[WIP] Inconsistency fixes for ZIPs 226 and 227

[AntoineRondelet]

ZIP 226 and 227 review: Overall comments

• Better draw the relationship between ZIP 226 and 227: Avoid to force the reader to bounce from 226 to 227 and back. Try to keep the relation between both ZIPs as linear as possible and define key common terms in 227, then refer to 227 from 226 (instead of defining things in both and bouncing from one to another)

  • 227 is the predecessor of 226
  • 226 builds in 227

• Use consistent capitalization when referring to terms defined in the TERMINOLOGY

• Change e.g.: to e.g.

• Make sure orders are all consistent when using tuples: some arguments orders are inconsistent.

• block chain -> blockchain (everywhere)

  • Fixed in 226
  • Fixed in 227

• Be consistent with indices over summations.

  • These are missing in many cases: Always specify them explicitly, that removes potential ambiguity and flag potential errors.
  • Use the \sum_{i=1}^n notation instead of \sum_{\forall i \in S} which is heavier and not consistent with the Zcash specs that use the \sum_{i=1}^{n} notation.

• Shouldn't we use the notations for the group operations defined in 4.1.7.2 of the Specs instead of sums everywhere?

• Some \forall are unnecessary and can safely be removed to simplify notations

• Be consistent in the order in which subscripts an hyperscripts are used. e.g. t_{i}^{n} and t^{n}_{i} are equivalent but inconsistent. It's better to have a systematic approach and e.g. always define the subscript first t_{i}^{n}

TODO: Check if we can use latex macros in rst files, this will standardize notations and save a lot of typos.

ZIP 226

• Page 3:
  • Orchard.Output must probably be NoteCommit^{Orchard}.Output
  • cm^{OrchardZSA} is that the same as cm_{ZSA}? Fixed in Corrections and addition of reference links #16
• Broken itemize in Backward compatibility section
• inconsistent notations for AssetBase. As per ZIP-227 an assetID maps to an AssetBase denoted AssetBase^{protocol}_{assetID}, the upper and subscripts are missing many times. To fix.
  • If the notation is too heavy, we can define AssetBase^{protocol} as an alias of AssetBase^{protocol}_{assetID} and also define AssetBase as an alias of AssetBase^{protocol}_{assetID} when the protocol is clear from context, e.g. in ZIPs 226 and 227, it is clear that the protocol that is built upon is Orchard, so it may be worth and clear enough to say that AssetBase = AssetBase^{Orchard}_{assetID} when the notations become too heavy (e.g. when assetBase needs to be used in a subscript or "exponent"). - DONE in ZIP227
• Page6: in the definition of cv^{net}, the input order to the ValueCommit function isn't consistent compared to bvk in Burn Mechanism section. Use convention: v first, AssetBase second (everywhere)
  • Fixed the tuple order in assetBurn to be consistent with the argument order of ValueCommit
• Page13: in bvk equality, assetBurn is defined a set (not a vector btw), so we sum over the set. Then do I get it properly that j is the index related to the the set assetBurn? What's the cardinality of this set? (n should correspond to the number of action descriptions with value commitment cv^{net}). I don't get the rcv_{i,j} notation don't we miss a term in the sum over assetBurn? Isn't it smthg like \sum_{j=1}^{|assetBurn|} cv_{j} ValueCommit ....? where |S| is the set cardinality.

ZIP 227 - EDIT: All changes related to ZIP 227 have been moved in a separate PR (#20)

• Page 1: No need for self reference in abstract (i.e. [6] refers to the actual current ZIP)
• Page 5: Should purpose be purpose'?
  • See: https://qed-it.github.io/zips/zip-0032.html#orchard-key-path
  • Since the ' indicates that BIP hardened derivation is used: https://github.com/bitcoin/bips/blob/master/bip-0043.mediawiki#purpose
  • Was the ' omitted deliberately here? Edit: I can see the ' was added on the constant 227' a few lines below. It's unclear and error prone IMHO to have m/purpose/coin_type'/account'. We should probably use all ' at the same place instead of spreading them over different lines.
• Page 7/8: The Size and Bytes columns are inconsistent. Stick to Bytes or Size (in bytes) and make sure only numbers are in the column (remove bytes suffix in column entries)
• Consolidate most of the terminology section in ZIP227.

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[vivek-arte]

I have created #79 to address updates to the use of capitalization for terminology like MUST etc. The other action points seem to have been addressed in subsequent updates, so I am closing this PR for now.