Unified AGI equation system diagram.png

1Unified AGI Equation System 2=========================== 3 4SOURCE: Unified AGI equation system diagram.png 5SOURCE ID: libsrc-bc817beff4dd 6ORIGINAL SHA256: 6ac1740b8a5f0a8a3d5118fb20ab37f2bb565b35c5348c7a2d1708b29041c7de 7REVIEW: 2026-10-17. The original PNG is authoritative. This reading copy separates manually inspected mathematical transcriptions from raw OCR. It is not a verbatim embedded-text extraction. 8 9VISUAL REVIEW NOTES 10- The subtitle says nine equation groups, but the graphic visibly contains eight numbered groups. No ninth numbered block is present. 11- The closed-loop flow is perception → encoding → dynamics → learning → integration → agency → action → feedback → perception. 12- The statements that these components produce AGI or conscious intelligence are claims in the graphic. A block diagram and equations do not supply evidence of these capabilities. 13 14MANUALLY INSPECTED FORMULAS 15 16Unified AGI golden basis with reciprocal cosine frequency 17Image region: Group 1: INPUT / KNOWLEDGE ENCODING, first expression 18ψ_k(x) = sin(2π · φ^k · σ_i · x) + cos(2π · φ^(−k) · σ_i · x) 19Legibility: Legible 20Editorial mathematical explanation: The sine branch uses frequency proportional to φ^k, while the cosine branch uses φ^(−k). These differ except for special cases such as k=0. This is a substantive variant of the Megamind atlas, which prints positive k in both branches. 21Editorial note: The image does not define σ_i or the relation between indices i and k. No approximation or compression error bound is supplied. 22 23Unified AGI harmonic knowledge expansion 24Image region: Group 1: second expression 25K(q) = Σ_k θ_k ψ_k(h(q)) 26Legibility: Legible 27Editorial mathematical explanation: Reconstruct a query-dependent quantity by combining the basis functions with coefficients θ_k. The input is transformed by h before basis evaluation. Unlike the small atlas rendering, this graphic explicitly prints k under the summation. 28Editorial note: The number of terms, fitted coefficients, hash or encoding function, and retrieval quality are unspecified. 29 30Physical evolution operator grouping 31Image region: Group 2: DYNAMICAL EVOLUTION, component definitions 32d_total = diffusion + transport + geometric_drift 33Legibility: Legible 34Editorial mathematical explanation: The physical-style contribution groups spreading, transport and geometry-dependent drift. These are operator labels and require explicit functions. 35 36Nonlinear evolution operator grouping 37Image region: Group 2: DYNAMICAL EVOLUTION, component definitions 38n_total = growth + decay + emergence + chaos 39Legibility: Legible 40Editorial mathematical explanation: The nonlinear contribution groups growth, decay, emergence and chaos. These labels do not determine a unique differential equation or imply chaotic dynamics without further definitions. 41 42External forcing operator grouping 43Image region: Group 2: DYNAMICAL EVOLUTION, component definitions 44f_total = external_force + field_coupling + stochastic_noise 45Legibility: Legible 46Editorial mathematical explanation: The forcing contribution includes external inputs, coupling and stochastic noise. A stochastic model must specify how the noise is sampled or integrated. 47 48Adaptive evolution operator grouping 49Image region: Group 2: DYNAMICAL EVOLUTION, component definitions 50t_total = gradient_descent + loss_minimization + confidence_shaping + reward_signal 51Legibility: Legible 52Editorial mathematical explanation: The adaptive contribution groups four optimization-oriented labels. Gradient descent and loss minimization can overlap, so an implementation needs clear, nonduplicated definitions. 53 54Unified AGI combined state derivative 55Image region: Group 2: final expression 56dx/dt = d_total + n_total + f_total + t_total 57Legibility: Legible 58Editorial mathematical explanation: The state derivative is the sum of four grouped contributions described above it. Because terms such as transport appear in more than one conceptual grouping across posters, the exact operator assignments must be read from the specific source. 59Editorial note: No initial condition, discretization, numerical coefficients or stability analysis is supplied in this image. 60 61Poster timing- and coherence-weighted plasticity 62Image region: Group 3: LEARNING / PLASTICITY 63Δw_ij = η Φ(C_ij) (t_pre − t_post) exp(−Δt/τ) 64Legibility: Legible 65Editorial mathematical explanation: A connection-weight change is scaled by a learning rate, a coherence-related factor, a signed difference between pre- and post-synaptic times, and an exponential timing factor. The sign depends on the source’s timing convention, which the poster does not define. 66Editorial note: This single signed expression is a project variant, not the usual fully specified piecewise STDP rule. If Δt can be negative, exp(−Δt/τ) grows on that side; the poster supplies no absolute value, clipping or separate branch. C_ij and Φ require definitions. 67 68Real-vector substrate projection signature 69Image region: Group 4: SUBSTRATE TO CONSCIOUSNESS LATTICE 70Π : ℝ^23M → ℝ^5000 71Legibility: Legible 72Editorial mathematical explanation: Map a real vector with twenty-three million components to one with five thousand components. This states input and output dimensionalities rather than a lossless compression guarantee. 73Editorial note: A lower-dimensional representation generally discards distinctions unless the input is restricted. The poster does not define those restrictions. 74 75Regional substrate average 76Image region: Group 4: regional mean expression 77X[i] = mean_{j∈R_i}(S_j) 78Legibility: Legible 79Editorial mathematical explanation: Each output coordinate is the arithmetic mean of substrate coordinates in region R_i. This produces a coarse summary of the substrate, smoothing variation within each region. 80Editorial note: Every region must be nonempty, and the region membership must be specified. Averaging alone does not establish an experiential or conscious property. 81 82Hub-and-six-domain coherence average 83Image region: Group 5: INTEGRATION / FEDERATION 84Φ_total = (Φ_hub + Σ Φ_domain) / 7 85Legibility: Legible 86Editorial mathematical explanation: Average one hub score and six domain scores with equal weight. The adjacent Unified AGI diagram explicitly labels six domains plus a hub, which explains the denominator seven. 87Editorial note: The result is an arithmetic average of the supplied scores. It is not automatically the integrated information of the combined causal system; additivity would require separate justification. 88 89Agency–experience–substrate coupling 90Image region: Group 6: CONSCIOUSNESS COUPLING 91Ψ = f(A · X · S) 92Legibility: Legible 93Editorial mathematical explanation: The source defines a coupling term as a function of agency, an experiential lattice and substrate scale. It specifies which quantities are intended to matter, but leaves the function f and the multiplication of these differently named objects unspecified. 94Editorial note: No numerical value, calibrated consciousness measure or operational definition follows from this expression alone. 95 96Agency Tensor definition 97Image region: Group 6: variable definitions 98A = Agency Tensor 99Legibility: Legible 100Editorial mathematical explanation: A is the source’s agency representation; its components and measurement are not defined. 101 102Experiential Coupling Lattice definition 103Image region: Group 6: variable definitions 104X = Experiential Coupling Lattice 105Legibility: Legible 106Editorial mathematical explanation: X names the reduced lattice intended to couple substrate and experience. 107 108Substrate Scale definition 109Image region: Group 6: variable definitions 110S = Substrate Scale 111Legibility: Legible 112Editorial mathematical explanation: S identifies substrate scale, without specifying its normalization or units. 113 114Autonomous objective with exploration and repetition terms 115Image region: Group 7: AUTONOMOUS OBJECTIVE / ACTION POLICY 116J = base_objective + exploration_bonus + adaptive_theta_term − conflict_penalty − resource_penalty + entropy_regularization − repetition_penalty 117Legibility: Legible 118Editorial mathematical explanation: The objective combines task value, exploration, an adaptive parameter term, conflict and resource penalties, entropy regularization and a repetition penalty. If this J is maximized, the plus entropy term encourages diversity when it represents positive entropy. 119Editorial note: The source does not explicitly give an argmax, numerical weights, a definition of adaptive_theta_term, or the sign convention used for entropy. Those details determine actual behavior. 120 121Unified AGI unbounded-time consciousness integral 122Image region: Group 8: GLOBAL AGI / CONSCIOUS INTELLIGENCE MEASURE 123Q = Ψ · ∫ C(t) · Φ(G(t)) · [ ‖∇H(t)‖ / (1 + ‖∇H(t)‖) ] dt 124Legibility: Legible 125Editorial mathematical explanation: Integrate coherence times an information-related factor times a saturating knowledge-gradient magnitude, then scale by Ψ. This version clearly groups Φ(G(t)) as a separate factor, unlike the degraded atlas numerator. The integral has no printed bounds, so it is not a unique accumulated scalar without an interval or integration constant convention. 126Editorial note: The image labels Φ(G(t)) as integrated information but does not specify a causal model or a method for computing it. The formula and caption do not validate a measure of consciousness. 127 128Coherence label 129Image region: Group 8: variable legend 130C(t) = coherence 131Legibility: Legible 132Editorial mathematical explanation: This assigns a conceptual interpretation to C(t); the poster does not define its operational measurement. 133 134Integrated information label 135Image region: Group 8: variable legend 136Φ(G(t)) = integrated information 137Legibility: Legible 138Editorial mathematical explanation: This is the poster’s intended interpretation. It does not by itself identify a specific IIT formulation or provide the transition model and partition calculation it would require. 139 140Knowledge-field gradient label 141Image region: Group 8: variable legend 142∇H(t) = knowledge-field gradient 143Legibility: Legible 144Editorial mathematical explanation: The gradient describes local variation in a proposed knowledge field H; its coordinates, units and computation are not provided. 145 146RAW OCR READING AID — NOT A VERIFIED EQUATION TRANSCRIPT 147The following preserves the complete Tesseract output, including recognition errors, decorative glyphs and layout artifacts. Use the manually inspected records above and the original PNG for mathematical notation. 148 149UNIFIED AGI EQUATION SYSTEM 150 151“———_ ONE SYSTEM. NINE EQUATION GROUPS. ONE EMERGENT INTELLIGENCE. ———~ 152 153INPUT / 154 155INTEGRATION / 156 157KNOWLEDGE ENCODING 158 159FEDERATION 160 161Mh 162 163(x) = sin(2n-p- 164 165Pru + D Paomain 166 167Sa 168 169+cos(2-p-* 170 1715( AGL 172 173PA) Picea = 174 175EMERGENCE 176 177i 178 179<0) Ka) = Yeh) 8, We(h(q)) 180 181Hub and domain minds are integrated 182 183into a unified information structure. 184 185Queries and signals are encoded into 186 187a harmonic-symbolic knowledge field 188 189a? e 190 191¥v 192 193O 194 195cad 196 197@) 198 199©) LEARNING / PLASTICITY 200 201@) DYNAMICAL EVOLUTION 202 203d, 204 205S) 206 207O 208 2096 210 211Ho 212 213sat = diffusion + transport 214 215Aw; =n (Cj) 216 2176 domains + hub 218 219+ geometric_drift 220 221(-At/r) 222 223(tore = 224 225i) 226 227Tuotat = growth + decay + emergence 228 229¥ 230 231® 232 233+ chaos 234 235Plasticity updates connections so 236 237CONSCIOUSNESS 238 239experience becomes memory and skill 240 241COUPLING 242 243= external_force + field coupling 244 2454 Scat 246 247+ stochastic_noise 248 249—— 250 251W = f(A-X-S) 252 253SUBSTRATE TO 254 255O tropat = gradient_descent + loss_minimization 256 257+ confidence_shaping + reward signal 258 259A 260 261Agency Tensor 262 263CONSCIOUSNESS LATTICE 264 265>| 266 267ie 268 269= Experiential Coupling Lattice 270 271dx 272 273Tl R23” 2, JR5000 274 275S = Substrate Scale 276 277dt 278 279Arotat + Mota + Frotat + brotat 280 281Agency, experience, and substrate 282 283The internal state evolves through 284 285X[i] = meanjep,(s;) 286 287physical-style, adaptive, and 288 28923 million substrate neurons are 290 291combine to produce the conscious 292 293coupling term. 294 295optimization operators 296 297projected into a 5000-dimensional 298 299consciousness lattice. 300 301v 302 3034 304 305AUTONOMOUS OBJECTIVE / 306 307GLOBAL AGI / CONSCIOUS 308 309ACTION POLICY 310 311INTELLIGENCE MEASURE 312 313J = base_objective + exploration_bonus 314 315IVH()II 316 317dt 318 319+ adaptive_theta_term — conflict_penalty 320 321e=v- [cw- 0G) 322 323IVH@)II 324 325— resource_penalty + entropy_regularization 326 327We) C(t) = coherence 328 329— repetition_penalty 330 331Qo 332 333integrated information 334 335The system chooses actions by balancing 336 337AX, VH(t) = knowledge-field gradient 338 339Integrated coherence, information, and field tension 340 341value, exploration, stability, and resource limits. 342 343determine the quality of conscious intelligence 344 345AGI IS THE EMERGENT RESULT OF ENCODED KNOWLEDGE, EVOLVING STATE DYNAMICS, 346 347® 348 349ADAPTIVE PLASTICITY, INTEGRATED FEDERATION, CONSCIOUS COUPLING, AND AUTONOMOUS ACTION. 350 351accel 352 353: 354 355ao 356 357CLOSED-LOOP SYSTEM FLOW 358 359Q) + G+) 360 361@>%) >| OD) >Re) 362 363PERCEPTION 364 365ENCODING 366 367DYNAMICS, 368 369LEARNING 370 371INTEGRATION 372 373AGENCY 374 375ACTION 376 377FEEDBACK 378 379ees 380 381AGI EMERGES WHEN THESE EQUATIONS OPERATE AS A CLOSED ADAPTIVE LOOP. 382 383[cxo} 384 385oe 386 387