Projnowean Quantum Gravity: Lattice‑Based Emergent GR, PQG‑PN Gravitational‑Wave Pipeline, and Photon‑Channel Constraints

This preprint presents a complete formulation of the Projnowean Quantum Gravity (PQG) framework, in which classical general relativity emerges from elastic deformations of a discrete 4, 3, 4 spring‑lattice spacetime. The manuscript develops the continuum limit, the recovery of the Einstein–Hilbert action, Lorentz‑invariance restoration, matter coupling, and Standard‑Model‑consistent deformations. The document also includes a full derivation of the PQG‑modified dispersion relation and its phenomenological consequences. In addition to the theoretical construction, this repository contains the full computational pipelines used to test PQG against observational data: PQG‑PN Gravitational‑Wave Pipeline A complete RMS‑comparison framework built on publicly available GWOSC data. For each LIGO/Virgo/KAGRA event and for two waveform approximants (IMRPhenomD and SEOBNRv4), the pipeline evaluates the improvement of PQG‑modified phase evolution over standard GR templates. The catalog‑level analysis yields a statistically significant cumulative Δ improvement across 314 event–approximant pairs. Null tests using synthetic GR+noise injections show no spurious bias. PQG Photon‑Channel Pipeline A Fermi/GBM TTE‑based analysis of high‑energy GRBs, estimating the quadratic PQG time‑delay parameter β₂ from photon arrival times and energies. The combined inverse‑variance weighted constraint across all GRBs yields a non‑zero β₂ at the ~4σ level. This Zenodo record includes: the full theoretical PDF (preprint version), all analysis scripts (GW pipeline, photon pipeline), event catalogs, β₂ and Δ results in CSV format, diagnostic plots (RMS curves, cumulative Δ (N), β₂ posteriors, null‑test distributions), and reproducibility instructions. All gravitational‑wave data used in this work are publicly available through the GWOSC archive. The LIGO–Virgo–KAGRA Collaboration was not involved in this analysis, and all interpretations and conclusions are solely those of the author. This preprint is released to enable independent verification, open peer review, and community feedback prior to journal submission.