An Anchor Theory of Value Sharing: Symmetry and the Structure of Shared Value

This paper proposes an anchor theory of value sharing. The central idea is that shared value is structured by an anchor—the segmented part of a proposition or object that carries the highest subjective value for an agent—and that whether value is preserved or changes depends on the symmetry of the anchor under transformations of time, space, and perspective. Each axis takes the value 1 (symmetry preserved) or 0 (symmetry broken), and value can be shared only while all three axes remain at (1, 1, 1). An anchor can be placed on any proposition or object, so the question is never whether an anchor exists but whether it survives symmetry operations. The three axes correspond by nature to three value components—credibility, narrativity, and importance—but historical attribution is not one-to-one: coarse-graining allows a breakdown to be attributed primarily to one axis, while fine-grained analysis may reveal the joint operation of several axes. The theory is applied to a range of phenomena: why scientific propositions can be said, why the lives of great figures can be said while those of ordinary persons cannot, why phlogiston became unsayable, why religion is communicable within a community but not outside it, why products that sell domestically may fail abroad and vice versa, why neglected theories may later be recognized, and why changing place can change a life. Sayability is treated as one application of the theory—the sharing of linguistic value—rather than as its sole subject. This paper is a proposal for a direction of research rather than a completed theory, and its limitations are explicitly stated.