Applications of a Large Graph Model

Project Nexus

2026 Sebastián Samaruga.

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Latest version available at:

https://github.com/sebxama/sebxama/raw/refs/heads/main/Objective.docx

See also:

https://sebxama.blogspot.com/2026/03/algebraic-embeddings.html

Executive Summary:

This project defines a next-generation data integration and intelligence framework. Unlike traditional ETL (Extract, Transform, Load) tools that move data from point A to point B, this framework creates a Dynamic Knowledge Facade. It ingests raw data from disparate backends, performs real-time mathematical inference (Augmentation) to discover hidden relationships, and provides a unified API (Facade) for applications to interact with. Crucially, it maintains a bi-directional sync, ensuring that actions taken in the Facade are reflected back in the source systems.

Project Nexus is not just another data pipeline; it is an intelligent, self-organizing data fabric. By investing in this architecture, we will drastically reduce integration overhead, surface hidden business insights mathematically, and provide our teams with a system that adapts to our business in real-time.

Modern enterprise data architecture is plagued by the "Silo Problem"—fragmented data spread across disparate applications that cannot talk to one another effectively. Current solutions use static ETL processes that move data but do not understand it.

Project Nexus is a reactive, semantic data integration framework designed to not just move data, but to Augment it. By applying Formal Concept Analysis (FCA) and Prime ID Embeddings, the platform automatically infers relationships, types, and state transitions, providing a dynamic API Facade that keeps all source systems in bi-directional sync.

Objective:

Develop a framework capable of ingest raw data from any integrated service or application backend, perform any possible "Augmentation" (Aggregation, Alignment and Activation) inferences on them, then provide a dynamic Facade for interacting on the inferred data and schemas, in "intra" or "inter" integrated applications (possibly inferred) use cases (Contexts) REST APIs and keep source integrated services or application back ends in sync with this interactions. Consolidate views of the same data (information) coming from or possibly stored in disparate systems (knowledge).

Use Cases:

If it sees an entity with "Name, Salary, and Manager," it infers this is an "Employee" without a human programmer having to define the database schema.

By analyzing historical contexts (e.g., "Yesterday's Price was Low", "Today's is Mid"), the system automatically predicts and aligns the next logical state ("Tomorrow's will be High").

The system understands business lifecycles. It knows that a "Junior" employee transitions to a "Semi-senior." It automatically exposes the actions required to trigger that state change.

Current State: Employee data is fragmented across Workday (payroll), Jira (performance), and internal directories. Nexus Application: The system ingests all three. Aggregation realizes "J. Doe" in Jira is "John Doe" in Workday by means of entity matching. Activation notices that based on Jira output, John is transitioning from Junior to Semi-senior. The Facade exposes a dynamic button to the HR manager: "Promote John." Clicking this automatically updates Workday and Jira simultaneously.

Current State: Pricing analysts manually pull historical vendor prices to guess tomorrow's material costs. Nexus Application: The platform ingests vendor pricing daily. The Alignment engine analyzes the axis of time (Yesterday: Low -> Today: Mid). It infers a relationship context and flags an Activation alert: "High probability of price spike tomorrow." The Procurement team uses the dynamic API to lock in purchasing contracts today, saving the company money.

Current State: Marketing has no single view of a customer because sales uses Salesforce, support uses Zendesk, and billing uses Stripe. Nexus Application: By using Rotated SPO Contexts (Person(buys, Product)), the system automatically infers that a Zendesk ticket creator is the exact same entity as a Stripe payer. It generates a real-time, unified Customer Profile API without any DBA writing a single SQL JOIN.

Technical Implementation Details

Reactive Services:

The whole framework is to be implemented as a series of reactive event driven micro services interacting with each other vía messages.

The Datasource Service is configured to produce / consume model event messages for the configured integrated application backends source data (JDBC, XML, API, JSON, etc. “connectors”)

One service, the Resource Model, acts as the main shared state repository to other services (vía helper services). It holds ingested (Datasource) and augmented (Augmentation Pipeline) resources. Augmented resources may have passed through manipulation through the Facade (IO API) Service.

The Augmentation Pipeline performs arithmetic inference over the raw source data: Aggregation (type inference, entity matching), Alignment (link / attribute prediction) and Activation (behavioral state management). It then updates the Resource Model with the aggregated, alignment and activated data.

Finally, the Facade Service exposes API Endpoints of the dynamic resources with their dynamic schemas coming from the augmented (integrated) datasource(s) original data in a REST fashion which enables to augment and sync back resources to datasource(s) data re-augmenting the endpoint interactions exchanged resources.

Service Endpoints Message formats:

Services Graph Messages:

RDF Quad: (Type : context URI, Instance : subject URI, Attribute : predicate URI, Value : object URI).

Datasource, Augmentation, Facade, Resource Model and Helper Services communicate using this message format.

RDF Quad Reification (as URI):

datasourceType://datasourceURI/[typeContextID]/[instanceSubjectID]/[attributePredicateID]/[valueObjectID]

URIs unique PrimeIDs Assignment. Registry Helper Service to / from ID / URI string resolution.

URIs pattern matching (partial paths, wildcards / expressions). Naming Helper Service resolves to, for example, a list of instanceSubjectIDs statements for a given typeContextID path.

Representations (Content Types): Index Helper Service provides for dynamic resources schema navigable (production) and activatable (consumption) of rendered URI resources representations.

Augmentation Pipeline Services (FCA) Messages:

FCA ContextPoint(s) instances.

Augmentation Pipeline Services (Aggregation, Alignment and Activation Services) internal communication format. Augmentation Service handles conversion from input / to output Services Graph Messages RDF Quad(s) while pipeline internally uses ContextPoint format Messages.

Services:

Datasources Service:

Ingestion / sync. Resource Model Service configured sources population / sources sync.

Publish / Consumes to Resource Model.

Augmentation Pipeline Services (FCA Contexts stream processing):

Augmentation Service: Aggregation, Alignment, Activation services pipeline wrapper (orchestration / helper services).

Consumes / Publish to Resource Model.

Aggregation (Augmentation Pipeline) Service:

Type Inference: FCA Concepts.

Entity Matching: Discover Equivalences.

Alignment (Augmentation Pipeline) Service:

Attribute / Link prediction. Contexts given axis inference.

Activation (Augmentation Pipeline) Service:

States transition change activations predictions. Attributes given axis shift inference.

Augmentation Pipeline Dataflow:

Aggregation <-> Alignment <-> Activation

Facade Service:

NakedObjects like (RESTful / HAL) Endpoint. Generic dynamic Endpoint API / Client. DCI (Data, Contexts and Interactions) semantics.

Activates (exposes) augmented resources in their dynamic endpoints (Naming) and their dynamic schema (discovery) for performing Resource CRUD which in turn gets augmented, persisted (Resource Model) and synced (Datasources).

Consumes / Publish to Augmentation.

Resource Model Service:

Main shared state repository. Graph (quads) backend.

Content Types / Addressing / Activation (Helper Services).

Services Functional Message Streams (Monads) State IO Helper Services:

. Naming (Helper) Service : Addressing

. Registry (Helper) Service : Repository

. Index (Helper) Service : Resolution.

This services handles utility methods for the Datasource ingestion / sync, Facade dynamic schema / data and Augmentation inferences interactions to / from the main Resource Model Service.

Services Dataflow (streams):

Datasources -> Resource Model

Resource Model -> Augmentation

Augmentation -> Facade

Facade -> Augmentation

Augmentation -> Resource Model

Resource Model -> Datasources

Augmentation Services Implementation:

FCA (Formal Concept Analysis):

FCA Contexts: Objects x Attributes matrix.

Context triples encoding:

ContextPoint : (context : ContextPoint, object : ContextPoint, attribute : ContextPoint);

ContextPoint: Augmentation Pipeline Events Message format.

ContextPoint class:

- uri : String

- primeID : long

- context : ContextPoint

- previousContext : Map<ContextPoint, ContextPoint> // Alignment

- nextContext : Map<ContextPoint, ContextPoint> // Alignment

- object : ContextPoint

- attribute : ContextPoint

- previousAttribute : Map<ContextPoint, ContextPoint> // Activation

- nextAttribute : Map<ContextPoint, ContextPoint> // Activation

- contextOccurrences : Set<Set<ContextPoint>>

- objectOccurrences : Set<Set<ContextPoint>>

- attributeOccurrences : Set<Set<ContextPoint>>

+ getContext() : ContextPoint

+ getObject() : ContextPoint

+ getAttribute() : ContextPoint

+ getContexts() : Set<ContextPoint>

+ getObjects() : Set<ContextPoint>

+ getAttributes() : Set<ContextPoint>

+ getPreviousContext(axis : ContextPoint) : ContextPoint

+ getNextContext(axis : ContextPoint) : ContextPoint

+ getPreviousAttribute(axis : ContextPoint) : ContextPoint

+ getNextAttribute(axis : ContextPoint) : ContextPoint

+ getPrimeIDEmbedding() : long

Aggregation (occurrences): ContextPoint context, object, attribute occurrences aggregated by FCA Formal Concept(s): Set<Set<ContextPoint>>. TODO: Subsumption Operations.

Occurrence Monad: ContextPoint (Context, Object, Attribute Occurrences) wrapper / filter / traversal streams reactive composition / activation.

Render SPO Graphs into FCA Contexts from input triples:

Each S, P, O from input triples with Contexts of their own. Example: Predicate Context, Subject Objects, Object Attributes (P, S, O). "Rotated" SPO Contexts.

(S, P, O) Context;

(P, S, O) Context;

(O, P, S) Context;

Prime ID Embeddings:

Each ContextPoint (singleton for a given URI) is assigned an unique incremental Prime Number Identifier.

For a given ContextPoint occurrence in a given Context its Prime ID Embedding is calculated as the product of this occurrence Prime ID with the Prime ID Embeddings of the other two parts of the occurrences.

For example: given an object in a given context its Prime ID Embedding is the product of its Prime ID (Embedding) by the Prime ID (Embedding) of the occurrence context by the Prime ID (Embeddings) of this object's attributes.

Augmentation Layers. Stream Pipelines:

Aggregation, Alignment, Activation steps. Leverage Prime ID Embeddings for reactive functional composition.

Augmentation Services:

Aggregation Service:

Type Inference (FCA Formal Concepts). Same attributes: same type. Attributes subset / superset: super / sub types. Aggregated rotated contexts for S / P / O Contexts type inference:

(aPerson(worksAt, anEmployeer))

(worksAt(aPerson, anEmployeer))

(anEmployeer(worksAt, aPerson))

Entity Matching:

“J. Doe” in data source A is the same as “John Doe” in data source B.

Alignment Service:

Attribute / Link prediction:

Type (upper ontology / hierarchies / order) inference / alignment.

Given type aggregated hierarchies and taking contexts into account as a given axis, predict objects attributes for an axis value shift:

(Yesterday(Price, Low))

(Today(Price, Mid))

(Tomorrow(Price, High))

Activation Service:

Transforms: available actors in roles in interaction context states transition change activations predictions:

(CurrentStateContext(PreviousStateContext x NextStateContext))

(Semisenior(Junior x Senior))

Appendix: Microservices Agentic Infrastructure (draft WIP)

The idea is to generate dynamic Agents "system prompts" (declarative use cases business logic / behaviors descriptions) from Augmentation aggregated, aligned and activated metadata used for specifying a formal dynamic grammar (from an "upper" grammar) whose possible productions are those of the description of the use case (prompt).

Then, the Interaction of an use case instance (user prompts) system and user completions (dialog) are meant to be constrained by the use case roles actors and their state with possible productions within this context and an Interaction instance derived grammar.

Resources (Pluggable Backends Ingestion / Sync Integrations)

Knowledge Graph: Resources Ingestion / Sync. Blackboard Pattern.

Message Broker. Resources CRUD Events / Schema Patterns.

Message Format: RDF Quads.

Message Events / Schema Patterns Listeners / Producers (Augmentation / Agents).

Listeners / Producers:

Events IO Context (incremental dialog across events).

Helper Services / Tools (Registry, Naming, Index).

Custom Embeddings.

Augmentation : Listener, Producer

Consumes KG CRUD Events. by Schema Patterns.

Publishes to Knowledge Graph.

Aggregates (entity types / roles, contexts)

Aligns contexts (ontology entity matching, links / attributes prediction, context roles)

Activates previous / running / possible behaviors (interactions: entities in roles in contexts / use cases types / instances)

Publishes augmentation results for further Augmentation.

Publishes aggregated / aligned activation use cases data, contexts and interactions (actors, roles and executions) metadata (events) for Agents to build system prompt (syntax, generative grammar productions constrained by metadata context parameters). Defines actor / roles behaviors in contexts (operations / transforms, business logic). 

Agents : Listener, Producer

Consumes KG CRUD Events. by Schema Patterns.

Publishes to Knowledge Graph.

Structured Inputs / Outputs: Schema Patterns Signatures.

Workflows defined by IO Events Schema Patterns Signatures. Auto (on event) or manual (waiting user event).

Implements activation use cases over aligned context roles of aggregated data.

Have tools for accessing and modifying augmented Knowledge Graph data (events).

Consumes aggregated / aligned activation use cases data, contexts and interactions (actors, roles and executions) metadata (events) for Agents to build system prompt (syntax, generative grammar productions constrained by metadata context parameters). Defines actor / roles behaviors in contexts (operations / transforms, business logic). 

Interactions: conversational contextual state dialog / exchange constrained by possible system prompt (grammar) productions and context state. Actual "prompts" querying / executing possible behaviors. Use case and context state driven possible prompt completions (choose from / input values).

Publishes interaction execution for further augmentation.

APIs: Exposes a Dynamic HATEOAS Interactions Endpoint. View past executions data and status and running / manual (waiting user event) executions. Start new possible executions.

Syndicated API Gateway: Agents Endpoints behaviors ordered according they workflows (executed, running, start new workflow).

Agents are instances of Augmentation use cases inference. They rely on Augmentation and helper Services (tools). And become "discoverable" tools for Augmentation and other agents.

Templates / Views / Transforms: Augmentation tools for building Agents context artifacts (prompts, tools, etc). Generative Grammar Tools: build “system prompts” (declarative use case business logic) and “interaction prompts” (use case interactions executions dialog completions grammars).

Example Use Cases

Integrated Systems (Backends from which Augmentation performs Aggregation, Alignment and Activation use case inferences):

Conference Registration System

Travel Agency System

Hotel Reservation System

Traveller Recreational Activities System

Local Transportation Service System

Inferred Use Cases (from integrated systems backends schema / data):

Register for Conference

Book Flight

Book Hotel Reservation

Book Recreational Activity

Airport Check-in / Travel

Hotel Check-in

Attend Recreational Activity

Attend Conference Sessions

Airport / Hotel / Activity / Conference Session from / to Transportation

Interactions (Use Case instances):

The user registers for Conference Sessions Attendance.

Travel Agency's system books a flight from user's source city to conference destination city.

User travels to conference’s city.

Hotel system books reservation for user in start / end conference's dates.

User check in into hotel for reservation dates.

Traveller Recreational Activities system appoints attendance to activity given user's preferences.

User attends to appointed recreational activities.

User attends to conference sessions.

Local Transportation service requested whenever necessary (from, to, distance).

All systems view an aligned entity for the same instances. User is: Traveller, Host, Attendant, Passenger.

All interactions (use case instances) perform declaratively generated use cases (roles) business logic (state transforms, updates, transitions).

Attendant registeredFor ConferenceSession

Traveller onBoard Flight

Host checkedIn Room

Tourist attending RecreationalActivity

Attendant listeningTo ConferenceSession

Passenger travelingWith TransportationService

All use case interaction details are inferred and defined into the agents specification:

Flight.destination : Conference.city

Conference, Flight, Hotel, Activity, Transportation Payments instantiated by User prompted available payment methods.