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 ↗
Layer or device behavior mapping
Defines the mapping from local inputs to behavior, an optimized state, or its associated minimized cost. The source-specific function and environment determine the returned value.
Layer or device behavior mapping
Defines the mapping from local inputs to behavior, an optimized state, or its associated minimized cost. The source-specific function and environment determine the returned value.
Layer or device behavior mapping
Defines the mapping from local inputs to behavior, an optimized state, or its associated minimized cost. The source-specific function and environment determine the returned value.
Layer sensitivity to an environment aspect
Uses a partial derivative of the layer loss with respect to an environment aspect as a sensitivity message. The derivative describes local effect on the objective; it does not itself specify a physical action.
Layer sensitivity to an environment aspect
Uses a partial derivative of the layer loss with respect to an environment aspect as a sensitivity message. The derivative describes local effect on the objective; it does not itself specify a physical action.
Layer sensitivity to an environment aspect
Uses a partial derivative of the layer loss with respect to an environment aspect as a sensitivity message. The derivative describes local effect on the objective; it does not itself specify a physical action.
Layer-neuron joint state–design minimization
For each layer, the selected state and design minimize behavior–design mismatch, weighted operating cost, state regularization and design regularization. The same environment is visible to every layer in this version. A shared objective form does not guarantee identical optima when layer-specific…
Learning-drive product
Scales learning by the product of activation, plasticity and confidence. The product couples readiness to learn with rate and evidence strength.
Link bandwidth utilization
Divides used bandwidth by available bandwidth. The two values need compatible units and the available value must be nonzero.
Local loss inherited from the global loss
This line states the intended relationship between a layer’s loss and the global objective. The right-hand side is descriptive text, so a numerical implementation still needs the restriction, projection or substitution that converts the global loss into the local one.
Loss-threshold active-neuron set
Includes each neuron whose conditional loss does not exceed threshold τ. This can activate multiple neurons and requires losses that are comparable across them.
MATHEMATICAL DEFINITIONS INSIDE THE NEURON MAP · M_{env}
The relation accumulates its integrand over the stated interval or closed loop. The result depends on the integrand, integration variable, limits and trajectory. In the archived notes, a loop integral represents the intended accumulation of state or error change; its consciousness interpretation…
MATHEMATICAL DEFINITIONS INSIDE THE NEURON MAP · \epsilon
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.
Maximum structural requirement
Takes the largest of the source’s U, V and dK structural parameters. This maximum becomes the dimension-like requirement used in the proposed neuron-cost expression.
Maximum structural requirement
Takes the largest of the source’s U, V and dK structural parameters. This maximum becomes the dimension-like requirement used in the proposed neuron-cost expression.
Maximum structural requirement
Takes the largest of the source’s U, V and dK structural parameters. This maximum becomes the dimension-like requirement used in the proposed neuron-cost expression.
Maximum-score routing rule
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…
Maximum-score routing rule
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…
Mind as self-coherence: conceptual limit
The source proposes that a recursively evaluated coherence score approaching perfect prediction should correspond to a mind. The expression names coherence, prediction and an error limit, but it does not define a measurable equivalence between the mathematical limit and experience. It is preserved…
Nested nine-filter coherence operator
Applies temporal, Bayesian-named, perceptual, predictive, distributed, pairing, helix, layer and logic filters in sequence, starting with the innermost temporal filter. This is the nested-function form of the source’s operator composition.
Network latency difference
Subtracts send time from receive time. This measures elapsed time only if the timestamps use a common synchronized time reference or an equivalent one-clock measurement.
Network-layer cost
Combines latency and normalized queue congestion. Its weights determine the tradeoff between time and occupancy; they also resolve the units of the summed terms.
Neuron-specific restriction of a layer loss
The loss for neuron i in layer ℓ is the layer loss evaluated with that neuron’s structural/input parameter Uᵢ and the environment slice Eℓ. This specialization is intended to retain one objective structure while changing the local inputs. It does not supply the missing form of the global loss or…
Nine-filter coherence composition
The state x, belief p and observation y pass through nine operators. Temporal processing appears on the right, followed by the Bayesian-named, perceptual, predictive, distributed, pairing, helix, layer and logic filters. Composition means that each filter acts on the previous result. The formula…
Normalized existing substrate coherence
Divides a substrate’s current coherence by the sum of all coherences plus ε. For nonnegative coherence and positive ε this is finite and emphasizes already established substrates.
Normalized learning pressure
Maps pressure Ψ to Ψ/(Ψ+ψ₀). For Ψ≥0 and ψ₀>0 it increases from zero toward one, reducing the influence of extreme pressure values.
Normalized queue occupancy
Divides current queue length by maximum queue length. It measures occupancy relative to capacity, with units canceling when the lengths share the same definition.
Novelty decay update
Multiplies the stored novelty by 0.99 at each application. After n repeated updates with no other changes, the retained novelty is 0.99^n times its original value.
Novelty weight ν
ν is the novelty factor used in allocating learning to substrate candidates. The source says brand-new substrates should be downweighted until stable, so this quantity serves a gating role rather than an automatic novelty reward. The mapping from observations to ν and the definition of stability…
Operation-success fraction
Divides successful operations by total operations. A consistent success criterion and a positive denominator are required for comparison across runs.
Physical-layer cost
Adds a bit-error penalty and an inverse signal-to-noise penalty. Better signal quality reduces the second term. SNR must be positive, and weights must put unlike quantities on an appropriate shared scale.
Physical-layer cost
Adds a bit-error penalty and an inverse signal-to-noise penalty. Better signal quality reduces the second term. SNR must be positive, and weights must put unlike quantities on an appropriate shared scale.
Power-sharpened allocation distribution
Raises each nonnegative allocation to power γ and renormalizes. For γ>1 this concentrates relative mass on larger entries. The denominator must remain positive; an all-zero vector needs a fallback.
Reported final state of the 5,000-tick run
The archived session reports these final diagnostic values after a 5,000-tick run. They describe that recorded run and do not establish the present runtime state.
Resource-intensive intelligence: rhetorical comparison
The original conversation groups spending, data centers, research staff and commercial barriers under an intelligence label. The plus signs form a rhetorical list and do not define quantities that can be added in a scientific model.
STAGE 4: COMPETITION SHARPENING + NORMALIZE · 2. Compute activation: χ
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.