feat: add built-in zero wire (Aux(0)) to constraint system

[sai-deng]

Reserve Aux(0) as a built-in zero variable, enforced with a single 0 * 0 = Aux(0) constraint at CS construction time. This makes AllocatedNum::zero() and alloc_zero() free (zero additional constraints or variables), mirroring AllocatedNum::one().

• Add CS::zero() -> Variable to ConstraintSystem trait + all impls
• All CS types (ShapeCS, WitnessCS, TestShapeCS, TestConstraintSystem) initialize with Aux(0)=0 and the enforcement constraint
• WitnessCS::extend() skips aux[0] like it skips input[0]
• AllocatedNum::zero() wraps CS::zero() with no constraints
• alloc_zero() delegates to AllocatedNum::zero()
• Net savings: ~7 constraints per augmented circuit

[Copilot]

Pull request overview

This PR introduces a built-in “zero wire” (Aux(0)) across the bellpepper-style constraint systems in this repo, enforced once at CS construction time via a 0 * 0 = Aux(0) constraint. This makes AllocatedNum::zero() / alloc_zero() effectively free and reduces constraint counts in Nova/Neutron augmented circuits.

Changes:

• Add ConstraintSystem::zero() -> Variable (defaulting to Aux(0)) and thread it through wrapper CS types.
• Initialize all CS implementations with Aux(0)=0 plus a single enforcement constraint 0 * 0 = Aux(0); ensure WitnessCS::extend() skips aux[0].
• Switch AllocatedNum::zero() and alloc_zero() to use the built-in zero wire; update expected digests/constraint-count tests accordingly.

Reviewed changes

Copilot reviewed 10 out of 10 changed files in this pull request and generated 4 comments.

Show a summary per file

File	Description
src/frontend/constraint_system.rs	Adds ConstraintSystem::zero() and forwards it through Namespace / &mut CS impls.
src/frontend/shape_cs.rs	Reserves Aux(0) and injects the single “zero enforcement” constraint into shapes.
src/frontend/util_cs/witness_cs.rs	Pre-initializes aux with 0 and updates extend() to skip aux[0].
src/frontend/util_cs/test_cs.rs	Test CS now starts with Aux(0)=0 and a built-in “ZERO” constraint.
src/frontend/test_shape_cs.rs	Test shape CS now reserves Aux(0) and records the built-in constraint/aux name.
src/frontend/gadgets/num.rs	Adds AllocatedNum::zero() and updates constraint-count assertions in tests.
src/frontend/gadgets/multieq.rs	Forwards zero() through the MultiEq CS wrapper.
src/gadgets/utils.rs	Makes alloc_zero() delegate to AllocatedNum::zero() (no alloc/enforce).
src/nova/circuit/mod.rs	Updates expected constraint counts reflecting net savings.
src/nova/mod.rs	Updates expected public-parameter digest test vectors due to shape/witness layout changes.

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