Bridge Expressiveness GapA possible mismatch between what an intermediary can express and what the connected interfaces can check. A language model may move information between a compliance database and a risk service without making their conventions or obligations explicit. The mismatch is present when the crossing lacks evidence needed to establish what survived, not merely because it uses a model. Explicit mappings, typed adapters, provenance, and institutional review can already supply parts of that evidence. Cheap composition does not establish that certification has become equally cheap; the difference must be shown for the particular pipeline and obligations.Composition BoundaryThe point where a component’s internal state is represented through an output interface for downstream use. Projection makes modular composition possible, but an omitted field or convention may matter to the task that consumes the output. A boundary therefore needs a declared account of what is exposed, what is assumed, and what evidence accompanies the handoff. In Bulla’s narrower schema model, a coboundary operator built from declared internal state and a loaded convention vocabulary is restricted to observable fields; the resulting rank difference measures disclosure or omission under those assumptions. It does not enumerate every unnamed convention or predict whether a live composition will fail.Locally Valid, Globally IncoherentA possible failure mode in which components or bilateral checks satisfy their local contracts while the combined result violates a requirement those checks did not cover. Local validity alone does not guarantee global coherence. Diagnosing a particular failure requires identifying the shared requirement, the information each check could inspect, and the assumptions lost at the handoffs. Better shared records, end-to-end observations, integration tests, or institutional review may expose or prevent the gap. The formal sheaf model and Bulla’s schema-level omission measure describe selected versions of this problem under different assumptions; neither supplies a universal numerical fee or establishes that every such composition must fail at runtime.Obligation TransportThe preservation of relevant commitments when a claim crosses contexts. A bill of exchange could carry a payment instruction and a chain of recourse, but endorsement, presentment, protest, and receiving law determined which obligations survived and against whom. Modern tool pipelines likewise may carry a payload while omitting its conditions, provenance, or the receiving institution's authority to act. A crossing must identify what was preserved, what was lost or never encoded, and which institution can hear a challenge. Fluency alone does not certify that transport; existing mappings, witnesses, and governance can supply parts of it.Semantic BurdenThe conventions, assumptions, and implicit agreements upon which a composition depends, including dimensions no single boundary exposes. A settlement pipeline may require shared day-count, jurisdiction, or rounding conventions that do not appear in every output schema. The term names the gap between what the whole task requires and what adjacent interfaces can check. A21 can record selected costs associated with that gap, but it supplies no universal measure of semantic burden and no guarantee that every hidden dependency will be detected.Similes of SymmetryWitnessed correspondences that can be inspected, transported, and disputed across contexts for a stated purpose. A simile asserts a likeness; a symmetry specifies transformations under which a relation is preserved. The phrase joins them as a discipline of comparison: identify the relevant correspondence, its scope, the evidence supporting it, and the conditions of its use. That evidence may be mathematical, documentary, or institutional, and the warrant of one kind does not become another merely because the same vocabulary describes both.The Bill of ExchangeA commercial instrument through which a payment instruction could travel between parties, places, and currencies. Later forms of endorsement recorded successive transfers and, under governing law, could add parties to conditional recourse after dishonor. The bill's standing depended on its terms, timely procedures, the credit of relevant parties, and recognition by receiving institutions. A signature did not guarantee every earlier signature, and verification alone did not determine the bill's value. Its history shows how transfer could be joined to liability and contest across distance.The Coherence FeeThe irreducible work required to make claims compose across contexts: authenticating, translating, storing, checking, adjudicating, or maintaining the crossing. Its form and measure depend on the domain. The term does not imply a universal physical or monetary unit, and Landauer's bound for logically irreversible erasure does not make institutional coherence a thermodynamic quantity. The coherence fee is distinct from the trust tax, the rent that can accrue when one party controls the practical route across a boundary.The Notary's SealOne of the four touchstones. The medieval notary pressed his seal into wax not to vouch for the truth of what the document claimed but to certify that the claim had been witnessed under specified conditions — the parties present, the date, the jurisdiction, the form of oath. The seal was not truth but attestation: a second-order claim that the first-order claim had passed through a verification procedure. This distinction between vouching for content and certifying process is the foundational insight of witness theory. The notary's seal teaches that witnesses can bind: attestation under specified conditions creates obligations that survive the attestor's departure, the parties' disagreement, and the passage of time.The Trust TaxThe extractable premium charged for controlling a verification chokepoint: rent disguised as coherence. It is parasitic on genuine witness, translation, storage, or adjudication work rather than proof that all intermediary cost is rent. Cheaper or more portable verification can reduce the premium, but it need not eliminate the intermediary, legal backstop, infrastructure, or institutional work at the boundary.Third ModeThe book's proposed discipline for admitting predicates, transporting claims under witnessed and scoped equivalence, composing local views, and accounting for coherence work. It organizes proposals, checks, receipts, and explicit failures into one architecture that could use relational, graph, logical, or hybrid components. Particular formal results support parts of that construction under their stated hypotheses; the name does not establish a complete working implementation or show that other architectures cannot satisfy the same obligations.