Proof step e-b76eec14ee8e8c71

basis_map_theorem → concludes about Square array A(n,r), the number of neighbors at a sharp Manhattan distance r in a finite n-hypercube lattice, read by upwards antidiagonals; A(n,r) = Sum_{k=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), 0]", "output_interval": "(-inf, 0]", "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 f2a1b6202373508ce5dca77951a88b85d65d09be9b769b87ce6e668be56ddfd8, 4,406 bytes (1,441 compressed); download JSON

Cited by

• n-a1540a6d32c29f8f (basis_map_preserver)