⚡ Proof-of-Concept

Can AI Derive Gravity? The 6-Step Proof-of-Concept

Challenge: Derive Einstein's equations from pre-1903 data.
C4 CDI Algorithm: 4 steps to STR, 6 steps to GTR.

1887 Michelson-Morley

→

1902 Mercury Data

→

→

1915 Einstein Field Eq

Algorithmic derivation: 1902 data → Einstein Field Equations in 6 cognitive steps

4 Steps to STR

6 Steps to GTR

≤6 Theorem 11 Bound

1902 Max Data Year

The Algorithm CDI: Creative Destructive Insights

Fingerprint

Identify current position in Z₃³ cognitive space

→

Target

Locate region where solution likely resides

→

Navigate

Use Theorem 9 (shortest path, ≤6 steps)

→

Destroy

Temporarily occupy "incompatible" states to break assumptions

→

Domain Transform

Find isomorphism between domains (geometry ↔ physics)

→

Reconstruct

Arrive at solution state with new understanding

Special Relativity

From Michelson-Morley to Lorentz Transformations

4 steps | Starting data: 1887 experiment

F⟨Past, Concrete, System⟩

Initial State: The Anomaly

Data (1887): Michelson-Morley experiment detects no "ether wind"

Hidden assumptions: Ether exists as absolute reference frame

Experiment Null result

Û_S (Concrete → Abstract)

F⟨Past, Abstract, System⟩

Step 1: Unpack Hidden Assumptions

"No ether wind detected" → "No privileged reference frame for electromagnetism"

Ontological shift: Remove "ether", "ether wind", "absolute frame"

Û_T (Past → Present)

F⟨Present, Abstract, System⟩

Step 2: Universal Law

Generalize to universal principle: "c = constant in all inertial frames"

Contradiction emerges: Maxwell (c=const) vs Newton (v' = v + u)

Û_S (Abstract → Meta)

F⟨Present, Meta, System⟩

Step 3: Question Foundation

If c = const (fact), then space and time are NOT absolute

Revolutionary leap: No absolute time, no absolute space, no absolute simultaneity

Û_T + Û_S^-1

F⟨Future, Meta, System⟩

Step 4: Mathematical Formalization

Transform meta-principle into equations:

Δt' = Δt / √(1 - v²/c²) Time dilation

L' = L √(1 - v²/c²) Length contraction

E = mc² Mass-energy equivalence

✓ Special Theory of Relativity derived in 4 steps

General Relativity

From Mercury's Perihelion to Einstein Field Equations

6 steps | Starting data: 1902 observations

F⟨Past, Concrete, System⟩

The Mercury Anomaly

Data (1902): Mercury's perihelion precession = 43"/century (unexplained by Newton)

Astronomy Anomaly

Û_S

F⟨Past, Abstract, System⟩

Generalization

"Mercury precesses 43"/century" → "Newton's law fails in strong gravitational fields"

Û_T

F⟨Present, Abstract, System⟩

Connection to STR

Gravity requires modifying Special Relativity (STR works for inertial frames only)

Û_S

F⟨Present, Meta, System⟩

Equivalence Principle

Gravity locally indistinguishable from acceleration. Einstein's elevator thought experiment.

4
DOMAIN TRANSFORM
F⟨Present, Meta, System⟩
Type II Isomorphism: Geometry ↔ Physics
                  Mathematics (Riemann, 1850s)
                  Physics (Einstein, 1915)
                

                  Metric gμν
                  Gravitational potential
                

                  Curvature Rρσμν
                  Gravitational field
                

                  Geodesic equation
                  Equation of motion
                

                This is NOT analogy — this is structural identity. Hamming distance: dH = 1
              

Û_T

F⟨Future, Meta, System⟩

Predictions

If gravity = curvature, then:

Mercury precession = 43"/century ✓
Light bending = 1.75" (verified 1919)
Gravitational redshift (verified 1959)

Û_S^-1 (Meta → Abstract)

F⟨Future, Abstract, System⟩

Einstein Field Equations

R_μν - ½Rg_μν = (8πG/c⁴)T_μν

Left side: Geometry (curvature of spacetime)
Right side: Matter (energy-momentum distribution)

✓ General Theory of Relativity derived in 6 steps
Maximum theoretical path (Theorem 11) — C4 space is complete!

Implications for AGI

Validation Test

Einstein Test serves as validation for AGI scientific reasoning capabilities. 6 steps = theoretical maximum in C4 space.

Algorithmic Discovery

C4 enables systematic generation of Einstein-class insights through principled cognitive navigation, not random search.

Domain Transfer

Type II isomorphisms (geometry ↔ physics) can be discovered algorithmically using Isomorphism Scanner.

Beyond Physics

CDI applies to biology, mathematics, art — any domain requiring conceptual leaps across distant cognitive states.