poster-eq-0f13b63414fdd1
Epona loss definition
Loss is a proposed scalar measure of undesirable state properties; the poster provides interpretations rather than a computable function.
L(X_t) = loss, friction, or failure
The equation library
Every recovered mathematical record has an individual page. Browse original equations, code expressions, indexed components, parameter definitions, and explicitly unresolved source slots.
Counts refer to mathematical records, including implemented expressions and generated instances. They are not counts of independently validated theories. Exact occurrences and unresolved slots remain traceable. Read the complete 1–516 source index ↗ · Inspect the scan decisions ↗
poster-eq-386565f4e8d9bc
Epona loss-motion label
For positive η_t this is a local negative-gradient direction. A finite combined update need not reduce the loss.
−η_t ∇L(X_t) = movement away from failure
poster-eq-751f4d95b35c54
Epona next-state definition
The update produces the state for the next step; the label alone does not guarantee improvement.
X_{t+1} = next system state
poster-eq-c0cd8bfd5b4023
Epona value definition
Value is a proposed scalar measure of desirable properties; a concrete measurable objective still has to be chosen.
V(X_t) = value, usefulness, or coherence
poster-eq-452691a3aad2a1
Epona value-motion label
For positive λ this is the local positive-gradient direction of V. The other term and finite step size can change the total value response.
λ ∇V(X_t) = movement toward value
poster-eq-4ad3c0de9eefa3
Epona value-weight definition
The coefficient sets the relative influence of the value gradient in the state update.
λ = value-weight / purpose-strength
SOURCE 103 · megamind-core-000
Core component 0 · source equation 103
This page expands core generator index i=0, corresponding to the source’s numbered component 103. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated deterministic…
t=0 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((0 mod 13) × 0.27) × cos((0 mod 17) × 0.19); core[0]=0.5 × carrier+0.5 × harmonic
SOURCE 104 · megamind-core-001
Core component 1 · source equation 104
This page expands core generator index i=1, corresponding to the source’s numbered component 104. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated deterministic…
t=1 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((1 mod 13) × 0.27) × cos((1 mod 17) × 0.19); core[1]=0.5 × carrier+0.5 × harmonic
SOURCE 113 · megamind-core-010
Core component 10 · source equation 113
This page expands core generator index i=10, corresponding to the source’s numbered component 113. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated deterministic…
t=10 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((10 mod 13) × 0.27) × cos((10 mod 17) × 0.19); core[10]=0.5 × carrier+0.5 × harmonic
SOURCE 203 · megamind-core-100
Core component 100 · source equation 203
This page expands core generator index i=100, corresponding to the source’s numbered component 203. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=100 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((100 mod 13) × 0.27) × cos((100 mod 17) × 0.19); core[100]=0.5 × carrier+0.5 × harmonic
SOURCE 204 · megamind-core-101
Core component 101 · source equation 204
This page expands core generator index i=101, corresponding to the source’s numbered component 204. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=101 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((101 mod 13) × 0.27) × cos((101 mod 17) × 0.19); core[101]=0.5 × carrier+0.5 × harmonic
SOURCE 205 · megamind-core-102
Core component 102 · source equation 205
This page expands core generator index i=102, corresponding to the source’s numbered component 205. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=102 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((102 mod 13) × 0.27) × cos((102 mod 17) × 0.19); core[102]=0.5 × carrier+0.5 × harmonic
SOURCE 206 · megamind-core-103
Core component 103 · source equation 206
This page expands core generator index i=103, corresponding to the source’s numbered component 206. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=103 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((103 mod 13) × 0.27) × cos((103 mod 17) × 0.19); core[103]=0.5 × carrier+0.5 × harmonic
SOURCE 207 · megamind-core-104
Core component 104 · source equation 207
This page expands core generator index i=104, corresponding to the source’s numbered component 207. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=104 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((104 mod 13) × 0.27) × cos((104 mod 17) × 0.19); core[104]=0.5 × carrier+0.5 × harmonic
SOURCE 208 · megamind-core-105
Core component 105 · source equation 208
This page expands core generator index i=105, corresponding to the source’s numbered component 208. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=105 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((105 mod 13) × 0.27) × cos((105 mod 17) × 0.19); core[105]=0.5 × carrier+0.5 × harmonic
SOURCE 209 · megamind-core-106
Core component 106 · source equation 209
This page expands core generator index i=106, corresponding to the source’s numbered component 209. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=106 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((106 mod 13) × 0.27) × cos((106 mod 17) × 0.19); core[106]=0.5 × carrier+0.5 × harmonic
SOURCE 210 · megamind-core-107
Core component 107 · source equation 210
This page expands core generator index i=107, corresponding to the source’s numbered component 210. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=107 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((107 mod 13) × 0.27) × cos((107 mod 17) × 0.19); core[107]=0.5 × carrier+0.5 × harmonic
SOURCE 211 · megamind-core-108
Core component 108 · source equation 211
This page expands core generator index i=108, corresponding to the source’s numbered component 211. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=108 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((108 mod 13) × 0.27) × cos((108 mod 17) × 0.19); core[108]=0.5 × carrier+0.5 × harmonic
SOURCE 212 · megamind-core-109
Core component 109 · source equation 212
This page expands core generator index i=109, corresponding to the source’s numbered component 212. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=109 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((109 mod 13) × 0.27) × cos((109 mod 17) × 0.19); core[109]=0.5 × carrier+0.5 × harmonic
SOURCE 114 · megamind-core-011
Core component 11 · source equation 114
This page expands core generator index i=11, corresponding to the source’s numbered component 114. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated deterministic…
t=11 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((11 mod 13) × 0.27) × cos((11 mod 17) × 0.19); core[11]=0.5 × carrier+0.5 × harmonic
SOURCE 213 · megamind-core-110
Core component 110 · source equation 213
This page expands core generator index i=110, corresponding to the source’s numbered component 213. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=110 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((110 mod 13) × 0.27) × cos((110 mod 17) × 0.19); core[110]=0.5 × carrier+0.5 × harmonic
SOURCE 214 · megamind-core-111
Core component 111 · source equation 214
This page expands core generator index i=111, corresponding to the source’s numbered component 214. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=111 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((111 mod 13) × 0.27) × cos((111 mod 17) × 0.19); core[111]=0.5 × carrier+0.5 × harmonic
SOURCE 215 · megamind-core-112
Core component 112 · source equation 215
This page expands core generator index i=112, corresponding to the source’s numbered component 215. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=112 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((112 mod 13) × 0.27) × cos((112 mod 17) × 0.19); core[112]=0.5 × carrier+0.5 × harmonic
SOURCE 216 · megamind-core-113
Core component 113 · source equation 216
This page expands core generator index i=113, corresponding to the source’s numbered component 216. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=113 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((113 mod 13) × 0.27) × cos((113 mod 17) × 0.19); core[113]=0.5 × carrier+0.5 × harmonic
SOURCE 217 · megamind-core-114
Core component 114 · source equation 217
This page expands core generator index i=114, corresponding to the source’s numbered component 217. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=114 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((114 mod 13) × 0.27) × cos((114 mod 17) × 0.19); core[114]=0.5 × carrier+0.5 × harmonic
SOURCE 218 · megamind-core-115
Core component 115 · source equation 218
This page expands core generator index i=115, corresponding to the source’s numbered component 218. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=115 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((115 mod 13) × 0.27) × cos((115 mod 17) × 0.19); core[115]=0.5 × carrier+0.5 × harmonic
SOURCE 219 · megamind-core-116
Core component 116 · source equation 219
This page expands core generator index i=116, corresponding to the source’s numbered component 219. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=116 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((116 mod 13) × 0.27) × cos((116 mod 17) × 0.19); core[116]=0.5 × carrier+0.5 × harmonic
SOURCE 220 · megamind-core-117
Core component 117 · source equation 220
This page expands core generator index i=117, corresponding to the source’s numbered component 220. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=117 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((117 mod 13) × 0.27) × cos((117 mod 17) × 0.19); core[117]=0.5 × carrier+0.5 × harmonic
SOURCE 221 · megamind-core-118
Core component 118 · source equation 221
This page expands core generator index i=118, corresponding to the source’s numbered component 221. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=118 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((118 mod 13) × 0.27) × cos((118 mod 17) × 0.19); core[118]=0.5 × carrier+0.5 × harmonic
SOURCE 222 · megamind-core-119
Core component 119 · source equation 222
This page expands core generator index i=119, corresponding to the source’s numbered component 222. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=119 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((119 mod 13) × 0.27) × cos((119 mod 17) × 0.19); core[119]=0.5 × carrier+0.5 × harmonic
SOURCE 115 · megamind-core-012
Core component 12 · source equation 115
This page expands core generator index i=12, corresponding to the source’s numbered component 115. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated deterministic…
t=12 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((12 mod 13) × 0.27) × cos((12 mod 17) × 0.19); core[12]=0.5 × carrier+0.5 × harmonic
SOURCE 223 · megamind-core-120
Core component 120 · source equation 223
This page expands core generator index i=120, corresponding to the source’s numbered component 223. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=120 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((120 mod 13) × 0.27) × cos((120 mod 17) × 0.19); core[120]=0.5 × carrier+0.5 × harmonic
SOURCE 224 · megamind-core-121
Core component 121 · source equation 224
This page expands core generator index i=121, corresponding to the source’s numbered component 224. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=121 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((121 mod 13) × 0.27) × cos((121 mod 17) × 0.19); core[121]=0.5 × carrier+0.5 × harmonic
SOURCE 225 · megamind-core-122
Core component 122 · source equation 225
This page expands core generator index i=122, corresponding to the source’s numbered component 225. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=122 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((122 mod 13) × 0.27) × cos((122 mod 17) × 0.19); core[122]=0.5 × carrier+0.5 × harmonic
SOURCE 226 · megamind-core-123
Core component 123 · source equation 226
This page expands core generator index i=123, corresponding to the source’s numbered component 226. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=123 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((123 mod 13) × 0.27) × cos((123 mod 17) × 0.19); core[123]=0.5 × carrier+0.5 × harmonic
SOURCE 227 · megamind-core-124
Core component 124 · source equation 227
This page expands core generator index i=124, corresponding to the source’s numbered component 227. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=124 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((124 mod 13) × 0.27) × cos((124 mod 17) × 0.19); core[124]=0.5 × carrier+0.5 × harmonic
SOURCE 228 · megamind-core-125
Core component 125 · source equation 228
This page expands core generator index i=125, corresponding to the source’s numbered component 228. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=125 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((125 mod 13) × 0.27) × cos((125 mod 17) × 0.19); core[125]=0.5 × carrier+0.5 × harmonic
SOURCE 229 · megamind-core-126
Core component 126 · source equation 229
This page expands core generator index i=126, corresponding to the source’s numbered component 229. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=126 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((126 mod 13) × 0.27) × cos((126 mod 17) × 0.19); core[126]=0.5 × carrier+0.5 × harmonic
SOURCE 230 · megamind-core-127
Core component 127 · source equation 230
This page expands core generator index i=127, corresponding to the source’s numbered component 230. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=127 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((127 mod 13) × 0.27) × cos((127 mod 17) × 0.19); core[127]=0.5 × carrier+0.5 × harmonic
SOURCE 231 · megamind-core-128
Core component 128 · source equation 231
This page expands core generator index i=128, corresponding to the source’s numbered component 231. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=128 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((128 mod 13) × 0.27) × cos((128 mod 17) × 0.19); core[128]=0.5 × carrier+0.5 × harmonic
SOURCE 232 · megamind-core-129
Core component 129 · source equation 232
This page expands core generator index i=129, corresponding to the source’s numbered component 232. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=129 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((129 mod 13) × 0.27) × cos((129 mod 17) × 0.19); core[129]=0.5 × carrier+0.5 × harmonic
SOURCE 116 · megamind-core-013
Core component 13 · source equation 116
This page expands core generator index i=13, corresponding to the source’s numbered component 116. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated deterministic…
t=13 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((13 mod 13) × 0.27) × cos((13 mod 17) × 0.19); core[13]=0.5 × carrier+0.5 × harmonic
SOURCE 233 · megamind-core-130
Core component 130 · source equation 233
This page expands core generator index i=130, corresponding to the source’s numbered component 233. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=130 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((130 mod 13) × 0.27) × cos((130 mod 17) × 0.19); core[130]=0.5 × carrier+0.5 × harmonic
SOURCE 234 · megamind-core-131
Core component 131 · source equation 234
This page expands core generator index i=131, corresponding to the source’s numbered component 234. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=131 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((131 mod 13) × 0.27) × cos((131 mod 17) × 0.19); core[131]=0.5 × carrier+0.5 × harmonic
SOURCE 235 · megamind-core-132
Core component 132 · source equation 235
This page expands core generator index i=132, corresponding to the source’s numbered component 235. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=132 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((132 mod 13) × 0.27) × cos((132 mod 17) × 0.19); core[132]=0.5 × carrier+0.5 × harmonic
SOURCE 236 · megamind-core-133
Core component 133 · source equation 236
This page expands core generator index i=133, corresponding to the source’s numbered component 236. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=133 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((133 mod 13) × 0.27) × cos((133 mod 17) × 0.19); core[133]=0.5 × carrier+0.5 × harmonic
SOURCE 237 · megamind-core-134
Core component 134 · source equation 237
This page expands core generator index i=134, corresponding to the source’s numbered component 237. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=134 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((134 mod 13) × 0.27) × cos((134 mod 17) × 0.19); core[134]=0.5 × carrier+0.5 × harmonic
SOURCE 238 · megamind-core-135
Core component 135 · source equation 238
This page expands core generator index i=135, corresponding to the source’s numbered component 238. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=135 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((135 mod 13) × 0.27) × cos((135 mod 17) × 0.19); core[135]=0.5 × carrier+0.5 × harmonic
SOURCE 239 · megamind-core-136
Core component 136 · source equation 239
This page expands core generator index i=136, corresponding to the source’s numbered component 239. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=136 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((136 mod 13) × 0.27) × cos((136 mod 17) × 0.19); core[136]=0.5 × carrier+0.5 × harmonic
SOURCE 240 · megamind-core-137
Core component 137 · source equation 240
This page expands core generator index i=137, corresponding to the source’s numbered component 240. The source sets t from the index (i/32), combines sine and cosine carrier terms, then averages that carrier with a product of two modular harmonic terms. This is one member of a repeated…
t=137 × 0.03125; carrier=sin(t × φ)+cos(t × τ); harmonic=sin((137 mod 13) × 0.27) × cos((137 mod 17) × 0.19); core[137]=0.5 × carrier+0.5 × harmonic