Degenerate Time Universe (DTU) — Papers I–III (v4.0): Foundations, Observational Interface, and Quantum Operator Layer

# Degenerate Time Universe (DTU) — Papers I–III (v4.0) **Author:** Lee Byoungwoo ## OverviewThis release provides the DTU (Degenerate Time Universe) three-paper set (v4.0). DTU introduces a **structural/measured time** \(T\) related to coordinate time \(t\) by a lapse field \(L>0\):\[dT = L\,dt,\qquad H_s := \frac{1}{a}\frac{da}{dT}=\frac{H}{L}.\]The central goal is a **referee-facing, testable dictionary** that separates:- an **operational (background-only) window** where the mapping is used as a measured-time inference convention, and- a **dynamical clock sector** where \(\psi := \ln L\) is promoted to a field producing genuine scale-dependent effects. This version is written to avoid overclaiming: observational fits are treated as **preliminary constraints**, and the quantum layer is presented as a **classification / sufficient-conditions program**, not a UV-complete quantum gravity claim. ## What is new in v4.0- Tightened “Witten-style” front-matter: **core statements, scope, and non-claims** are made explicit.- Cleaned operational vs dynamical separation: - operational regime emphasizes **measured-time inference** through \(H_s\), - dynamical regime is isolated as a clock-sector EFT.- Paper II: removed “Figure ??”/reference hygiene issues; upgraded the observational narrative with - a **non-degenerate signature note** (chronometers + distance probes), - an **EFT embedding paragraph** (\(\psi(N)\simeq \alpha+\beta N\)), - a referee-facing **limitations** paragraph (no detection claim), - a minimal **reproducibility pack** checklist.- Document build/formatting hygiene and placeholder conventions improved (manual PDF image insertion friendly). ## Contents### Paper I — Foundations and minimal EFTPaper I defines the DTU dictionary and fixes the operational/dynamical split:- **Operational mapping:** background observables are routed through \(H_s=H/L\) under a measured-time convention.- **Dynamical completion:** \(\psi=\ln L\) is promoted to a scalar in a minimal Einstein-frame EFT with a Jordan coupling,\[S=\int d^4x\sqrt{-g}\left[\frac{M_{\rm Pl}^2}{2}R-\frac{\xi}{2}(\nabla\psi)^2 - V(\psi)\right]+ S_m[\tilde g_{\mu\nu},\Psi_m],\qquad \tilde g_{\mu\nu}=A(\psi)^2 g_{\mu\nu},\]with \(\xi>0\) and standard health conditions (no ghost; \(c_T^2=1\) in the regime of interest). ### Paper II — Observational interface (operational window)Paper II is an **interface paper**: it keeps the perturbation sector in the background-only operational window\[\mu=\gamma=1,\]and tests clock-based background drift through a phenomenological \(L(a;\alpha,\beta)\), interpreted via\[\bar\psi(N)=\ln L \simeq \alpha+\beta N,\qquad N=\ln a.\]The paper emphasizes that current constraints are preliminary and that the key robustness direction comes from**combining chronometer-based \(H(z)\)** with **ruler/candle distance probes** (BAO/SN), which reduces degeneracyrelative to single-probe inference. ### Paper III — Quantum operator layer (classification / sufficient conditions)Paper III introduces the clock–generator split and a structural-time generator\[\hat K_T := \hat L^{-1/2}\,\hat H\,\hat L^{-1/2},\]and develops a boundary-agnostic operator framework for minisuperspace / effective settings:- self-adjoint extension as a classification problem (deficiency data),- boundary \(S\)-matrix as a representation of extension choices,- explicit non-claims about full UV completion beyond the stated scope. ## Reproducibility and figuresThis release is designed to support a manual PDF-insertion workflow for figures:- placeholder boxes can be used in LaTeX, and PNG/JPG figures can be inserted later via a PDF editor.Paper II includes a minimal reproducibility-pack checklist (parameter YAML, pipeline script, placeholders, manifest hashes). ## Scope and non-claims (referee-facing)- Operational mapping alone does not claim new dynamics; it is used as a **measured-time inference convention**.- Dynamical clock effects are isolated to the \(\psi=\ln L\) sector and are model-dependent through \(A(\psi)\), \(V(\psi)\).- Paper II does **not** claim a detection; it provides a transparent observational interface and preliminary constraints.- Paper III does **not** claim UV-complete quantum gravity; it provides classification results and sufficient conditions in the stated minisuperspace/effective setting. ## Files- Degenerate_Time_Universe_Paper1_v4.0.pdf / .tex- Degenerate_Time_Universe_Paper2_v4.0.pdf / .tex- Degenerate_Time_Universe_Paper3_v4.0.pdf / .tex ## CitationLee Byoungwoo, “Degenerate Time Universe (DTU) — Papers I–III (v4.0): Foundations, Observational Interface, and Quantum Operator Layer,” Zenodo (v4.0). (email: leeclinic@protonmail.com)