Glossary:

Hypothesis:

A working hypothesis, in short called hypothesis, is asserted merely as a provisional conjecture to guide investigation. A hypothesis can be tested using an interactive protocol between proposer and challenger. The outcome of the protocol defines whether the protocol is supported. 

Propose:

Proposing a hypothesis means to introduce it into the pool of hypotheses.

Oppose:

Opposing a hypothesis means to either strengthen it or trying to discount it.

Strengthen:

Strengthening hypothesis A to hypothesis B means that B must imply A.

Discounting/Supporting:

A hypothesis is discounted if the outcome of the discounting protocol results ina win of the opposer. Otherwise the hypothesis is supported.

Discounting Protocol

A protocol where the proposer and opposer alternate to produce witnesses that 
decide between discounting and supporting.

Reputation:

Each scholar gets an initial reputation. Reputation is gained when 
the offerer successfully supports his hypothesis or when a hypothesis is strengthened without being subsequently successfully discounted.
Reputation is zero-sum.

Provide

A step in the 

Solve