P Party Puzzle!

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Across
  1. 3. Canonical conic
  2. 5. One of Patrick’s favorite artistic activities, meant to convey information
  3. 6. Foundational part of Patrick’s childhood
  4. 7. Top food
  5. 9. Royal friend of one of Patrick’s favorite characters
  6. 11. One of Patrick’s favorite teams at OpenAI
  7. 12. Previous city
  8. 13. Mom or Dad, e.g.
Down
  1. 1. Objects generated from the Mersenne twister have this property
  2. 2. All good Bayesians have one
  3. 3. 2^136,279,841 − 1
  4. 4. Patrick’s favorite sushi backwards
  5. 5. Mitochondria meme
  6. 8. Index sixteen?
  7. 9. Tetrahedron?
  8. 10. Patrick’s spirit animal
  9. 11. This answer for this clue, in some sense?