Simplified Taproot DLC structure

Oracle setup:
  1. Oracle publishes: R = k·G  (nonce point for the event)
  2. Oracle publishes: V = v·G  (oracle public key)

For each outcome o_i, the oracle will reveal:
  s_i = k + hash(R || o_i) · v   (scalar announcement)

This reveals a point: s_i·G = R + hash(R || o_i)·V

Adaptor signature: an incomplete signature that becomes valid
when combined with a secret scalar (the oracle's outcome scalar)

Creating an adaptor signature for outcome o_i:
  1. Compute anticipated oracle point: S_i = R + hash(R || o_i)·V
  2. Create adaptor signature: σ' = sign(tx_i, privkey) adapted to S_i
  3. σ' is verifiable but not yet a valid Bitcoin signature

When oracle announces s_i:
  Complete signature: σ = σ' + s_i
  This signature is valid for spending CET (Contract Execution Transaction)

Funding output script:
OP_2 <alice_pubkey> <bob_pubkey> OP_2 OP_CHECKMULTISIG

or in Taproot (preferred):
OP_1 <MuSig2(alice, bob)>  <- aggregated key

Contract Execution Transactions (CETs):
  One CET per possible outcome
  Each CET pays Alice and Bob according to that outcome

Refund transaction:
  Timelocked fallback if oracle never announces
  NSEQUENCE or CHECKLOCKTIMEVERIFY

1. Alice and Bob agree on contract terms and outcomes

2. They create and sign all CETs (one per outcome)

3. They fund the multisig output on-chain

4. Oracle observes the real-world event

5. Oracle publishes s_i for outcome o_i

6. Alice (or Bob) uses s_i to complete their adaptor sig on CET_i

7. CET_i becomes broadcastable; funds distributed per outcome

8. Oracle never sees the funding transaction or CETs

Privacy properties:
  - Oracle cannot link its announcement to any specific contract
  - Blockchain shows only a 2-of-2 multisig spend
  - Contract terms are off-chain

# Simplified Taproot DLC structure
internal_key = musig2_aggregate(alice_key, bob_key)
# Each CET output is also a Taproot key path spend
# The signature on each CET uses adaptor technique with Schnorr
# On-chain: indistinguishable from any ordinary Taproot spend