Finite Screen Spacetime: Entropy-Response Geometry from Causal-Screen Ledgers

FDS--G1 Complete Series presents a finite-screen entropy-response framework for gravity and late-time dark-sector residuals. The series develops Finite Screen Spacetime as a bridge program in which the primitive gravitational object is a finite causal-screen entropy ledger, and geometry is treated as the integrable hydrodynamic response envelope of that ledger. The archive includes the Core paper, Companions A--F, the G1fit-real data-confrontation paper, and the D0--D7 dark-sector closure sequence. Together these papers formulate the finite-screen response chain, screen statistical mechanics, stochastic screen transition dynamics, scalar-capacity EFT interface, likelihood-ready falsification tests, horizon occupancy residuals, holographic dictionaries, modular anomaly-inflow calibration targets, finite-access sheaf geometry, the 3/4 projection law, the screen influence functional, Weyl-normalized Ward completion, maximum-caliber memory quotient, and a finite Markov-screen realization prototype. The current leading empirical dark-sector branch is the projection-locked G1DE-M3/4 model. Its locked late-time residual pattern is: s < 3, μ(a,k) = 1, Σ(a,k) − 1 = −(3/4)(3 − s) RbH(a), RbH(1) = 1. Here RbH(a), also denoted R̂H(a) or Xb(a) in theory/code-facing notation, is the normalized horizon-response output shape. It is not assumed to be a uniquely identified microscopic source--kernel factorization. D6 formalizes this output/lift distinction through a memory quotient and maximum-caliber horizontal lift, while D7 gives a finite-state detailed-balance Markov-screen realization prototype for an admissible passive lift. The current exact-pilot evidence result compares six late-time cosmology models under matched medium-prior nested evidence: M3/4 > Mκ > const-Σ > G1DE-2 > CPL > ΛCDM. This should be read as a preliminary exact-pilot, theory-structured evidence selection result, not as final cosmological confirmation. The archive explicitly identifies pending work: production nested-evidence refinement, full wide-prior baseline sensitivity, expanded weak-lensing / EG / 3×2pt likelihoods, CMB/BBN and nonlinear production validation, and independent pipeline replication. The purpose of this release is to provide a timestamped, internally organized, falsifiable research archive for the FDS--G1 finite-screen gravity program and the G1DE-M3/4 dark-sector branch. The framework is conditional on stated bridge assumptions and includes explicit demotion criteria: failure of the 3/4 projection lock, preference for constant-Σ, unsuppressed μ-channel response, requirement of a free A(a,k), or loss to CPL / ΛCDM under production-level evidence would weaken or demote the relevant branch. Recommended entry points are: Core for the finite-screen entropy-response architecture, G1fit-real for the exact-pilot evidence comparison, D0 for the modular calibration route, D5 for the Weyl-normalized production rules, D6 for memory-output identifiability, and D7 for the finite Markov-screen realization prototype. Official website: distinctiontheory.orgPublic portal for the start guide, papers, claim status, failure registry, prior-art boundary, and citation resources. Canonical GitHub repository:https://github.com/yiningwu-research/Distinction-Theory