Chunk budget on one AxNum/TabAt axis

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J6Seg.ChB.chunk_budget_at

by Ethan Cheung Wang · Oct 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

budgetj6segkappa-r6

On a single round-six axis carrying an AxNum package and a table-size fact TabAt, the chunk half of the axis budget holds at the uniform constant $K_{\mathrm{ch}}$ .

Fix a plan $ap$ with ChunkPlan6 and ChunkPlanB, and an axis with $d_P(n)=D+1$ . Combining the Proved size package chunk_facts, the natural cost bound chunk_cost_nat, and the real comparison cY_le, one obtains

\texttt{ChunkBudgetAt}\ P\ ap\ n\ src\ D\ k\ \bigl(K_{\mathrm{ch}}(P,ap)\cdot cU_6(P,n,2)/(D+1)\bigr).

The comparison uses $d+\ell\le N_{\mathrm{cost}}$ and the definition $cU_6(P,n,2)=T_P\cdot p\cdot N_{\mathrm{cost}}\cdot(\log\lg n+1)^2$ .

Preamble

import Definitions.Def_IntMul_Kappa_R6_Defs70

set_option autoImplicit false
set_option relaxedAutoImplicit false
set_option maxHeartbeats 1000000

open J6Seg J6Seg.ChB
open IntMul NLogN NLogN.KIL NLogN.KFB IntMul.Kappa.R6 J6Seg J6Seg.KR
variable {P : Prm} {n : ℕ} {src : ℕ → ℕ} {D k : ℕ} (ap : AxPlan6) (h : Side.AxNum P n src D k)
include h

Formal statement

theorem J6Seg.ChB.chunk_budget_at (hT : J6Seg.Ax.TabAt P n src k) (hc : AxCh.ChunkPlan6 ap) (hcb : ChunkPlanB ap)
    (hD : dP6 P n = D + 1) :
    ChunkBudgetAt P ap n src D k (Kch P ap * cU6 P n 2 / (D + 1)) := by sorry

Source

xuanji round-six (Solutions.J6SegAxBud7); consumes Proved J6Seg.ChB.chunk_facts / chunk_cost_nat / cY_le; feeds chunkBudget6_all

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