recursion-v2: add PCS aggregation checks

[hero78119]

Problem

Recursion v2 aggregation needs to verify the child proof PCS opening path, not only the VM public values, main claims, and tower checks inherited from the base branch.

Design Rationale

This PR maps the native PCS verifier flow into explicit recursion-v2 preflight records, AIRs, and lookup/permutation buses. The design keeps transcript order and proof-shape data owned by preflight replay, then constrains each PCS phase with row-local checks plus cross-module bus bindings. This keeps the verifier logic auditable while avoiding a broad backend fork.

Change Highlights

• ceno_recursion_v2: add PCS preflight records, buses, AIR modules, and circuit wiring for base input openings, Merkle paths, basefold queries, sumcheck claims, jagged helpers, and final claims.
• ceno_recursion_v2: bind PCS transcript values and commitment heights into the existing aggregation flow.
• ceno_zkvm: update test-only field constructors for the upgraded Plonky3/field trait surface.

Benchmark / Performance Impact

Not a performance optimization PR. The new PCS AIRs add prover work; release shard runs remain the relevant sanity check.

Operation

Operation	master (s)	this PR (s)	Improve (master -> this PR)
N/A	N/A	N/A	N/A

Layer

Layer	master (s)	this PR (s)	Improve (master -> this PR)
N/A	N/A	N/A	N/A

Benchmark command(s):

# No benchmark comparison in this PR body.

Environment (CPU/GPU, core count, rust toolchain, commit hash):

raw data:

• master: N/A
• this PR: N/A

Testing

cargo fmt --all --check
RUSTFLAGS="-Dwarnings" cargo check --workspace --all-targets
RUSTFLAGS="-Dwarnings" cargo check --workspace --all-targets --release
RUSTFLAGS="-Dwarnings" cargo make clippy
RUSTFLAGS="-Dwarnings" cargo clippy --workspace --all-targets --release
RUSTFLAGS="" cargo make tests
RUSTFLAGS="" cargo make tests_goldilock
taplo fmt --check --diff
git diff --exit-code Cargo.lock

Risks and Rollout

The main risk is verifier soundness from mismatched transcript or PCS phase ordering. Rollout should keep the current shard aggregation tests as the gate and treat new PCS AIR changes as verifier-path changes requiring focused proof fixtures.

Follow-ups (optional)

• TODO: reduce PCS trace size and prove-time cost after correctness lands.
• TODO: add narrower PCS phase regression tests so failures localize before full aggregation prove.

Copilot Reviewer Directive (keep this section)

When Copilot reviews this PR, apply .github/copilot-instructions.md strictly.

[hero78119]

Recursion-v2 aggregation timing update from the local Keccak fixture.

Environment:

• Fixture regenerated as a real 2-shard keccak_syscall proof with --max-cycle-per-shard=1600; the earlier 2-shard failure was caused by cycling a 1-shard fixture, which duplicated a final shard and violated VmPvsAir continuation adjacency.

Verification:

• agg_prover_single_shard: passed, elapsed=100.12s
• agg_prover_two_shards: passed, elapsed=155.29s
• CENO_REC_V2_DEBUG_CONSTRAINTS=1 agg_prover_two_shards: passed

Single-shard timing split:

• generate_proving_ctx: 2.17s
• prove: 97.59s
• verify: 0.36s
• total trace cells: 30,778,586

Bottleneck by trace cells:

AIR	cells	share
MainFrontloadTermAir	12,320,768	~40%
Poseidon2Air	9,863,168	~32%
PcsJaggedAssistQAir	3,276,800	~11%
PcsCommitPhaseMerkleAir	1,638,400	~5%
PcsEqProductAir	950,272	~3%
ForkedTranscriptAir	770,048	~2.5%
PcsSuffixProductAir	688,128	~2%

Conclusion: the ~100s single-shard runtime is dominated by the prove phase, not generate_proving_ctx. The largest trace surfaces are MainFrontloadTermAir, Poseidon2Air, and jagged PCS tables. The ECC/selector AIRs are not the main cell-count bottleneck in this run (MainEccRtEquationAir: 13,632 cells; MainSelectorFormulaAir: 80,896 cells).