Calibration and Topological Residual Analysis of Late-Universe Supernova Probes

Abstract:We present a methodological framework for resolving cross-survey systematics in Type Ia Supernova (SN Ia) data using a discrete topological transcoder and a sequence alignment algorithm. We analyze the full Pantheon+ (1590 SNe) and DESY5 (1820 SNe) compilations. By cross-matching 378 overlapping supernova anchors, we identify and correct a systematic zero-point offset of Δμ=−0.1045Δμ=−0.1045 mag between the two datasets. To isolate the underlying cosmological signal from instrument-specific noise, we extract the residuals against a reference flat ΛΛCDM model and discretize them into 50 redshift bins. Applying the Needleman-Wunsch dynamic programming algorithm to the resulting structural phases yields a 73.5% global alignment coherence, confirming that both datasets encode identical underlying geometry. We then perform a joint 2D grid search on the dark energy equation of state, parameterized as w(z)=−1+β0+β1zw(z)=−1+β0+β1z. Using robust median binning to equalize epoch weights, the joint unnormalized χ2χ2 minimization converges to β0=0.300β0=0.300 and β1=0.100β1=0.100 with a minimal χ2=56.21χ2=56.21. This result indicates a preference for a quintessence regime (w(z)=−0.7+0.1zw(z)=−0.7+0.1z) over both the standard ΛΛCDM and previously reported local phantom signals (β=−0.120β=−0.120). The open-source Delphi implementation is provided for independent verification. Key Findings: Identification of a systematic zero-point offset (Δμ=−0.1045Δμ=−0.1045 mag) between Pantheon+ and DESY5 using 378 anchor supernovae. Topological coherence of 73.5% between the residual profiles of the two datasets, confirming structural consistency. Joint 2D fit of the equation of state yields a quintessence regime with w(z)=−0.7+0.1zw(z)=−0.7+0.1z. The previously reported phantom signal in Pantheon+ is shown to be a localized artifact of calibration. Full simulation source code (Unit1.pas, Unit2.pas) is attached for reproducibility.