1 min read
| Status | Active — read in full 2026-10-27 (NOTE-1221), from arXiv v3; worth reading as the source of the consistency radius and of sheaf-based data fusion as the nearest global section, with a clear worked example. It is expository: "canonical" is argued by positing axioms whose models are sheaves, not proved, and the paper calls sheaves one of "many co-universal information representations". The demonstration is one simulated scenario; its uniqueness result for linear fusion (Proposition 25) does not follow from its proof. |
| Version | 2 |
| Tags | mathematics, information-theory |
| Cited as “paper” by | NOTE-1221 — Robinson — Sheaves are the canonical data structure for sensor integration |
| Cited as “source” by | THEORY-1060 — Robinson's claim that sheaves are the canonical data structure for sensor integration rests on an axiomatization, not a theorem: six axioms are posited as what an integrated sensor system must be and a sheaf is defined as whatever satisfies them, the paper calls sheaves one of many co-universal information representations, and its consistency and fusion tools need only a presheaf, THEORY-1077 — On a presheaf of pseudometric spaces, the consistency radius of an assignment, the largest distance between an observation and the restriction of another, is zero exactly for assignments induced by global sections (in metric spaces) and, when the restrictions are K-Lipschitz, bounds the assignment's sup-distance from every global section below by ε/(1 + K); so fusing data into a consistent state must move it at least that far, and the bound needs no sheaf condition, THEORY-1092 — Read over the sensor domains, the discrepancies between each observation and the restrictions of others can single out a faulty sensor where the consistency radius alone does not: in Robinson's simulated search, a 2° bearing bias was attributed to the right sensor, without prior knowledge of it, because every large discrepancy involved that sensor's domains, while the radius was lower than in the unbiased case |
Robinson, M. (2017). Sheaves are the canonical data structure for sensor integration. Information Fusion, 36, 208–224. doi:10.1016/j.inffus.2016.12.002.
Read in full on 2026-10-27 (NOTE-1221).
A21 §5 called it “almost the practical engineering version of our abstract proposal”: distributed local observations supporting global inference without a privileged observer, with residuals as evidence against the correspondence model. It bears on CLAIM-471 and QUESTION-285.