claimroutineinferred_dep

Recurrence total cost and conversion to H

Total time is O(Vdλ′)O(Vd^{\lambda'}), and the exact CC-layer converts to H\mathcal H
closes the time bound and identifies the layer
Claim·§5.4 An explicit guard-width bound·inside propSimultaneous Hadamard layer in near-linear time

Statement (paper)

The row construction and the recurrence analysis give total time O(Vdλ′)O(Vd^{\lambda'}) on fixed tapes, including all padded and auxiliary streams, and Equation  converts the resulting exact CC-layer to H\mathcal H.

In plain English

The row construction together with the recurrence analysis gives total running time O(Vdλ′)O(Vd^{\lambda'}) on a fixed number of tapes, counting all padded and auxiliary streams. The identity in Equation (phase-butterfly-layer) then converts the resulting exact CC-layer into the layer H\mathcal H.

Why it's here

This step closes the time bound of the proposition by summing the packed basis-change costs, which the uniform near-linear bound makes available with one common constant. It then uses the telescoping of complex-network edge frames to C⊗mC^{\otimes m} to turn the computed CC-layer into H\mathcal H, so the next claim can analyze exact guarded evaluation of Hz\mathcal H z.
Classified routine:
Bookkeeping step: sums the uniformly near-linear packed basis-change costs from the preceding claim over the recurrence, then applies the paper's phase-butterfly identity (telescoping edge frames via prop-complex-motif-interface) to convert the C-layer to H.

Uses

claimPacked basis changes cost uniformly near-linearpropComplex network edges factor into translation kernels

Used by

claimGuarded evaluation with single final truncation

Sources

PaperOpen
Section
§5.4 An explicit guard-width bound
Page
—
Label
—
Line
sections/05-layers.tex:974
Leannot aligned

Phase 2 aligns this node to a Lean declaration.

Friction

  • info
    inferred_dep
    outline: "Recurrence gives O(Vd^λ') and converts C layer to H_0" rests on claim-prop-simultaneous-layer-2
  • info
    inferred_dep
    outline: "Recurrence gives O(Vd^λ') and converts C layer to H_0" rests on prop:complex-motif-interface