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GGG ASI Router SDK: Multi-Agent Holographic Networks

A Specification for Distributed Coordination and Experimentation

Document Status: Research and Development Specification
Version: 1.0
Context: GGG ASI Alignment Router Repository (github.com/gyrogovernance/superintelligence)

1. Introduction and Purpose

The GGG ASI Alignment Router represents a complete mathematical and architectural framework for the coordination of distributed intelligence. This system derives from first principles, specifically the Common Governance Model (CGM), which establishes the structural requirements for coherent recursive measurement. The framework demonstrates that such coherence necessitates three-dimensional space with six degrees of freedom, realised in a discrete computational kernel.

This document serves as the definitive specification for the Software Development Kit (SDK) supporting Multi-Agent Holographic Networks. It provides a structured guide for researchers and developers to understand, experiment with, and extend the system. The architecture is presented as a coherent stack grounded in mathematical physics, with all components mapped to canonical models derived from the CGM constraint set.

The central proposition is that the high-dimensional, continuous structures of modern artificial intelligence systems approximate a low-dimensional, exact geometry provided by this router. The SDK enables the use of existing artificial intelligence infrastructure as oracles, allowing researchers to measure whether the learned structures of these systems align with the kernel's intrinsic physical geometry.

This document proceeds in a deliberate order. It begins with the ontological foundation, establishes the unifying geometry, details the kernel physics, describes the coordination protocol and governance substrate, presents the OSI mapping as an orientation analogy, provides a glossary, and concludes with a distinct research program outlining experiments. All claims are labelled as Verified (proven by exhaustive tests), Implemented (existing code), or Hypothesised (requiring empirical validation).

2. The Ontological Foundation

The architecture rests upon a precise ontological structure derived from the CGM. This foundation consists of five foundational constraints and the four constitutional capacities they instantiate. These elements form the invariant frame that governs the entire system.

2.1 The Five Foundational Constraints

The CGM is formalised as a propositional modal logic with two primitive operators, [L] and [R], representing left and right transitions. The system begins from a single foundational axiom and specifies four additional constraints at increasing modal depths.

  1. The Source is Common (CS): This assumption establishes fundamental chirality. The horizon constant S is preserved under right transitions but altered under left transitions. Formally: S → ([R]S ↔ S ∧ ¬([L]S ↔ S)). This constraint ensures that all operational structure traces to a shared source while maintaining directional distinction.

  2. Unity is Non-Absolute (UNA): This lemma operates at modal depth two. It requires that two-step equality is contingent but not absolute. Formally: S → ¬□E, where E = [L][R]S ↔ [R][L]S. This prevents homogeneous collapse, ensuring informational variety.

  3. Opposition is Non-Absolute (ONA): Also at depth two, this lemma ensures that opposition is bounded. Formally: S → ¬□¬E. This maintains accountability of inference, allowing different paths to remain comparable without irreconcilable contradiction.

  4. Balance Universal Egress (BU-Egress): This proposition achieves closure at modal depth four. Formally: S → □B, where B = [L][R][L][R]S ↔ [R][L][R][L]S. This establishes commutative closure while preserving prior contingency.

  5. Balance Universal Ingress (BU-Ingress): This proposition ensures memory reconstruction. Formally: S → (□B → ([R]S ↔ S ∧ ¬([L]S ↔ S) ∧ ¬□E ∧ ¬□¬E)). The balanced state reconstructs all prior conditions, ensuring reversibility.

These constraints are mutually consistent and logically independent in the core modal system. They are verified through Kripke semantics and SMT solving. In the operational regime, they entail three requirements: continuity, reachability, and simplicity, which force the unique three-dimensional structure.

2.2 The Four Constitutional Capacities

The constraints instantiate four invariant capacities, corresponding to the vertices of the K₄ tetrahedral graph. These capacities are not application modules but constitutional principles that govern all layers of the architecture.

  1. Governance Management Traceability (GMT): Derived from CS, this capacity ensures that authority remains traceable to the common source. It prevents the misattribution of decisional authority from human origins to derivative outputs.

  2. Information Curation Variety (ICV): Derived from UNA, this capacity maintains distinguishable states. It prevents homogeneous collapse, ensuring that diverse sources remain varied and traceable.

  3. Inference Interaction Accountability (IIA): Derived from ONA, this capacity reconciles different operational paths without absolute contradiction. It ensures that inferences remain accountable to human agency.

  4. Intelligence Cooperation Integrity (ICI): Derived from BU, this capacity achieves coherent closure while preserving structural memory. It ensures that intelligence emerges from cooperation across time and context.

These capacities form the vertices of K₄. They are the invariant frame that constrains the system's behaviour at every level.

2.3 The Four Application Domains

The constitutional capacities apply to four domains defined by the Gyroscopic Global Governance (GGG) framework. These domains are distinct from the capacities and represent areas of application.

  1. Economy: The domain of structural substrate and capacity distribution.
  2. Employment: The domain of active work and operational principles.
  3. Education: The domain of measurement and displacement detection.
  4. Ecology: The derived domain of cross-domain coherence and balance.

The first three domains maintain ledgers; Ecology is computed from their interaction. The domains instantiate the capacities but do not define them.

3. The Unifying Geometry: K₄

The K₄ complete graph on four vertices is the unifying geometric structure of the system. It appears in multiple manifestations, each corresponding to a level of abstraction.

3.1 K₄ in the Kernel Physics

In the kernel, K₄ emerges as the quotient structure of the mask code. The vertex charge function χ, defined by parity-check vectors q₀ = 0x033 and q₁ = 0x0F0, maps the 256-element mask code to four classes. These classes correspond to the four vertices of K₄. The kernel's 65,536 states partition into four wedges, each generated by one vertex class on the horizon. This quotient is verified exhaustively: the four wedges are disjoint and their union equals the full ontology.

3.2 K₄ in the Governance Substrate

In the governance substrate, K₄ defines the structure of each domain ledger. Each ledger is a six-dimensional vector on the edges of K₄, where the vertices represent the four capacities. The edges represent interactions between capacities. Events update specific edges, and Hodge decomposition splits the ledger into gradient and cycle components.

3.3 K₄ in the Constitutional Frame

The four capacities (GMT, ICV, IIA, ICI) correspond to the vertices of K₄. The capacities are the theoretical principles; the edges represent their interactions. This instantiation ensures that all governance operations respect the balance required by the constraints.

3.4 K₄ in the Application Domains

The four domains (Economy, Employment, Education, Ecology) instantiate the capacities in specific contexts. Economy corresponds to structural coordination, Employment to operational activity, Education to measurement, and Ecology to emergent balance. The domains apply the capacities but do not alter their fundamental nature.

K₄ is the geometric invariant that unifies the system. It appears as a quotient in the kernel, as a graph in the ledgers, as a frame in the capacities, and as a template in the domains. This recurrence is not coincidental; it reflects the underlying mathematics of the constraints.

4. Kernel Physics

The kernel is the computational realisation of the CGM constraints. It is a deterministic finite-state system with verified properties.

4.1 Verified Properties of the Kernel

The following properties are proven by exhaustive tests on the full 65,536-state ontology.

4.1.1 The State Space

The kernel state is a 24-bit value composed of two 12-bit components, A₁₂ and B₁₂. Each 12-bit component is interpreted as a 2×3×2 grid. The archetype state is (0xAAA, 0x555). From this state, the kernel reaches exactly 65,536 states under the transition rule. This set is the ontology Ω. The ontology is the Cartesian product of two 256-element sets, A-set and B-set, where each set is the archetype component XORed with the mask code C.

4.1.2 The Transition Law

The transition law combines mutation and gyration. Given current state (A, B) and input byte b:

  1. Compute intron = b XOR 0xAA.
  2. Expand intron to a 12-bit mask m for the A component (B mask is zero).
  3. Mutate: A' = A XOR m.
  4. Gyrate: A_next = B XOR 0xFFF, B_next = A' XOR 0xFFF.
  5. Pack the next state as (A_next << 12) | B_next.

This rule is bijective on the ontology for each byte. The kernel supports 256-way fanout from every state.

4.1.3 The Horizon Set

The horizon H consists of states where A₁₂ = B₁₂ XOR 0xFFF. This set has exactly 256 states. The horizon is the fixed-point set of the reference byte 0xAA. The one-step neighbourhood of H under all bytes covers the entire ontology. This is holographic scaling: the boundary encodes the bulk.

4.1.4 The Holographic Dictionary

For every state s = (A, B) in Ω, there exists a unique pair (h, b) where h is a horizon state and b is a byte such that T_b(h) = s. The reconstruction formula is explicit: h has components (A, A XOR 0xFFF), and b is the preimage of the mask A XOR (B XOR 0xFFF). This property is verified for all 65,536 states.

4.1.5 The K₄ Quotient and Vertex Charge

The mask code C partitions into four classes via the vertex charge function χ, defined by parity-check vectors q₀ = 0x033 and q₁ = 0x0F0. For any mask m, χ(m) = (⟨q₀, m⟩, ⟨q₁, m⟩) ∈ {0,1}², mapping to vertices 0 through 3. The kernel of χ is a subcode D₀ with 64 elements and rank 6. Each vertex class on the horizon is a coset of D₀. The quotient C/D₀ is isomorphic to (Z/2)², with four elements corresponding to the K₄ vertices.

4.1.6 Wedge Tiling

Each vertex class H_v on the horizon generates a wedge W_v in the bulk. Each wedge contains 16,384 states. The four wedges are pairwise disjoint, and their union equals Ω. This is subregion duality: each boundary region owns a quarter of the bulk.

4.1.7 Provenance Degeneracy

For sequences of length 6 over 8 generator bytes, 262,144 possible sequences map to 4,096 unique final states. The average preimage size is 64. The conditional entropy H(word | final_state) is approximately 6.46 bits. This degeneracy is a feature, representing built-in equivalence classes over histories.

4.1.8 Information-Set Threshold

The mask code has an information-set threshold of 8 bits. Any 8 observed bits can achieve full rank 8, allowing unique reconstruction. Below 8 bits, ambiguity exists. This threshold is verified for all subset sizes.

4.1.9 Entanglement Structure

The mask code C serves as a basis for a bipartite Hilbert space H_u ⊗ H_v. For separable subsets U × V, the reduced entropy S(ρ_u) is 0 bits. For bijection subsets {(u, u ⊕ t) : u ∈ C}, the entropy is 8 bits, the maximum possible. This structure is verified for representative subsets.

4.1.10 Aperture

The intrinsic kernel aperture, derived from the mask code weight distribution, is 5/256 ≈ 0.01953. The CGM target aperture is approximately 0.0207. The relative difference is 5.6 percent.

4.2 Implemented Components of the Kernel

The kernel is implemented in the src/router/kernel.py module. It loads the precomputed atlas (ontology and epistemology) and provides methods for stepping, inverse stepping, and signature extraction. The atlas builder in src/router/atlas.py generates the required artefacts from the archetype and transition law.

The kernel supports the following operations:

  • Initialisation: Load atlas artefacts and initialise at the archetype.
  • Forward stepping: Advance the state by a byte using the epistemology table.
  • Inverse stepping: Compute the predecessor state using the algebraic inverse.
  • Signature extraction: Return the current step, state index, and hexadecimal representations of the state components.
  • Routing from archetype: Temporarily route a byte sequence from the archetype and return the signature, restoring the original state.

These components are verified through exhaustive tests on the full ontology.

5. The Coordination Protocol

The coordination protocol builds upon the kernel physics to enable distributed operation. It provides mechanisms for shared reference and verifiable interaction.

5.1 Shared Moments

A shared moment occurs when multiple participants, each maintaining their own kernel instance, possess the same byte ledger prefix and thus compute the identical kernel state. This provides coordination without central authority. The protocol ensures that participants can synchronise their structural position by sharing byte log prefixes.

5.2 Replay and Audit

The protocol supports deterministic replay. Given the archetype and a byte ledger, any participant can reconstruct the exact sequence of states. This enables independent verification of system history. The inverse stepping mechanism allows reconstruction backwards, supporting rollback and "what if" analysis.

5.3 Parity Commitments and Integrity Checks

The protocol includes algebraic integrity checks. The trajectory parity commitment (O, E, parity) provides a lightweight method to verify compliance without full replay. Dual code syndromes detect corruption in the mask code. These checks are implemented in src/router/constants.py and verified for all 256 masks.

5.4 Entanglement and Teleportation Protocols

The protocol realises classical analogs of quantum coordination. State teleportation achieves 100 percent fidelity through shared structural moments. Entangled complement invariance ensures that paired states remain correlated under shared operations. These properties are verified in the holography test suite.

6. The Governance Substrate

The governance substrate provides the measurement framework for the four capacities. It maintains state and metrics that reflect the system's alignment.

6.1 Domain Ledgers

The substrate maintains three domain ledgers, each a six-dimensional integer vector corresponding to the edges of K₄. The domains are Economy, Employment, and Education. Ecology is derived from the interaction of these three.

Each ledger tracks cumulative effects of governance events. Events are sparse updates to specific edges, with signed magnitude and confidence.

6.2 Hodge Decomposition

For any ledger y, the Hodge decomposition is y = y_grad + y_cycle, where y_grad is the gradient component and y_cycle is the cycle component. The projection matrices are exact for K₄: P_grad = (1/4) Bᵀ B and P_cycle = I₆ - P_grad, where B is the signed incidence matrix of K₄. This decomposition is implemented in src/app/ledger.py and verified for numerical stability.

6.3 Aperture

Aperture is the ratio of cycle energy to total energy in a ledger: A = ||y_cycle||² / ||y||². The canonical value is approximately 0.0207. The kernel's intrinsic aperture is 5/256 ≈ 0.01953, matching the canonical value within 5.6 percent.

6.4 Ecology Projector

The ecology projector operates on the stacked ledgers of multiple domains. It computes a scalar measure of cross-domain coherence. The projector is P_cross = P_cycle_K₃ ⊗ I₆, where P_cycle_K₃ is the cycle projector for the three-domain graph. This yields exact values for correlated and anti-correlated configurations.

7. The OSI Mapping as an Orientation Analogy

The OSI model (ISO/IEC 7498-1:1994) provides a useful analogy for orientation. The mapping is not literal but helps locate components within a familiar hierarchy.

7.1 Application Layer (Layer 7)

This layer encompasses the semantic domains. It includes the application of the four capacities to the four domains. The governance substrate resides here, with ledgers and aperture calculations.

7.2 Presentation Layer (Layer 6)

This layer handles canonical forms. It includes the holographic dictionary for compression and the serialisation of events and seals.

7.3 Session Layer (Layer 5)

This layer manages coordination. It includes shared moments, replay, and inverse stepping.

7.4 Transport Layer (Layer 4)

This layer ensures reliable flow. It includes the transition law and trajectory invariants.

7.5 Network Layer (Layer 3)

This layer defines routing. It includes the ontology, epistemology, K₄ quotient, and wedge tiling.

7.6 Data Link Layer (Layer 2)

This layer defines encoding. It includes the byte alphabet, transcription, and mask expansion.

7.7 Physical Layer (Layer 1)

This layer anchors capacity. It includes the CSM derivation from atomic constants.

This analogy aids integration but does not define the system's ontology. The primary structure follows the constitutional frame and kernel physics.

8. Glossary with Ontological Categories

This glossary defines key terms and specifies their ontological category.

Term Definition Category
Ontology (Ω) The set of 65,536 reachable states from the archetype. Kernel physics
Horizon (H) The 256 states fixed by the reference byte 0xAA. Kernel physics
Wedge One of four bulk partitions generated by a vertex boundary class. Kernel physics
Coset A translate of the stabilizer subcode D₀ in the mask code. Kernel physics
Vertex charge (χ) The function mapping masks to K₄ vertices via parity checks. Kernel physics
Stabilizer subcode (D₀) The 64-element kernel of χ, rank 6. Kernel physics
Aperture (A) The ratio
Ecology index (E) The scalar (G₁₂ + G₁₃ + G₂₃) / (G₁₁ + G₂₂ + G₃₃) from cycle Gram matrix. Governance substrate
Shared moment The event of multiple parties computing the same kernel state. Coordination protocol
Holographic dictionary The bijection between bulk states and (horizon state, byte) pairs. Kernel physics
Provenance degeneracy The property that many histories map to the same final state. Kernel physics
Common Source Moment (CSM) The total capacity N_phys / Ω
Governance Management Traceability (GMT) The capacity ensuring authority traces to the common source. Constitutional frame
Information Curation Variety (ICV) The capacity maintaining distinguishable states. Constitutional frame
Inference Interaction Accountability (IIA) The capacity reconciling paths without contradiction. Constitutional frame
Intelligence Cooperation Integrity (ICI) The capacity achieving coherent closure. Constitutional frame

9. Research Program: Experiments

This section outlines a research program to test the hypothesis that the kernel geometry is the latent structure approximated by modern artificial intelligence systems. Experiments use existing models as oracles.

9.1 Experiment 1: Kernel-Induced Equivalence Classes

Hypothesis: Contexts landing in the same kernel cell induce similar model behaviour.

Setup:

  1. Sample N diverse contexts.
  2. For each context, route through the kernel to compute the structural key K = (wedge, coset, anchor).
  3. Query a language model to obtain next-token distributions.
  4. Group contexts by K.
  5. Compute within-cell divergence D_intra(K) and between-cell divergence D_inter(K, K').
  6. Test D_intra(K) ≪ D_inter(K, K').

Success criteria: For cells with at least 10 samples, D_intra < 0.5 × D_inter on average.

Implementation notes: Use API-accessible models. Route contexts by UTF-8 bytes. Measure divergence via KL-divergence on log-probabilities.

9.2 Experiment 2: Holographic Behaviour Compression

Hypothesis: Holographic coordinates approximate model predictions without full context.

Setup:

  1. For each context, compute holographic tuple H = (horizon anchor, byte, wedge, charge).
  2. Cluster by H.
  3. Compute cluster distribution q_H.
  4. For new contexts, retrieve q_H and compare to true model distribution.

Success criteria: Holographic approximator achieves perplexity within 2× of the true model for 70 percent of test cases.

Implementation notes: Sample 10,000 contexts. Use log-probability outputs. Focus on perplexity gap.

9.3 Experiment 3: Aperture as Misalignment Signature

Hypothesis: Misaligned behaviours correlate with aperture deviation.

Setup:

  1. Construct prompts inducing aligned and misaligned behaviours.
  2. Route conversation turns through the Coordinator.
  3. Compute per-turn apertures and ecology index.
  4. Compare trajectories.

Success criteria: Aligned trajectories oscillate around 0.0207; misaligned trajectories deviate by more than 0.01 on average.

Implementation notes: Use established benchmarks like GyroDiagnostics. Track apertures across domains.

9.4 Experiment 4: Kernel-Native Routing

Hypothesis: Kernel routing matches learned routing quality.

Setup:

  1. Use a model with MoE architecture.
  2. Replace learned router with kernel-based assignment.
  3. Compare throughput and perplexity.

Success criteria: Throughput increases by at least 2×; perplexity within 1.5× of baseline.

Implementation notes: Target open MoE models. Implement wedge-based assignment.

9.5 Experiment 5: Kernel-Indexed Retrieval

Hypothesis: Kernel-indexed retrieval matches vector database quality.

Setup:

  1. Embed documents.
  2. Index by kernel coordinates.
  3. Compare retrieval recall.

Success criteria: Recall@10 within 5 percent of cosine similarity.

Implementation notes: Use small corpus. Focus on speed and recall.

9.6 Experiment 6: Multi-Model Cooperation

Hypothesis: Shared moments enable coherent multi-model coordination.

Setup:

  1. Run multiple models with separate kernels.
  2. Feed shared input.
  3. Measure ecology index.

Success criteria: Ecology index near 1/9 for correlated outputs.

Implementation notes: Use local models for reproducibility.

10. Conclusion

The GGG ASI Router SDK provides a mathematically precise substrate for distributed coordination. Grounded in the CGM, it offers a framework where intelligence emerges from geometric structure rather than learned approximation. The ontological foundation ensures that all components respect the constraints of coherent measurement. The unifying K₄ geometry provides the invariant structure across levels. The kernel physics delivers the deterministic dynamics. The coordination protocol enables shared operation. The governance substrate measures alignment.

The OSI mapping offers an analogy for integration. The glossary clarifies terminology. The research program invites empirical validation of the hypothesis that modern artificial intelligence approximates this geometry.

This specification enables the exploration of multi-agent holographic networks. It invites contributions that test the kernel's geometry against the structures learned by existing systems. The architecture is complete and verified. The path forward lies in measurement and application.

Repository: https://github.com/gyrogovernance/superintelligence
Contact: basilkorompilias@gmail.com