{
  "handle": "Gradient",
  "mechanism": "The directional rate of change of a scalar field across a differentiable space. For any sufficiently smooth field f over a differentiable space, the gradient ∇f at a point is the vector whose direction is the one of steepest ascent of f and whose magnitude is the rate of increase in that direction. Substrate property: gradients exist wherever fields exist, whether or not anyone measures them. Specific cases include {{entropy}} gradients (the direction of maximum disorder increase), attention gradients, credibility gradients, information-density gradients. Higher patterns use gradients for hill-climbing search, attention allocation, credit assignment, and flow routing.",
  "gloss": "The directional rate of change of a scalar field — substrate for hill-climbing, attention flow, and credit assignment",
  "invariants": [
    "Existence: every sufficiently smooth field on a differentiable space has a gradient defined at every interior point.",
    "Direction: ∇f points in the direction of steepest ascent of f.",
    "Magnitude: |∇f| is the rate of change in the direction of steepest ascent."
  ],
  "_meta": {
    "tier": 1,
    "ring": 0,
    "path": [
      "Physics",
      "Primitives"
    ],
    "supersedes": [
      "sema:Gradient#mh:SHA-256:dcf04816f4c8639244be889bb5030889bcd786600046a64a67b3ad59a679bb96"
    ]
  },
  "sema_id": "sema:Gradient#mh:SHA-256:ecfc2cd2d9eb95778ef04ede8a7e872c33822f174a9e3273fa7bba92b3a30e36",
  "sema_ref": "Gradient#ecfc",
  "sema_stub": "ecfc",
  "dependencies": {
    "references": {
      "entropy": "sema:Entropy#mh:SHA-256:d5f7482e6c06a1e48eadbf28e6dca0cc0eb176bf75c70e7e467284f656d20bae"
    }
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  "sema_layer": "Physics",
  "sema_category": "Primitives",
  "used_by": {
    "references": {
      "Judge": "sema:Judge#mh:SHA-256:704cbb71588d7a3bafa08b71c863005e31ec4400860b9cb8b094e660da9c7c6c",
      "MemeticSeed": "sema:MemeticSeed#mh:SHA-256:5271ca15f0285d5846715e7bbfdccd4f165c44e02f3ab2df037b9c3f9f325e1c",
      "Optimize": "sema:Optimize#mh:SHA-256:38771f5e8f583966cfb8af8ff0d2e6737c8d0bf87329ddc49d8049450e852674",
      "SurprisalUpdate": "sema:SurprisalUpdate#mh:SHA-256:26e53ade88809ac3ba9293b45db768fdbdb384a53cda1217c3a0dfc61d5f8408"
    }
  }
}