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  "assumptions": [
    "Finite binary64 model. Common degree angles and17 listed normalized binary64 radian magnitudes within2π andtheir signed counterparts use symbolic recognition; generic radian values use Math.tan. No epsilon pole window or tiny-result cleanup.",
    "Inverse tangent is the separate published Arctan capability. Typing calculates locally; shareURLs andREST/MCP send parameters andmayenterlogs."
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  "limitations": [
    "Finite binary64 angle;deg(default) orrad. Strict decimal/scientific text<=512characters;unknownkeys/conflictingaliases reject. Null/blank numeric rejects;null/blankunit defaultsdeg. Nonzero source text rounding0 rejectsNUMERIC_UNDERFLOW.",
    "Degree reduction before conversion,stable tan/cotangent offsets;exact odd90degree poles rejectUNDEFINED without epsilon.17 listed normalized binary64 radian magnitudes within2pi andsignedcounterparts use symbolic recognition;only pi/2 and3pi/2 pole tokens andtheir negatives reject. Genericradians useMath.tan.",
    "Nonzero finite input producingzero rejectsRESULT_UNDERFLOW except declaredsymboliczero identities. Nonfinite result rejectsRESULT_OVERFLOW. Finite output is scalar;|value|>5729.57789313059 returns{value,warnings:[NEAR_SINGULARITY]}.",
    "121 independent Decimal420/620 Taylor/Machin referencevectors:2ULPfixedvector budget;zero/sign/types/warnings strict,actualULP reported;16legacyO3values retainedseparately. Noall-domain/cross-runtime guarantee. Nearpoles inputuncertainty strongly amplifies;huge inputspacing losesphase beforecomputation.",
    "Display12significantdigits fallsbacktofullbinary64 if rounding erases nonzero orchanges±1. Fullscalar/warnings/rawinputs preservedin native exports. Graph omitted when|theta|>1e6 or|value|>8,not calculation failure.",
    "Inverse tangent usespublished Arctan capability viaexplicitnavigation. Typinglocal;shareURLs/REST/MCP sendinputs andmayenterlogs."
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    "Exact theta=90+180k degrees =>UNDEFINED. Listed radian ±π/2/±3π/2 tokens =>UNDEFINED. Adjacent finite floats remain finite with warnings if magnitude exceeds5729.57789313059.",
    "Finite results are scalar numbers, or {value,warnings:[{code,severity,detail,suggestion}]} near singularity. Scalar limits are never silently replaced byzero."
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      "title": "NIST Digital Library of Mathematical Functions, Chapter 4",
      "kind": "reference"
    },
    {
      "title": "NIST DLMF §4.14",
      "kind": "reference"
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      "title": "CalculatorX mathematical conventions",
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