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@@ -10,6 +10,8 @@ at a finality round on top of [CometBFT](https://github.com/cometbft/cometbft).
 Similar to any native PoS validator,
 a finality provider can receive voting power delegations from BTC stakers, and
 can earn commission from the staking rewards denominated in Babylon tokens.
+The core logic of a finality provider instance can be found in
+[Finality Provider Core](./docs/fp-core.md).
 
 The finality provider toolset does not have
 any special hardware requirements
diff --git a/docs/fp-core.md b/docs/fp-core.md
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@@ -0,0 +1,92 @@
+# Finality Provider Core
+
+This doc is to provide basic invariants and heuristics one should follow to
+build the finality provider. This part should be agnostic to any consumer
+chains.
+
+## Status Transitions
+
+A finality provider has the following 5 possible states: `Registered`,
+`Inactive`, `Active`, `Jailed`, `Slashed`. The state transition is depicted
+in the following diagram.
+
+![Finality Provider Status Transition](./fp-status-transition.png).
+
+## Invariants
+
+We define invariants that the finality provider should satisfy:
+
+- The finality provider should submit a finality signature for a block if:
+  - the block is not finalized,
+  - the finality provider has positive voting power for this block,
+  - the finality provider has not cast a finality signature for this block, and
+  - the finality provider has cast finality votes for all non-finalized blocks
+    prior to this block for which it has voting power.
+
+- The finality provider should commit public randomness for a block if:
+  - the block is not finalized, and
+  - the finality provider has not committed any randomness for this block
+
+- A finality provider instance should not be running if it’s status is `slashed`
+  or `jailed` on Babylon.
+
+### Internal variables
+
+The finality provider maintains the following internal variables.
+* `last_voted_height`: the last block height on which the fp has cast a vote,
+* `last_processed_height`: the last block height on which the fp either has
+  cast a vote or it does not have voting power, and
+* `next_height`: the next block to poll.
+
+Internal variables need to satisfy the following rules:
+* `last_processed_height >= last_voted_height` should always hold, and
+* `next_height = max{latest_finalized_height, last_processed_height} + 1` should
+  always hold.
+
+## Heuristics
+
+### Sending finality votes
+
+* The poller polls blocks from `start_height` one by one monotonically.
+* `start_height` should be the least height that satisfy
+  `start_height = max{latest_finalized_height, last_processed_height} + 1`.
+* For the next block from the poller, the finality provider retries to send
+  a finality signature until the invariant is not satisfied.
+
+### Committing public randomness
+
+* Finality providers should start to send public randomness commit right
+  after it is registered on Babylon. This is because a public randomness commit
+  only takes into effect after the committed epoch is finalized. So the finality
+  provider should start sending the commit as soon as possible.
+* If the remaining randomness is not sufficient (defined by config) by the
+  current babylon height, the finality provider should make a new commit.
+* The next commit should be made with `start_height` right after the last
+  committed height. This is to ensure no gap between each commit.
+
+The above approach of committing public randomness may cause waste of some
+public randomness in cases where the finality provider does not have voting
+power for some heights, but given that the randomness are constructed in a
+merkle-tree and the commit only contains the root hash of the tree. Therefore,
+the waste is negligible.
+
+### Fast sync
+
+Fast sync is needed for bootstrap and in case the finality provider falls
+behind due to network latency.
+
+* The finality provider enters fast sync if:
+  * the finality provider is bootstrapping, or
+  * the `current_block_height - last_processed_height > gap` (configured value).
+  This condition might not be needed if we can do batching in normal processing
+  loop.
+
+During fast sync:
+1. block the poller,
+2. find a range of blocks starting from `last_processed_height + 1` to
+   `current_block_height`,
+3. check invariant against each of the blocks, batch signature messages, and
+   send it to Babylon,
+4. clear the buffer of the poller and reset the next height of the poller to
+   `last_processed_height + 1`, and
+5. unblock the poller.
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