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    "Real z in the ROC",
    "Table of named pairs, not a CAS",
    "The Result Card includes an engine-linked figure of X(z) on the real ROC (pole at |z|=|a|) or a stem of x[n] (at most 16 indices). Same table as REST/MCP.",
    "Not DFT / FFT",
    "Not Laplace",
    "Not residue / two-sided",
    "Not a pole-zero Argand of complex z"
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    "Finite real z strictly outside conservative ROC radius on either real branch, including degenerate zero sine; a,z dimensionless, omega radians per sample",
    "Binary64 approximate evaluation,12 significant digits;2e-11 relative fixture tolerance, no uniform accuracy theorem; conditioned near poles and trig zeros",
    "Coded decimal input underflow and numerical range/phase/quantization refusals; inverse subnormal relative precision may be refused despite representability",
    "Aliases must agree; null, nondecimal scalar forms and unknown fields rejected; inverse URL locks mode",
    "Arbitrary symbolic sequence and contour/residue inversion are outside this named table"
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    {
      "title": "ISO 80000-2:2019 Quantities and units — Mathematics",
      "url": "https://www.iso.org/standard/64973.html",
      "supports": "Mathematical symbols and notation. This standard is not numerical verification or an endorsement of this implementation.",
      "kind": "standard",
      "publisher": "International Organization for Standardization",
      "reference_scope": "all"
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      "title": "Oppenheim & Schafer, Discrete-Time Signal Processing — unilateral Z table",
      "supports": "Z{a^n}=z/(z−a); Z{1}=z/(z−1); ROC |z|>pole",
      "kind": "reference",
      "reference_scope": "model",
      "oracle_class": "O1"
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    {
      "title": "MIT Signals and Systems — Lecture 22: The z-Transform",
      "url": "https://ocw.mit.edu/courses/res-6-007-signals-and-systems-spring-2011/resources/lecture-22-the-z-transform/",
      "supports": "The z-transform, its relation to the discrete-time Fourier transform, inverse transform and region of convergence. A rational expression alone does not identify the time sequence without its ROC. Mathematical reference only; not validation or endorsement of this implementation.",
      "kind": "reference",
      "publisher": "Massachusetts Institute of Technology"
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