computer-science

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Gradient

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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.

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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: “the browser-eyeball step is genuinely asymmetric — overkill for schema PRs, load-bearing for interaction PRs” with the operational heuristic “does this PR change how something feels in the hand, or just what something contains?”
• Inflection / threshold — a parameter on a gradient hits a step-function (“the math inverts at X%,” “tips the balance”).
• Asymmetric-stability — the user names asymmetric stability (“if one choice gives us more stability… i’d lean that way”); the agent elevates to a doctrine: for genuinely fuzzy questions where there’s no ‘right’ answer, prefer whichever choice the extractor/LLM produces consistently. This sub-shape generalizes across decision domains (identity rules, filter-vs-label, even visual-grammar where symmetric/asymmetric marks have predictable semantic loadings — “boat heading somewhere” vs “stamp on a document”).

Agent-initiated: Engine 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).

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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.

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Structure

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Relationships

• asymmetric-gate — the specific higher-order concept where gradient meets a gating mechanism (one direction cheap, the other expensive).
• local-minimum — gradient + attractor; every local direction looks worse, but the global landscape has better attractors.

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Examples