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.

2,910 recordsSource snapshot 2026-10-17

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 ↗

2,910 records · page 55 of 59Search the source archive ↗

rhiannon-neuron-cost-74

Rhiannon neuron 74: environment and pattern cost

This is the documented cost template instantiated for neuron 74 in the environment and pattern group. The source provides U=4, V=4 and dK=3, so the maximum structural requirement is 4. Substituting those parameters reduces the proposed cost to 36+4·dx. The coherence driver dx remains an input; the…

Rhiannon neuron cost instancesdocumented formula instance

U_74=4, V_74=4, dK_74=3; r_min,74=max(U_74,V_74,dK_74)=4; C_74=r_min,74²+r_min,74(dK_74+dx+2)

rhiannon-neuron-cost-75

Rhiannon neuron 75: environment and pattern cost

This is the documented cost template instantiated for neuron 75 in the environment and pattern group. The source provides U=5, V=3 and dK=3, so the maximum structural requirement is 5. Substituting those parameters reduces the proposed cost to 50+5·dx. The coherence driver dx remains an input; the…

Rhiannon neuron cost instancesdocumented formula instance

U_75=5, V_75=3, dK_75=3; r_min,75=max(U_75,V_75,dK_75)=5; C_75=r_min,75²+r_min,75(dK_75+dx+2)

rhiannon-neuron-cost-76

Rhiannon neuron 76: internal math cost

This is the documented cost template instantiated for neuron 76 in the internal math group. The source provides U=3, V=3 and dK=3, so the maximum structural requirement is 3. Substituting those parameters reduces the proposed cost to 24+3·dx. The coherence driver dx remains an input; the table does…

Rhiannon neuron cost instancesdocumented formula instance

U_76=3, V_76=3, dK_76=3; r_min,76=max(U_76,V_76,dK_76)=3; C_76=r_min,76²+r_min,76(dK_76+dx+2)

rhiannon-neuron-cost-77

Rhiannon neuron 77: internal math cost

This is the documented cost template instantiated for neuron 77 in the internal math group. The source provides U=4, V=4 and dK=3, so the maximum structural requirement is 4. Substituting those parameters reduces the proposed cost to 36+4·dx. The coherence driver dx remains an input; the table does…

Rhiannon neuron cost instancesdocumented formula instance

U_77=4, V_77=4, dK_77=3; r_min,77=max(U_77,V_77,dK_77)=4; C_77=r_min,77²+r_min,77(dK_77+dx+2)

rhiannon-neuron-cost-78

Rhiannon neuron 78: internal math cost

This is the documented cost template instantiated for neuron 78 in the internal math group. The source provides U=5, V=4 and dK=3, so the maximum structural requirement is 5. Substituting those parameters reduces the proposed cost to 50+5·dx. The coherence driver dx remains an input; the table does…

Rhiannon neuron cost instancesdocumented formula instance

U_78=5, V_78=4, dK_78=3; r_min,78=max(U_78,V_78,dK_78)=5; C_78=r_min,78²+r_min,78(dK_78+dx+2)

rhiannon-neuron-cost-79

Rhiannon neuron 79: internal math cost

This is the documented cost template instantiated for neuron 79 in the internal math group. The source provides U=4, V=5 and dK=3, so the maximum structural requirement is 5. Substituting those parameters reduces the proposed cost to 50+5·dx. The coherence driver dx remains an input; the table does…

Rhiannon neuron cost instancesdocumented formula instance

U_79=4, V_79=5, dK_79=3; r_min,79=max(U_79,V_79,dK_79)=5; C_79=r_min,79²+r_min,79(dK_79+dx+2)

rhiannon-neuron-cost-07

Rhiannon neuron 7: system and device cost

This is the documented cost template instantiated for neuron 7 in the system and device group. The source provides U=6, V=2 and dK=3, so the maximum structural requirement is 6. Substituting those parameters reduces the proposed cost to 66+6·dx. The coherence driver dx remains an input; the table…

Rhiannon neuron cost instancesdocumented formula instance

U_7=6, V_7=2, dK_7=3; r_min,7=max(U_7,V_7,dK_7)=6; C_7=r_min,7²+r_min,7(dK_7+dx+2)

rhiannon-neuron-cost-80

Rhiannon neuron 80: internal math cost

This is the documented cost template instantiated for neuron 80 in the internal math group. The source provides U=3, V=4 and dK=2, so the maximum structural requirement is 4. Substituting those parameters reduces the proposed cost to 32+4·dx. The coherence driver dx remains an input; the table does…

Rhiannon neuron cost instancesdocumented formula instance

U_80=3, V_80=4, dK_80=2; r_min,80=max(U_80,V_80,dK_80)=4; C_80=r_min,80²+r_min,80(dK_80+dx+2)

rhiannon-neuron-cost-08

Rhiannon neuron 8: system and device cost

This is the documented cost template instantiated for neuron 8 in the system and device group. The source provides U=3, V=4 and dK=2, so the maximum structural requirement is 4. Substituting those parameters reduces the proposed cost to 32+4·dx. The coherence driver dx remains an input; the table…

Rhiannon neuron cost instancesdocumented formula instance

U_8=3, V_8=4, dK_8=2; r_min,8=max(U_8,V_8,dK_8)=4; C_8=r_min,8²+r_min,8(dK_8+dx+2)

rhiannon-neuron-cost-09

Rhiannon neuron 9: system and device cost

This is the documented cost template instantiated for neuron 9 in the system and device group. The source provides U=5, V=3 and dK=3, so the maximum structural requirement is 5. Substituting those parameters reduces the proposed cost to 50+5·dx. The coherence driver dx remains an input; the table…

Rhiannon neuron cost instancesdocumented formula instance

U_9=5, V_9=3, dK_9=3; r_min,9=max(U_9,V_9,dK_9)=5; C_9=r_min,9²+r_min,9(dK_9+dx+2)

SOURCE 277 · megamind-supplemental-000

Supplemental component 0 · source equation 277

This page substitutes i=0 into the supplemental generator, which the source numbers as equation 277. It averages a sine term, a cosine term and a sine–cosine product. The result is placed at binding_field[174], following the 174 core components. It is an indexed member of the same source-defined…