Lord of the Circles

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Across
  1. 3. Collapsed countryside's cardinal catamorphism
  2. 5. To call a unique torus
  3. 7. loga​(x)=loga​(x)? Confusing for a ring-bearer.
  4. 10. The Spanish truncate without you, King Elf.
  5. 11. Commute np𝜋² for a hobbit
  6. 12. Where you walk to if you add some dor to Gondor
Down
  1. 1. Breaking limit with HR creates superior mail
  2. 2. Dimension in Greek corner or men's kingdom?
  3. 4. Hi, I transmit disordered capital.
  4. 6. First becomes lost from number that contains no divided kingdom
  5. 7. Ordered sequence of symbols, without any real numbers, spells trouble for Orcs
  6. 8. Tree(3)
  7. 9. Hobbit's radius in permuted meal