claimroutine
Numerical places recovered with one scratch
Numerical places regenerated using one -bit scratch tuple
numerical-record case of regenerability
Claim·§11.4 Certificates for the estimator recipes·inside lemControl records replay with later-salt independence
Statement (paper)
Numerical paths, which specify arithmetic operands, gates, digit places and the early-prefix modes of a reciprocal, are regenerable by finite index rules from Theorem : an absolute place is recovered from the root clock and the path or offset, and descriptor selections that used the cursor are stored as bounded choices before movement. At every step the tuple and temporary integers have bits, so a single current tuple kept in scratch and overwritten as each record is processed, with repeated scans reconstructing an ancestor or selected candidate chain, suffices, at the cost of one scratch facility rather than one absolute pointer, input-head position or tuple per frame.
In plain English
Numerical paths (arithmetic operands, gates, digit places, and early-prefix modes of a reciprocal) are regenerable by finite index rules, so a single current tuple of bits in scratch, overwritten as records are processed, suffices without a pointer, input-head position or tuple per frame.
Why it's here
This is the numerical-record case of the regenerability lemma: by the arithmetic interface, an absolute place is recomputed from the root clock and the path or offset, and cursor-based descriptor choices are stored as bounded choices before movement. Ancestors and selected candidate chains are rebuilt by repeated scans, so only one scratch facility is needed instead of per-frame storage.
Classified routine:
A bookkeeping step within the regenerability lemma. It follows directly from the paper's arithmetic interface (thm-arith-interface) together with the standard log-space recomputation technique of rebuilding ancestors by repeated scans instead of storing a stack.
Uses
Used by
Nothing in the paper
Sources
PaperOpen
- Section
- §11.4 Certificates for the estimator recipes
- Page
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- Label
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sections/implementation.tex:1118
Leannot aligned
Phase 2 aligns this node to a Lean declaration.