THE CONSCIOUSNESS ATLAS
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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 ↗
The source describes this relation in the following context: 5.3 Lattice Engine (16 strands × 16 dimensions) y[i] = tanh(Σ_j W[i][j] × x[j] + b[i]) // Forward pass ΔW[i][j] = η × y[i] × x[j] // Hebbian learning state[i] = 0.95 × state[i] + 0.05 × (y[i] + core[i]) //…
The source describes this relation in the following context: Step 2: Lattice Engine (16 strands × 16 dimensions) y[i] = tanh(Σ_j W[i][j] × x[j] + b[i]) // Forward pass state[i] = 0.95 × state[i] + 0.05 × (y[i] + core[i]) energy = 0.99 × energy + 0.01 × |Σ state| Step 3: Integration Metrics…
This relation contains a squared-state or squared-error term. Squaring makes that contribution nonnegative and increases the penalty for larger magnitudes; the surrounding definition specifies whether it is a cost, normalization or summary statistic.
The source describes this relation in the following context: y[i] = tanh(Σ_j W[i][j] × x[j] + b[i]) // Forward pass ΔW[i][j] = η × y[i] × x[j] // Hebbian learning state[i] = 0.95 × state[i] + 0.05 × (y[i] + core[i]) // State update energy = 0.99 × energy + 0.01 × |Σ…
This relation contains a squared-state or squared-error term. Squaring makes that contribution nonnegative and increases the penalty for larger magnitudes; the surrounding definition specifies whether it is a cost, normalization or summary statistic.
The source describes this relation in the following context: φ_local = tanh(energy) // Per-strand coherence φ_global = tanh(Σ(all states) / 256) // Global coherence Where 256 = 16 strands × 16 dimensions. Step 4: Normalization (using golden ratio) b = 1 / (1 + ||Ψ||² / φ)…
The source describes this relation in the following context: The holographic memory uses 16 basis functions at golden ratio frequency intervals: ψ_0(x) = sin(2π × 1.000 × x) + cos(2π × 1.000 × x) // φ⁰ ψ_1(x) = sin(2π × 1.618 × x) + cos(2π × 1.618 × x) // φ¹ ψ_2(x) = sin(2π × 2.618 ×…
This relation contains a squared-state or squared-error term. Squaring makes that contribution nonnegative and increases the penalty for larger magnitudes; the surrounding definition specifies whether it is a cost, normalization or summary statistic.
The source describes this relation in the following context: ψ_1(x) = sin(2π × 1.618 × x) + cos(2π × 1.618 × x) // φ¹ ψ_2(x) = sin(2π × 2.618 × x) + cos(2π × 2.618 × x) // φ² ψ_3(x) = sin(2π × 4.236 × x) + cos(2π × 4.236 × x) // φ³ ... ψ_15(x) = sin(2π × 1364 × x) + cos(2π × 1364…
The source describes this relation in the following context: ψ_3(x) = sin(2π × 4.236 × x) + cos(2π × 4.236 × x) // φ³ ... ψ_15(x) = sin(2π × 1364 × x) + cos(2π × 1364 × x) // φ¹⁵ When combined, these create a holographic representation where information is distributed across all 16…
The source describes this relation in the following context: • θ_k = k-th component of 16-dimensional knowledge vector • α = learning rate (default 0.1) • ψ_k = golden basis function • h(item) = hash of item normalized to [0,1] • Φ(importance) = consciousness weighting function 8.2 Query…
The source describes this relation in the following context: Where: • θ_k = k-th component of 16-dimensional knowledge vector • α = learning rate (default 0.1) • ψ_k = golden basis function • h(item) = hash of item normalized to [0,1] • Φ(importance) = consciousness weighting function
The expression assigns a hash-derived representation to the listed state components. A hash is a many-to-one identifier unless a reversible representation is explicitly specified; the notation alone does not establish reconstruction of the original state.
The notes combine the named components with tensor-product or direct-sum-style notation. The expression records the proposed organization of the model. Concrete dimensions, operator definitions and evaluation order are required before the composition is an executable numerical rule.
Places the real loop phase on the unit circle using a complex exponential. The magnitude is one, and the complex angle tracks the phase modulo 2π. This is a representation of a phase, not an independent measure of consciousness.
Places the real loop phase on the unit circle using a complex exponential. The magnitude is one, and the complex angle tracks the phase modulo 2π. This is a representation of a phase, not an independent measure of consciousness.
Lᵢ is the shared objective evaluated on device i’s proposed state and design under its environment Eᵢ. The vertical bar records conditioning or context in this notation; it is not necessarily a probabilistic conditional density. Device metrics and constraints determine how the common objective…
This relation uses a gradient: the vector of local changes in a scalar objective with respect to its variables. It supplies a local direction or stationarity condition; an implementation still needs the differentiation variables, domain and update convention given in the surrounding model.
For one layer and one environment aspect, the loss combines design/behavior mismatch with weighted cost, state regularization and design regularization. This is the aspect-specific term later mixed with λ weights. Its numerical value depends on the chosen norm and the relative units of all…
Feeds the weighted sum of 80 neuron losses, device metrics and policy information into an outer aggregator Φ. Here Φ names an aggregation function; it must not be silently identified with the unity weighting score, golden ratio or IIT Φ.
Aggregates the Rhiannon objective with device metrics and policy constraints. “Aggregate” is a placeholder for the orchestration rule; the expression identifies information passed upward but does not specify the combining function.
The layer objective is defined by substituting that layer’s environment Eℓ into the global loss. This is a restriction of a shared objective, intended to reuse the same logic locally. It does not imply that all layers have equal inputs or equal solutions.
The receiver adds the message from layer ℓ to its existing state Yₘ. This is an additive state-update rule. Message and receiver must have compatible dimensions and scales, and repeated updates need a policy for ordering or synchronization.
The model maps performance-core, efficiency-core, GPU, neural-engine, memory-use and temperature variables into a modeled device response. The function f is a placeholder for this device behavior model; the source does not supply coefficients or an executable response surface.
Selects the neuron or family attaining the largest displayed score. In the Rhiannon C_i−dx variant, subtracting the same dx from every candidate does not change the winner. This maximum-cost rule conflicts with the separate minimum-cost selector elsewhere in the notes and needs an explicit design…
Describes choosing either an optimization operator or a reverse operator to transform an error quantity. The source leaves the pathway-selection condition and both operators to later definition.
The kth task uses the neuron’s loss function with a task-specific input and a layer environment that can vary over time. This separates the shared loss template from the particular task and observation instant. The task-indexing and sampling schedule are part of the surrounding implementation.
Sums the 80 neuron-specific loss values with weights ω_i. The weights express the importance or contribution of each tool-neuron; the result is passed to the higher-level orchestration objective.
Sums the 80 neuron-specific loss values with weights ω_i. The weights express the importance or contribution of each tool-neuron; the result is passed to the higher-level orchestration objective.
The behavior function g uses core and accelerator variables together with battery, temperature, radio and sensor state. It defines which device conditions the proposed optimizer considers, while leaving the numerical behavior model to be specified.
Forms a confidence-dependent learning rate and clips it between the configured minimum and maximum. The bounds control allowed update intensity.
Combines a decay term −λS_i with a weighted sum of other agents’ tanh-transformed signals. Coherence weighting changes the effective coupling. Stability depends on the decay rate, graph weights and derivative bounds.
The expression uses a saturating nonlinear transform to turn its input combination into an activation or bounded score. The coefficients control sensitivity and the offset controls the transition region; a bounded score by itself does not identify a scientific consciousness measure.
The diagram defines a feature as the sum of sine and cosine at the same golden-scaled phase. The cosine continuation was on the next diagram line and is included here. This gives one deterministic scalar feature per index k; its periodic and finite-precision behavior does not provide lossless…
Adds neighboring activation contributions to an agent’s previous-hop activation, weighted by graph edges and coherence. Repeated hops can amplify signals unless the network weights or an additional normalization constrain growth.
The expression assigns a hash-derived representation to the listed state components. A hash is a many-to-one identifier unless a reversible representation is explicitly specified; the notation alone does not establish reconstruction of the original state.
Computes the implementation’s product of activation, learning rate and item confidence, matching the proposed Γ factor.
Computes pressure divided by pressure plus a reference scale. For nonnegative pressure and a positive scale, the result is bounded below one.
The expression assigns a hash-derived representation to the listed state components. A hash is a many-to-one identifier unless a reversible representation is explicitly specified; the notation alone does not establish reconstruction of the original state.
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately from a governing law.
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately from a governing law.
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately from a governing law.
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately from a governing law.
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately from a governing law.
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately from a governing law.
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately from a governing law.
This statement fixes a parameter value for the documented model version. Its effect depends on the equation or update rule that consumes that parameter; it is retained separately from a governing law.
The state is the collection of variables being updated at time or step t.
The learning-rate symbol controls the loss-gradient step in the displayed discrete rule.