test: Add invariant tests for SumTree structure in PDPVerifier

[Hany-Almnaem]

Summary

This PR introduces a suite of tests to validate the correctness and stability of the sumTreeCounts structure in the PDPVerifier smart contract.

The tests ensure that each node in the SumTree maintains the invariant:

• sumTreeCounts[setId][index] == sum of rootLeafCounts[setId][j] for the correct range derived from the node’s height.

This directly addresses and resolves issue: #45

Summary of Changes

Core Tests (Basic Coverage)

• testSumTreeInvariantAfterAddsAndRemovals()
  • Adds a controlled set of roots, removes a few, and asserts the sumtree structure.
• assertSumTreeInvariant(uint256 setId)
  • Shared invariant validation used across tests.
• testAdvancedSumTreeInvariant()
  • Simulates multiple add/remove rounds using dynamic values.
• testFuzzedSumTreeInvariant(uint256 seed)
  • Uses seeded randomness to test with pseudo-random leaf counts and root IDs.

Advanced Suite (Tagged [ADVANCED])

Implemented in a separate SumTreeEnhancedTest contract:

• testSumTreeStressTest()
  • Applies add/remove operations over several rounds with increasing load.
• testSumTreeEdgeCases()
  • Verifies correctness under very small, very large, and alternating root sizes.
• testSumTreePerformance()
  • Executes 100 add/remove operations and logs gas usage.
• testSumTreeRandomized(uint256 seed)
  • Interleaves randomized add/remove logic with proving period progression.
• Shared internal assertSumTreeInvariant() with more detailed error messaging for diagnostics.

Benefits

• Validates the structural integrity of the SumTree under normal and edge-case usage.
• Improves test coverage for internal tree logic, including depth-aware summation.
• Reduces regression risk from future updates to root addition/removal logic.
• Keeps invariant assertions reusable and centralized for clarity and reliability.

Notes

• Tests pass locally using forge test
• No contract logic has been modified—only test coverage has been added.
• Code has been linted and follows existing style conventions.
• Advanced tests are separated to keep the default suite performant and focused.

Please let me know if you prefer these broken into separate PRs or test files.