/claim #183

Summary

• End-to-end nullable bigint proof using NaiveEvaluationProof mixing nullable and non-nullable columns with validity filtering.
• Canonical null enforcement preserved while supporting nullable plus non-nullable arithmetic helpers.
• PoC repro, logs, and unicode control scan captured in deliverables for reviewers.
• Changes scoped to nullable column path and validity handling to reduce blast radius.

Acceptance criteria (Issue #183)

• Nullable mechanism: NullableOwnedColumn/NullableColumn with validity masks and canonical null checks in crates/proof-of-sql/src/base/database/validity.rs.
• Nullable arithmetic: helpers for nullable columns and mixed nullable plus non-nullable sums live in crates/proof-of-sql/src/base/database/owned_column.rs and related tests cover both paths.
• Non-trivial proof: PoC below proves a query over nullable bigint data plus a non-nullable column with validity-driven filtering.

Non-trivial proof PoC

• Location: crates/proof-of-sql/src/base/database/nullable_column_proof_test.rs::test_nullable_bigint_proof_with_nulls_and_nonnullable_mix.
• Command: cargo test -p proof-of-sql –no-default-features –features=“arrow cpu-perf test” – test_nullable_bigint_proof_with_nulls_and_nonnullable_mix –nocapture
• Expectation: proof builds and verifies; summed outputs for valid rows are 10, 16, 22.

Notes on canonical null invariant + validity masks

Canonical nulls stay represented by a fixed sentinel value and every nullable column carries a validity mask; arithmetic helpers gate contributions by this mask so nulls never affect aggregates, and mixed nullable plus non-nullable operations honor the mask before combining values.