{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp06_four_proposal_generalization60_20260803","cell_id":"representation_independent_interface_contract__mathematics","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_id":"uniform_labeled_graph_sampler_contract_v0","proposal_index":4,"version":0,"title":"Measure-Level Contract for Uniform Finite-Graph Sampling","problem":"An experimental graph-theory project tests conjectures by sampling simple graphs on n labeled vertices. Its current sampler independently draws adjacency-matrix entries, while a proposed replacement chooses an unlabeled isomorphism class and then assigns labels. Both return objects called graphs, but they induce different probability measures because isomorphism classes contain different numbers of labeled graphs. Downstream analyses also inspect adjacency-array order and treat a fixed seed as if it had representation-independent meaning, so replacing the sampler can silently change both the sampled population and the replayed sequence.","actors":["Mathematicians designing the computational experiment","Researchers interpreting sampled graph properties","Implementers of graph samplers and graph representations","Reviewers checking the experiment's population and reproducibility claims","Custodians preserving sampled datasets and replay metadata"],"observable_state":"For a fixed n, two nominal sampler implementations produce different exact frequencies over labeled graphs when their finite randomness spaces are exhaustively enumerated. Analysis code iterates storage rows or internal edge lists rather than using abstract adjacency, and replay documentation records only a seed without the sampler contract and implementation version. The experiment lacks a binding declaration of whether its population is labeled graphs, isomorphism classes, or another weighted collection.","consequence":"A backend replacement can alter the mathematical population underlying reported exploratory frequencies even though function signatures remain unchanged. Exact replay may also fail for incidental reasons when edge ordering, random-bit consumption, or pseudorandom-state layout changes.","affected_objective":"Keep the sampled graph population and interpretation of exploratory results fixed while permitting graph storage and uniform-sampling algorithms to change.","intervention":"Create an opaque UniformLabeledGraphSampler(n) contract. Its abstract sample space is all simple graphs on the fixed labeled vertex set V={0,...,n-1}, and its binding probability law assigns equal mass 1/2^binomial(n,2) to every graph. The public surface exposes initialization from a declared randomness source, next-sample production, abstract adjacency and edge-set observations, vertex relabeling, implementation-scoped replay metadata, and typed failures. The behavioral laws require simple-graph validity, the exact uniform pushforward measure, independence of successive samples when the supplied source satisfies its stated independence premise, and invariance of the distribution under vertex permutations and graph complementation. Concrete adjacency matrices, bit sets, graph ranks, rejection strategies, edge enumeration, pseudorandom state, caches, and bit-consumption traces remain hidden. A seed alone is explicitly not portable across implementations; exact experiments preserve sampled abstract edge sets or a versioned implementation-scoped replay bundle. Each implementation supplies a semantic mapping to labeled graphs and a proof or bounded exact calculation connecting its randomness inputs to the declared measure. A common conformance suite checks laws without demanding identical sample sequences.","structural_mapping":[{"archetype_element":"Abstract component","domain_realization":"A sampler for the uniform probability space of simple graphs on a fixed labeled vertex set."},{"archetype_element":"Observable operation surface","domain_realization":"Sampler initialization, next-sample production, abstract adjacency, abstract edge-set extraction, vertex relabeling, complement, status, and replay metadata."},{"archetype_element":"Abstract state model","domain_realization":"The fixed population declaration, randomness-source assumptions, opaque continuation state, contract version, and implementation-scoped replay identity."},{"archetype_element":"Behavioral laws","domain_realization":"Every output is a simple labeled graph, each graph has the declared equal probability, successive outputs satisfy the stated independence condition, and relabeling or complement preserves the target distribution."},{"archetype_element":"Hidden representation","domain_realization":"Adjacency arrays, packed bits, integer ranks, unlabeled catalogs, edge order, rejection loops, pseudorandom state layout, caches, and entropy-consumption counts."},{"archetype_element":"Representation invariant and abstraction function","domain_realization":"Each concrete graph state must denote exactly one simple labeled graph, and each sampler must map admissible randomness to graphs with the contractually declared pushforward measure."},{"archetype_element":"Error semantics","domain_realization":"Unsupported n, invalid randomness-source configuration, corrupt replay metadata, and entropy exhaustion have distinct typed outcomes; no failed draw may be reported as a sample from the target measure."},{"archetype_element":"Side-effect limits","domain_realization":"Sampling uses only the supplied source and returned opaque continuation; it does not consult hidden global random state, network services, or ambient iteration order."},{"archetype_element":"Conformance oracle","domain_realization":"A shared suite combines exhaustive small-n probability tables, representation-independent graph laws, metamorphic transformations, and deliberately biased sampler mutants."},{"archetype_element":"Substitutability rule","domain_realization":"An implementation may replace another for distribution-level experiments when it realizes the same labeled sample space, exact target measure, independence premise, failure policy, and observation laws; equality of seed-to-sequence mappings is not required."}],"mechanism_mapping":[{"mechanism_slug":"abstract_data_type_specification","role":"Defines the sampler through its labeled-graph probability space and observable operations, then requires concrete graph and randomness states to map to that abstract meaning.","counterfactual_removal":"Without the abstract sample space and semantic mapping, the word uniform could refer incompatibly to labeled graphs, isomorphism classes, encodings, or generator states."},{"mechanism_slug":"design_by_contract_clause","role":"States the randomness-source premises, sample postconditions, independence promise, and failure policy for initialization and drawing.","counterfactual_removal":"Without explicit clauses, path-dependent exhaustion, invalid replay state, or hidden fallback behavior could selectively remove outcomes and bias the returned population."},{"mechanism_slug":"opaque_type_or_module_boundary","role":"Restricts clients to adjacency and other declared graph observations while hiding storage, edge enumeration, and random-state layout.","counterfactual_removal":"Without opacity, analysis scripts could continue using matrix row order, packed-bit positions, or pseudorandom internals as unofficial sampler behavior."},{"mechanism_slug":"black_box_contract_test_suite","role":"Runs graph-validity, observation, error, replay-scope, and bounded distribution checks against every implementation solely through the public surface.","counterfactual_removal":"Without one shared suite, each sampler could be tested against examples chosen under its own implicit population definition."},{"mechanism_slug":"property_based_conformance_test","role":"Generates graph observations, relabelings, complements, repeated draws, invalid configurations, and representation conversions to test the declared laws.","counterfactual_removal":"Without generated cases, storage-dependent failures and interactions among relabeling, complement, and repeated sampling could escape the fixed examples."},{"mechanism_slug":"metamorphic_behavior_test","role":"Checks that vertex permutations and complementation transform samples according to relations that preserve the uniform labeled-graph measure, without expecting identical individual outputs.","counterfactual_removal":"Without distribution-preserving relations, conformance would lean on concrete output sequences and risk freezing the incumbent sampler."},{"mechanism_slug":"reference_implementation_differential_test","role":"Uses direct enumeration of all labeled graphs for small n as an independent probability oracle and compares event counts rather than internal encodings or draw order.","counterfactual_removal":"Without the enumerated reference, two samplers could share the same population-weighting error while agreeing on general symmetry properties."},{"mechanism_slug":"representation_leakage_probe","role":"Audits adjacency iteration, serialization, timing, random-bit consumption, seed mapping, error text, and replay tokens for observable but unpromised dependencies.","counterfactual_removal":"Without the probe, clients could convert a deterministic seed sequence or edge order into a de facto compatibility requirement that blocks valid samplers."},{"mechanism_slug":"semantic_versioning_and_deprecation_gate","role":"Versions changes to the population definition, randomness premises, observation laws, and replay format, distinguishing semantic breaks from internal sampler rewrites.","counterfactual_removal":"Without governed versions, an archived seed or dataset could be interpreted under a changed probability contract while retaining the same sampler name."},{"mechanism_slug":"abstraction_barrier_code_review","role":"Requires reviewers to classify every experimental dependency as a promised graph or measure property, implementation-scoped replay behavior, or prohibited reach-through.","counterfactual_removal":"Without review, convenient access to an edge array or generator state could reintroduce representation coupling around the mechanical boundary."}],"causal_chain":["The current experimental workflow identifies a sampler by its code and output type rather than by a declared probability space.","Different graph-generation representations therefore induce different weights while appearing interchangeable at the signature level.","Downstream scripts also depend on storage order and seed-to-sequence behavior, turning sampler internals into experimental assumptions.","The intervention makes the labeled sample space, exact measure, observation laws, randomness premises, and replay scope the binding interface.","Each implementation maps its concrete randomness and graph storage to that abstract probability model and is checked by the same small-n oracle and behavioral laws.","Opacity and leakage review prevent edge ordering, bit consumption, and implementation-specific seeds from being mistaken for population semantics.","A conforming sampler can then replace another for distribution-level analysis while exact historical replay remains tied to stored graphs or an explicitly versioned replay bundle."],"baseline":"Freeze the adjacency-matrix sampler, pseudorandom generator, edge enumeration, seed, and runtime version for every experiment, treating that entire execution stack as the operational definition of the sampled population.","nearest_rivals":["Define the intended graph population in prose but continue testing samplers independently without a shared behavioral oracle.","Store every sampled graph to guarantee exact replay while leaving future sampler distributions unspecified.","Choose one canonical adjacency-matrix sampler and prohibit backend substitution.","Sample isomorphism classes and apply post-hoc weights intended to reconstruct the labeled-graph measure.","Write pairwise distribution comparisons whenever a new sampler replaces the incumbent."],"remaining_contrastive_claim":"Compared with freezing one sampler, merely storing outputs, or conducting pairwise comparisons, the testable claim is that an exact labeled-graph measure contract plus representation-independent observations is sufficient for a direct edge-bit sampler and an independently implemented graph-rank decoder to support the same predeclared distribution-level analyses, despite different storage, edge enumeration, entropy consumption, and seed-to-sequence mappings.","authority_safety":{"decision_authority":"The mathematicians responsible for the experiment decide whether labeled-uniform sampling is the intended population. Sampler maintainers approve implementations, and reviewers retain authority over how exploratory frequencies may be interpreted; conformance does not turn sampling evidence into proof.","authorized_first_step":"Create an isolated, non-conclusion-bearing pilot for n=4 and n=5 with a frozen population statement, randomness assumptions, event list, two independent sampler implementations, and an exhaustive conformance harness.","excluded_actions":["Changing between labeled-uniform and isomorphism-class-uniform populations without a new contract version","Reporting statistical non-rejection as proof that an implementation is exactly uniform","Claiming that identical seeds must yield identical graphs across implementations","Overwriting or reinterpreting archived sampled datasets","Using sampling results as deductive proof of a conjecture","Silently discarding failed or resource-exhausted draws","Using hidden global randomness or ambient graph-iteration order","Changing the predeclared event list after inspecting implementation disagreements"],"halt_rollback":"Stop if a concrete graph has multiple abstract interpretations, exhaustive small-n counts disagree with the declared measure, failures selectively suppress outcomes, or analysis code requires hidden representation access. Roll back by removing the isolated pilot implementations and harness; retain all existing samplers and datasets unchanged."},"negative_tests":{"strongest_counterevidence":"A short experiment protocol that explicitly states the labeled sample space and probability measure, combined with preservation of every sampled edge set, may already provide adequate meaning and reproducibility. If alternative samplers can prove that measure directly and downstream analyses use only abstract adjacency, a separate sampler component and conformance portfolio may add little.","problem_falsifier":"The existing experiment already declares its probability space formally, saves each abstract sampled graph, uses no storage-order or seed-portability assumptions, and accepts a second independently implemented sampler after an unchanged measure-level verification.","intervention_falsifier":"Two implementations satisfy every stated operation law and pass the exhaustive conformance oracle but induce different exact probabilities for a predeclared graph event under the same randomness-source assumptions. That result would show the contract or acceptance oracle is insufficient.","risks":["Uniform labeled graphs may be the wrong population for the mathematical question even if implemented perfectly.","Small-n exhaustive checks may not expose an arithmetic, rejection, or state-transition defect that appears for larger n.","A pseudorandom source may fail the ideal independence premise even when the sampler's transformation is correct.","Variable resource exhaustion or rejection behavior may condition the returned outputs and introduce bias.","Independence across successive samples may be underspecified when implementations transform or buffer entropy differently.","A canonical edge-set export may accidentally freeze vertex or edge ordering beyond what analysis requires.","Ordinary sampling variation may be misdiagnosed as nonconformance when implementations legitimately produce different sequences.","Implementation-scoped replay tokens may be lost, misversioned, or mistaken for portable seeds.","The enumerated reference and a candidate sampler may share graph-property code and agree on the same observation defect."]},"next_evidence_step":"Freeze the labeled-uniform population, randomness-source assumptions, failure policy, and eight graph events before implementation. Build one sampler that consumes independent edge bits and another that decodes a uniformly selected graph rank using a deliberately different edge ordering and storage type. For n=4 and n=5, exhaust the finite rank space, map every result to an abstract edge set, and compare exact counts for every graph and predeclared event with direct enumeration. Apply all vertex relabelings and complementation as metamorphic checks, verify repeated-draw state handling separately, and run a deliberately biased weighting mutant to test whether the oracle rejects it. Record every mismatch, hidden dependency, replay ambiguity, and exhausted draw; do not modify any existing experiment or dataset.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"Proposal 1 concerned representation-dependent polynomial theorem proofs and used coefficient-function semantics for an algebraic object. Proposal 2 concerned competing constructions of metric completion and used a universal extension property plus unique isometry. Proposal 3 concerned computer-assisted inequality evidence and used a deterministic obligation-state machine with exact certificate verification. This proposal concerns the probability measure underlying an experimental graph-sampling process. Its binding surface is stochastic behavior, population identity, independence premises, abstract graph observations, and replay scope; its causal path runs from hidden representation-induced weighting through an explicit pushforward measure to distribution-level sampler substitution. It neither abstracts polynomial values, transports completion theorems, nor verifies proof certificates, and it can be adopted independently within a graph-sampling experiment.","revision_record":{"parent_version":null,"progress_targets_addressed":["Fourth complete proposal","Materially different experimental-mathematics problem","Distinct measure-level intervention and stochastic causal path","Explicit diversity from proposals 1, 2, and 3","Bounded reversible evidence plan"],"conceptual_changes":["Initial version defines sampler identity by an exact probability space and observation laws rather than by code, encoding, or seed sequence."],"operational_changes":["Initial version restricts the pilot to n=4 and n=5, two independently represented samplers, eight frozen events, and exhaustive finite checks."],"evidence_changes":["Initial version combines exact probability tables, metamorphic relabeling and complement checks, repeated-state tests, leakage review, and a deliberately biased mutant."],"claim_changes":["The claim is limited to measure-preserving substitution in the bounded pilot and makes no assertion of novelty, prevalence, demand, or effect size."]}}