1 min read
| Status | Active — read in full 2026-10-27 (NOTE-1222), from the arXiv preprint; worth reading as the clearest formal case of agreement on what is expressed without identity of what is held, and of correspondence maps revised by interaction. Mathematics with toy examples, no data; its expression learning reaches coherence with nothing outside the loop to check it, which the authors call "learning to lie". |
| Version | 2 |
| Tags | mathematics, network-science, society-and-governance |
| Cited as “paper” by | NOTE-1222 — Hansen & Ghrist — Opinion dynamics on discourse sheaves |
| Cited as “source” by | THEORY-1062 — On a discourse sheaf, where each agent expresses a private opinion through a linear map into each edge's space of topics, sheaf-Laplacian opinion diffusion converges to the orthogonal projection of the initial opinions onto the global sections, which are agreement in what each pair expresses and not in what they hold; stable polarized or incomparable private opinions are therefore possible, and when the sheaf has no nonzero global section the only limit is all opinions zero, THEORY-1088 — When the expression maps of a discourse sheaf diffuse to reduce disagreement, with opinions held fixed they converge to the nearest sheaf, in Frobenius distance, of which the opinions are a global section, so apparent consensus is reached by changing what is said ("learning to lie"); with opinions diffusing too the joint flow is gradient descent on ½‖δx‖², and conserved diagonal blocks of αδᵀδ − βxxᵀ keep the opinions from collapsing to zero; nothing in either flow checks an expression against the opinion it expresses |
Hansen, J., & Ghrist, R. (2021). Opinion dynamics on discourse sheaves. SIAM Journal on Applied Mathematics, 81(5), 2033–2060. doi:10.1137/20M1341088. Preprint: arXiv:2005.12798.
Read in full on 2026-10-27 (NOTE-1222).
A22 §11 listed it among the prior art to elevate, for “Richer observation and communication maps, including selective expression”: compatibility on what is shared without identity of what is held. It bears on CLAIM-471.