[Ethereum] ethminer never seems to mine – repeated DAG generation

This sounds like your graphics card is running out of memory, I had something similar when my miner was trying to use my onboard graphics card. You will need a graphics card with more than 4gb minimum to mine.

To recap, your mining pool will respond to the eth_getWork call with the following information:

DATA, 32 Bytes - current block header pow-hash
DATA, 32 Bytes - the seed hash used for the DAG.
DATA, 32 Bytes - the boundary condition ("target"), 2^256 / difficulty.

This information will be used to generate the DAG.

From here on I've referenced the Yellow Paper, rather than the Ethash wiki page. From the Yellow Paper, we can confirm the basis for your query:

J.3. Dataset generation. In order the generate the dataset we need the cache c, which is an array of bytes. It depends on the cache size csize and the seed hash s ∈ B32.

And:

J.2. Size of dataset and cache. The size for Ethash’s cache c ∈ B and dataset d ∈ B depend on the epoch, which in turn depends on the block number.

From section J.2. of the Yellow Paper you'll see that the size of the cache is constant for all mining performed during a given epoch, where an epoch is defined as 30,000 blocks (~100 hours). You therefore don't need to know the block number to calculate the cache size, only the current epoch number. The same holds true for the size of the DAG itself, which is also dependent on the current epoch number.

So... How do we locally find the epoch number?

We're told the seed hash by eth_getWork, but we can't reverse the hash to get the block number from which it was created. So we use trial and error. Starting with a block we know to be in epoch 0 - because we know epoch 0 is from block 0 to block 30,000 - we locally create a seed hash and check whether it matches the seed hash we've been sent.

An example in the code is as follows.

• A call to getWork is made in MinerAux.h, and the 3 variables, including the seed hash, is returned
• EthashAux::full() is called, and the seed hash from getWork is passed in
• The action jumps to EthashAux.cpp, where the main functions are defined
• In EthashAux::full() we call EthashAux::computeFull(), again passing through the seed hash
• Here we calculate the (approximate) block number using blockNumber = EthashAux::number(_seedHash)

The pertinent part of EthashAux::number() is the following line:

for (h256 h; h != _seedHash && epoch < 2048; ++epoch, h = sha3(h), get()->m_epochs[h] = epoch) {}

... which loops through epoch numbers, hashes to create a seed hash, and checks it against the hash sent by getWork.

The function then returns an approximate block number: return epoch * ETHASH_EPOCH_LENGTH;.

We then later use this value to calculate the cache size, which in turn can be used in generating the cache.

Edit - Addendum:

Parity - the client written by Ethcore - does include the block number in its implementation of eth_getWork.