Overlap Compatibility Test¶
Consistency test — instantiates Patchwise Global Certification
Checks that local verdicts agree wherever patches meet, walking the seams in a fixed order, so the boundaries between patches cannot hide a global failure.
The Overlap Compatibility Test checks that wherever two patches share territory, their local verdicts agree — so the seams between patches cannot conceal a contradiction that no single patch is positioned to see. It works pairwise, or across shared boundaries, in a defined traversal order, comparing what each patch asserts on the region they hold in common. It presupposes that each patch already carries a witness, and it does not produce those witnesses; it asks the one question the interior checks structurally cannot: do the parts agree where they touch?
Example¶
A long novel is split among four translators, each taking a run of chapters. Every translator's chapters pass their own editorial checklist — fluent, faithful, idiomatic in isolation. But the novel is one work, and its unity lives in the handoffs: a character's nickname, an invented term, the formality of a recurring form of address must be consistent across the boundaries between translators. The Overlap Compatibility Test walks the chapter seams in reading order and, at each one, compares the two translators' choices for every shared entity. Where chapter 12 (translator A) hands to chapter 13 (translator B), it checks the carried-over terminology, the tense of the framing narrative, and the honorifics. A mismatch — A writes "Mr. Fox," B writes "Reynard" — is a seam failure even though both chapters read beautifully alone. The test's substance is two things: the traversal order over the seams (front to back, plus a glossary-wide sweep) and the equivalence relation that decides what "agree" means for a shared term.
How it works¶
- Locate the seams. Take the overlaps and shared boundaries from the cover's structure.
- Define the equivalence relation. State precisely what it means for two patches' witnesses to "agree" on the shared region — exact match, or a tolerant/semantic match.
- Fix a traversal order. Choose how the seams are visited — local pairwise adjacency, a global shared-boundary sweep — since the order decides which conflict surfaces first and how conflicts cascade.
- Flag disagreements. Emit each seam conflict, to be routed to the register.
Tuning parameters¶
- Equivalence strictness — exact versus tolerant matching; strict catches subtle conflicts but flags harmless variation, loose passes real contradictions.
- Seam granularity — every pairwise overlap versus a sampled subset of seams; more seams, more assurance, more cost.
- Traversal order — adjacency-local versus a global sweep; the order changes which conflict appears first and how repairs propagate.
- Overlap depth — how much shared context is compared at each seam.
When it helps, and when it misleads¶
Its strength is that it catches the failures that live only between patches — the ones where every local unit passes yet the assembled whole fails at an interface. That class of failure is invisible to any interior check, and the seam is exactly where local success is most misleading.
Its failure mode runs in both directions: a compatibility relation that is too weak passes contradictory seams as agreement, while one that is too strict buries real conflicts under cosmetic mismatch. The classic misuse is skipping seams because every patch passed locally — treating interior success as license to ignore the boundary. The guarding discipline is to derive the equivalence relation from the global property itself, and to treat an unchecked seam as uncovered, not as passing. The mathematical statement of exactly this requirement is the sheaf compatibility condition.[n1]
How it implements the components¶
overlap_compatibility_condition— its core: the relation that decides whether adjacent patches agree on shared territory, and the verdict it returns per seam.composition_order_or_traversal_rule— it fixes the order in which seams are compared, the traversal over overlaps that determines how conflicts surface.
Does not implement local_witness_record — producing each patch's own pass/fail evidence is the job of Local Witness Checklist, its nearest twin. The checklist validates one patch's interior; this test validates the boundary two patches share.
Related¶
- Instantiates: Patchwise Global Certification — the test certifies the seams the aggregation rule will later glue across.
- Consumes: Local Witness Checklist supplies the local witnesses that are compared at each seam.
- Sibling mechanisms: Patch Cover Inventory · Local Witness Checklist · Gluing or Recomposition Workflow · Obstruction Register Review · Coverage Completeness Audit · Global Certificate Template · Local-to-Global Dashboard
Editorial Notes¶
Form Classification¶
Form family: Assessment, Review & Assurance
Rationale: The mechanism evaluates local verdicts on shared seams against a declared equivalence relation and emits conflicts requiring correction.
Nearest alternative: Experiment, Test & Rehearsal — It is called a test, but it reviews existing patch outputs without deliberately perturbing or rehearsing the target.
Review outcome: Adjudicated after independent review; high confidence.
Origin Attribution¶
Primary origin: Mathematics
Origin pattern: Cross-disciplinary synthesis
Present-day reach: Specialized
Rationale: Overlap Compatibility Test is most directly rooted in mathematics' axiomatic study of abstract structure, relations, and formal operations. The lineage fits its defining practice: Checks that local verdicts agree wherever patches meet, walking the seams in a fixed order, so the boundaries between patches cannot hide a global failure.
Related originating lineages:
- Computer Science & Software Engineering — Overlap Compatibility Test also draws materially on computer science and software engineering's formal and practical treatment of computation, interfaces, data, and reliable systems, which shaped this mechanism rather than merely adopting it as an application.
Review resolution: Both independent reviews agree on primary origin mathematics; reconciliation resolves encyclopedia_synthesis_disagreement. Formative alternate lineages retained: computer_science. The broader reach of later applications is kept separate as domain_reach=specialized; origin_mode=cross_disciplinary_synthesis records how the formative lineages relate. Confidence is conservatively reconciled to high, and encyclopedia_synthesis=true preserves the reviewers' boundary judgment.
Encyclopedia synthesis: The exact catalogued form synthesizes established practice rather than reproducing a single standard historical label.
Review outcome: Reconciled after independent review; high confidence.
Notes¶
[n1] In sheaf theory, the compatibility (gluing) axiom requires that local sections agreeing on their overlaps determine a unique global section. It is the formal statement of what this test enforces on the ground: there is no legitimate whole unless the parts agree on the seams. ↩