This is the standard's definition of "heat". That is, in this standard, a Heat (of steel) is defined as [all] material originating from a final melt, or for remelted alloys, the raw material originating from a single re-melted ingot.
If you are using continuous cast material, it would not be considered a remelted alloy, so all continuous cast blooms that resulted from the final molten refining operation are considered a single heat. In the special case of remelted alloys (VAR, VIM, or VIM-VAR) only that material that came from the final remelt ingot are to be considered a heat. I doubt there are many any remelt alloys that are processed by the continuous casting route in the final melt.
This particular section, 3.1.3, does not restrict the steel making methods; this section only defines what is meant by the term "Heat" in the standard. The acceptable steelmaking methods are defined elsewhere in the standard, depending on whether you are producing BSL-1, BSL-2, or BSL-3. For BSL-1, they would be covered by the applicable ASTM standard and for BSL-2 and BSL-3, by the manufacturer's material specification, as described by section 5.2.
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