R.I.P. L5R

Hammer is too much influence for 3x but you could put one in instead of a favor. Every card in the deck is irrelevant except ancestry, logistics, ingenuity and calling. The rest were literally only chosen to be zero cost and always playable so you can cycle your deck. What they actually are doesn't matter so much. If you pull it off you won't even resolve a single conflict to actually trigger hammer. You just sit there and cycle through your own deck endlessly without honour loss moving cards from an opponent's province until they have to refill, but have none left in deck or discard. Then they lose.

Hammer is only 2 influence. The same as Oracle. If you replace it with 13 influence (keeper) having currently only spent 9, I think you would be fine. Technically you just need two logistics anyway. Play one at one card left. Then play the next. It reshuffles as soon as there is need.

That's our understanding how it works. When their whole dynasty is out and a province empties, then they try to refill, lose 5, have nothing to shuffle and then just keep losing 5. However even if it was ruled that only happens once, earth role lets you take Sabotage so a 1x of that will let you keep feeding them one card to reshuffle so they do lose the 5 and then you just keep going and they will lose without relying on the empty deck = unlimited honour loss.

At the moment the game doesn't allow for you to have nothing in a province. But possibly the rules do need updating to allow that 5 honour loss to happen once and then you just keep going without refilling, until it's possible for you to do so. It might even be necessary: if the opponent also plays divine ancestry then the game just breaks as they keep trying to reshuffle infinitely without losing honor.

But I do think 1x sabotage makes the loop work even if the rules were changed.

It's a bonkers Phoenix card previewed in a marketing fan image for coils of power:
https://store.us.asmodee.com/catalogue/l5r-lcg-coils-of-power_3295/

0F, discard your hand. Until the end of the phase you can see and play the top card of your deck.

So you trigger Divine Ancestry to make sure you don't lose honor when you reshuffle. Play Calling The Storm, and then your whole deck is 0 cost except the two characters and you can play it all. You get the whole lot out on the table and then so long as you have logistics as your last card, or in hand, or some way of drawing a card, eventually you need to draw a card from the effect, which reshuffles your deck. At that point your only cards left in deck are copies of Logistics. You can then play one, to draw another. Keep doing that: you play one in your hand, which shuffles the one in your discard into the deck, which you draw to hand. Do it forever until your opponent has no dynasty left.

I think TI is useful for making sure the sequencing at the end of your deck works properly. But Courtyard can also guarantee a Logistics at the bottom.

If they changed the rules so you can only lose 5 honor once a round for running out of cards in a deck, that would stop something like this working.

Please don't actually play or try to play something like this though. It's just a thought experiment cause that Calling card is silly.