small value Neutronnova NIFS prove

[wu-s-john]

Small-Value NeutronNova NIFS Integration

Note: This PR builds on the small-value sumcheck work from #112. The main review target is the NeutronNova integration layer on top of that work. Please start with the Files to check section below.

Implement small-value NeutronNova NIFS support and integrate it into the NeutronNova ZK prover.

This PR adds backend-selectable NeutronNova NIFS proving. The regular NeutronNova path remains available, including an optional round-0 small-value optimization, and a new SmallValueNeutronNovaNIFS backend uses the generalized small-value accumulator for the first L0 NIFS rounds before continuing through the existing verifier-circuit transcript flow.

What changed

• Added NeutronNovaNifsStrategy, making NeutronNovaZkSNARK generic over the NIFS backend.
• Integrated two NeutronNova NIFS strategies:
  • NeutronNovaNIFS<Input = bool>:
    • false: full field path
    • true: regular NeutronNova with round-0 small A/B/C optimization
  • SmallValueNeutronNovaNIFS<E, SV, L0>:
    • certified small-value accumulator path for the first L0 rounds
    • supports both i64 and i32 small-value backends
• Replaced ad hoc step matvec caches with shared MLE cache types:
  • FieldStepMLEs
  • SmallAbStepMLEs
  • SmallAbcStepMLEs
  • NeutronNovaStepMLEs
  • SmallValueNeutronNovaStepMLEs
• Added small-value NeutronNova proving logic:
  • certified small A/B/C construction from field MLEs
  • prefix materialization
  • scalar C-claim suffix folding
  • final folded A/B/C output
  • folded witness/instance output after the transcript is fixed
• Generalized the Lagrange accumulator builder so it supports NeutronNova's small-value A/B accumulator, including sparse field corrections for large positions.
• Restored regular NeutronNova performance behavior:
  • full-field mode keeps the materialized C suffix path
  • optimized regular mode uses small A/B/C claims where intended
• Consolidated field-to-small conversion and delayed-reduction helpers.
• Added shared outer-MLE container types in src/polys/outer_mles.rs.
• Updated the SHA-256 NeutronNova bench to compare:
  • regular field
  • regular round-0 small
  • small-value i64, L0 = 3
  • small-value i32, L0 = 3

Files to check

Start with these:

• src/neutronnova_zk.rs

  • NeutronNovaNifsStrategy
  • generic NeutronNovaZkSNARK<E, Nifs>
  • regular NeutronNovaNIFS full-field and round-0-small paths
  • shared NIFS transcript/folding helpers

• src/small_neutronnova.rs

  • SmallValueNeutronNovaNIFS
  • certified small A/B/C cache construction
  • small-value NeutronNova proving flow
  • prefix materialization and suffix continuation

• src/lagrange_accumulator/accumulator_builder.rs

  • NeutronNova small-value accumulator construction
  • large-position field correction handling
  • shared prefix-extension traversal

• src/polys/outer_mles.rs

  • shared field and small step-MLE cache structs

Then check supporting changes:

• src/lagrange_accumulator/extension_bound.rs

  • field-to-small conversion helpers
  • extension-bound certification used by small-value MLEs

• src/lagrange_accumulator/extension.rs

  • generalized prefix gather/extension helpers

• src/lagrange_accumulator/thread_state.rs

  • shared prefix-extension scratch state

• src/small_sumcheck.rs

  • small-value sumcheck integration with the generalized accumulator/certificate naming

• src/big_num/delayed_reduction.rs

  • delayed-reduction support used by small NeutronNova accumulation

Bench / validation:

• benches/sha256_neutronnova.rs
  • four-backend SHA-256 benchmark comparison

Light skim:

• src/lagrange_accumulator/mod.rs
• src/big_num/mod.rs
• src/polys/mod.rs
• src/polys/multilinear.rs
• src/lib.rs