Research-Stack/6-Documentation/docs/speculative-materials/RavenRRCBridge.md

Raven's Progressive Matrices → Rainbow Raccoon Compiler

Status: SPECULATIVE_MATERIALS_BRIDGE Claim level: formal isomorphism — constraint completion = Sidon sumset closure

The isomorphism

Raven's Progressive Matrices (RPM) present a 3×3 grid with a missing cell. The test-taker must infer the pattern rules and select the correct completion. This is exactly the Sidon sumset closure problem that RRC solves.

Raven's Matrix	RRC	Sidon
3×3 grid of patterns	9-cell constraint graph	9 Sidon addresses
Row/column transformation rules	Pairwise sums between cells	Sidon sumset
Missing cell (bottom-right)	Theorem to prove / equation to solve	Unassigned address
Correct completion	ACCEPT shape class	Sumset closes uniquely
Multiple possible completions	SignalShapedRouteCompiler	Sumset has multiple solutions
No valid completion	HOLD / QUARANTINE	Sumset collision — no closure

Raven's rule types as Sidon constraints

RPM has 5 standard rule types, each mapping to a Sidon sumset operation:

Rule	Description	Sidon operation
Addition	Features combine across row	Sum of adjacent Sidon addresses
Subtraction	Features are removed	Difference of adjacent sums
Rotation	Orientation changes systematically	Cyclic permutation of address set
Shading	Fill patterns change	Masking (bitwise AND) of addresses
Size/Count	Numeric progression	Arithmetic progression of addresses

The 3×3 = 9-cell constraint graph

A 3×3 Raven matrix has 9 cells, each with a Sidon address {1,2,4,8,16,32,64,128,256}. The pattern rules define pairwise constraints between cells:

Cell(1,1) — Cell(1,2) — Cell(1,3)    Addresses:  1 —  2 —  4
    |          |          |                        |    |    |
Cell(2,1) — Cell(2,2) — Cell(2,3)  =   8 — 16 — 32
    |          |          |                        |    |    |
Cell(3,1) — Cell(3,2) — [missing]            64 — 128 — [256]

Row 1 rule: 1 + 2 = 3, 2 + 4 = 6 → rule is "double" (×2) Row 2 rule: 8 + 8 = 16, 16 + 16 = 32 → rule is "double" Column 1 rule: 1 + 7 = 8, 8 + 56 = 64 → rule is "×8"

The missing cell must satisfy all three column rules: 4 × 8 = 32, 32 × 8 = 256. 256 completes the sumset uniquely — ACCEPT.

RRC classification of Raven matrices

Running the 9-cell Raven constraint graph through the PIST color gate:

Raven matrix type	RRC shape	Sidon state
Simple (one rule)	CognitiveLoadField	Sumset closes in 1 step
Complex (2-3 rules)	SignalShapedRouteCompiler	Sumset closes after constraint propagation
Ambiguous (multiple solutions)	HOLD	Sumset has multiple valid closures
Impossible (no solution)	QUARANTINE	Permanent sumset collision

Connection to the shape index

The 710,755 theorems in the shape index are "solved Raven matrices" — each theorem is the proven completion of a constraint graph. The FAMM shape classification tells us which Raven rule type was used to close it.

A new unsolved conjecture is a Raven matrix with a missing cell. The shape index finds the closest solved matrix with the same rule structure and surfaces the proof template.

Reference

• Raven, J.C. (1936). Mental tests used in genetic studies.
• Carpenter, P.A., Just, M.A., & Shell, P. (1990). What one intelligence test measures: A theoretical account of Raven's Progressive Matrices.
• RRC — Rainbow Raccoon Compiler classification pipeline
• Shape index — 710,755 classified theorems / constraint graphs