Proof step e-e8da6a4618f02a9d

preserver_image reversal, shift 0 → concludes about 3n + 1 preceded by n zeros. JSON

Theorem

Affine, reversal and Möbius substitutions (elementary) polytool ?

Lean (RealRooted): route reversed RealRooted.X_pow_mul_reverse_eq_zero_or_splits, RealRooted.reflect_eq_zero_or_splits

Operation

Image under a real-rootedness preserver

{
  "index_shift": 0,
  "operation": "preserver_image",
  "operator": "{\"shape\":\"reversal\",\"schedule\":{\"first_index\":0,\"first_degree\":0,\"step\":1}}"
}

Premises

• a(n) = 1 if n is a triangular number, otherwise 0. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: preserver_image, SHA-256 8ef455a903933ffabe4b1a6cb69ea8046e64c1c4a72f288b946c4fe29062d6f1, 5,734 bytes (1,731 compressed); download JSON

Cited by

• n-ccc86c3dcf2ac685 (real_rooted)
• n-ccc86c3dcf2ac685 (one_signed_coefficients)
• n-ccc86c3dcf2ac685 (hadamard_kernel)