TYPE 0x0402 · RECURSION FAMILY

RECURSE_MODIFIED

Covenant with controlled mutations. Output must match input conditions except for specified numeric parameter changes. Each mutation applies an additive delta to a targeted parameter at a specific (rung, block, param) position. No Tapscript equivalent.

Recursion Invertible

Ladder Diagram

Fields

Field	Data Type	Size	Side	Description
max_depth	NUMERIC	1-4 B	Conditions	Maximum recursion depth (> 0). Bounds the chain of modified spends.
block_idx	NUMERIC	1-4 B	Conditions	Target block index within rung 0 (legacy) or per-mutation target (new format).
param_idx	NUMERIC	1-4 B	Conditions	Target parameter index within the block.
delta	NUMERIC	1-4 B	Conditions	Additive delta applied to the target parameter. Can be positive or negative.

Legacy format: max_depth, block_idx, param_idx, delta (4 NUMERICs, single mutation targeting rung 0).
New format: max_depth, num_mutations, then per mutation: rung_idx, block_idx, param_idx, delta (2 + 4N NUMERICs).

Wire Format Breakdown

0x0402 0 4 NUMERIC · max_depth NUMERIC · block_idx NUMERIC · param_idx NUMERIC · delta Conditions (legacy) = 24 bytes

0x0402 0 0 Witness = 4 bytes

Total 28 bytes (legacy, single mutation)

Evaluation Logic

1.Read max_depth from first NUMERIC field

2.If max_depth ≤ 0 → UNSATISFIED

3.Parse mutation specs: detect legacy (4 fields, rung 0 implicit) or new format (2 + 4N fields)

4.For each mutation, record target position (rung_idx, block_idx, param_idx) and delta

5.Deserialize output conditions from spending output

6.Verify: all non-targeted parameters match input exactly

7.Verify: each targeted parameter equals input_value + delta

8.All checks pass → SATISFIED

9.Any mismatch → UNSATISFIED

Worked Example

Decrementing a counter: rung 0, block 1, param 0, delta = -1

Input has param[0][1][0] = 5. Expected output param = 5 + (-1) = 4.

max_depth = 10 > 0 → proceed

Target: rung=0, block=1, param=0, delta=-1

Output param[0][1][0] = 4 == 5 + (-1) → SATISFIED

Output tries delta = -2 instead of -1:

Output param[0][1][0] = 3 ≠ 5 + (-1) = 4 → UNSATISFIED

JSON Wire Format

{
  "type": "RECURSE_MODIFIED",
  "fields": [
    { "type": "NUMERIC", "value": 10 },
    { "type": "NUMERIC", "value": 1 },
    { "type": "NUMERIC", "value": 0 },
    { "type": "NUMERIC", "value": -1 }
  ]
}

Legacy format shown: max_depth=10, target rung 0 (implicit) block 1 param 0, delta=-1 (decrement by 1 each spend).

Use Cases

Decrementing Counters

A covenant parameter decreases by 1 each spend. When it reaches 0, another block (e.g., a conditional check) can trigger a different execution path. Useful for countdown-gated releases.

Progressive Timelock Relaxation

Each spend reduces a CSV timelock parameter by a fixed amount, progressively shortening the required wait between spends. Creates a decaying cooldown curve over the covenant chain.

Evolving Covenant Parameters

Any numeric parameter in the covenant can be systematically evolved. Threshold values, ratios, or counts can increase or decrease with each spend according to a deterministic schedule.

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