Log-Periodic Dimuon Residual in CMS Open Data: Cross-Period Replication and a Prospective Phase-Locked Holdout

Cross-Period and Prospective Phase-Locked CMS Open-Data Replication of a Log-Periodic Dimuon Residual Motivated by a Pre-Existing Wave Confinement Theory Collider Prediction
Richard J. Reyes - September 1, 2026

GitHub Repository: github.com/rickyjreyes/wct-cms

This paper develops a progressively constrained replication test for log-periodic structure in the inclusive opposite-sign dimuon invariant-mass spectrum of CMS Run-2 open data. After rejecting an initial low-frequency boundary solution as a continuum-model degeneracy, a certified Run2016H discovery sample identifies a resolved interior frequency near ωₘ ≈ 7.03. That numerical frequency is then frozen and tested in an unused Run2016H file, preregistered across the Run2016G period, and finally extended to a prospective holdout in which frequency, phase, amplitude sign, and target-file selection are all fixed before inspection.

Established in the paper
Frozen Predictive Log-Frequency:

ωₘ = 7.0258258258

with the prospective phase-locked prediction

ϕₗₒ꜀ₖ = −0.2313916853 rad, A > 0

The G2 holdout fits only the signed amplitude; neither frequency nor phase is refit to the target data.

Key results
• The certified Run2016H discovery sample identifies an interior log-periodic candidate at ωₘ = 7.0258258258 with Aᵣ = 0.7543 and Δχ² = 75.76, spanning approximately 4.57 cycles across the analyzed logarithmic mass interval.
• An unused Run2016H file reproduces the frozen frequency with Aᵣ = 0.9367 and Δχ² = 118.91, with zero exceedances in 1000 residual permutations and 500 parametric background-refit pseudoexperiments.
• A preregistered Run2016G cross-period test again reproduces the same frozen frequency with Aᵣ = 0.9349 and Δχ² = 115.89, extending the result beyond the original CMS run period.
• The prospective Run2016G G2 holdout freezes the frequency, phase, positive amplitude direction, file-selection rule, cuts, resonance masks, continuum model, and null settings before target inspection. It returns A = 0.9708618 and Δχ² = 126.2832.
• Under the implemented fixed-waveform reference model, the G2 result has a one-sided local analytic probability p = 1.33 × 10⁻²⁹, corresponding to Z = 11.24σ. However, the empirical ensembles contain zero exceedances in only 1000 permutation and 500 refit-bootstrap trials, so they establish Monte Carlo floors near 10⁻³–2 × 10⁻³ rather than an empirical >5σ tail.
• The genuine replication amplitudes are notably stable: Aᴴ² = 0.9367, Aᴳ¹ = 0.9349, and Aᴳ² = 0.9709, while the analysis becomes progressively more constrained from discovery through the phase-locked prospective holdout.

Contribution
Provides a reproducible progression from exploratory discovery to frozen-frequency replication, cross-period preregistration, and a prospective fixed-frequency, fixed-phase, fixed-sign holdout in CMS open data. The work substantially weakens a one-file statistical-fluctuation explanation under the implemented analysis pipeline and provides positive empirical support for the pre-existing WCT prediction class of collider log-periodicity. It does not establish WCT as the unique physical cause, nor does it claim an empirical >5σ anomaly. Stable CMS, Standard Model, acceptance, reconstruction, trigger-efficiency, and continuum-model structure remain active conventional explanations, motivating adversarial background tests, detector and efficiency controls, deeper end-to-end null calibration, and independent-detector replication such as ATLAS.

Keywords
CMS; CERN Open Data; dimuon invariant mass; log-periodic structure; discrete scale invariance; frozen replication; prospective holdout; phase-locked prediction; cross-period replication; gravitational-wave-independent collider validation; Wave Confinement Theory.

For correspondence regarding this work, please contact Richard J. Reyes at reyes.ricky30@gmail.com.
ORCID iD: 0009-0005-5975-8718.