SRT Part II: PRE-REGISTRATIONSRT Complexity Correlation Test (SN Ia + Weak Lensing)

Abstract

This document is a formal pre-registered falsification protocol for the State-Rewrite Theory (SRT) using Type Ia supernova (SN Ia) Hubble residuals and weak-lensing mass-map tomography.

The protocol is designed to isolate an SRT-specific signal from standard General Relativity (GR) + LambdaCDM weak-lensing effects by explicitly defining:

1. Frozen observables
2. Fixed models
3. A GR + LambdaCDM null distribution for the complexity statistic
4. Hard rejection thresholds defined before analysis

1) Ground truth: GR + LambdaCDM expectations (baseline)

GR + LambdaCDM predicts that line-of-sight (LOS) matter inhomogeneity produces both:

(A) A mean magnification channel that correlates SN Ia Hubble residuals with convergence (kappa).

(B) An additional lensing-induced scatter channel whose magnitude increases with LOS structure.

This baseline has been detected in multiple datasets, including a 3.6σ correlation in Pantheon and a 6.0σ detection in DES-SN5YR lensing analyses.

Baseline references (factual, not interpretive):

• Shah, Lemos, Lahav, “Weak lensing magnification of Type Ia Supernovae from the Pantheon sample” (arXiv:2203.09865)
• DES Collaboration, “Detection of weak lensing magnification of supernovae and constraints on dark matter haloes” (arXiv:2406.05047)

2) Observables and sign conventions (FROZEN)

2.1 Primary observable

Distance-modulus residual for supernova i:

mu_res_i = mu_obs_i − mu_LCDM_i

Computed after standard light-curve standardization and selection corrections used by the dataset release.

Positive mu_res means the supernova appears dimmer than predicted.

2.2 Uncertainty term

sigma_mu_i is the published per-supernova uncertainty (as released), used only as defined below.

2.3 Weak-lensing predictors from LOS tomography

From a fixed mass-map product producing kappa_i(z) in tomographic bins:

• kappa_eff_i = weighted mean / sum of convergence along the LOS (exact weights locked below)
• K_i = LOS “complexity” defined as multi-plane variance across tomographic bins:
  K_i = Var_z[ kappa_i(z) ]

2.4 kappa(z) estimation protocol (FROZEN)

kappa_i(z) is computed from a fixed released mass-map product using:

• Aperture: 10 arcmin radius
• Gaussian smoothing: sigma = 5 arcmin

If the release provides already smoothed or binned kappa products, the release-native smoothing or bins are used and no re-smoothing is performed.

The 10 arcmin aperture and sigma = 5 arcmin defaults apply only when kappa is computed directly from raw mass maps.

3) The dual-channel test (FROZEN models)

3.1 Endpoint A: Mean-shift (baseline lensing channel)

mu_res_i = a + gamma1 · kappa_eff_i + b1 · z_i + b2 · HostMass_i + SurveyIndicators + eps_i

GR expectation: gamma1 < 0
(overdense LOS magnifies; the supernova appears brighter; mu_res decreases)

3.2 Endpoint B: Complexity excess (SRT-only claim under test)

To avoid distribution artifacts from squaring a noisy quantity, Endpoint B uses a locked transformation.

Primary B outcome (FROZEN):

y_i = log( (mu_res_i / sigma_mu_i)² + y_floor )

where y_floor = 1e-6 (fixed) to avoid log(0).

Endpoint B model (FROZEN):

y_i = a + gamma2 · K_i + delta · kappa_eff_i + b1 · z_i + b2 · HostMass_i + SurveyIndicators + eps_i

SRT requirement: gamma2 > 0 and must exceed the GR + LambdaCDM null expectation defined below.

Document hash

Document Hash: SRT-PREREG-V3-K-EXCESS-TEST-2026-LiMiT

License

License: CC BY 4.0
Copyright © 2026 LiMiT

References (primary)

• arXiv:2203.09865 — Shah, Lemos, Lahav, Weak lensing magnification of Type Ia Supernovae from the Pantheon sample
• arXiv:2406.05047 — DES Collaboration, Detection of weak lensing magnification of supernovae and constraints on dark matter haloes