate that moves with the Higgs mass ratio would show the quoted number is an artifact of the $m_H/m_W = 4.65$ choice rather than a property of the transition.","supporting_citations":[{"cited_title":"Phys. Rev. Lett . 76, 1011 (1996); I.I. Tkachev, Phys. Lett. B 376, 35","cited_arxiv_id":null,"evidence_quote":"Supplies the entire baryogenesis scenario being tested: the CP-odd operator, the effective chemical potential, and the estimate this paper is trying to substantiate numerically."},{"cited_title":"Phys. Lett. B 510, 271","cited_arxiv_id":null,"evidence_quote":"Paper I of this series, which establishes the scalar-sector dynamics, the lump-to-bubble picture, and the justification for turning on classical evolution at $mt_i = 5$."},{"cited_title":"Pseudonatural Inflation","cited_arxiv_id":"hep-th/0302034","evidence_quote":"Establishes that preheating after hybrid inflation proceeds by spinodal instability rather than parametric resonance, which is the premise for the tachyonic growth of long-wavelength Higgs modes."},{"cited_title":"Phys. Lett. B 244, 479 (1990); Nucl. Phys. B353, 346","cited_arxiv_id":null,"evidence_quote":"States the objection the paper is written against, namely that coupled gauge fields drive an ultraviolet cascade that would make the classical lattice description cutoff-dependent."},{"cited_title":"Do We Understand the Sphaleron Rate?","cited_arxiv_id":"hep-ph/0009161","evidence_quote":"Supplies the window of $m_W L$ and $m_W a$ values, and the claim that sphalerons survive as $m_H to infty$, which licenses running at $m_H/m_W = 4.65$."},{"cited_title":"Phys. Rev. D 65, 103517","cited_arxiv_id":null,"evidence_quote":"Provides the Abelian $(1+1)$-dimensional precedent for the Chern-Simons measurement and the procedure for imposing the Gauss constraint on initial data used in Appendix B."},{"cited_title":"Initial conditions for simulated `tachyonic preheating' and the Hartree ensemble approximation","cited_arxiv_id":"hep-ph/0112057","evidence_quote":"Supplies the gauge-invariant lattice discretization of the classical equations of motion on which the whole simulation rests."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Source of the dimension-six CP-violating operator and the Boltzmann-like treatment used in Section V to convert the Chern-Simons rate into a baryon asymmetry."}],"lane_accuracy":{"status":"not yet measured","lane":{"model":"selfhosted/deepseek-v4.1-flash","input_kind":null},"url":"https://pith.science/accuracy"},"review_version":1}