[ip] Generalize IPVerifierChannel to have an Elem type #1402
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The F parameter was only used for Mul<F> and MulAssign<F> bounds, which were redundant for Field types (where F = Self). Move scalar multiplication bounds directly to PackedField where they are actually needed.
Generalize IPVerifierChannel to have an associated type Elem: FieldOps<F>. All recv_* and sample_* methods now return Self::Elem instead of F. This allows for future symbolic field element types in verification. Add assert_zero method that returns Error::InvalidAssert if the value is not zero. For all concrete implementations, Elem = F is used.
Change IPVerifierChannel::Elem bound from Copy to Clone. Generalize sumcheck and mlecheck verify functions to accept any channel type without requiring Elem = F, enabling future support for symbolic field elements. Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
Extend the channel generalization pattern from sumcheck/mlecheck. Use C::Elem instead of requiring Elem = F, and replace equality checks with channel.assert_zero() for FieldOps compatibility. - Add extrapolate_line function with FieldOps bound to binius-math - Remove Field bounds from claim structs Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
Remove Elem = F requirement from IOPVerifierChannel trait. Update finish method to take (Oracle, Self::Elem) tuples and return symbolic claims. Generalize spartan-verifier and verifier protocols accordingly. Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
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This is intended to be used in subsequent changes as a symbolic field element. This will help in verifier logic analysis and recursion circuit building.