Proof step e-45ba9d9d510f2f6c

basis_map_theorem → concludes about Table a(d,m) of number of points of L1 norm m in cubic lattice Z^d, read by antidiagonals (d >= 1, m >= 0). 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 - sqrt(2), -1 + sqrt(2)]", "output_interval": "(-inf, +inf)", "statement": "every real polynomial with all roots in E = [-1 - sqrt(2), -1 + sqrt(2)] has a real-rooted image" }
• { "claim": "basis_map_preserver", "input_interval": "[-1 - sqrt(2), -1 + sqrt(2)]", "output_interval": "[-3 - 2 sqrt(2), -3 + 2 sqrt(2)]", "statement": "every real polynomial with all roots in E = [-1 - sqrt(2), -1 + sqrt(2)] has an image with all roots in I = [-3 - 2 sqrt(2), -3 + 2 sqrt(2)]" }
• { "claim": "basis_map_preserver", "input_interval": "[-1 - sqrt(2), 0]", "output_interval": "[-3 - 2 sqrt(2), -3 + 2 sqrt(2)]", "statement": "every PF input with all roots in [-1 - sqrt(2), 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 0e7cbd977a505346047db192fb12e6f7224c14ae18ee11e36d8e7456fd969deb, 5,850 bytes (1,517 compressed); download JSON

Cited by

• n-e073e5e0b021f36a (basis_map_preserver)