claimroutine
Environment regenerated from walk words
Effective environment is rebuilt from stored walk words
regenerates environments without conditioning addresses
Claim·§11.4 Certificates for the estimator recipes·inside lemControl records replay with later-salt independence
Statement (paper)
For averaging edges, the effective environment is regenerated from the stored generator and wrap word by applying these fixed transformations in order to the current environment; their descriptors are independent of the indicated endpoint, with membership and wrap consistency tested separately on visits to that vertex, so no discarded conditioning address is needed. For an old-prefix edge the tuple is that of the same row calculation, a gate or column multiplier at final assembly uses this common tuple rather than the internal variant leading to a selected representative, and an action-owner tag lets an endpoint-local calculation replay just to that ancestor tuple.
In plain English
For averaging edges, the effective environment is recovered from the stored generator and wrap word by applying fixed transformations in order to the current environment, with descriptors independent of the chosen endpoint. For old-prefix edges the tuple equals that of the same row calculation, and an action-owner tag lets an endpoint-local calculation replay to that ancestor tuple.
Why it's here
This shows the stored walk data suffices to rebuild each record's effective environment, so no extra conditioning address has to be kept. That regenerability is what the parent lemma needs, and later claims such as the later-salt independence one build on it.
Classified routine:
A bookkeeping step inside the control-record replay lemma: it recovers the environment by replaying the stored generator and wrap word through fixed transformations. This is a direct consequence of how the records are defined, not a new idea.
Uses
Nothing else in the paper
Used by
Sources
PaperOpen
- Section
- §11.4 Certificates for the estimator recipes
- Page
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- Label
—- Line
sections/implementation.tex:1107
Leannot aligned
Phase 2 aligns this node to a Lean declaration.