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Verification script for 'Meta-Automatic Sequences'
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Generating 300000 terms of Q, M1, M2...

Section 2: DFAO checks
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  [PASS] Q : DFAO matches sequence on 300000 terms; minimized states = 3
  [PASS] M1: DFAO matches sequence on 300000 terms; minimized states = 4
  [PASS] M2: DFAO matches sequence on 300000 terms; minimized states = 4

Section 3: Morphism checks
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  [PASS] M1: morphism agrees with sequence through 4^8 = 65536 terms
  [PASS] M2: morphism agrees with sequence through 4^8 = 65536 terms

Section 4: Closed digit formula for M2
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  [PASS] M2(n) = t(q(n)) and base-4 digit formula agree with sequence on 300000 terms

Section 5: Initial factor-complexity values
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  [PASS] p_Q (1..15) = [2, 4, 6, 10, 12, 16, 20, 23, 26, 30, 34, 38, 42, 45, 48]
  [PASS] p_M1(1..15) = [2, 4, 6, 9, 12, 17, 22, 28, 34, 40, 46, 52, 58, 64, 70]
  [PASS] p_M2(1..15) = [2, 4, 6, 10, 12, 14, 16, 18, 20, 24, 28, 32, 36, 40, 44]

Section 6: Piecewise formula for p_Q
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  [PASS] Proposition Q-complete: p_Q(n) matches formula for 16 <= n <= 64

Section 7: Piecewise formula for p_M2
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  [PASS] Proposition M2-complete: p_M2(n) matches formula for 1 <= n <= 64

Section 8: Right-special factor counts
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  [PASS] RS_Q (n) values for n <= 63: [2, 3, 4]
  [PASS] RS_M2(n) values for n <= 63: [2, 4]

Section 9: Appendix table (minimal MSB-first DFAO size for the 25
           specializations of the base-4 skeleton)
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F(n)            | G(n)            | DFAO   | Nested
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a(n)            | a(n)            | 2      | 0     
a(n)            | a(2n)           | 3      | 0     
a(n)            | a(2n+1)         | 2      | 0     
a(n)            | a(2n+a(n))      | 4      | 1     
a(n)            | a(2n+1-a(n))    | 4      | 1     
a(2n)           | a(n)            | 4      | 0     
a(2n)           | a(2n)           | ---    | 0     
a(2n)           | a(2n+1)         | 2      | 0     
a(2n)           | a(2n+a(n))      | 3      | 1     
a(2n)           | a(2n+1-a(n))    | 3      | 1     
a(2n+1)         | a(n)            | 5      | 0     
a(2n+1)         | a(2n)           | 3      | 0     
a(2n+1)         | a(2n+1)         | 5      | 0     
a(2n+1)         | a(2n+a(n))      | 5      | 1     
a(2n+1)         | a(2n+1-a(n))    | 5      | 1     
a(2n+a(n))      | a(n)            | 4      | 1     
a(2n+a(n))      | a(2n)           | 4      | 1     
a(2n+a(n))      | a(2n+1)         | 4      | 1     
a(2n+a(n))      | a(2n+a(n))      | 4      | 2     
a(2n+a(n))      | a(2n+1-a(n))    | 4      | 2     
a(2n+1-a(n))    | a(n)            | 5      | 1     
a(2n+1-a(n))    | a(2n)           | 4      | 1     
a(2n+1-a(n))    | a(2n+1)         | 5      | 1     
a(2n+1-a(n))    | a(2n+a(n))      | 5      | 2     
a(2n+1-a(n))    | a(2n+1-a(n))    | 5      | 2     

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End of verification.
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