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Fix typos on 17 files.
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@@ -241,16 +241,16 @@ Disallowing a node with two SKIP branches eliminates what would otherwise be a s
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The number of hashing operations required to verify a proof is one less than the number of hashes (SKIP and VERIFY combined),
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and is exactly equal to the number of inner nodes serialized as the beginning of the proof as N.
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The variable-length integer encoding has the property that serialized integers, sorted lexigraphically, will also be sorted numerically.
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Since the first serialized item is the number of inner nodes, sorting proofs lexigraphically has the effect of sorting the proofs by the amount of work required to verify.
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The variable-length integer encoding has the property that serialized integers, sorted lexicographically, will also be sorted numerically.
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Since the first serialized item is the number of inner nodes, sorting proofs lexicographically has the effect of sorting the proofs by the amount of work required to verify.
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The number of hashes required as input for verification of a proof is N+1 minus the number of SKIP hashes,
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and can be quickly calculated without parsing the tree structure.
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The coding and packing rules for the serialized tree structure were also chosen to make lexigraphical comparison useful (or at least not meaningless).
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The coding and packing rules for the serialized tree structure were also chosen to make lexicographical comparison useful (or at least not meaningless).
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If we consider a fully-expanded tree (no SKIP hashes, all VERIFY) to be encoding a list of elements in the order traversed depth-first from left-to-right,
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then we can extract proofs for subsets of the list by SKIP'ing the hashes of missing values and recursively pruning any resulting SKIP,SKIP nodes.
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Lexigraphically comparing the resulting serialized tree structures is the same as lexigraphically comparing lists of indices from the original list verified by the derived proof.
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Lexicographically comparing the resulting serialized tree structures is the same as lexicographically comparing lists of indices from the original list verified by the derived proof.
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Because the number of inner nodes and the number of SKIP hashes is extractible from the tree structure,
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both variable-length integers in the proof are redundant and could have been omitted.
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