timefirstgravity

#!/usr/bin/env sage -python
# -*- coding: utf-8 -*-
# ------------------------------------------------------------
# COMPUTATIONAL Validation of the Spherical Flux Law
# From "Gravity as Temporal Geometry" (GATG)
#
# This script COMPUTES all mathematical objects to rigorously validate:
#     ∂_t Φ = (4πG/c⁴) r T^t_r
#
# Key clarifications in comments:

timefirstgravity

# validate_lorentz_from_phi.sage
# SageMath script to verify the Lorentz-factor derivation from the time-first lapse Φ
#
# Metric (zero shift, spherical, radial motion):
#   ds^2 = -A dt^2 + A^{-1} dr^2  with  A = e^{2Φ(x,t)}
#
# Static clock:  dτ_stat = sqrt(A) dt
# Local ruler:   dl      = dr / sqrt(A)
# Local speed:   v = (dl/dτ_stat) = (dr/dt) / A
# Worldline:     dτ^2 = A dt^2 - A^{-1} dr^2 = A dt^2 (1 - v^2)

timefirstgravity

#!/usr/bin/env sage -python
# -*- coding: utf-8 -*-
# ------------------------------------------------------------
# Schwarzschild from a single ODE in lapse-first variables
# and equivalence to the standard two-function derivation.
#
# Gauge/ansatz (lapse-first, spherical, zero shift, areal r):
#   ds^2 = -A(r) dt^2 + A(r)^{-1} dr^2 + r^2 dΩ^2,
# with   A(r) := e^{2Φ(r)}  (Φ is the temporal potential).
#

timefirstgravity

# Gravity as Temporal Geometry (Part I, lapse-first GR)

## HEADER
```yaml
title: Gravity as Temporal Geometry (Part I, lapse-first GR)
signature: "- + + +"
units_default: "G=c=1 (restore for experiments)"
scope: "Classical equivalence to GR; spherical ODE; flux law; rotation-as-shift; linearized TT; FRW map"
doi: "https://doi.org/10.5281/zenodo.16878018"
dependencies: []