> ## Documentation Index > Fetch the complete documentation index at: https://agentconcepts.io/llms.txt > Use this file to discover all available pages before exploring further. # gradient > Anti-symmetry schema: a dimension with direction — cheap one way, expensive the other; one state attracts, another repels. computer-science physics # Gradient ## Description The structural property that a dimension has direction — moving one way is cheap, the other expensive; one state attracts, another repels; one outcome is more likely than the symmetric alternative. The gradient concept is the anti-symmetry schema: when you see a situation where the symmetric framing feels off, gradient is often the correct framing. Often used as a corrective to "binary" or "symmetric" framings that lose information. ## Triggers **User-initiated:** Gradient is overwhelmingly a *re-framing reach* on the agent's side rather than a lexically marked prompt cue. The concept fires when the user describes a binary or symmetric framing and the agent recognizes the actual structure is directional, or vice versa. Three recurring sub-shapes: * **Cost-asymmetric direction** — cheap forward, expensive backward (this is the asymmetric-gate higher-order concept's home base). Example: a manual review step that is redundant for a change altering only *what* a system contains but load-bearing for one altering *how* it behaves — the same check, asymmetric in value by the class of change it faces. * **Inflection / threshold** — a parameter on a gradient hits a step-function ("the math inverts at X%," "tips the balance"). * **Asymmetric-stability** — a choice between options with no clearly correct answer, where one option is more *stable* than the other; the agent elevates it to a doctrine: *for genuinely fuzzy questions with no right answer, prefer whichever option a process yields consistently.* This sub-shape *generalizes* across decision domains — naming conventions, classification boundaries, even visual grammar, where symmetric vs. asymmetric marks carry predictable semantic loadings ("a boat heading somewhere" vs. "a stamp on a document"). **Agent-initiated:** Agent notices the user is reaching for a binary/symmetric framing of a directional situation; surfaces gradient as the corrective. Often arises in orchestrator-evaluating-worker contexts (an orchestrator evaluating a worker's directional cost/risk analysis). **Vocabulary cues:** "asymmetric," "asymmetry," "gradient," "directional," "one direction cheap," "expensive in the other direction," "tips the balance," "math inverts," "asymmetric stability," "stability beats correctness," "ratchet," "threshold," "inflection," "tipping point." **Situation-shape signals:** A decision being framed in binary terms when the underlying structure has a cost or stability differential along a continuous axis; a doctrine being proposed as universal when it should be artifact-class-conditional (cheap-and-overkill for class X, load-bearing for class Y). ## Exclusions * **Genuine symmetry** — mirror-image systems, undirected graphs; forcing a gradient frame loses information. * **Constant landscape** — if there's no actual variation along the dimension, gradient is degenerate. ## Structure Internal structure of gradient: a table of its component slots and the concepts that fill them. ## Relationships Relationship neighborhood of gradient: a graph of the concepts it connects to and the concepts it is a part of. * [asymmetric-gate](/concepts/asymmetric-gate) — the specific higher-order concept where gradient meets a gating mechanism (one direction cheap, the other expensive). * [local-minimum](/concepts/local-minimum) — gradient + attractor; every local direction looks worse, but the global landscape has better attractors. ## Examples A temperature gradient is a dimension with a built-in direction. Heat flows spontaneously down it — from hot to cold — for free, but moving heat the other way, cold to hot, takes work: a heat pump, a refrigerator, an energy bill. The axis is not symmetric; one direction is cheap and the reverse is expensive, which is exactly the anti-symmetry the gradient schema names. Wherever a quantity varies across space or time and travelling each way along it costs differently, the same shape recurs. threshold observation: gradient becomes a step-function at a specific point.