Properties-certificate-retrieval
Some properties of the certificate retrieval operations,
when applied to unequivocal sets of certificates.
Some of these come in two forms:
one involving retrieval from two sets of certificates in subset relation
where the superset (and consequently the subset) is unequivocal;
and one involving retrieval from two sets of certificates
that are mutually unequivocal.
The significance of the first kind is that,
as the DAG of a validator grows,
the retrieval of existing certificates is unaffected,
i.e. always yields the same results as the DAG grows.
The significance of the second kind is that,
across DAGs of different validators,
the retrieval of common certificates yields the same results.
In other words, there is a ``stability'', or ``consistency'',
in certificate retrieval,
both within a validator and across validators.
These properties are the basis for proving
some higher-level properties of paths and histories in DAGS,
namely that those are also stable and consistent
within a validator as its DAG grows
as well as across different validators.
Subtopics
- Certificates-with-authors+round-of-unequivocal-superset
- If certificates with certain authors and a certain round
are retrieved from a subset of an unequivocal set of certificates,
the same certificates are retrieved from the superset.
- Certificates-with-authors+round-of-unequivocal-sets
- If certificates with certain authors and a certain round
are retrieved from both of two mutually unequivocal certificate sets,
the same certificates are retrieved from both sets.
- Certificate-with-author+round-of-unequivocal-sets
- If a certificate with a certain author and round
is retrieved from both of two mutually unequivocal certificate sets,
it is the same certificate from both sets.
- Certificate-with-author+round-of-unequivocal-superset
- If a certificate with a certain author and round
is retrieved from a subset of an unequivocal set of certificates,
the same certificate is retrieved from the superset.
- Certificate-with-author+round-of-element-when-unequivocal
- If a certificate is in an unequivocal set,
retrieving a certificate with the certificate's author and round
will return the certificate itself.
- Certificate-set-unequivocalp-of-certificates-with-round
- The certificates with a given round of an unequivocal DAG
is also an unequivocal set of certificates.
- Certificate-set-unequivocalp-of-certificates-with-authors
- The certificates with given authors of an unequivocal DAG
is also an unequivocal set of certificates.
- Cardinality-of-certificates-with-authors+round-when-subset
- The number of certificates in a round with given authors,
in an unequivocal DAG,
is equal to the number of authors,
if there is a certificate for each author in that round.
