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Root 1Root 2Root 3Root 4Root 5Root 6Root 7Root 8Root 9Root 10Root 11Root 12Root 13Root 14Root 15Root 16Root 17Root 18Root 19Root 20Root 21Root 22Root 23Root 24Root 25Root 26Root 27Root 28Root 29Root 30Root 31Root 32Root 33Root 34Root 35Root 36Root 37Root 38Root 39Root 40Root 41Root 42Root 43Root 44Root 45Root 46Root 47Root 48Root 49Root 50Root 51Root 52Root 53Root 54Root 55Root 56Root 57Root 58Root 59Root 60Root 61Root 62Root 63Root 64Root 65Root 66Root 67Root 68Root 69Root 70Root 71Root 72Root 73Root 74Root 75Root 76Root 77Root 78Root 79Root 80Root 81Root 82Root 83Root 84Root 85Root 86Root 87Root 88Root 89Root 90Root 91Root 92Root 93Root 94Root 95Root 96Root 97Root 98Root 99Root 100Root 101Root 102Root 103Root 104Root 105Root 106Root 107Root 108Root 109Root 110Root 111Root 112Root 113Root 114Root 115Root 116Root 117Root 118Root 119Root 120Root 121Root 122Root 123Root 124Root 125Root 126Root 127Root 128Root 129Root 130Root 131Root 132Root 133Root 134Root 135Root 136Root 137Root 138Root 139Root 140Root 141Root 142Root 143Root 144Root 145Root 146Root 147Root 148Root 149Root 150Root 151Root 152Root 153Root 154Root 155Root 156Root 157Root 158Root 159Root 160Root 161Root 162Root 163Root 164Root 165Root 166Root 167Root 168Root 169Root 170Root 171Root 172Root 173Root 174Root 175Root 176Root 177Root 178Root 179Root 180Root 181Root 182Root 183Root 184Root 185Root 186Root 187Root 188Root 189Root 190Root 191Root 192Root 193Root 194Root 195Root 196Root 197Root 198Root 199Root 200Root 201Root 202Root 203Root 204Root 205Root 206Root 207Root 208Root 209Root 210Root 211Root 212Root 213Root 214Root 215Root 216Root 217Root 218Root 219Root 220Root 221Root 222Root 223Root 224Root 225Root 226Root 227Root 228Root 229Root 230Root 231Root 232Root 233Root 234Root 235Root 236Root 237Root 238Root 239Root 240
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Connections join points. Fibers show curved paths. Subsets show smaller shapes within the same map.

Connections join neighboring roots. Fibers show paths inside the S7 → S4 Hopf fibers. Both use the same fixed root IDs. These mathematical relationships do not establish shared meaning.

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How Looking Glass uses these words

Find meanings sends your words to the dictionary service. Choose the definitions that fit, or leave a word open. Nothing is saved to your account. Review in my space keeps a temporary draft for you to review and save there. This view looks up dictionary definitions; it has no voice input or AI-written reply.

Fibers sends the 240 E8 representatives through the retained S⁷→S⁴ calculator. Beads follow a declared path inside each fiber. Connections shows their fixed E8 Coxeter-plane positions and mathematical neighbors. Subsets selects a named root system. Numbers preserve each root’s identity; different points can overlap in a projection.

After every word has a chosen, mapped definition, the result marked in Fibers follows the same calculator using the exact octonion product. The drawing and the clarification questions are separate outputs; neither establishes sentence meaning.

Color highlights possible dictionary meanings. Thin root-neighbor lines describe geometry. Stronger word links join consecutive chosen records in your sentence and appear only after you choose both definitions. Neither kind establishes equivalent meaning or agreement.

Dictionary wording was compressed into eight coordinates by the existing experimental atlas. Several senses can occupy one root. A root choice and its octonion product are not measurements of a person, consent, or truth.

Your response stays on this page. Changing words, language, or dictionary choices clears it. Review in my space separately keeps a temporary draft in this tab; it is not an agreement or a saved explanation.

Geometry, dictionary version & source hashes
{
  "geometry": {
    "schema": "looking-glass.e8-coxeter-geometry/v1",
    "sourceFile": "E8 Coxeter Plane.html",
    "sourceSha256": "2e0668f6764369e241acb36b9df7fed2770475264c59e117fd5bc357d2ab1eeb",
    "sourceBytes": 45942,
    "modelGeometryDigest": "sha256:fd8ac2058aee11bfb68ed69dec7aa424db56db465e8e61724cfdbda89e58472a",
    "geometryDigestEncoding": "sha256 of e8-plane-data.json UTF-8 bytes including final newline",
    "donorCommit": "1394c395fdfb6e55a30a4578900fcc939866883c",
    "donorPath": "lib/math/e8-octavian.ts",
    "donorSourceSha256": "2f1cea4852320ba674a4e493e267cb695345db8e859f6b4d9146c384e14c7a7e",
    "coordinateConvention": "standard E8 roots; roots2 = 2r; r has squared norm 2",
    "planeConvention": "Q rows 2p and 2p+1; p=0,1,2,3; exponents 1,7,11,13",
    "assignmentConvention": "exact max dot(integer vector, roots2); ties ordered lexicographically; zero unassigned",
    "assignmentScope": "240 root sectors, not nearest point in the full E8 lattice"
  },
  "hopfDisplay": {
    "version": "looking-glass/mirror-s7-s4-trajectory/v1",
    "geometryDigest": "sha256:fd8ac2058aee11bfb68ed69dec7aa424db56db465e8e61724cfdbda89e58472a",
    "hopfVersion": "looking-glass/hopf-s4/S-sub/height-first/v1",
    "split": "S-sub",
    "outputOrder": "height-first",
    "splitMap": "q1=(x0,x1,x2,x4); q2=(x3,x7,x5,-x6)",
    "formula": "H(q1,q2)=(|q1|²-|q2|²,2q1 conjugate(q2)) for |q1|²+|q2|²=1",
    "charts": "h>=0: a=sqrt((1+h)/2) real, b=conjugate(c)/(2a); h<0: b=sqrt((1-h)/2) real, a=c/(2b)",
    "gauge": "north: lambda=q1/a; south: lambda=q2/b; (a lambda,b lambda) recovers the original S7 point",
    "trajectory": "lambda(t)=lambda(0) exp(i t) exp(j 2t) exp(k 3t); one closed trajectory within the full right-unit-quaternion S3 fiber",
    "period": 3.14159265359,
    "samples": 192,
    "projection": "R8 -> R3: scale .62 times orthonormal DCT-II rows k=1,2,3; then the shared rotating orthographic camera",
    "projectionRows": [
      [
        0.490392640202,
        0.415734806151,
        0.27778511651,
        0.0975451610081,
        -0.0975451610081,
        -0.27778511651,
        -0.415734806151,
        -0.490392640202
      ],
      [
        0.461939766256,
        0.191341716183,
        -0.191341716183,
        -0.461939766256,
        -0.461939766256,
        -0.191341716183,
        0.191341716183,
        0.461939766256
      ],
      [
        0.415734806151,
        -0.0975451610081,
        -0.490392640202,
        -0.27778511651,
        0.27778511651,
        0.490392640202,
        0.0975451610081,
        -0.415734806151
      ]
    ],
    "scale": 0.62,
    "view": {
      "centerX": 360,
      "centerY": 346,
      "radius": 310,
      "screenScale": 440,
      "pitch": 0.62,
      "yaw": -0.55,
      "roll": 0.22
    },
    "boundary": "Float64 drawing derived from the declared exact S7/S4 calculation. The path is not the whole S3 fiber. Distinct points and fibers can overlap after projection; no collision offsets or semantic relationships are inferred."
  },
  "displaySignificantDigits": 12,
  "atlas": null
}

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