This record is part of the Mass, Proper Time, and Gravity series. Full series community:https://zenodo.org/communities/mass-proper-time-gravity/ This part gives the synthesis of the frozen-frame route developed after the effective causal-history partition function of Part LII. The claim is not that ADM constraints, gravitational decoherence, or quantum measure theory are new. The contribution is the operational causal-set chain that places them in one sequence: causal order -> proper time -> frozen screen -> energy density -> spatial 3-geometry -> gravitational self-energy of the geometric difference -> decoherence functional. A causal order supplies a proper-time slicing; on a frozen screen the ADM Hamiltonian constraint ties energy to spatial geometry; a matter superposition therefore becomes a superposition of screen geometries; and classicality is read as decoherence between gravitationally distinguishable geometry branches (Diosi-Penrose), not as objective collapse. Each link is graded explicitly as established, prototype-level, conjectural, or open. This is a continuation of Parts I-LII of the same program.
This record is part of the Mass, Proper Time, and Gravity series. Full series community:https://zenodo.org/communities/mass-proper-time-gravity/ This part gives the synthesis of the frozen-frame route developed after the effective causal-history partition function of Part LII. The claim is not that ADM constraints, gravitational decoherence, or quantum measure theory are new. The contribution is the operational causal-set chain that places them in one sequence: causal order -> proper time -> frozen screen -> energy density -> spatial 3-geometry -> gravitational self-energy of the geometric difference -> decoherence functional. A causal order supplies a proper-time slicing; on a frozen screen the ADM Hamiltonian constraint ties energy to spatial geometry; a matter superposition therefore becomes a superposition of screen geometries; and classicality is read as decoherence between gravitationally distinguishable geometry branches (Diosi-Penrose), not as objective collapse. Each link is graded explicitly as established, prototype-level, conjectural, or open. This is a continuation of Parts I-LII of the same program.
This record is part of the Mass, Proper Time, and Gravity series. Full series community: https://zenodo.org/communities/mass-proper-time-gravity/ This part identifies a precise compatibility condition (the frozen-screen condition) under which a causal history admits a frozen proper-time screen with a pinned clock mode and a Green elastic shape sector. On such a screen the gravitational decoherence functional is Sorkin-admissible (positive, I3=0) and takes the form D(A,B) ~ exp(-gamma_IR E_grav). The screen fluctuation covariance equals gamma_IR L_Sigma^+ as an operator on the infrared sector (verified numerically, robust to resolution, density and curvature on T3/S3/H3), so the screen behaves as a Gaussian elastic field, and the central proper-time slice is the cleanest elastic screen. Classical objects are read as geometry-compatible decohered branches: matter distributions readable on a frozen screen, while alternatives with distinguishable geometries lose interference. The condition is stated, not derived; its derivation from the full histories measure mu(C) exp(iS/hbar) remains the open analytic gate. Supplementary Python scripts included.
This record is part of the Mass, Proper Time, and Gravity series. Full series community: https://zenodo.org/communities/mass-proper-time-gravity/ Part LVII isolates the single microscopic input of the frozen-screen programme: the operator identity H_Sigma = c L_Sigma, relating the Hessian of the coarse-grained action on the screen shape sector to the intrinsic spatial Laplacian of the screen. The naive target c -> 1 is shown to be a boundary illusion: once the reading is restricted to the interior of the screen and to its infrared modes, the constant stops drifting and settles at a definite, finite value c_ast = 0.04, robust across estimators. The physical content is that H_Sigma = c_ast L_Sigma makes the frozen slice an elastic medium: the clock mode is pinned while the spatial shape stays elastic, and c_ast is its stiffness. Because the screen propagator is the inverse of the stiffness, C_Sigma = c_ast^-1 L_Sigma^+, the Diosi-Penrose energy of a branch difference scales as c_ast^-1: a soft screen turns two energy alternatives into two geometries more easily, so the discreteness amplifies gravitational decoherence relative to the naive baseline (by about 25 for c_ast = 0.04). Diosi-Penrose thereby becomes not merely a self-energy formula but the elastic response of a frozen causal screen. Results are reported as a finite-N prototype: c_ast is a first estimate, the fermionic log-det correction is computed and found not to close the identity, and the exact continuum constant remains an open, well-posed analytic problem. Each result has a reproducible Python script (included). Part of the Mass, Proper Time, and Gravity series.
This record is part of the Mass, Proper Time, and Gravity series. Full series community: https://zenodo.org/communities/mass-proper-time-gravity/ Part LVIII turns the frozen-screen rigidity into an experimental prediction. Because the screen propagator is the inverse of the stiffness, C_Sigma = c_ast^-1 L_Sigma^+, the Diosi-Penrose energy of a branch difference is amplified by c_ast^-1, so the critical mass at which interference is lost shifts to m_ast^causal = sqrt(c_ast) m_ast^DP. A large-N continuum reading gives c_ast ~ 0.05, hence m_ast^causal ~ 0.2 m_ast^DP: decoherence sets in at a mass about five times below standard Diosi-Penrose. The mechanism is pure decoherence: a large-N analysis and a dispersion-plus-pinning argument give a vanishing dissipative coefficient eta -> 0, so the screen does not heat or radiate and automatically evades the spontaneous-radiation bounds (Gran Sasso, LISA Pathfinder) that constrain collapse models. The distinctive, falsifiable signature is gravitational-scaling visibility loss without heating, at one-fifth of the DP mass; a MAQRO-class space interferometer at m ~ 10^10-10^11 amu, Delta x ~ 100 nm, T ~ 100 s is the concrete device that would test it. QGEM acts as a one-sided falsifier: any positive gravitational-entanglement signal refutes the model. Results are reported at the honest level of a finite-N prototype: c_ast and eta -> 0 are prototype readings, and the exact continuum c_ast is the one number left to fix. Each result has a reproducible Python script (included). Part of the Mass, Proper Time, and Gravity series. Changes in v2: the QGEM cross-test is reframed around the entanglement witness <W> that the protocol actually measures. The causal self-decoherence Gamma enters the total decoherence rate gamma; if gamma*tau >> 1 then exp(-gamma*tau) -> 0 and <W> -> 1/4 (separable). It is presented as two rival predictions for a future measurement (standard QGEM: <W> < 0; causal model: <W> -> 1/4 if Gamma is at the estimated scale), noting that QGEM is not yet performed and that c_*^-1 is a finite-N prototype number. A witness script (causal_lviii_qgem_witness.py) is added.
This record is part of the Mass, Proper Time, and Gravity series. Full series community: https://zenodo.org/communities/mass-proper-time-gravity/ Part LXV closed the operator-to-equation arc, ending with the causal Einstein equation G_munu^caus + Lambda_eff g_munu^caus = (8 pi G_ind/c_obs^4) T_munu^read and naming one remaining conceptual gap: the history measure mu(C). Part LXVI carries the programme across that gap and out to phenomenology in one continuous arc. It first defines the physical readability functional whose minimizer selects the physical history and reads gravity as the Green response of an induced causal screen L_Sigma^eff = a I - Pi_SJ (Sec. 1); fixes the normalization principle, the suppression threshold and the critical coarse-graining rule that turn readability into a measure principle (Secs. 2-4); establishes the spectral-gap/leakage bridge, the dynamical saturation principle and the posterior reading of the constants, with their universality and stability (Secs. 5-8); calibrates the Newton/Diosi-Penrose decoherence interface and the matter, gauge and vacuum sectors (Secs. 9-12); and finally assembles the constrained finite quantum measure mu(A) = D(A,A) and reads its experimental windows (Secs. 13-14). Throughout, the Barbu phase Phi_B = e^{-i m c^2 tau_C/hbar} rides on the order-intrinsic proper time and no fundamental graviton is introduced; the structural constant c_C stays dimensionless and only the observed c_obs = lim c_C carries the Einstein coefficient. The result closes the measure gap left open by Part LXV and gives the first phenomenological windows of the causal-gravity programme. This record unifies the former Parts LXXV-LXXXVIII into one article; the attached scripts are self-contained and reproduce the finite results.
This record is part of the Mass, Proper Time, and Gravity series. Full series community: https://zenodo.org/communities/mass-proper-time-gravity/ Part LIX serves two roles. First, a status map of the programme: eight results (proper time, the neutralization of Kleitman-Rothschild domination, the Einstein/Lovelock form, the Planck scale, the 3+1 selection, rest mass, quantum interference, gravitational decoherence), each stated with its headline, its logic, an honest status label (exact / analytic / prototype / mechanism), and a link to the Zenodo part where it is built, ordered by position in the series. Second, a focused study of the two frontier items. The history measure mu(C) is taken to be conditioned by the order and the action, mu = mu[C,S], and is shown to factorize, mu(C,S) ~ exp(-E_layer[C]) exp(-E_mat[C,S]): the order capacity E_layer (a log-count in nats, coupling fixed by normalization lambda=1) exactly neutralizes the KR multiplicity (E_layer^KR/N^2 -> (ln2)/4 = ln(#KR)/N^2, so e^{-E_layer} #KR ~ O(1), not a brute suppression); the action phase alone cannot (KR is a phase-coherent plateau); and the 3+1 choice lives in the separate exact term e^{-E_mat} (#E=#B <=> d_sp=3). The matter-sector dynamics is illustrated by a testable screen identity, C_Sigma P_IR ~ gamma_IR L_Sigma^+ P_IR => |D| ~ exp(-gamma_IR E_grav) (finite-N prototype, O(10%)). The single analytic gate that remains open is that this factorized suppressor and this covariance follow from the full measure mu(C) e^{iS/hbar} itself, with the manifold-like sector dominating Z. Results are stated at their honest level (exact, prototype, or mechanism); reproducible Python scripts are included. The part concludes with the interpretation of time as the causal DNA of a 4D world.
This record is part of the Mass, Proper Time, and Gravity series. Full series community: https://zenodo.org/communities/mass-proper-time-gravity/ This part proves no new theorem about the measure; it establishes one identification and draws the reading it forces. The Barbu phase of Parts LXIX-LXXI is a single object read in three registers: the internal clock Phi_B = e^{-i omega_B tau_C} (omega_B = mc^2/hbar, with the physical c), the phase of the history amplitude A(C) = W(C) e^{-i phi_B(C)}, and the mass kernel on worldlines. The old role is kept and lifted: the clock of mass becomes the phase of the causal history. The identification is checked numerically -- the history amplitude's phase responds to omega_B with exactly the clock's proper time (d(arg A)/d omega_B = sum_x depth(x), while normalized ratios are nearly clock-free); the dephasing rate between histories is linear in omega_B (Gaussian visibility law, rms 0.002); and branch separation grows with omega_B inside a readable window that closes exactly at omega_B = 2pi, where the integer clock aliases and the overlap revives. The reading it forces: not geometries in superposition, but phased causal histories in superposition, with geometry as the crystallized branch -- C is the combinatorial history, (C, phi_B) the interfering quantum branch, mu selects the readable branches, g_{mu nu} the resulting classical crystal. Mass is the rate at which causal order becomes phase, and numerically the rate at which branches of the blur become distinguishable. The extension breaks nothing: the new objects inherit the relabeling covariance and the quantum-measure structure of the old. The dynamical half is separate and already derived: the crystallized branch obeys the Einstein equation obtained through the readable Dirac operator (coefficient 8 pi G_ind / c_obs^4). The value of m is a declared input throughout; what is new is named as what it is -- an identification, seven gates of measurement, and a reading. Each result has a reproducible Python script (included).