claimroutineinferred_dep

Each side reconstructs its advice input

Each side recovers its advice input from

r

and its own questions

makes strategies depend only on their own questions

Claim·§6.2 Vanishing advice on clean coordinates·inside lemAdvice agreement decays with clean coordinates

Statement (paper)

Conditional on

R=r

, the equation side can reconstruct the full input

U

(both padded advice maps, with the full intercept

c_U

) from

r

and its occurrences

e_i

i\in I

, without using any clean selected position or variable question. Likewise, the variable side can reconstruct the full input

O

(both advice maps, with the original intercept) from

r

and the variable questions for

i\in I

, without using any clean equation.

In plain English

Given the recorded randomness

R=r

, the equation side can recover its full advice input

U

(both padded advice maps with the full intercept

c_U

) from

r

and its occurrences

e_i

for

i\in I

, without using clean selected positions or variable questions. Symmetrically, the variable side can recover its full advice input

O

from

r

and its variable questions for

i\in I

, without using any clean equation.

Why it's here

This lets each local strategy's advice input be treated as a function of

r

and its own question, independent of the other side's clean questions. Together with the independence of clean pairs, it allows the agreement probability conditional on

R=r

to be bounded by the value of the repeated game on the clean coordinates, as used in the next claim.

Classified routine:

Bookkeeping step in the standard Raz/Holenstein-style correlated-sampling analysis of parallel repetition with advice, where the conditioning variable R is chosen so each player's extra input is determined by r and its own non-clean questions.

Uses

claimClean pairs are independent game questions

Used by

claimConditional agreement bounded by repeated game

Sources

PaperOpen

Section: §6.2 Vanishing advice on clean coordinates
Page: —
Label: —
Line: sections/05-clean.tex:167

Leannot aligned

Phase 2 aligns this node to a Lean declaration.

Friction

info
inferred_dep
outline: "Each side reconstructs its advice input" rests on claim-lem-clean-3