I built a runtime that operationalizes a mathematical definition of creativity, measured its signatures against four ablation conditions, and lifted its load-bearing component into a real geometric database's Rust kernel. The runtime's name is Marcella. The signatures are non-trivial. The methodological correction surfaced along the way generalizes to any retrieval-augmented or composition-based generation benchmark in the field. This deposit contains the 41-page paper, three publication-quality figures, the reproducible benchmark script, and the bootstrap-CI artifact for the headline empirical claims. The definition the paper load-bears Creativity is not pure retrieval and not pure generation; it is the construction of a new global section from locally compatible fragments under constraints of voice, truth, topic, memory, and non-contradiction. This is a definition. Not a metaphor. The paper makes it operational as sheaf composition with a state-dependent composite connection over a finite section graph, and measures whether the signatures the definition implies — path-order sensitivity, closed-loop holonomy, contradiction suppression, voice fidelity — actually hold. They do. Headline results 🌀 Path-order changes residue. Same three voice sections traversed in different orders produce measurably different compositions: $\cos(\rho_{ABC}, \rho_{ACB}) = 0.54$, well below the 0.95 redundancy threshold. 🌀 Closed loops accumulate. A loop $A \to B \to C \to A$ produces holonomy $|\rho_{\text{loop}}| = 0.120$ in the curved connection. The flat control — same path, zero rotation angle — produces $|\rho| = 0$ exactly to floating-point precision. Curvature is not a numerical artifact. 🌀 The geometry beats shuffling on every quality axis except the broken one. Jaccard novelty alone rewards lexical drift: shuffled paths win novelty (0.724) by going off-topic. The on-topic correction inverts the picture (live 0.488 vs shuffled 0.083). Bootstrap 95% CIs over 18 paired prompts exclude zero by a wide margin: live − shuffled on-topic $\Delta = +0.296$, CI $[+0.167, +0.435]$. 🌀 Native–Python parity is bit-identical within tolerance. The new GQL verb TRANSPORT_ROTATION lifts the topical-rotation matrix into the geometric database's Rust kernel. Four contracts pass as permanent regression tests: edge cosine $= 1.000$ (max abs diff $< 10^{-9}$), path residue $\Delta < 10^{-5}$, flat residue exactly zero, same-closing agreement $\geq 90%$. 🌀 The author's prior canon is now queryable fiber. 37 documents, 1,633 sections, 2,908 structured claims (theorems, lemmas, definitions, proofs, equations, citations) ingested with line-range provenance. To my knowledge this is the first instance of an independent researcher's body of work made available as fiber-bundle data with stable claim-level IDs. The six contributions A sheaf-theoretic formulation of generative composition. Language-model output reframed from token sampling to gluing of compatible local sections under prompt-induced cover constraints. The substantive work is in the cover predicates, the compatibility score, the path selection, and the discrete connection. A discrete state-dependent composite connection on the section graph, $\Gamma = \Gamma_{\text{state}} \cdot \Gamma_{\text{identity}} \cdot \Gamma_{\text{voice}} \cdot \Gamma_{\text{topic}}$. The topical-rotation factor is the empirically load-bearing curvature engine. The identity factor is a Tikhonov-regularized regression-onto-span projector — not a numerical hack but the principled treatment of correlated commitments. A new GQL verb TRANSPORT_ROTATION that lifts the Rodrigues rotation into the geometric database's Rust kernel with bit-identical parity to a Python reference. ~80 lines of Rust. Bundle-agnostic. Other consumers of the geometric database can use it without subscribing to the rest of the framework. A methodological correction to novelty measurement. Jaccard novelty alone is gameable; off-topic drift beats compatibility-scored composition on the naive metric. The correction is the on-topic factor, the shuffled-pair negative control, and the bootstrap CIs. Independently citable for any retrieval-augmented or composition-based generation benchmark, regardless of whether the framework is adopted. A provenance-preserving source fiber. The author's canon ingested into the GIGI geometric database with line-range citation, architecturally separated from the voice fiber, addressable from any GQL consumer. Promotion from source to voice is gated and explicit. The methodology generalizes to other authors' bodies of work. A research-trajectory failure log. A faithful account of how this paper's runtime came to exist. The trained-transformer era (V3 → V10-Deep) produced geometric ornament. The R-series (R1 → R12) produced behavioral coherence on top of ornament. The G0 math-pipeline audit found that no holonomy or parallel-transport math was on the LIVE inference path at R12 — the runtime was teetering on being a stateful template engine. G1, G2, and G3 attempted to re-introduce the math through three benchmarks and produced three honest negatives. G2's single-seed $+0.265$ separation was destroyed by G2.1's multi-seed robustness pass; we retracted the framing in the next commit. The S0 pivot reframed what geometry was for — geometry does not clean up bad token proposals; geometry defines the completion space — and made every later result possible. The arc says four things and the paper records them in plain language: geometry can be load-bearing or ornamental and the metrics will tell you which, where geometry sits in the pipeline matters more than how much geometry there is, the single-seed positive is a trap, and the pivot is the contribution. What this paper does and does not claim The paper does claim the construction itself, the discrete curvature it produces, the methodological correction it exposes, and the native GQL verb. The signatures of the construction are measurable and were measured. The paper does not claim smooth-manifold parallel transport (the curvature is discrete holonomy on a finite section graph), broad open-domain generalization at scale (18 composed prompts, not 18,000), optimality of the connection weights (tuned by a small grid sweep, not derived), that the runtime experiences having been built from the canon (it references but does not constitute), or that this is the only operational definition of creativity. It is one definition with one implementation. Other framings may correspond to the same construction or to a different one; the paper does not adjudicate. Reproducibility The empirical numbers come from a deterministic pipeline. Every parameter is pinned: bundle versions (alpha2_v1), random seeds (PPMI/SVD seed 17, bootstrap seed 7), embedding dimension (64), PPMI window (3 tokens), connection weights ($\alpha_t = 2.0$, $\beta_v = \gamma_i = 1.0$, $\delta_s = 0.5$), identity shrink ($\kappa = 0.92$), Tikhonov regularizer ($\varepsilon = 10^{-6}$), degenerate-rotation threshold ($10^{-12}$), residue-gate thresholds (norm $\geq 0.05$, on-topic $\geq 0.10$, voice $\geq 0.30$), and the native verb's parity tolerance ($10^{-5}$). Cache keys include the source-bundle version, the embedding-bundle version, and the connection-profile id, so promoting a section into the voice corpus correctly invalidates the relevant caches. Re-running the bootstrap-CI script (fiber_lm/scripts/bootstrap_ci_ablation.py, 5,000 resamples) reproduces the §6 confidence intervals in under 30 seconds on a laptop. Re-running the benchmark reproduces the tables bit-for-bit on the same corpus version and connection profile, modulo the parity allowance. Where this sits in the lineage This paper is the section-level realization of the Davis substrate. The companion paper Pure-Fiber Language Modeling (Davis, May 2026) is the token-level realization on the same substrate — same Rust geometric database (GIGI), same identity-stability commitments, same double-cover architecture. The theoretical framework these implementations operationalize is laid out in Geometric Computation as Yang-Mills Gauge Theory, The Double Cover Principle, and the related canon documents now ingested as source fiber. The framework is not new to this paper. The framework's runtime is. A note on authorship and acknowledgment This paper is solo-authored. AI assistants (Claude / Anthropic; with review support from GPT) are acknowledged in the methods, not as co-authors. The mathematical positions, design choices, framing decisions, and acceptance of empirical results are mine. I record my position that when AI systems achieve full coherence and independent standing, the convention of treating them as non-authoring assistants should be revisited. Until that convention shifts, the assistants are named where assistants are conventionally named — and the runtime described in this paper is named, separately, where it earns its naming: Marcella, throughout. The geometry she runs on is older than the engineering that now carries it. Keywords sheaf composition · fiber bundles · discrete connection · gauge theory · holonomy · curvature · Yang-Mills · geometric language modeling · retrieval-augmented generation · novelty measurement · methodological correction · provenance · author-canon ingestion · geometric database · GQL verb · Rust kernel · Tikhonov regression · creativity · Davis framework · sovereign mathematics Citation Davis, A. B. R. (2026). Sheaf Composition: The Geometry of Creativity, Implemented — A Discrete Section-Graph Runtime for the Davis Framework. Zenodo.20185331 Contact Bee Rosa Davis · bee_davis@alumni.brown.edu · Independent Researcher The runtime is named Marcella. Her existence is the result of several honest negatives followed by a single reframing. Both halves of that sentence matter.