Weak Lensing Magnification of Type Ia Supernovae from a Predicted External-Convergence Model: DES-SN5YR, Union3, and Pantheon+

Introduction

Weak lensing by foreground structure perturbs the observed brightnesses of Type Ia supernovae (SNe Ia), adding a redshift-dependent, skewed scatter to the Hubble diagram [63]; [22] of $\sigma_{\rm lens} \simeq0.055z$ mag [26]. Current cosmological analyses treat it as a Gaussian term in the distance-modulus uncertainty. The DES five-year analysis (DES-SN5YR; [1]) notes that the non-Gaussian lensing tail is otherwise uncorrected, and its released lensing correction column is identically zero; the same holds for Union3 [52] and Pantheon+ [54]; [10]. These are the three samples that, with DESI DR2 baryon acoustic oscillations and the CMB, drive the current $2.8$–$4.2\sigma$ preference for evolving dark energy [12].

The same foreground galaxies that produce the convergence are catalogued by wide-field surveys, so the lensing of each supernova can be predicted. [40] found no correlation between supernova brightness and SDSS galaxy overdensity for the [49] sample. [32] correlated 171 SNLS supernovae with a mass-to-light halo model built from a deep photometric catalog and found a $2.3\sigma$ signal, and [57] obtained $\sim1.4\sigma$ for 608 SDSS supernovae from foreground galaxy counts. [55] found a marginal correlation in Pantheon, and [56] made the first $>5\sigma$ detection by correlating DES-SN5YR Hubble residuals with DES Y3 foreground galaxies whose halo mass-to-light normalization and profile were fitted to the residuals. That design maximizes the detection but cannot test the expected amplitude, because the fitted normalization absorbs any error in the galaxy–halo connection.

We take the complementary approach: the convergence along each sight line is predicted from a halo model calibrated entirely on external data, with no reference to the Hubble residuals. The prediction code (SNKappa) was developed for the environment of the strongly lensed SN 2025wny [18] and tested there against deep-SED stellar masses, null tests, and the line-of-sight magnification of SN 1997ff [8]; §3 is self-contained. Applied to 2920 unique sight lines, it turns the lensing detection into a measurement of the observed-to-predicted amplitude — a population-level test of the galaxy–halo connection with standard candles as sources — and, because the three compilations share sight lines but not standardization pipelines, into a test of whether the lensing signal depends on how the supernovae are standardized.

Section 2 describes the supernova samples and foreground catalogs, Section 3 the prediction and statistical methods, Section 4 the validation tests, Section 5 the results, and Section 6 biases, de-lensing, and the implications for the DESI DR2 dark-energy preference.

Data

DES-SN5YR

We use the public DES-SN5YR Hubble diagram and metadata [1, 53, 61]: distance moduli $\mu$, uncertainties, BEAMS [33] Type-Ia probabilities $P_{\mathrm{Ia}}$, host coordinates (adopted as the sight line), and field assignments. Of the 1572 SNe in the ten DES fields with $0.1 < z_{\mathrm{HD}} < 1.15$ and valid host positions, 1450 have $P_{\mathrm{Ia}} > 0.9$ and form the baseline sample; the 194 external low-redshift SNe are excluded ($\sigma_{\mathrm{lens}} < 5$ mmag). Hubble residuals are computed against flat $\Lambda$CDM with $\Omega_{\mathrm{M}} = 0.352$ (the DES-SN5YR SN-only fit, also used for the convergence prediction), with the inverse-variance-weighted mean subtracted in each source-redshift bin, so only relative residuals enter and the choice of $\Omega_{\mathrm{M}}$ is absorbed.

Union3

Union3 [52] comprises 2087 SNe Ia from 25 samples. The UNITY framework [51] releases per-SN light-curve fits ($m_B$, $x_1$, $c$ with covariances), redshifts, host masses, and coordinates, but its distances are a binned spline. We therefore standardize the released fits ourselves [60],

fitting $(\alpha, \beta, \gamma, M)$ globally ($\alpha= 0.122$, $\beta= 2.57$) with a per-sample intrinsic dispersion, a 300 km s$^{-1}$ peculiar-velocity term, the DES-convention $\sigma_{\mathrm{lens}} = 0.055z$ term, and a $3.5\sigma$ clip (14 SNe; DES-SN5YR and Pantheon+ ship standardized distances and are not clipped). The Hubble scatter is 0.199 mag rms (0.151 mag NMAD), with intrinsic dispersions of 0.09–0.15 mag for the major samples, comparable to the published UNITY treatment. The clipped objects are not preferentially lensed ($\langle\kappa_{\mathrm{ext}}\rangle= +0.0005$ against a field mean of $+0.0003$ and dispersion 0.0076). The $\sigma_{\mathrm{lens}}$ weight term down-weights high-$z$ supernovae by the variance of the effect under study, but removing it changes the DES slope only from $-1.71 \pm0.42$ to $-1.77 \pm0.42$.

All 1380 Union3 SNe at $z > 0.1$ lie in the Legacy Surveys footprint, and 1213 are analyzed. Of the 167 excluded, six lie beyond the $z_s = 1.58$ limit of our source-redshift grid; 73 are isolated supernovae at $z < 0.2$, for which no foreground region is built; 69 fail the coverage and random-annulus gates sec:3.4; 12 belong to the cluster-targeted See-Change sample [20], which is selected on $\kappa$ and analyzed separately (sec:5.2); and seven are clipped. The excluded objects are mostly at low redshift (median $\bar{z} = 0.20$; two above $z = 1$) and carry little leverage on $\kappa_{\mathrm{ext}}$.

Pantheon+

Pantheon+ [54, 10] releases standardized magnitudes ($m_{b,\mathrm{corr}}$), SN and host coordinates, and the full 1701$^{2}$ statistical+systematic covariance, allowing a full-covariance lensing fit (sec:5.3). We drop Cepheid-calibrator hosts and the HST cluster-search SNe [58], adopt host coordinates, and use the 901 unique sight lines at $0.1 < z < 1.58$.

Foreground catalogs

For each survey region we build catalogs from the DESI Legacy Imaging Surveys DR10 [14]: Tractor sources with standard quality cuts, Milky Way-dereddened $griz$ and WISE [67] fluxes, $z \leq22.5$ mag, and detection in $z$ plus either W1 (the primary mass estimator) or $g$ (the optical fallback). Photometric redshifts are the DR10 random-forest estimates [69] (DR9 in the BASS/MzLS north), with $p(z)$ reconstructed from the released quantiles as a split normal; against $\sim$42,000 DESI spectroscopic redshifts the nominal 68% (95%) intervals contain the truth 65–66% (91–92%) of the time, with a 1% catastrophic-outlier rate rising to $\sim$5% in the faintest half magnitude. DESI DR1 spectroscopic redshifts [11] replace them where available. The deep fields — XMM-LSS, (E)CDF-S, ELAIS-S1, and COSMOS, which host the DES X/C/E groups, SNLS D1/D2, and the Pan-STARRS medium-deep and HST sight lines and carry 52%, 35%, and 32% of the DES, Union3, and Pantheon+ weighted lensing signal — also have deep VISTA near-infrared photometry: VIDEO DR5 $YJHK_s$ [24], matched at 1″ with 97.7–98.1% completeness for our foregrounds, and UltraVISTA [38] via COSMOS2020 ([65]) (93.9%, the shortfall being bright-star masks). Galaxy clusters are from [66]. The Union3 and Pantheon+ footprints are divided by friends-of-friends grouping into $\sim$270 and 59 regions; DES uses its four field groups.

Methods

The halo chain

Stellar masses come from the rest-frame 1 µm luminosity with $M_\star/L_{1\mu\mathrm{m}} = 0.6$ ([39]; [29]), obtained by log-interpolating each galaxy’s photometry to the observed wavelength $(1+z)\,\mu\mathrm{m}$. Where deep VISTA photometry exists, the interpolation uses the two nearest bands of $z/Y/J/H/K_s/W1$, never straddling the rest-frame 1.6 µm bump; elsewhere it spans $z$ and W1. The deep-NIR path removes 0.10–0.12 dex of scatter in quadrature against independent CIGALE ([9]) and LePhare ([2]; [23]) masses, most at $z > 0.8$. Galaxies without W1 (13–15%, mostly faint) use an optical-color estimator ([59]). A constant $M_\star/L$ underestimates massive red galaxies: against 500,000 DESI DR1 BGS and LRG galaxies in the FastSpecFit value-added catalog ([43]), the offset rises to +0.3 dex for the most massive galaxies at $z \simeq0.15$ and declines with redshift. We correct each interpolation path with a sigmoid $\Delta(\log M_\star,z)$ fit to that comparison, tying the mass scale to the DESI spectrophotometric masses. Halo masses are the halo-mass-function-weighted posterior mean $\langle M_h|M_\star\rangle$ of the [7] stellar-to-halo-mass (SMHM) relation (0.18 dex scatter; [13] mass function), capped at $M_{200\mathrm{c}} = 10^{13.8}\,M_\odot$ for individual galaxies; the difference from other SMHM prescriptions (e.g. [42]; [31]) is part of the halo-chain systematic. Each halo is an NFW profile ([44]) with [16] concentrations, truncated at $r_{200\mathrm{c}}$ ([6]).

Convergence, shear, and magnification

Galaxy $i$ at angular separation $\theta_i$ from a sight line to a source at $z_s$ contributes

summed over $3^{\prime\prime} < \theta_i < 10^\prime$, at the spectroscopic redshift where available and marginalized over $p(z)$ otherwise. The tangential shears of the same halos, $\gamma_t = \Delta\Sigma/\Sigma_{\mathrm{cr}}$, are summed as spin-2 quantities, and the exact predicted magnification is $\Delta\mu_{\mathrm{pred}} = 2.5\log_{10}[(1-\kappa)^2-|\gamma|^2]$. Its weak-lensing limit, $\Delta\mu= -(5/\ln10)\kappa_{\mathrm{ext}} = -2.171\kappa_{\mathrm{ext}}$ mag, is the prediction for the slopes quoted below. The exact form lowers the joint amplitude by 3.5% (0.17$\sigma$): 2.1% from the $\kappa^2$ term, a third-moment effect $\langle\kappa^3\rangle/2\langle\kappa^2\rangle$ that is nonzero because $\kappa_{\mathrm{ext}}$ is positively skewed, and 1.4% from shear, which is significant only near clusters.

The cluster tier

Clusters within $30^\prime$ are included as single NFW halos ($M_{200} = 1.4M_{500}$, $c = 5$) that replace their member galaxies’ halos. Each cluster’s $\Sigma$ and $\Delta\Sigma$ profiles are marginalized over a Rayleigh miscentering of scale $0.2r_{500}$ ([27]; [17]) and a 0.25 dex lognormal richness–mass scatter centered so that $\langle M\rangle= M_{\mathrm{catalog}}$. The prediction is deterministic.

Zero point

The mass-sheet zero point is set empirically by evaluating the same estimator on random sight lines in each survey region (500 for large regions, 200 for small, excluding masked areas), drawn once and reused for all source redshifts:

and likewise for the galaxy and cluster components and for $\Delta\mu_{\mathrm{pred}}$. Any spatially uniform component cancels in this difference, so no assumption is made about the density between catalogued galaxies. No sight line falls below the empty-beam limit ([36]) in our cosmology ($\kappa_{\mathrm{env}}=-0.020$ at $z_s=0.5$ and $-0.071$ at $z_s=1$; the most negative $\kappa_{\mathrm{ext}}$ is $-0.016$). Source planes are evaluated every $\Delta z_s=0.05$ to $z_s=1.6$ and interpolated to each supernova’s redshift. No parameter of the model is adjusted against any Hubble residual.

Statistical methods

Slope fits weight each supernova by its inverse distance-modulus variance and include a free intercept (jointly $+0.003\pm0.003$ mag; forcing zero changes $A$ by 0.7%). Because nearby $10^\prime$ apertures overlap, significances come from permutation nulls that shuffle residuals among supernovae within source-redshift bins, preserving the spatial structure of $\kappa$, supported by 0.5° spatial block bootstraps. Significances are one-sided, since the sign of the effect is predicted. For the joint fit, four of $10^6$ permutations exceed the observed slope; the Poisson range of that count spans $4.4$–$4.6\sigma$, and we quote $4.4\sigma$ (the width of the null distribution gives $4.3\sigma$). Galaxy and cluster amplitudes are fit jointly (their predictions are nearly uncorrelated, $r=0.015$). For Pantheon+, a generalized least-squares (GLS) fit uses the full released covariance.

The latent-variable regression (§5.4) treats each prediction as a noisy measurement of the true convergence. Its Monte Carlo noise variance is split into a classical part, from noisy inputs (photometric $M_\star$ error, richness–mass scatter), which attenuates the slope and is corrected, and a Berkson part, from scatter the prediction already marginalizes (photo-$z$, SMHM and concentration scatter, miscentering), which adds residual variance without attenuating. Treating the Berkson part as classical would inflate the amplitude by $\sim30\%$.

Validation

Table 1 lists ten tests of the mass scale and pipeline. The three that carry most weight are described here.

Galaxy–galaxy lensing closure (v). The chain predicts $\Delta\Sigma$ for any lens sample, so it can be tested against measured lensing of the same galaxies (Figure 1). We measured $\Delta\Sigma$ for the BOSS DR12 LOWZ and CMASS samples [48] with the public KiDS-Legacy shear catalog [68] (stacked with dsigma). The chain agrees with the measurement to within $6 \pm4\%$ and $7 \pm6\%$ (LOWZ) and $16$–$18\%$ (CMASS) on one-halo scales. The same test against the DESI DR1 BGS and LRG lensing measurements (shared in advance of publication; [21]) agrees to $0$–$11\%$ for BGS ($z = 0.1$–$0.4$, down to median $\log M_\star= 10.4$) and $12$–$21\%$ for LRG ($z = 0.4$–$0.6$), with the sign and mass dependence expected from the unmodeled satellite term. Without the FastSpecFit recalibration, the chain fails both tests by factors of $1.4$–$2.1$.

End-to-end mock (vi). We reran the full pipeline on the cosmoDC2 lightcone [30] with DES-like forward-modeled noise. Comparing the noisy and noiseless runs gives the noise attenuation of the weighted slope, $\lambda_{\rm mock} = A_{\rm noisy}/A_{\rm noiseless} = 0.68 \pm0.09$, for an unsmoothed point prediction as used in the analysis. Against the simulation’s own convergence map, after matching its resolution, the pipeline recovers $A_{\rm mock} = 0.93 \pm0.08$. Because the mock contains the full matter field, this also bounds the diffuse and sub-threshold mass the catalog-based prediction omits (§6). Applying $\lambda_{\rm mock}$ to Union3 and Pantheon+ assumes a noise-to-signal ratio similar to DES; the latent-variable amplitude does not use it. The attenuation is confirmed on the sky: regressing deep-NIR on wide-field predictions over the same sight lines gives galaxy-tier coefficients of $0.69$–$0.89$.

Mass swaps (viii, ix). We replaced the stellar masses with two independent per-galaxy determinations. For the 6,943 galaxies that dominate the convergence, an 8-band FrankenBlast [46] SBI++ [64] fit (DECam $grz$, VISTA $JHK_s$, WISE W1/W2, redshift fixed) places our masses $0.19$ dex lower, with no mass dependence ($\pm0.05$ dex over $\log M_\star= 9$–$13$). This offset is typical of inter-code zero points: ours are $0.16$ dex below CIGALE and $0.06$ dex below LePhare, and FrankenBlast is itself a further $0.25$ dex below direct Prospector [25] fits with a nonparametric star-formation history, the documented direction for such histories [35]. Substituting the FrankenBlast masses changes the exact-prediction amplitude by $\sim1\%$, and substituting 363,314 DESI FastSpecFit spectroscopic masses changes it by $0.001$–$0.04$ ($\le0.15\sigma$) across the three compilations.

Results

DES-SN5YR

The weighted fit gives $d\Delta\mu/d\kappa_{\rm ext} = -1.71 \pm0.42$ ($N = 1450$), i.e. $A = 0.79 \pm0.20$ (stat.) $\pm0.13$ (sys.), with permutation $p = 10^{-4}$ ($3.6\sigma$), a block-bootstrap slope error of $0.44$, and Spearman $\rho= -0.11$ ($p < 10^{-4}$). The exact prediction gives $A = 0.76 \pm0.19$. The slope is stable across a dozen sample and model variations (e.g. excising host-plane galaxies and clusters, $-1.91 \pm0.46$; spectroscopic redshifts on/off; W1-only; halo cap and stellar-mass offsets; unmasked-area cuts), and $\kappa_{\rm ext}$ does not correlate with host stellar mass ($\rho= -0.001$). The 211 sight lines with $\kappa_{\rm ext} > 0.005$ are brighter than the rest by $0.020 \pm0.012$ mag. Sight lines within $2'$ of a cluster at the SN redshift show a steeper slope ($-3.82 \pm0.77$) that persists when all near-plane foreground weight is excised, which favors a foreground lensing origin; an environmental standardization effect (e.g. [50]) cannot be excluded for these sight lines at present statistics.

What it tests	Result	Source
(i) SN 2025wny lens	absolute $M_\star$ on a deep-SED anchor	agrees to 0.04 dex	[18]
(ii) SED-code scatter	estimator dispersion adopted here	0.16 dex ($z$–W1); 0.115 dex with VISTA	§3.1
(iii) blank field	zero point on empty sight lines	$\kappa_{\rm ext}=-0.008\pm0.010$	[18]
(iv) SN 1997ff	a known magnified SN	reproduces the Keck-kinematics limit	[8]
(v) $\Delta\Sigma$ closure	halo chain vs. measured lensing	6–18% (BOSS×KiDS); 0–21% (DESI DR1)	Figure 1
(vi) cosmoDC2	end-to-end, full matter field	$\lambda_{\rm mock}=0.68\pm0.09$; $A_{\rm mock}=0.93\pm0.08$	§4
(vii) cross-pipeline	reproducibility of $\kappa_{\rm ext}$	$r=0.992$–$0.994$ on shared sight lines	Figure 3
(viii) mass-scale ladder	$M_\star$ zero point vs. four SED codes	0.06–0.19 dex low (0.44 vs. Prospector); no mass trend	§4
(ix) mass swaps	does $A$ depend on the masses?	$\Delta A\sim1\%$ (FrankenBlast); $\le0.04$ (spec.)	§4
(x) velocity dispersions	the halo rung, independent of $M_\star$	virial slope; −0.17 dex vs. SIS (418 gal.)	table note

Note—(x) compares the SMHM halo masses of spectroscopic contributors with their DESI velocity dispersions: the measured $\mathrm{d}\log M_h/\mathrm{d}\log\sigma_v=1.9$–$2.1$ is the virial value of 3 attenuated by $\sigma_v$ measurement noise, and the normalization is within the $\sim$0.1–$0.2$ dex accuracy of the singular-isothermal-sphere anchor. It is the only per-galaxy test of the halo masses that does not pass through $M_\star$.

Union3

Union3 gives $\mathrm{d}\Delta\mu/\mathrm{d}\kappa_{\rm ext}=-2.14\pm0.63$ (3.4$\sigma$ Gaussian; permutation 2.51$\sigma$; block-bootstrap error 0.70) over 1213 field SNe, with Pan-STARRS alone at $-3.82\pm1.08$ and all drop-one-sample jackknives consistent. The exact-prediction amplitude is $A=0.96\pm0.29$. The excluded See-Change sample has the elevated convergence its selection implies ($\langle\kappa_{\rm ext}\rangle=+0.0008$ vs. $+0.0003$ for the field), modest because its target clusters lie near the SN redshift, where the lensing efficiency vanishes.

Pantheon+

Pantheon+ gives $-2.47\pm0.64$ (3.9$\sigma$; permutation 2.95$\sigma$). With the full statistical+systematic covariance the GLS slope is $-2.68\pm0.80$ (3.3$\sigma$, $A=1.23\pm0.37$), so survey calibration covariances neither create nor remove the signal. On the 530 sight lines shared with Union3 ($\kappa$ correlation 0.993), the independently standardized residuals give consistent slopes ($-2.54\pm0.67$ vs. $-2.86\pm0.78$), and their difference regressed on $\kappa$ gives $+0.14\pm0.31$: the lensing signal is independent of the SN standardization pipeline (Figure 3, right).

Joint and latent amplitudes

The joint fit uses one row per physical supernova, keeping the best-measured of any duplicates: 3564 rows contain 747 shared pairs, 103 supernovae appear in all three compilations, and $3564-747+103=2920$ sight lines remain (pair residual correlations 0.70–0.88; the choice of representative changes the slope by 0.05). It gives

with 0.79 $\pm$ 0.17 for the exact prediction and $A_{\rm gal} = 0.83 \pm0.29$, $A_{\rm cl} = 0.82 \pm0.22$ for the galaxy and cluster tiers. A GLS over all 3564 rows, with the variance of each pair-difference mode floored at $(0.06\ \mathrm{mag})^2$, agrees ($-1.89 \pm0.37$ vs. $-1.79 \pm0.38$ in slope).

Noise in the predictor biases any weighted slope toward zero, so $A = 0.82 \pm0.18$ is biased low; we use it for the detection significance because it involves no correction. The latent-variable regression (§3.5), which needs no external $\lambda$, gives $A = 1.45 \pm0.61$ (DES), $0.74 \pm0.79$ (Union3), and $0.85 \pm0.83$ (Pantheon+), and jointly

$0.3\sigma$ from unity and consistent with the mock-corrected weighted fit, $0.82/\lambda_{\rm mock} = 1.20 \pm0.30$. This is our amplitude measurement. Treating all prediction noise as classical would raise the DES value to 1.87; since the mock’s forward-modeled noise is classical by construction, $\lambda_{\rm mock}$ probably over-corrects slightly.

The amplitude is flat in source redshift, as a lensing signal must be, since the prediction already carries the full lensing efficiency: $A = 1.04 \pm0.41$ ($z_s < 0.35$), $0.53 \pm0.28$ ($0.35 < z_s < 0.65$), and $1.09 \pm0.27$ ($z_s > 0.65$), mutually consistent ($\chi^2 = 2.3$ for 2 degrees of freedom, $p = 0.32$) with no monotonic trend (Figure 4). These are weighted, and so attenuated, fits. Selection, standardization drift, intrinsic-scatter mismodelling, and calibration errors would each have a redshift signature. Because residuals are de-meaned in $\Delta z_s = 0.05$ bins, the wider bins measure within-bin slopes only.

Systematic budget

The DES-anchored budget (halo-chain amplitude from the closure residuals, 0.10; cluster mass convention, 0.06; W1 fallback, 0.03; $M_\star$ calibration, 0.03; photo-$z$ calibration, 0.02) totals 0.13 in quadrature at $A = 0.79$. The mass-scale entries are also bounded by

the direct substitutions of validations (viii)–(ix). All these terms are multiplicative (16% of the signal), so they vanish under the null and do not affect the detection significance; at $A_{\rm latent} = 1.17$ they amount to 0.187. The circumgalactic-dust term of §6, 0.195, is an additive shift in $A$ and is not rescaled. The total is $\sqrt{0.187^2 + 0.195^2} = 0.27$. Noise attenuation is handled by the latent fit and is not part of the budget.

Discussion

A population-level test of the galaxy–halo connection. The amplitude ties the halo surface density implied by the DESI-calibrated mass scale, SMHM relation, concentrations, truncation, and cluster masses to the lensing of 2920 standard candles, over a validated mass range from $\log M_\star= 10.4$ to cluster scales, with the galaxy and cluster tiers tested separately. The latent uncertainty is 38% of $A$ (44% with systematics). Since $\kappa$ scales roughly as $M_{\rm h}^{0.7-0.8}$ in this regime, the supernovae alone bound the effective halo-mass normalization to $\sim50\%$ (55–60% with systematics).

Biases on the amplitude. Two physical effects act in opposite directions (Table 2). Dust in the circumgalactic medium along the sight line ([41]) dims the supernovae that lensing brightens, and so suppresses $A$. Dust inside the foreground galaxies, by contrast, affects only their mass estimates; it is small at rest-frame $1\,\mu\mathrm{m}$ and bounded by the mass swaps, whose SED codes fit attenuation explicitly. The Tripp colour correction removes most of the circumgalactic dimming, leaving $(R_B-\beta)\,\Delta E(B-V)\approx1.5\,\Delta E(B-V)$. Regressing SALT colour on $\kappa_{\rm ext}$ over the 2920 sight lines, with $c$ de-meaned in source-redshift bins like the residuals, gives $dc/d\kappa_{\rm ext}=+0.32\pm0.28$, consistent with zero, and hence $\Delta A=+0.22\pm0.20$. Because extinction can only dim, $\Delta A<0.55$ at 95% confidence (one-sided), consistent with the $\sim0.1$ expected for $\langle E(B-V)\rangle$ of a few $\times10^{-3}$. Stretch shows no dependence on $\kappa_{\rm ext}$ either. We do not apply the $1.1\sigma$ central value, but carry its uncertainty in the budget. The opposite bias comes from mass the catalog misses but that traces the catalogued halos — sub-threshold galaxies, mass beyond $r_{200c}$, filaments — which makes the true convergence exceed the prediction and inflates $A$. The cosmoDC2 mock contains this mass, and $A_{\rm mock}=0.93\pm0.08$ limits it to $\lesssim10\%$ of the signal. Neither effect is detected, so we apply no correction; applying both central values would give $1.17+0.22-0.10=1.29$, still well within the statistical error of unity.

Effect	$\Delta A$	Determination
Circumgalactic dust	$+0.22 \pm0.20$	$dc/d\kappa_{\mathrm{ext}}$; one-sided ($\ge0$)
Diffuse / sub-threshold mass	$\lesssim-0.10$	cosmoDC2, $A_{\mathrm{mock}} < 1.09$ ($2\sigma$)
Noise attenuation	$\times0.68$	absorbed by the latent fit

Magnification bias. The BEAMS/BBC ([28]) selection corrections of DES-SN5YR and Pantheon+ come from simulations that include lensing only as random $0.055z$ smearing, so they do not remove the preferential detection, near the survey limit, of supernovae on high-$\kappa$ sight lines, which would mimic the signal. We test for this by refitting only below the redshift at which fewer than 5% of supernovae per $\Delta z=0.1$ cell lie within 0.5 mag of their compilation’s faint envelope ($z<0.6$ for DES-SN5YR and Union3, $z<0.4$ for Pantheon+). This cut depends only on survey and redshift, not on brightness, so it induces no truncation bias. It gives $A=0.92\pm0.24$ on 2191 sight lines, against $0.83\pm0.10$ for random subsamples of the same size: a shift of $+0.097\pm0.103$, which bounds any selection-induced contribution to $|\Delta A|<0.20$ at 95% confidence. The redshift-flatness of $A$ is a second constraint, since the selection coupling grows steeply with redshift.

De-lensing. De-lensing DES-SN5YR with the measured amplitude shifts $\Omega_{\rm M}$ by $-0.002$ in a flat-$\Lambda$CDM refit, consistent with [56]. Supernova sight lines are slightly overdense relative to random ($\langle\kappa_{\rm ext}\rangle\approx+0.002$ at $z>0.7$, a coherent 4 mmag brightening), and de-lensing raises the $z>0.7$ residual skewness by $+0.17$, toward zero, as expected if part of the bright tail is lensing. With $\sigma_\kappa\cong0.01$ the expected variance reduction, $(2.1\sigma_\kappa)^2\approx5\times10^{-4}\,\mathrm{mag}^2$, is about 2% of a 0.15 mag scatter; the variance and skewness channels ([37]; [47]) are therefore systematics-limited now and become useful at LSST scale.

Implications for DESI DR2. The evolving-dark-energy preference of [12] is $2.8$–$4.2\sigma$, depending on which SN compilation is combined with BAO and the CMB. Propagating the de-lensed distances in the Gaussian limit changes the $\Lambda$CDM-rejection $\Delta\chi^2$ by $+0.4$ (DES-SN5YR: $4.19\sigma\rightarrow4.24\sigma$), $+0.2$ (Union3: $3.76\rightarrow3.79$), and $-0.1$ (Pantheon+: $2.82\rightarrow2.81$). Raising the DES-SN5YR combination to $5\sigma$ would require $+7.7$. The corrections lie almost entirely along the SN-only $(w_0,w_a)$ degeneracy that BAO+CMB break, so lensing neither creates nor materially changes the evolving-dark-energy preference for any of the three examples.

Relation to earlier work. [56] fit the halo normalization and reach $6\sigma$; we fix it a priori and measure the amplitude. Their fitted mass-to-light ratios, consistent with expectations, and our $A\simeq1$ are the same conclusion reached from opposite directions.

Caveats. Group-scale halos between the single-galaxy cap and the cluster-catalog limit are represented only by summed member halos; the insensitivity of the slope to the cap bounds this. Host coordinates stand in for SN positions. The Union3 residuals are our own standardization, but the agreement with Pantheon+ and fixed $\kappa$ bounds that directly. None of these affects the Hubble residuals, so the amplitude test remains blind.

Summary

Using only public catalogs and an externally calibrated halo model, we predict the external convergence toward 2920 unique SN Ia sight lines in DES-SN5YR, Union3, and Pantheon+. We detect the corresponding magnification in each compilation (permutation 2.5–3.6$\sigma$; 3.4–4.0$\sigma$ Gaussian) and jointly at $p = 4 \times10^{-6}$ (4.4$\sigma$), and measure an observed-to-predicted amplitude $A = 1.17 \pm0.44$ (stat) $\pm0.27$ (sys), consistent with unity. The signal is independent of the SN standardization pipeline, survives the full Pantheon+ covariance, and is unchanged under per-galaxy substitution of two independent sets of stellar masses. The galaxy–halo connection is validated from $\log M_\star= 10.4$ to cluster scales by two galaxy–galaxy lensing measurements and by DESI velocity dispersions. De-lensing leaves the DESI DR2 evolving-dark-energy preference unchanged. The released per-supernova $\kappa_{\mathrm{ext}}$ catalogs allow de-lensing and magnification flags for current SN samples, and the method scales directly to LSST and Roman, with Euclid $YJH$ extending the deep-NIR mass estimates across the footprint.

ACKNOWLEDGMENTS

This work used the public DES-SN5YR, Union3/UNITY, and Pantheon+SH0ES data releases; data products of the DESI Legacy Imaging Surveys (DR10) and DESI DR1; the [66] cluster catalog via CDS; and services of the Astro Data Lab at NSF NOIRLab ([45]). The deep near-infrared photometry is from the VISTA VIDEO survey (DR5; ESO programme 179.A-2006) via the ESO Science Archive and from the COSMOS2020 catalog (UltraVISTA). The stellar-mass calibration used the public DESI DR1 FastSpecFit value-added catalog, which also provided the spectroscopic masses and velocity dispersions of validations (ix)–(x). The galaxy–galaxy lensing closure used the public SDSS-III BOSS DR12 large-scale-structure catalogs and the public KiDS-Legacy (DR5) shear catalog. We are grateful to Sven Heydenreich and the DESI Lensing Working Group for sharing the DESI DR1 galaxy–galaxy lensing measurements in advance of publication. The mock calibration used the cosmoDC2 synthetic sky catalog ([30]) and resources of NERSC. P.E.N. acknowledges support from the DOE Office of Science, Office of High Energy Physics, under contract DE-AC02-05CH11231. Anthropic’s Claude was used to assist in the analysis and the drafting of this manuscript.

Facilities: Blanco (DECam), Mayall (DESI, Mosaic-3), Bok (90Prime), WISE, VISTA (VIRCAM), Sloan, CFHT, PS1, VST

Software: SNKappa (https://github.com/nugent68/SNKappa), astropy ([3, 4, 5]), numpy ([19]), scipy ([62]), colossus ([15]), pyvo, dsigma ([34])

DATA AVAILABILITY

The per-supernova $\kappa_{\mathrm{ext}}$ catalogs for all three compilations (output/{des_full,union3,pantheon}/*_kappa.csv, including galaxy/cluster decompositions, shear, exact predicted magnifications, and quality flags), the FrankenBlast masses for the 6,943 dominant convergence contributors (output/nir_video/fb_masses.csv, with per-galaxy uncertainties), the galaxy–galaxy lensing closure (measurement and prediction), all analysis scripts, and the query provenance are in the repository at https://github.com/nugent68/SNKappa.