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80 lines
3.6 KiB
Markdown
80 lines
3.6 KiB
Markdown
# Raven's Progressive Matrices → Rainbow Raccoon Compiler
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**Status:** SPECULATIVE_MATERIALS_BRIDGE
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**Claim level:** formal isomorphism — constraint completion = Sidon sumset closure
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## The isomorphism
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Raven's Progressive Matrices (RPM) present a 3×3 grid with a missing cell.
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The test-taker must infer the pattern rules and select the correct completion.
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This is exactly the Sidon sumset closure problem that RRC solves.
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| Raven's Matrix | RRC | Sidon |
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|----------------|-----|-------|
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| 3×3 grid of patterns | 9-cell constraint graph | 9 Sidon addresses |
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| Row/column transformation rules | Pairwise sums between cells | Sidon sumset |
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| Missing cell (bottom-right) | Theorem to prove / equation to solve | Unassigned address |
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| Correct completion | ACCEPT shape class | Sumset closes uniquely |
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| Multiple possible completions | SignalShapedRouteCompiler | Sumset has multiple solutions |
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| No valid completion | HOLD / QUARANTINE | Sumset collision — no closure |
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## Raven's rule types as Sidon constraints
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RPM has 5 standard rule types, each mapping to a Sidon sumset operation:
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| Rule | Description | Sidon operation |
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|------|-------------|-----------------|
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| **Addition** | Features combine across row | Sum of adjacent Sidon addresses |
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| **Subtraction** | Features are removed | Difference of adjacent sums |
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| **Rotation** | Orientation changes systematically | Cyclic permutation of address set |
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| **Shading** | Fill patterns change | Masking (bitwise AND) of addresses |
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| **Size/Count** | Numeric progression | Arithmetic progression of addresses |
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## The 3×3 = 9-cell constraint graph
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A 3×3 Raven matrix has 9 cells, each with a Sidon address {1,2,4,8,16,32,64,128,256}.
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The pattern rules define pairwise constraints between cells:
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```
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Cell(1,1) — Cell(1,2) — Cell(1,3) Addresses: 1 — 2 — 4
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| | | | | |
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Cell(2,1) — Cell(2,2) — Cell(2,3) = 8 — 16 — 32
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Cell(3,1) — Cell(3,2) — [missing] 64 — 128 — [256]
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```
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Row 1 rule: 1 + 2 = 3, 2 + 4 = 6 → rule is "double" (×2)
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Row 2 rule: 8 + 8 = 16, 16 + 16 = 32 → rule is "double"
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Column 1 rule: 1 + 7 = 8, 8 + 56 = 64 → rule is "×8"
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The missing cell must satisfy all three column rules: 4 × 8 = 32, 32 × 8 = 256.
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256 completes the sumset uniquely — ACCEPT.
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## RRC classification of Raven matrices
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Running the 9-cell Raven constraint graph through the PIST color gate:
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| Raven matrix type | RRC shape | Sidon state |
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|-------------------|-----------|-------------|
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| Simple (one rule) | CognitiveLoadField | Sumset closes in 1 step |
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| Complex (2-3 rules) | SignalShapedRouteCompiler | Sumset closes after constraint propagation |
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| Ambiguous (multiple solutions) | HOLD | Sumset has multiple valid closures |
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| Impossible (no solution) | QUARANTINE | Permanent sumset collision |
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## Connection to the shape index
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The 710,755 theorems in the shape index are "solved Raven matrices" —
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each theorem is the proven completion of a constraint graph. The FAMM
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shape classification tells us which Raven rule type was used to close it.
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A new unsolved conjecture is a Raven matrix with a missing cell.
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The shape index finds the closest solved matrix with the same rule
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structure and surfaces the proof template.
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## Reference
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- Raven, J.C. (1936). Mental tests used in genetic studies.
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- Carpenter, P.A., Just, M.A., & Shell, P. (1990). What one intelligence
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test measures: A theoretical account of Raven's Progressive Matrices.
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- RRC — Rainbow Raccoon Compiler classification pipeline
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- Shape index — 710,755 classified theorems / constraint graphs
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