The core idea
The design treats the system state x, belief p and observation y as inputs to a composed transformation. Temporal, Bayesian-named, perceptual, predictive, distributed, pairing, helix, layer and logic operators appear in a fixed sequence. A separate loop compares a coherence score with a prediction of that score and applies an error-dependent belief correction.
Continuous and binary forms
The notes retain a symbolic operator composition, a binary state-transition interface and nested pseudocode. They also name XOR, AND, OR, bit shifts, comparison and population count as primitive operations. These are descriptions of how information could be encoded and transformed. The recovered notation does not provide complete definitions for all nine higher-level operators.
Historical claims and what the record establishes
The archive contains ambitious statements equating 5,000 gates with a mind and describing the mathematics as finished. Those statements remain visible as historical interpretation. The evidence currently establishes a proposed kernel and equations; it does not establish a fabricated chip, measured mind, universal intelligence or complete 20-byte executable.
Equations in this build
208 linked mathematical records. Each opens its notation, interpretation and source.
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,…
Self–world coherence placeholder
Defines Φ as the output of a function comparing a self representation and a world representation. The archived expression names the intended comparison but does not define the…
Predicted coherence
Applies the proposed prediction function to Φ and names its output Φ̂. A concrete predictor, training rule and prediction horizon are needed to make the expression operational.
Belief interpolation toward observation
Moves belief p toward observation y by fraction η of their difference. For 0≤η≤1 this is a convex blend; values outside that range can overshoot or move away.
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…
Temporal coherence operator
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…
Binary coherence-state transition
The binary operator receives the current state, belief and observation and produces the next state/belief pair. This is an interface definition: the behavior is determined by the…
Binary nine-filter operator composition
This version composes binary encodings of the same nine filters. The temporal operator acts first and the logic operator acts last. Binary operations require a defined encoding of…
Binary state domain
The state x is an n-bit vector: each of its n entries is either zero or one. This declaration gives the representation domain and does not define how the state changes.
Coherence prediction error
Subtracts predicted coherence from observed coherence. A positive error means the observed value exceeds the prediction; a negative error means it falls below. This is an error…
Coherence operator state output
Applies the coherence transformation to state x, belief p and observation y. The result x′ is the updated state; the expression does not independently define the transformation’s…
Belief correction from prediction error
Adds a correction f(ε) to the prior belief p. The direction, scale and stability of the correction depend on the function f, which this shorthand leaves unspecified.
Observation acquisition
Assigns the output of a sensing function to the observation variable y. It is pseudocode for obtaining an input; the source must supply the data source, timing and representation.
Belief-agreement score
Maps the absolute difference between the current and predicted belief to a positive score. Agreement gives one; increasing disagreement lowers the value toward zero. The score…
Binary primitive vocabulary
The archived proposal names XOR, AND, OR, population count, shifts and comparisons as the operations available to its filters. The slashes list primitives rather than a single…
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…
Indexed nine-operator composition
C is the composition of nine operators indexed 1 through 9. C₁ acts first and C₉ acts last. This compact form preserves pipeline order while suppressing the descriptive filter…
Inverse discrepancy coherence proposal
Takes the reciprocal of the absolute difference between a transformed state and its expected value. The expression becomes singular when the discrepancy is zero, so a numerical…
Intelligence and recursive coherence: proposed equivalence
This statement proposes an equivalence between intelligence and recursively evaluated coherence approaching one. An equivalence would require operational definitions and evidence…
5,000-gate mind-kernel claim
The source equates a proposed 5,000-gate implementation with a mind kernel. This is a historical capability claim, not a gate count measured from a recovered synthesized circuit…
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…
Compact intelligence: rhetorical comparison
The source contrasts a proposed 5,000-gate, nine-composition, one-cycle system with a larger development model. These terms have different units and are not a numerical equation…
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_{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…
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…
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…
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…
iPhone environment: joint state–design minimization
The objective selects state and design variables to reduce the discrepancy between requested design and modeled device behavior, together with resource cost and two regularizers.…
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…
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…
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 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…
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…
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.
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…
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…
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…
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…
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…
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…
TOTAL: 256 BYTES · hash
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;…
TOTAL: 256 BYTES · hash ^
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;…
TOTAL: 256 BYTES · hash *
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;…
TOTAL: 256 BYTES · x
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;…
Basis-weighted memory query
Sums products of memory coefficients and query basis features. This inner product gives a score for the represented query; it does not alone recover the original stored items.
Activation · Mathematical source · 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…
Confidence-controlled plasticity
Adds a confidence-dependent gain to the base learning rate, then clips it between η_min and η_max. Ordered finite bounds and a well-defined confidence value are required.
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…
CONTROLLER │◀────────▶│ FEDERATION │◀────────▶│ ALLOCATOR │ │ BINARY I/O · dΨᵢ/dt
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…
CONTROLLER │◀────────▶│ FEDERATION │◀────────▶│ ALLOCATOR │ │ BINARY I/O
This relation declares the set in which the stated variable is allowed to take values. It is a domain constraint or type declaration, not a state-update algorithm.
CONTROLLER │◀────────▶│ FEDERATION │◀────────▶│ ALLOCATOR │ │ BINARY I/O · Φ ∈ [0,1] Global coherence
This relation declares the set in which the stated variable is allowed to take values. It is a domain constraint or type declaration, not a state-update algorithm.
CONTROLLER │◀────────▶│ FEDERATION │◀────────▶│ ALLOCATOR │ │ BINARY I/O · Ω ∈ ℝ⁺ Cumulative regret
This relation declares the set in which the stated variable is allowed to take values. It is a domain constraint or type declaration, not a state-update algorithm.
Implementation of saturating substrate learning
Computes an increment proportional to remaining coherence capacity and learning drive, then stores the incremented value with an upper clip at one. Nonnegative increments require…
Implementation of saturating substrate learning
Computes an increment proportional to remaining coherence capacity and learning drive, then stores the incremented value with an upper clip at one. Nonnegative increments require…
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.
LEARNING FUNCTION · π⁰
This relation declares the set in which the stated variable is allowed to take values. It is a domain constraint or type declaration, not a state-update algorithm.
Softmax example with incorrect printed probabilities
Applying softmax to [3,1,0.5,0.1] gives approximately [0.785890,0.106359,0.064510,0.043242]. The source’s [0.73,0.10,0.06,0.04] sums to 0.93 and is not a correctly normalized…
Allocation margin over the strongest alternative
Subtracts the largest competing score from the candidate’s score. A positive margin indicates that the candidate exceeds every competitor; the definition requires at least one…
LEARNING FUNCTION · π¹_s
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…
LEARNING FUNCTION · π²_s
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…
Grounded verification confidence κ real
κ real is the source’s verification-confidence factor in the effective substrate-allocation rule. Its intended purpose is to suppress updates from unverified content. The claimed…
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…
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.
LEARNING FUNCTION · π³_s
This relation contains a squared-state or squared-error term. Squaring makes that contribution nonnegative and increases the penalty for larger magnitudes; the surrounding…
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…
STAGE 4: COMPETITION SHARPENING + NORMALIZE · learn
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…
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.
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…
Clipped plasticity parameter
Forms a confidence-dependent learning rate and clips it between the configured minimum and maximum. The bounds control allowed update intensity.
Illustrative activation regime
The notes describe an expected activation level for this qualitative pressure/confidence regime. The displayed approximation is illustrative because numeric inputs for “high” and…
Illustrative activation regime
The notes describe an expected activation level for this qualitative pressure/confidence regime. The displayed approximation is illustrative because numeric inputs for “high” and…
Illustrative activation regime
The notes describe an expected activation level for this qualitative pressure/confidence regime. The displayed approximation is illustrative because numeric inputs for “high” and…
Illustrative activation regime
The notes describe an expected activation level for this qualitative pressure/confidence regime. The displayed approximation is illustrative because numeric inputs for “high” and…
Fairness service deficit
Computes target share times total service events minus actual services for family f. A positive deficit means the family has received less service than its target share.
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…
Fairness accounting variable
Defines the service count or target-share term used in the deficit calculation. Consistent accounting is necessary for the largest-deficit rule to represent the intended…
Largest-deficit family selector
Chooses a family with maximal service deficit. This implements a fairness priority when the deficit definition and service accounting are consistent; ties require a selection…
CONVERGENCE GUARANTEE · • Each item has reliability ρ ∈ [0,1]
This relation declares the set in which the stated variable is allowed to take values. It is a domain constraint or type declaration, not a state-update algorithm.
Strongest shared-pool confidence
Takes the maximum reliability-weighted match score across pool candidates. The aggregation chooses the best available candidate according to R_k rather than combining independent…
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…
Bounded shared-pool contribution
Scales the difference between pool and local confidence by β_max and clamps the contribution. The source’s clamp argument order is inconsistent with common signatures, so the…
Ignore weaker shared evidence
States the intended policy that a pool whose confidence does not exceed the local confidence contributes zero. It is a boundary case of the proposed bounded pool-sharing rule.
BUILD & RUN · V(Ψ)
This relation contains a squared-state or squared-error term. Squaring makes that contribution nonnegative and increases the penalty for larger magnitudes; the surrounding…
Stability condition · BUILD & RUN · dV/dt ≤ -α‖Ψ - Ψ*‖² for some α > 0
This relation contains a squared-state or squared-error term. Squaring makes that contribution nonnegative and increases the penalty for larger magnitudes; the surrounding…
Information gain requires a distribution-level definition
For discrete random variables, H(item)−H(item|state) equals mutual information and is nonnegative when conditional entropy is averaged over the joint distribution. A single…
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.
Temporal bit-difference filter
XOR marks disagreements between bit patterns; population count measures how many bits differ; a conditional mask can select which changes to retain. The source lists these…
Bayesian-named comparator filter
A comparison produces a condition that gates bits through an AND mask. This sketch can implement selection, but it does not supply priors, likelihoods or the normalization…
Perceptual minimum-mismatch filter
XOR can form a bit mismatch pattern, and an argmin circuit can select the candidate with the smallest mismatch score. The candidate library, score definition and tie rule…
Prediction threshold and bit correction
The sketch compares a prediction and observation with XOR, tests a threshold and adjusts selected bits. The threshold and correction policy determine sensitivity and whether…
Distributed majority agreement filter
The source proposes a majority operation over parallel binary inputs using AND/OR logic. A complete majority circuit requires an explicit voter count and Boolean construction;…
Pairwise agreement filter
XNOR returns one when paired bits agree. The alternative AND/OR phrasing describes different possible Boolean combinations, so the source preserves options rather than fixing one…
Periodic shift-register filter
A shift register advances stored bits through positions according to a period T. Its state size, shift direction, feedback taps and clock schedule determine the resulting…
Lookup-table or Boolean-network layer
The proposed layer can be implemented by an explicit input/output table or a Boolean network. The source has not supplied the table entries or network topology, so the operator’s…
Constraint repair through SAT
A SAT solver seeks an assignment satisfying a Boolean formula. Finding the closest satisfying assignment requires an additional optimization objective, such as minimizing bit…