Evidence for Six-fold Phase Alignment Geometry in ATLAS Mercedes Jets and GW170817: A Test of the Allen Orbital Lattice

This paper reports a Branch A geometry-validation test of Pattern Field Theory (PFT), the Allen Orbital Lattice (AOL), and Phase Alignment Lock (PAL) using reconstructed ATLAS 2010 Open Data 7 TeV 3-jet event geometry and a GW170817 neutron-star compactness cross-check.

The study defines two collider observables: the six-axis angular residual R6min, measuring residual alignment to the kπ/3 hexagonal grid, and the tensor residual ||ΔT||, measuring global event-shape coherence under QuantaHex projection. ATLAS Mercedes 3-jet topology shows R6_min enrichment ratio 2.717 in data versus 1.718 in Pythia8 Monte Carlo, with KS p = 0.706. Inclusive/exact-3jet topology shows ||ΔT|| enrichment ratio 1.514 in data versus 1.424 in Monte Carlo, with reported significance 8.2σ and Mann-Whitney p = 2.28 × 10^-48.

Rank-shuffled null controls preserve jet pT and η distributions while destroying phase coherence, confirming that the 58.1% Mercedes R6_min excess and the 6.3% inclusive ||ΔT|| excess represent substrate-level PAL geometry not captured by pT-ordered shower models.

The paper also links the collider geometry result to the companion GW170817 structural compactness analysis, where the empirical compactness ceiling Lmax = 0.446 ± 0.004 is compared with the PFT/AOL prediction π/7 = 0.4488, giving approximately 0.6% agreement.

A central distinction of the paper is parameter status. Conventional collider reconstruction, Monte Carlo tuning, background modelling, detector calibration, and compact-object inference rely on fitted, tuned, or externally calibrated parameters. By contrast, the PFT/AOL target relations tested here introduce no fitted parameters into the target geometry. The tested quantities are fixed prior geometric consequences of AOL geometry, PAL closure, six-axis angular spacing, the 6+1 closure structure, and the compactness ratio π/7.

This publication is Branch A of the PFT/AOL Collider Program and is a companion to the separate Branch B 7.3 TeV chamber-resonance prediction and ATLAS-style pseudo-analysis.

Data: ATLAS Open Data 2010 7 TeV. The Mercedes analysis screens 25,707 events, with 22 events passing the Mercedes topology cuts. The inclusive/exact-3jet analysis screens 25,708 events, with 2,069 exact-3jet candidates.

Prediction and ATLAS-Style Pseudo-Analysis of a Non-Standard 7.3 TeV Resonance
https://zenodo.org/records/20031950

A Data-Derived Structural Ceiling for Neutron Star Compactness and Tidal Deformability from GW170817
https://zenodo.org/records/20789186

Beyond Universal Scaling: A Structural Solution to the Galaxy Rotation Problem
https://zenodo.org/records/20055899