Proof step e-03d40cd0c568ac28

basis_map_theorem → concludes about A convolution triangle of numbers based on A001906 (even-indexed Fibonacci numbers). JSON

Theorem

Affine-current basis map theorem polytool RealRooted orderTwoConstants_nonneg_iff ?

Operation

Basis map theorem for the node's own rule

{
  "operation": "basis_map_theorem"
}

Premises

None: this step is a direct theorem check.

Claims

• { "claim": "basis_map_preserver", "input_interval": "[-1, 1]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-1, 1] has a real-rooted image" }
• { "claim": "basis_map_preserver", "input_interval": "[-1, 1]", "output_interval": "[-5, -1]", "statement": "every real polynomial with all roots in E = [-1, 1] has an image with all roots in I = [-5, -1]" }
• { "claim": "basis_map_preserver", "input_interval": "[-1, 0]", "output_interval": "[-5, -1]", "statement": "every PF input with all roots in [-1, 0] has a PF image; no larger [-R, 0] works" }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map_theorem, SHA-256 d320275609f49d4003dac21feb3ade35bb58dcc3b8789a3103d981526a9fceae, 5,283 bytes (1,349 compressed); download JSON

Cited by

• n-f287bed89e07609f (basis_map_preserver)