[TS PBT] Guide relational and metamorphic properties across multiple executions #401

Part of the full #345 delivery. Builds on #395, #351/#352/#353 and the observation/projection contracts in #396/#398.

Delivery stage

This is a stage-two extension of #345. Complete and record the core assessment in #405 before accepting this extension's end-to-end integration and results. Literature, interface design and focused experiments may start earlier; the extension never blocks #355 or #405.

Reuse the completed core contracts. This issue owns any extension-specific changes to observation, binding, scheduling, replay, shrinking and feedback integration, with focused follow-up PRs; do not retroactively broaden #351/#352 or require already completed core issues to reopen. A negative or inconclusive pilot is recorded honestly and informs design; it does not silently cancel this full-roadmap obligation.

Publish a separately identifiable extension configuration and evaluate it against the same original oracle with the extension disabled. Its final held-out evaluation belongs to #357 and is reported separately from the development pilot.

Goal

Exploit human-written relations between executions, including round-trip, idempotence, commutativity and reference equivalence, as first-class search and observation contexts.

Scope

• Reuse original TypeScript predicates that call the tested program multiple times. Add declarative relation/context metadata only where it enables pairing or selection; do not require a second manually rewritten oracle.
• Model shared symbolic base inputs and the stated transformations between executions. Preserve correlation instead of treating the calls as independent random samples.
• Specify when calls share predicate-local state and when independent runs need fresh state. Follow ordinary user-code semantics; never silently clone away intended aliasing/mutation.
• Pair observed intermediate/results across related calls, preserving call identities, original inputs, transformations and assertion identity. Feed scoped relational hypotheses to [TS PBT] Infer property-relevant relational hypotheses from PBT observations #397/[TS PBT] Project observed relations and assertion goals into exact EtsIR bindings #398.
• Compare direct search for the relational assertion with observation-guided search for its relevant intermediate relations. Correctly classify a false law/specification separately from a known implementation defect.
• Include finite-float cases where a mathematical identity is false under JavaScript, NaN-sensitive equality, duplicate-sensitive collections and a relation requiring more than one execution.
• Shrink the shared base input or related input tuple while preserving the transformation/relationship and the same failed assertion.

Definition of Done

• Round-trip and idempotence plus at least one of reference equivalence/commutativity have meaningful real or curated examples with original concrete oracles.
• A multi-execution observation changes a symbolic target and its candidate is confirmed through the complete TypeScript relation.
• Correlation, mutation/isolation, wrong relation scope and unsupported transformations have explicit fixtures.
• [TS PBT] Build a property-rich development and held-out benchmark with validated faults #356/[TS PBT] Evaluate causal contributions of property-aware feedback and bounded extensions #357 include paired held-out evaluation against the same relational properties with observation feedback disabled; no improvement is inferred merely from having a stronger oracle.