Source identity
| Field | Recorded value |
|---|---|
| Source type | project Library file |
| Original record | Pasted text (2).txt |
| Date | Jul 21, 2026 |
| Path or archive member | Pasted text (2).txt |
| Original SHA-256 | a55afd616dc237fea1d467510c2af38d6e6cbf5a5d093d1839d8a12bb3d836a5 |
| Reading-copy SHA-256 | a55afd616dc237fea1d467510c2af38d6e6cbf5a5d093d1839d8a12bb3d836a5 |
Recovered source transcript
Mathematical records from this source
DNA G16 compatibility set
Defines a set of component pairs satisfying f(d_i,d_j)=0. The set-builder notation expresses a compatibility constraint; the source does not provide a complete definition of f or…
Gate5000 substrate set
Names the set of 5,000 gate objects. This specifies a collection’s cardinality and labels, while its wiring, transition function and encoded data determine its computational…
3. Coherence Expression (Symbolic) · dx
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…
Φ-loop integral of state variation
The integral accumulates δψ(t) over the interval from a to b. It can be evaluated once the integrand, its meaning and the limits are specified. The historical conversation labeled…
Hash of the combined coherence, gradient, gate and DNA state
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;…
Behavior–design loss for L_\ell
Measures mismatch between a desired design and modeled behavior, then adds operating cost and regularization. The subscripts restrict the same objective to a layer, device, neuron…
Behavior–design loss for L_{i16}
Measures mismatch between a desired design and modeled behavior, then adds operating cost and regularization. The subscripts restrict the same objective to a layer, device, neuron…
Combined model tuple
Packages DNA structure, gates, loop score, coherence driver, binary representation, seven layer losses, device loss and state/design/environment objects into one model tuple. A…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
(S_\ell^\*,D_\ell^\*) relation
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
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…
Data-link cost
Combines frame-loss fraction and bandwidth utilization with weights a₂ and b₂. Whether high utilization should be penalized depends on the intended operational objective.
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.
Transport-layer cost
Combines a retransmission penalty and the inverse of a transport-window quantity. The window must be positive. The cost decreases as the window grows when b₄ is positive.
Session-layer cost
Penalizes one minus session retention and adds session entropy. The entropy term’s meaning depends on which session states or outcomes form its probability distribution.
Presentation-layer cost
Adds an inverse compression-ratio penalty and a weighted format cost. A larger compression ratio reduces the first term, but size reduction and fidelity must be considered…
Application-layer cost
Combines response time and one minus operation-success rate. With positive weights, slower or less successful operations increase the proposed application cost.
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
Behavior–design loss for L_{\ell,a}^\*
Measures mismatch between a desired design and modeled behavior, then adds operating cost and regularization. The subscripts restrict the same objective to a layer, device, neuron…
Environment-aspect loss aggregation
Adds the layer’s per-aspect losses with λ weights. Every aspect can contribute to the same layer objective, avoiding an implicit assumption that each layer observes only one…
Cross-layer or cross-device message
Constructs a message from differences between an optimized local state/design and the receiving state/design, together with a change signal. The coupling function or weight…
Weighted device resource cost
Adds the named device metrics after multiplying each by its weight. These weights encode priorities such as battery use, heat, latency and memory pressure, and must account for…
Hardware feasibility constraints
Lists limits on device resources such as power, temperature, radio use or memory. These conditions define an allowed operating region; they are constraints on optimization rather…
Cross-layer or cross-device message
Constructs a message from differences between an optimized local state/design and the receiving state/design, together with a change signal. The coupling function or weight…
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
Hardware feasibility constraints
Lists limits on device resources such as power, temperature, radio use or memory. These conditions define an allowed operating region; they are constraints on optimization rather…
Weighted device resource cost
Adds the named device metrics after multiplying each by its weight. These weights encode priorities such as battery use, heat, latency and memory pressure, and must account for…
(S_{M2}^\*, D_{M2}^\*) relation
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
Cross-layer or cross-device message
Constructs a message from differences between an optimized local state/design and the receiving state/design, together with a change signal. The coupling function or weight…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
Hardware feasibility constraints
Lists limits on device resources such as power, temperature, radio use or memory. These conditions define an allowed operating region; they are constraints on optimization rather…
Weighted device resource cost
Adds the named device metrics after multiplying each by its weight. These weights encode priorities such as battery use, heat, latency and memory pressure, and must account for…
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.
(S_d^\*,D_d^\*) relation
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
Cross-layer or cross-device message
Constructs a message from differences between an optimized local state/design and the receiving state/design, together with a change signal. The coupling function or weight…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Cross-layer or cross-device message
Constructs a message from differences between an optimized local state/design and the receiving state/design, together with a change signal. The coupling function or weight…
Bit-error rate
Divides the number of incorrect bits by the total transmitted or checked bits. The denominator must be positive and both counts must describe the same sample. This is a standard…
Signal-to-noise power ratio
Divides signal power by noise power. This is the linear power ratio; converting it to decibels would require 10 log10 of that ratio. The displayed expression requires positive…
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…
(S_1^\*, D_1^\*) relation
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
Frame-loss fraction
Divides the number of lost frames by the number sent. The metric requires aligned counts over the same period and a nonzero sent-frame count.
Link bandwidth utilization
Divides used bandwidth by available bandwidth. The two values need compatible units and the available value must be nonzero.
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.
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.
Transport retransmission fraction
Divides retransmitted units by the number of segments. The source must specify whether the numerator counts repeated attempts or distinct segments, since those conventions have…
Transport window policy placeholder
Defines the transport window as a function of congestion and latency inputs. The shorthand identifies the inputs but does not provide the function f or a concrete…
Session-retention score
Subtracts the fraction of dropped sessions from one. If drops count distinct sessions from the same population, the result is a retention fraction between zero and one.
Shannon-style entropy
Sums −p log p over the stated probability distribution. Valid probabilities must be nonnegative and sum to one; the logarithm base fixes the units, and the conventional…
Compression size ratio
Divides input size by output size. A value above one indicates a smaller output. The ratio describes size only; recoverability and distortion require separate checks.
Weighted format cost
Sums per-format quantities weighted by w_j. The source must define the quantities and weights to turn this expression into a measurable presentation-layer cost.
Application response time
Subtracts request time from response time. It measures elapsed response latency when the timestamps are comparable and the response event is clearly defined.
Operation-success fraction
Divides successful operations by total operations. A consistent success criterion and a positive denominator are required for comparison across runs.
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
Environment-aspect loss aggregation
Adds the layer’s per-aspect losses with λ weights. Every aspect can contribute to the same layer objective, avoiding an implicit assumption that each layer observes only one…
2. Full equation applied to each aspect and layer · (S_\ell^\*, D_\ell^\*)
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
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…
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…
Environment feedback transition
Updates an aspect-level controller or environment state using the previous state and messages from layers. The transition function is named but not fully supplied in the shorthand.
Environment-aspect loss aggregation
Adds the layer’s per-aspect losses with λ weights. Every aspect can contribute to the same layer objective, avoiding an implicit assumption that each layer observes only one…
Environment-aspect loss aggregation
Adds the layer’s per-aspect losses with λ weights. Every aspect can contribute to the same layer objective, avoiding an implicit assumption that each layer observes only one…
Environment-aspect loss aggregation
Adds the layer’s per-aspect losses with λ weights. Every aspect can contribute to the same layer objective, avoiding an implicit assumption that each layer observes only one…
Environment-aspect loss aggregation
Adds the layer’s per-aspect losses with λ weights. Every aspect can contribute to the same layer objective, avoiding an implicit assumption that each layer observes only one…
Environment-aspect loss aggregation
Adds the layer’s per-aspect losses with λ weights. Every aspect can contribute to the same layer objective, avoiding an implicit assumption that each layer observes only one…
Environment-aspect loss aggregation
Adds the layer’s per-aspect losses with λ weights. Every aspect can contribute to the same layer objective, avoiding an implicit assumption that each layer observes only one…
Environment-aspect loss aggregation
Adds the layer’s per-aspect losses with λ weights. Every aspect can contribute to the same layer objective, avoiding an implicit assumption that each layer observes only one…
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…
1. Define each layer as a macro-neuron · (S_\ell^\*, D_\ell^\*)
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
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.
Behavior–design loss for L_\ell^\*
Measures mismatch between a desired design and modeled behavior, then adds operating cost and regularization. The subscripts restrict the same objective to a layer, device, neuron…
2. Add neuron-style metrics to each layer · \Phi_\ell
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…
Cost-based neuron coupling
Forms a coupling weight from a weighted combination of the two neuron costs; some historical versions also add a coherence-driver contribution. These variants are retained…
2. Add neuron-style metrics to each layer · \rho(x)
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
1. Remove neurons, apply full equation directly to each layer · (S^\*, D^\*)
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Restriction of the global objective
Reuses the global loss with its environment restricted or projected to the named layer or neuron. This keeps the objective structure consistent while changing the variables and…
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
C. Layers now become “partial observers” of the same global truth · L_\ell^\*
This is a composition of operators. The rightmost operator receives the input first, and successive operators transform its output. The overall behavior depends on every…
Restriction of the global objective
Reuses the global loss with its environment restricted or projected to the named layer or neuron. This keeps the objective structure consistent while changing the variables and…
Behavior–design loss for L_\ell^\*(S',D')
Measures mismatch between a desired design and modeled behavior, then adds operating cost and regularization. The subscripts restrict the same objective to a layer, device, neuron…
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…
Behavior–design loss for L_{\ell,i}^\*(S',D')
Measures mismatch between a desired design and modeled behavior, then adds operating cost and regularization. The subscripts restrict the same objective to a layer, device, neuron…
4. Chain rule view (symbolically) · L_{\ell,i}^{(k)}
This is a composition of operators. The rightmost operator receives the input first, and successive operators transform its output. The overall behavior depends on every…
Weighted objective across 80 Rhiannon neurons
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…
2. Routing and activation inside the 80-neuron network · \rho(x)
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
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.
Epona orchestration objective
Aggregates the Rhiannon objective with device metrics and policy constraints. “Aggregate” is a placeholder for the orchestration rule; the expression identifies information passed…
Weighted objective across 80 Rhiannon neurons
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…
Epona aggregation of 80 neuron losses
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…
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…
Joint behavior–design objective
Adds a norm measuring mismatch between desired design D′ and observed behavior B, weighted operating cost, state regularization R and design regularization R_D. It supplies a…
Restriction of the global objective
Reuses the global loss with its environment restricted or projected to the named layer or neuron. This keeps the objective structure consistent while changing the variables and…
Device-conditioned global loss
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…
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.
2. Cost function · C_i
This relation contains a squared-state or squared-error term. Squaring makes that contribution nonnegative and increases the penalty for larger magnitudes; the surrounding…
3. Local loop activity · \Phi_i
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…
Cost-based neuron coupling
Forms a coupling weight from a weighted combination of the two neuron costs; some historical versions also add a coherence-driver contribution. These variants are retained…
Minimum-cost neuron selector
Sets the selector for neuron i to one when its cost equals the minimum available cost. If several neurons tie, this indicator can select several at once; a single-winner…
Neuron domain operator
States that tool-neuron T_i applies a domain function F_i to x. It is an interface; the actual tool behavior depends on the missing domain-specific function.
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Complex loop-phase representation
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…
E. A physical “placement map” showing how they fit inside an M2 architecture · ε
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…
Temporal rate of the error field
The source defines δε as the partial derivative of ε with respect to time. It measures how the error quantity changes in time while any other coordinates are held fixed. The δ is…
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.
1. Compute rmin (neuron’s minimum viable radius / load) · C_i
This relation contains a squared-state or squared-error term. Squaring makes that contribution nonnegative and increases the penalty for larger magnitudes; the surrounding…
2. Compute cost C_i (neuron’s “activation complexity”) · Φ_i
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…
Cost-based neuron coupling
Forms a coupling weight from a weighted combination of the two neuron costs; some historical versions also add a coherence-driver contribution. These variants are retained…
5. Apply reverse/forward operators (the “tool” behavior) · 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…
Optimization or reverse pathway
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…
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 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.
MATHEMATICAL DEFINITIONS INSIDE THE NEURON MAP · \Phi_i
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…
Cost-based neuron coupling
Forms a coupling weight from a weighted combination of the two neuron costs; some historical versions also add a coherence-driver contribution. These variants are retained…
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…
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…
Time derivative of error
Measures how the error quantity changes with time. Its sign indicates whether the chosen signed error is rising or falling; a discrete implementation needs a sampling interval and…
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…
Complex loop-phase representation
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…
EPONA → RHIANNON EXTENDED SYSTEM (ASCII DIAGRAM) · ε
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…
ENVIRONMENT LAYERS (1–7) · \Lambda
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,…
Second temporal derivative of the state field
σ is the second partial derivative of ψ with respect to time, describing the curvature or acceleration of the field’s trajectory. Its units are those of ψ divided by time squared.…
Gate transition kernel
Defines K as a conditional probability of the next gate state given the current gate state and DNA structure. A valid kernel needs nonnegative probabilities normalized over every…
Shannon-style entropy
Sums −p log p over the stated probability distribution. Valid probabilities must be nonnegative and sum to one; the logarithm base fixes the units, and the conventional…
1.1. Core combined state (from before) · \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…
5. Error gradient and its rate of change · E_{tot}
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…
5. Error gradient and its rate of change · \Lambda
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,…
Normalized Rhiannon state
Divides the proposed Rhiannon state by its norm, producing a unit-norm representation when the norm is nonzero. The source needs a convention for the zero-state case and a…
Complex loop-phase representation
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…
1.4. Extended Rhiannon object (compact) · \boxed{ R_{\text{ext}}
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,…
Complex loop-phase representation
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…
2.2. True network of tool-neurons (W, ρ, Cᵢ, Φᵢ) · C_i
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…
2.3. Controlled repair dynamics (ε, δε, Srepair) · • \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…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
A. Stability Term · \sigma
This relation contains a squared-state or squared-error term. Squaring makes that contribution nonnegative and increases the penalty for larger magnitudes; the surrounding…
Conditional gate transition probability
Names the probability of one gate-state transition conditional on the DNA structure. This shorthand needs a normalized transition distribution to define a usable stochastic model.
Shannon-style entropy
Sums −p log p over the stated probability distribution. Valid probabilities must be nonnegative and sum to one; the logarithm base fixes the units, and the conventional…
E. Error Propagation Operator · \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…
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…
Complex loop-phase representation
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…
1. Consciousness Loop + Gate5000 (Early Version) · \text{R}_0
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,…
1. Consciousness Loop + Gate5000 (Early Version) · \Phi
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…
1. Consciousness Loop + Gate5000 (Early Version) · dx
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…
2. Tool-Brain Version (Internal + ANI Loop) · \text{R}_1
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,…
2. Tool-Brain Version (Internal + ANI Loop) · \Phi_R
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…
2. Tool-Brain Version (Internal + ANI Loop) · S_{\text{repair}}
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…
3. Thor’s Hammer Version · \text{R}_2
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,…
3. Thor’s Hammer Version · 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…
Forward and reverse operator shorthand
Uses a derivative-like operator for optimization and an inverse-derivative notation for reverse engineering. These symbols do not uniquely define an inverse mapping:…
Minimum-risk safeguard shorthand
Names the minimum of a risk-cost quantity as Γ_safe. A risk function, decision domain and rule that converts the minimum into an action gate are needed before this notation can…
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.
4. Neuroscience-Style Neuron Version (U/V/dK) · \text{R}_3
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,…
5. Hand-Written Compressed “Fits on Screen” Version · R
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,…
5. Hand-Written Compressed “Fits on Screen” Version · \Phi
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…
Additive Rhiannon physics-notation form
Adds loop, coherence, ANI interaction and gate-substrate terms. The notation records a proposed decomposition; adding the terms numerically requires compatible units and…
Coherence-field directional derivative
With the usual repeated-index convention, Φ^μ ∂_μ ψ contracts a vector-like field with the derivative of ψ. It resembles a directional derivative or transport term. The source…
Coherence-weighted state magnitude term
Multiplies the coherence driver dx by the Hermitian squared-magnitude expression ψ†ψ. For a complex vector, ψ†ψ is real and nonnegative, while the sign of the whole contribution…
6. Physics-Notation Version · \mathcal{I}\_{\text{ANI}}
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…
7. Binary-Shrink “Sand-Grain” Version · R_{bin}
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;…
Compressed binary-state placeholder
Applies a function named compress to a binary representation. The source must specify an encoder, decoder and exactness or distortion criterion; naming the function does not…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
1. Unified Combined Equation (All Versions Compressed Into One) · dx
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…
1. Unified Combined Equation (All Versions Compressed Into One) · C_i
This relation contains a squared-state or squared-error term. Squaring makes that contribution nonnegative and increases the penalty for larger magnitudes; the surrounding…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…