This is a five-step reconstruction of gravitational structure from discrete geometry, starting from event ordering and ending with a source-driven field equation.

The Core Result. Gravitational structure — temporal ordering, observer-dependent kinematics, metric-like separation, curvature, and source-driven dynamics — is reconstructed from the phase-overlap geometry of two conjugate 600-cell copies. No spacetime manifold, metric tensor, or Lorentz symmetry is assumed. Each layer is derived from the discrete constraint geometry.

The Route in Five Steps

  1. 1
    Event Structure (GR-I)
    Two 600-cell copies rotate. Where vertices align, events are born. Their birth-angle ordering is a strict partial order — emergent time from geometry.
    → Read GR-I
  2. 2
    Observer Frames (GR-II)
    Different observers complete the partial order differently. Relativity of simultaneity proved. Time-dilation analogue exhibited. Worldlines as maximal chains.
    → Read GR-II
  3. 3
    Metric Emergence (GR-III)
    Three separation constructions: chain-length (temporal), observer-disagreement (spatial precursor), transition-cost (full metric). Distance from event order.
    → Read GR-III
  4. 4
    Curvature (GR-IV)
    Flatness as local uniformity. Curvature as deviation. Volume-growth, branching, geodesic concentration. Geodesics concentrate through bottlenecks — the free-fall analogue.
    → Read GR-IV
  5. 5
    Dynamics (GR-V)
    Source content defined. Accessibility potential via discrete graph Laplacian field equation. Source tells geometry how to distort. Geometry tells geodesics how to propagate.
    → Read GR-V
What Has Been Established
  • Temporal ordering from geometry (proved)
  • Observer-dependent kinematics (proved)
  • Metric-like separation (three constructions)
  • Curvature from accessibility (three indicators)
  • Source-driven field dynamics (discrete field equation)

This forms a complete gravitational scaffold derived from event-order structure.

Event Structure
→
Observers
→
Metric
→
Curvature
→
Dynamics

What Is Not Claimed

  • Derivation of Einstein’s field equations
  • Lorentz invariance or continuous Lorentz symmetry
  • Equivalence with general relativity
  • Newtonian limit or post-Newtonian corrections
  • Gravitational waves or black hole solutions
Connection to the Programme. The gravity programme builds on the same 600-cell geometry that produces: 13 particle masses at 0.014% error (Papers I–V), Standard Model structural correspondences (Papers VI–XI), quantum dynamics and Schrödinger recovery (Papers XII–XXI), and the programme synthesis (Paper XXII). Gravity is the final sector.

Unification: Paper XXVIII

The gravitational and quantum tracks share a common origin. Paper XXVIII shows that temporal ordering, metric, curvature, and field dynamics (this programme) arise from the same event-order geometry as Schrödinger evolution and interference (the quantum programme). The regime transition is parameterised by the degree of constraint ordering. Read the unification paper →

No spacetime assumed. Five papers. A gravitational scaffold — and a bridge to quantum structure — from event-order geometry.

Related Work
Paper XXII Programme Synthesis The full synthesis: integer selection, coupling constants, generation structure, mass formulas. Overview Quantum Structure The route from closure dynamics to the Schrödinger equation in eight steps. Paper X Gravity Gravitational correspondence from closure geometry.
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