Docket Map
Paper 1: SCPI — Structured Concept Predicate Invention
Full title: Structured Concept Predicate Invention: Descent Under Sheaf Constraints
Claims substantiated: C4 (Compositional Failure)
Formal contribution: When agents independently invent predicates to describe the same domain, the predicates may not align. SCPI formalizes predicate invention as a descent problem under sheaf constraints and classifies the obstructions to alignment using Čech cohomology (H^1). If H^1 vanishes for the relevant covering, the predicates align. If H^1 is nontrivial, the obstruction is computable, classifiable, and in some cases repairable through conservative extension.
Relevant chapter: Chapter 3 (The Witness Protocol), where the sheaf condition is introduced in accessible language and the compositional failure claim is stated.
What the reader gains: A computable diagnostic for concept alignment across agents. The paper provides the mathematical machinery that turns C4 from a structural claim into a testable one.
Paper 2: Bridge — The Coherence Fee in LLM-Database Interaction
Full title: The Bridge Problem: Bilateral Validation and Compositional Failure in LLM-Database Systems
Claims substantiated: C4 (Compositional Failure), C3 (Trust Tax)
Formal contribution: Empirically demonstrates "Edge-Local Blindness" in LLM-database interactions: bilateral validation (checking each component independently) misses compositional failures that manifest only at the interface. Formalizes the coherence fee as the dimension of H^1 for the covering defined by the interacting systems. Shows that compositional failures can be repaired by "bridge concepts" that collapse the obstruction.
Relevant chapters: Chapter 3 (The Witness Protocol), where the coherence fee is given formal content; Chapter 2 (The Trust Tax), where the coherence fee is distinguished from the trust tax.
What the reader gains: Empirical evidence that real systems fail at composition despite passing bilateral checks, and the failure is quantifiable.
Paper 3: Seam — Operationalizing the Coherence Fee for Agent Pipelines
Full title: The Seam Protocol: Fraud Proofs and Semantic Manifests for Agent Pipeline Composition
Claims substantiated: C4 (Compositional Failure), C9 (Predictable Failure)
Formal contribution: Operationalizes the coherence fee for multi-agent pipelines by identifying "invisible dimensions" — encoding, line-ending, implicit schema — in Filesystem-Git composition. Proposes the Seam Protocol: a system of semantic manifests and fraud proofs that makes compositional failures detectable and attributable. When a pipeline fails at a seam, the Seam Protocol can identify which component produced the inconsistency and generate a fraud proof that is independently verifiable.
Relevant chapters: Chapter 3 (The Witness Protocol), where composition is specified as a witness property; Chapter 12 (Three Ways Receipts Fail), where the hardening of receipt regimes against failure is discussed.
What the reader gains: A concrete protocol for detecting and attributing compositional failures in agent systems. The paper demonstrates that the receipt regime's requirements can be implemented at the technical level.
Paper 4: SHEAF — Structured Heterogeneous Consensus Among Agents
Full title: SHEAF: A Protocol for Structured Consensus Among Heterogeneous Agents Using Sheaf-Theoretic Diagnostics
Claims substantiated: C4 (Compositional Failure), C7 (Domination Without a Dominator), C8 (Receipt Minimum)
Formal contribution: Proposes a protocol for structured consensus among heterogeneous agents (agents with different objectives, different logics, different representations) using H^1 as a diagnostic. When agents' local assessments fail to glue into a global consensus, the SHEAF protocol uses Laplacian diffusion to propose resolutions and a topology auction to assign the cost of corrections to the agents whose assessments contribute most to the obstruction. The protocol produces impossibility certificates when consensus is formally unachievable, preventing indefinite negotiation.
Relevant chapters: Chapter 3 (The Witness Protocol), where coordination without consensus is specified; Chapter 10 (The Kind Master Problem), where the emergent behavior of composed systems is analyzed; Chapter 11 (The Receipt Regime), where the constitutional minimum is stated.
What the reader gains: A working protocol for coordination among agents that do not share objectives. The paper demonstrates that the constitutional requirement of coordination without consensus (the sheaf condition applied to agent systems) can be implemented as a protocol with computable diagnostics and auditable outputs.
Summary Table
| Paper | Claims | Formal Apparatus | Key Chapter |
|---|---|---|---|
| SCPI | C4 | Čech cohomology, descent | Ch 3 |
| Bridge | C3, C4 | H^1 dimension, bridge concepts | Ch 2, Ch 3 |
| Seam | C4, C9 | Semantic manifests, fraud proofs | Ch 3, Ch 12 |
| SHEAF | C4, C7, C8 | Laplacian diffusion, topology auction | Ch 3, Ch 10, Ch 11 |