Project Stars

Official live demo: https://iusmusic.github.io/stars/

Project Stars is a browser-based research atlas for modeling thoughts, concepts, and references as structured objects within a reviewable conceptual framework.

It is designed as a research interface for examining how conceptual structures may be represented simultaneously as:

• structured objects with attributes and provenance,
• nodes in a reviewed and reviewable graph,
• points in a semantic space,
• elements in a dynamic layout,
• and local sources in a continuous activation field.

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Contents

1. Abstract
2. Research Framing
3. Formal Model
4. Thought Objects
5. Geometry of Thought
6. Relation Layers
7. Edge Objects as Evidence-Bearing Entities
8. Candidate-Link Inference
9. Modeling Principles
10. Layout Dynamics
11. Visual Encoding as Epistemic Encoding
12. Wave Field and Activation
13. Receiver Quality and Experimental Metrics
14. Inspector as Research Interface
15. Add-Thought Workflow as Curation Mechanism
16. Multi-View Navigation
17. Export Semantics
18. External Research-Source Layer
19. Research Foundations and Scientific Framing
20. Scientific Contribution
21. Limitations
22. Future Extensions
23. Implementation Mapping
24. Updates — 28/03/2026
25. Copyright

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1. Abstract

Project Stars formalizes thoughts as attributed objects embedded in a semantic space and linked through two distinct relation layers:

1. a confirmed layer of reviewed structural relations,
2. a candidate layer of explainable but unconfirmed hypotheses.

The system couples these layers to:

• a deterministic candidate-link scoring function,
• a force-driven visual embedding defined by confirmed structure,
• and a field-like background representation of activation and propagation.

This produces a research graph in which:

• nodes are evidence-bearing thought objects,
• edges are typed, provenance-aware relation objects,
• candidate links arise from explicit signals rather than randomness,
• and visualization is treated as a dynamic embedding of the graph rather than the graph itself.

2. Research Framing

Project Stars studies a central question:

How can thoughts be represented as mathematically structured objects inside a research graph that preserves provenance, uncertainty, review state, and interpretable inference?

The system takes the view that a thought is not merely a label or note. A thought is a structured object with:

• semantic content,
• ontology placement,
• evidence and provenance,
• graph relationships,
• and visual or dynamical behavior.

3. Formal Model

3.1 Formal hypothesis

The current Project Stars framing is best understood as a formal hypothesis rather than a strict theorem-proof claim.

Semantic precision is modeled as an emergent property of a dynamical conceptual system, and depends jointly on structural constraints, local activation, and receiver-state tuning.

In this framing:

• thoughts are structured attributed objects,
• feelings correspond to local activation, amplification, and propagation behavior,
• goals correspond to attractor-like low-energy configurations or stabilized trajectories,
• and precision increases when receiver state is sufficiently tuned to the structure being activated.

The full system can be described as:

M = (Theta, A, d, Rc, Rp, S, p(t), phi, Q, Xi)

Where:

• Theta = the set of thoughts,
• A = the attribute structure carried by each thought,
• d = a multi-part similarity or distance structure,
• Rc = the set of confirmed relations,
• Rp = the set of candidate relations,
• S = the candidate-link scoring function,
• p(t) = the time-dependent visual embedding into the display plane,
• phi = a continuous activation or wave field over the visual space,
• Q = receiver quality, a scalar tuning parameter in [0,1],
• Xi = experiment and observability metrics such as precision, coherence, convergence, and receiver state.

This is intentionally a hybrid model. It is not only a graph, not only a metric space, and not only a simulation. It combines:

• an attributed object space,
• a layered graph,
• an epistemic model of review status,
• a dynamic layout process,
• a field-based activation layer,
• and an explicit receiver-state variable that can be experimentally manipulated.

4. Thought Objects

Let Theta be the set of all thoughts or concepts in the system.

Each thought theta is modeled as:

theta = (L, D, e, C, M)

Where:

• L(theta) = label,
• D(theta) = description,
• e(theta) = semantic embedding vector,
• C(theta) = category or ontology class,
• M(theta) = metadata bundle.

The metadata bundle includes fields already present in the node schema, such as:

• references,
• provenance,
• evidence class,
• consensus,
• review state,
• source type,
• and layout state.

In implementation terms, the current node model already approximates this through fields such as:

• id
• label
• cat
• desc
• ref
• evidence
• consensus
• sourceType
• reviewState
• provenance
• x, y, vx, vy
• pinned, alpha, visible

5. Geometry of Thought

The model treats thoughts as points in a semantic feature space through the embedding map:

e : Theta -> R^d

A simple semantic dissimilarity can be defined as:

d_sem(theta_i, theta_j) = 1 - cosine_similarity(e(theta_i), e(theta_j))

More generally, the system is better understood as a multi-metric space:

d(theta_i, theta_j) = sum over k of lambda_k * d_k(theta_i, theta_j)

The component distances may include:

• semantic distance,
• citation or reference distance,
• topic distance,
• ontology distance,
• temporal distance,
• graph-structural distance.

This matters because Project Stars does not infer relations from one notion of similarity alone.

6. Relation Layers

Project Stars maintains two distinct relation layers.

6.1 Confirmed relations

The confirmed relation layer is:

Rc subset of Theta x Theta x RelationTypes

A confirmed relation represents a reviewed or accepted relationship. These are the only relations treated as structurally binding in the layout system.

6.2 Candidate relations

The candidate relation layer is:

Rp subset of Theta x Theta x RelationTypes x [0,1] x Evidence

Where:

• the value in [0,1] is a confidence or composite score,
• Evidence is the bundle describing the basis of inference.

Candidate relations are hypotheses:

• they are generated deterministically,
• they are reviewable,
• they are visually subordinate,
• they are never auto-promoted to confirmed.

This makes the graph not only structural, but also epistemic.

7. Edge Objects as Evidence-Bearing Entities

Edges are not anonymous line segments. They are structured relation objects.

The current implementation already stores rich edge-level information through fields such as:

• relation
• status
• confidence
• basis
• notes
• rationale
• citations
• evidenceClass
• consensus
• provenance
• review
• scoreComponents

A relation object can be written as:

r_ij = (theta_i, theta_j, type, status, basis, provenance)

This matters because the graph stores relationship meaning and justification, not just connectivity.

8. Candidate-Link Inference

Candidate relations are computed by a deterministic scoring function.

8.1 Signal extraction

For each thought theta, define extracted signal sets such as:

• Tok(theta) = token set from label and description,
• Ref(theta) = reference or citation set,
• Top(theta) = topic set,
• Year(theta) = representative temporal signal.

These correspond to the signal extraction described through computeNodeSignals(node) and fields like:

• tokenSet
• refSet
• topicSet
• yearAvg

8.2 Scoring function

Define the candidate-link score as:

S(theta_1, theta_2) =

• 0.28 * s_sem
• + 0.24 * s_cit
• + 0.18 * s_top
• + 0.16 * s_nei
• + 0.09 * s_ont
• + 0.05 * s_rec

Where each component is normalized to the range [0,1], and:

• s_sem = semantic similarity,
• s_cit = citation overlap,
• s_top = shared topic signal,
• s_nei = shared confirmed-neighbor signal,
• s_ont = ontology or domain match,
• s_rec = recency weight.

A candidate edge is admitted only when:

S(theta_1, theta_2) >= tau

With the current threshold:

tau = 0.46

8.3 Determinism and explainability

A key principle is:

Candidate relations must arise from explicit, reviewable signals rather than random suggestion.

More precisely, a candidate relation exists only if:

• the score is above threshold, and
• the basis of inference is not empty.

This captures the current design: candidate links are deterministic, thresholded, and preserve why they were created.

9. Modeling Principles

The following principles define the scientific stance of Project Stars.

9.1 Thoughts are structured objects

A thought is not just a label. It is an attributed object with semantic, relational, evidential, and review-bearing structure.

9.2 Inference is not confirmation

Candidate links are epistemic hypotheses. Confirmed links are reviewed commitments.

9.3 Explainability is required

Every candidate link must preserve the reasons it was surfaced.

9.4 Only confirmed structure shapes stable layout

Hypothetical relations may be shown, but they should not deform the stable topology of the graph.

9.5 Provenance is part of the model

Sources, review state, citations, evidence class, and rationale are not optional extras. They are part of the scientific object.

9.6 Visualization is an embedding, not the ontology itself

The visible 2D layout is a dynamic projection of the relational system, not the thought system in full.

10. Layout Dynamics

The displayed graph is not identical to the thought space. It is a time-dependent visual embedding of the graph into 2D.

Define:

p(t) : Theta -> R^2

Where p(t)(theta) is the rendered position of thought theta at time t.

Each thought also carries velocity:

v_theta(t) = d/dt p_theta(t)

The current force-layout design can be expressed as:

m_theta * p_theta'' =

• sum of pairwise repulsion forces
• + sum of spring forces over confirmed edges only
• + weak centering force
• - damping term

Where:

• repulsion prevents collapse,
• confirmed-edge springs preserve reviewed structure,
• centering keeps the graph bounded,
• damping reduces instability.

10.1 Confirmed-only spring axiom

A central axiom of the layout is:

Spring force is zero unless the relation is confirmed.

This formalizes a key design choice: uncertain hypotheses may annotate the map, but they should not determine its equilibrium geometry.

10.2 Energy interpretation

The layout can also be understood as approximately minimizing an energy function made from:

• spring energy on confirmed edges,
• pairwise repulsion,
• weak centering.

That gives the visualization a more rigorous basis than just “animated nodes.”

11. Visual Encoding as Epistemic Encoding

The interface uses visual hierarchy to distinguish certainty levels:

• confirmed edges = solid,
• possible edges = faint and dashed,
• selected possible edges = slightly more visible,
• candidate-neighbor labels = faint and conditional.

This should be understood as an epistemic encoding scheme, not mere styling.

11.1 Structural layer

Confirmed edges and confirmed topology represent accepted relational structure.

11.2 Hypothesis layer

Possible edges and faint related labels represent epistemic hypotheses above threshold.

11.3 Activation layer

Selection, hover, and wave disturbances represent temporary local activation rather than truth status.

12. Wave Field and Activation

The animated wave background is meant to evoke:

• oscillation,
• propagation,
• emergence,
• resonance,
• disturbance.

When a node is selected, the node acts as a local disturbance source.

A formal way to express this is through a scalar field:

phi(x, t)

over the 2D visual plane, behaving like a damped driven wave.

In practical terms:

• the graph provides discrete relational structure,
• the background provides a continuous activation field,
• selected thoughts act like local excitations in that field.

This supports the conceptual reading that ideas are not isolated points but sources of local influence in a surrounding system.

13. Receiver Quality and Experimental Metrics

The finalized atlas introduces an explicit receiver-state control.

13.1 Receiver quality

Receiver quality is represented by a scalar:

Q in [0,1]

Q is intended as a controllable tuning parameter for testing how well the current system state supports coherent activation and stable conceptual resolution.

In the current atlas framing:

• low Q corresponds to weak tuning and noisier local resolution,
• high Q corresponds to stronger tuning and cleaner emergence of coherent local structure.

13.2 Experimental interpretation

This turns a philosophical claim into a manipulable computational hypothesis:

precision depends not only on structure, but also on receiver-state tuning.

Rather than asserting this as a theorem, Project Stars now exposes it as an interactive experimental variable.

13.3 Live metrics

The atlas also introduces an observability bundle Xi, which can include:

• precision,
• coherence,
• convergence,
• receiver state.

These metrics make the system more testable by allowing the user to compare different receiver states under the same conceptual structure.

14. Inspector as Research Interface

The detail inspector is the main explanatory surface of the application.

For a selected node it shows:

• domain,
• confirmed degree,
• evidence class,
• consensus,
• review state,
• candidate count,
• description,
• references,
• confirmed connections,
• possible related thoughts,
• relationship notes.

Scientifically, the inspector is where the graph becomes interpretable. It translates:

• graph structure into readable relation lists,
• candidate inference into inspectable evidence,
• node metadata into explicit epistemic context.

15. Add-Thought Workflow as Curation Mechanism

The add-thought workflow allows new node creation and optional confirmed-edge creation with rationale, citations, provenance, and review metadata. Candidate edges are recomputed after addition.

This means the system is not just an observer of thought structure. It is also a curation environment.

Each addition extends the current graph by:

• adding a new thought object,
• optionally adding a reviewed confirmed relation,
• recomputing the candidate layer.

This makes Project Stars a dynamic research object rather than a static diagram.

16. Multi-View Navigation

The current implementation supports several navigation modes, including:

• constellation view,
• domain view,
• focus view,

along with:

• search,
• filters,
• zoom,
• fit,
• home reset,
• minimap,
• pause or resume,
• manual rearrangement.

These are not just view presets. They are different ways of projecting the same underlying system:

• global structural inspection,
• domain grouping,
• local neighborhood analysis.

17. Export Semantics

The export layer preserves:

• categories,
• nodes,
• edges,
• metadata,
• integration configuration,
• and the distinction between confirmed and candidate relationships.

It also preserves:

• provenance,
• uncertainty,
• review state,
• rationale,
• relation type,
• score components,
• and receiver-state or experiment metrics where available.

This is scientifically important. A graph export that discards uncertainty or provenance is weak as a research artifact.

18. External Research-Source Layer

The current build models an external-source integration layer through:

• OpenAlex,
• Crossref,
• Semantic Scholar,
• Wikidata.

These sources support future or parallel workflows such as:

• citation overlap,
• metadata resolution,
• author-neighborhood analysis,
• recommendation expansion,
• ontology or entity matching.

This staged design is methodologically sound:

1. define the internal semantics,
2. define the scoring and review model,
3. connect live data once the evidence structure is stable.

19. Research Foundations and Scientific Framing

The design draws from several research areas:

• graph drawing and information visualization,
• link prediction,
• bibliometrics and citation structure,
• similarity and retrieval,
• ontology matching,
• human-centered knowledge systems.

These map onto the model as follows:

19.1 Graph drawing

Force-directed layout motivates the dynamic embedding p(t).

19.2 Link prediction

Candidate-link generation is interpretable link prediction over a layered graph.

19.3 Bibliometrics

Citation overlap and neighborhood structure support research-grounded relation signals.

19.4 Information retrieval

Semantic and token-level similarity provide a retrieval-style basis for conceptual adjacency.

19.5 Ontology matching

Category and entity alignment help distinguish true conceptual relation from lexical coincidence.

19.6 Human review

Human review defines the hard boundary between surfaced hypotheses and accepted structure.

19.7 Isomorphism to established frameworks

The current atlas is best interpreted as a computationally analogous or partially isomorphic system rather than a full identity claim.

Free Energy Principle

The layout dynamics can be read as an energy-minimizing process over a structured state space. Confirmed-edge springs, repulsion, damping, and centering together define a low-energy settling process that is broadly analogous to variational or predictive-error minimization.

Predictive processing / active inference

The candidate-link layer functions like a structured hypothesis layer, while confirmed structure functions like stabilized commitment. In this reading, candidate scores act as interpretable update pressures rather than opaque suggestions.

Dynamical systems neuroscience

The evolving embedding p(t) and activation field phi(x,t) can be interpreted as a metastable conceptual dynamics. Receiver quality Q provides a controllable parameter for testing how tuning changes the emergence of coherent local structure.

20. Scientific Contribution

The main contribution of Project Stars is the coupling of several ideas into one interpretable system:

1. Thoughts as structured research objects
   Nodes carry provenance, evidence, review, and ontology-bearing metadata.

2. Epistemically separated relation layers
   Confirmed and candidate relations are kept distinct both visually and structurally.

3. Explainable candidate inference
   Candidate links are generated from explicit weighted signals and preserve their basis.

4. Structural vs perceptual separation
   Only confirmed relations shape equilibrium layout; candidate relations remain inspectable but non-deforming.

5. Field-based activation metaphor
   Selection and local activity are modeled through a wave-like background rather than collapsed into graph structure.

6. Receiver-state experimentation
   Receiver quality and live metrics make the central claim computationally testable rather than purely rhetorical.

7. Research-preserving export
   The JSON schema retains rationale, provenance, review state, uncertainty, and score components.

This makes Project Stars interpretable as a research system for thought relations rather than merely a browser visualization.

21. Limitations

The current build has important limits:

1. it is client-side only,
2. the force simulation is intentionally lightweight,
3. token-based similarity is interpretable but not state-of-the-art,
4. candidate quality depends on the quality of underlying text and references,
5. the build prioritizes interpretability over automation.

Additional limitations include:

• the embedding layer may be approximate or implicit,
• the score is interpretable but hand-weighted,
• the ontology layer is still modest,
• the field layer is partly metaphorical,
• there is no persistent collaborative review backend,
• large-scale graph behavior is not yet the main target.

22. Future Extensions

Natural next steps include:

• stronger embedding-based retrieval,
• calibrated or learned score weights,
• typed morphisms between thoughts,
• explicit cluster or tightness measures,
• richer ontology structure,
• field behavior tied more directly to graph activation.

A deeper theoretical extension would reinterpret confirmed relations as morphisms:

r : theta_i -> theta_j

Another would treat the semantic space as curved rather than flat, so conceptual distance depends on local structure.

23. Implementation Mapping

A practical mapping from theory to implementation is:

• Theta -> node collection (SEED_NODES plus added nodes),
• A -> node fields such as label, description, references, evidence, review, and provenance,
• Rc and Rp -> edge collection with relation status,
• S -> recomputeCandidateEdges() and stored score components,
• p(t) -> node position, velocity, and animation tick,
• phi -> background wave canvas and selected-node disturbance logic,
• Q -> receiver-quality control,
• Xi -> live experiment metrics,
• export semantics -> JSON schema preserving relation layer and evidence metadata.

24. Updates — 28/03/2026

The README and live atlas were updated on 28/03/2026 to reflect the finalized theory framing and interface changes.

Added to the atlas

• Receiver Quality control (Q) with low, medium, and high experimental presets,
• live experiment metrics for precision, coherence, convergence, and receiver state,
• finalized mathematical framing in the interface using the language of a formal hypothesis rather than an overclaimed proof,
• science-link framing connecting the atlas to free-energy, predictive-processing, and dynamical-systems interpretations,
• extended export semantics so receiver-state and experiment metrics travel with the exported research artifact,
• responsiveness and stability improvements to improve minimap interaction and overall browser robustness.

Why this matters

These updates move Project Stars from a compelling conceptual visualization toward a more testable computational research instrument. The atlas now makes the central claim experimentally manipulable:

precision depends not only on structure, but also on receiver-state tuning.

Repository note

The interactive file prepared on 28/03/2026 is intended to serve as the current hosted index.html for the project.

25. Copyright

Unless otherwise stated for third-party materials, services, or marks:

Copyright (c) 2026 Pezhman Farhangi

See LICENSE and THIRD_PARTY_NOTICES.md for governing terms and ownership boundaries.