The best replacement for thesis statement is topic sentence.

The best alternatives to thesis statement are rated as following:
★★★★★  topic sentence
★★  purpose statement
★★  hypothesis
★★  introduction
★  main idea
★  topic
★  research question
★  topic statement
★  theme
  thesis
  claim
  specific purpose
  problem statement
  research paper
  question
  preview statement
  thesis statement
  thematic statement
  sentence

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Speaking about thesis statement, one probably shouldn't forget about outline.

Other search terms related to thesis statement and their ratings are:
★★★★★ outline
★★ outline sample
★ introduction
★ topic
★ an outline
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thesis statement
topic sentence
purpose statement