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Merkle tree for custom predicate batches (#471)

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Resolve https://github.com/0xPARC/pod2/issues/466

Now batches are identified by the root of a merkle tree that contains all the predicates (using sequential indices as keys).  This means that the format to identify a custom predicate reference is still a hash + index, but the calculation of the hash is different.
The MainPod circuit now isn't limited by number of batches but instead number of custom predicates; and for each one we verify a merkle proof to verify the batch id.

I've removed a bunch of tests from lang that were testing splitting into multiple batches because there's no longer any need for that.  In a future PR we'll remove the code that handles batch splitting.

Each custom predicate needs 148.2 gates (which is very close to my estimate of 142.7 in https://github.com/0xPARC/pod2/issues/466#issuecomment-3823531286 where I actually made a mistake and considered 5 predicates per batch instead of 4 in the previous Params).
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Eduard S. 2026-02-04 11:12:32 +01:00 • committed by GitHub
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book/src/custom.md
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@ -22,7 +22,7 @@ See [examples](./customexample.md)
## Hashing and predicate IDs
Each custom predicate is defined as part of a _group_ of predicates. The definitions of all statements in the group are laid out consecutively (see [examples](./customexample.md)) and hashed. For more details, see the pages on [hashing custom statements](./customhash.md) and [custom predicates](./custompred.md).
Each custom predicate is defined as part of a _group_ of predicates. The definitions of all statements in the group are merklelized (using sequential indices as keys) (see [examples](./customexample.md)) and the root of the merkle tree is used as the identifier. For more details, see the pages on [hashing custom statements](./customhash.md) and [custom predicates](./custompred.md).
## How to prove an application of an operation

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book/src/customexample.md
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@ -37,7 +37,7 @@ SELF.1(?1, ?2, ?3, ?4, ?5, ?6) = OR(
```
and similarly for the other two definitions.
The above definition is serialized in-circuit and hashed with a zk-friendly hash to generate the "group hash", a unique cryptographic identifier for the group.
The above definition is serialized in-circuit and merkelized with a zk-friendly hash to generate the "group hash", a unique cryptographic identifier for the group.
Then the individual statements in the group are identified as:
```