Research
The mathematics behind Bulla, plus the papers it operationalizes.
Bulla is the runtime. The pages below are the calibration data and architecture briefs that make the runtime trustworthy. The papers further down are the underlying program.
Glyph research pages
Calibration Study
Boundary fee = 0 has zero annotated convention mismatches across 678 pairwise compositions of 38 real MCP servers. Spearman ρ = 0.996 against annotation-derived mismatch labels (schema-derived, not execution-derived).
Verification Stack
How a schema-level rank invariant (the coherence fee) composes upward into receipts, audit, and settlement. The whole stack in one read.
BABEL Benchmark
Frozen benchmark of 932 instances across seven workflow families; ground truth computed by a deterministic symbolic executor, no human annotation. The public reference to beat.
Methodology
How a claim gets on this site: CI claims gates, a single sourced facts file, and the public ledger of what is validated, what was tested and falsified, and what is open.
Wire Spec + Golden Vectors
ActionReceipt v0.1, verifiable from the spec alone: one canonicalization rule, four hashes, the modality law, and an in-browser verifier running the reference checks against published golden vectors.
Papers
Each paper sits on the Res Agentica research site. Click through for the full PDF or web version. Bulla implements the measurement and receipt layers in Python; the math is machine-checked in Lean 4.
Local Validity Does Not Compose ↗
Impossibility theorem for bounded AI audit. Locally valid checks compose into globally invalid pipelines; one separation theorem, one abstract result, six lemmas.
Witness Geometry Beyond Scalar Fee ↗
Per-field leverage, concentration index, coloops, matroid-greedy disclosure basis. The fee is one projection of a richer object; the paper exhibits the others.
The Stitching Defect ↗
How seams between locally consistent components produce globally inconsistent outputs in the bypass-analysis regime, with the LaTeX-grade proof.
A Witness Logic for Semantic Composition ↗
The full doctrine paper. Sets up the sheaf, the coboundary, and the composition rule that the rest of the program operationalizes.
Seam ↗
The originating paper. Defines the seam between two tools and the algebraic invariant that detects it.
The Coherence Fee ↗
The fee in plain English. Why a single number lands the architectural argument that long-form proofs cannot.
The full program
The papers above are the spine of a larger research program at resagentica.com/research, which collects 20+ papers on the witness-logic, sheaf-theoretic, and matroid-structural threads. Bulla ships the subset that runs on a developer's laptop today.