Clarify and reformat

0029-multisignature-keys.md

@@ -38,8 +38,8 @@ applications not listed above.
 This change should not affect any current Hotspot owners or HNT holders as it
 is a purely additive change to existing key types.
 
-We believe that this feature will enable new ownership organization of HST, HNT and
-Hotspots on the network.
+We believe that this feature will enable new ownership organization of HST, HNT
+and Hotspots on the network.
 
 # Detailed Explanation
 [detailed-explanation]: #detailed-explanation
@@ -64,11 +64,11 @@ Roughly, the schemes are:
 1. Multi-signature public key: `| net-type | key-type | m | n | multihash-digest-of-n-public-keys |`;
 2. Multi-signature: `| public-key[0]..public-key[n-1] | isig[1]..isig[m] |`.
 
-More precisely, given a sequence `n` public keys: `public-key[0]..public-key[n-1]`,
-a `multihash-digest-of-n-public-keys` is its multihash digest and `isig[1]..isig[m]`
-is a sequence of triples: `i | len | sig` where `i` is the index into the
-preceding sequence of public keys, `len` is the length of the following
-signature (in bytes) and `sig` is the signature.
+More precisely, given a sequence of `n` public keys:
+`public-key[0]..public-key[n-1]`, a `multihash-digest-of-n-public-keys` is its
+multihash digest and `isig[1]..isig[m]` is a sequence of triples: `i | len |
+sig` where `i` is the index into the preceding sequence of public keys, `len`
+is the length of the following signature (in bytes) and `sig` is the signature.
 
 #### Illustration:
 
@@ -95,10 +95,12 @@ requires knowledge of:
 ### Verification
 
 After parsing the scalar components of the multi-pub-key and multi-signature,
-we consider the signature to be valid if all of the following is true:
+we consider the multi-signature to be valid if _all_ of the following
+conditions are true:
 1. we have at least `M` scalar signatures within the composite multi-signature;
-2. _all_ of the provided signatures _uniquely_ point to a public key within
-   `0..N-1`;
+2. _all_ of the provided scalar signature triples _uniquely_ point to a public
+   key within `0..N-1` range (i.e. any isig containing an-already-seen index -
+   invalidates the multi-signature);
 3. at least `M` of the scalar signatures pass verification.
 
 # Drawbacks
@@ -118,7 +120,6 @@ time, intend to update `vars_v1` but may do so at a later date.
 # Unresolved Questions
 [unresolved]: #unresolved-questions
 
-
 # Deployment Impact
 [deployment-impact]: #deployment-impact