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Complexitylib.Metacomplexity.MCSP.Magnification.AntiChecker.Counter.HashCell.Circuit.Affine.Defs

Affine hash-cell circuit fragments -- definitions #

This module specializes the generic affine-zero compiler to the packed input layout of anti-checker hash-cell predicates. The labeled samples precede the row-major affine seed, and the powered-survivor witness occupies the final primary-input block.

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def Complexity.GapMCSP.Magnification.AntiCheckerLemma.HashCellAffineCircuit.seedBase (arity prefixLength : ℕ) :
ℕ

First wire of the affine seed inside the public hash-cell prefix.

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    def Complexity.GapMCSP.Magnification.AntiCheckerLemma.HashCellAffineCircuit.coefficientRef (beta : PositiveRationalScale) (arity prefixLength rangeWidth : ℕ) (row : Fin rangeWidth) (coordinate : Fin (counterSurvivorPowerWidth beta arity + 1)) :
    ℕ

    Primary-input wire carrying one row-major affine coefficient.

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      def Complexity.GapMCSP.Magnification.AntiCheckerLemma.HashCellAffineCircuit.witnessBase (beta : PositiveRationalScale) (arity prefixLength rangeWidth : ℕ) :
      ℕ

      First wire of the powered-survivor witness after the public prefix.

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        def Complexity.GapMCSP.Magnification.AntiCheckerLemma.HashCellAffineCircuit.witnessRef (beta : PositiveRationalScale) (arity prefixLength rangeWidth : ℕ) (coordinate : Fin (counterSurvivorPowerWidth beta arity)) :
        ℕ

        Primary-input wire carrying one powered-survivor coordinate.

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          def Complexity.GapMCSP.Magnification.AntiCheckerLemma.HashCellAffineCircuit.compileRaw (beta : PositiveRationalScale) (arity prefixLength rangeWidth : ℕ) :
          CircuitCode.RawCircuit

          Raw affine-zero fragment over the packed hash-cell primary inputs.

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            def Complexity.GapMCSP.Magnification.AntiCheckerLemma.HashCellAffineCircuit.gateCount (beta : PositiveRationalScale) (arity rangeWidth : ℕ) :
            ℕ

            Exact number of gates in the specialized affine-zero fragment.

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              def Complexity.GapMCSP.Magnification.AntiCheckerLemma.HashCellAffineCircuit.outputWire (beta : PositiveRationalScale) (arity prefixLength rangeWidth : ℕ) :
              ℕ

              Absolute wire carrying the specialized affine-zero decision.

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