ResearchFrontier structures and internal systems
Unified Music Library
Canonical merged graph across theory content, track catalog, and legacy JSON datasets. This replaces parallel loaders with one source of truth.
Generated: 3/5/2026, 8:31:09 PM
Nodes
21,199
Edges
79,218
Sources
367
Issues
0(0 errors)
Embedding Dimension
192
Concept Models
3
Concept Labels
12
Formula Families
10,308
Family Relations
25,366
Math Audit
PASS
Deep Cycles
4,989
Spectral Gap
0.915
Node Kinds
Formula Family10,308
Formula10,273
Concept205
Knowledge Node191
Track122
Dataset Artifact40
Artist30
Taxonomy Category15
Album9
Difficulty Level4
Learning Path2
Relation Types
Contains Formula31,116
Related25,959
References20,757
Connects To481
Prerequisite248
Has Difficulty204
Categorized As202
Performed By122
Contains Track47
Composed By37
Contains Step17
Next Step15
Originated By13
Mathematical Extraction
Automated theorem candidates and structural invariants extracted from the formula/family corpus.
Error groups
0
Warning groups
0
Max invariance
12
Transpositional Duality Identity
verified
For every formula, limitedTranspositionCount × transpositionalInvarianceCount = 12.
Interval-Vector Pair Identity
verified
For every formula, Σ(intervalVector) = C(cardinality, 2).
Cross-Octave Motif Invariance
verified
Cross-octave families preserve a single canonical motif across all member formulas.
Extension Graph Macro-Connectivity
verified
Extension/truncation operations create large connected manifolds over the formula space.
Global Structural Integrity
verified
Formula identifiers, interval/set invariants, and family membership constraints are internally coherent.
Deep Dynamical Extraction
Library-of-Babel style finite-state analysis: deterministic lift, periodic attractors, quotient compression, and novelty frontiers over the formula manifold.
Cycle count
4989
Max preperiod
7
State entropy
0.79089409
Compression (formula→trajectory)
19.94757282
formula:6-10x3@48
0.4482
(A4 m7)x3
small family orbit context
formula:3-10-11x2@48
0.4354
(T m7 M7)x2
small family orbit context
formula:3-11-10x2@48
0.4354
(T M7 m7)x2
small family orbit context
formula:4-11-9x2@48
0.4354
(M3 M7 M6)x2
small family orbit context
formula:4-9-11x2@48
0.4354
(M3 M6 M7)x2
small family orbit context
formula:5-10-9x2@48
0.4354
(P4 m7 M6)x2
small family orbit context
formula:5-11-8x2@48
0.4354
(P4 M7 m6)x2
small family orbit context
formula:5-8-11x2@48
0.4354
(P4 m6 M7)x2
small family orbit context
Top Categories
Formula Family
10,308
Formula System
10,273
Rhythm
60
Original
54
Classical
31
Instruments
24
Analysis
19
Chords
19
Cover
17
Form
16
Symmetry
16
Intervals
15
Harmony
12
Scales
12
Composers
9
Demo
8
Formula Root Matrix
Exhaustive periodic formulas in bounded 12-TET space with transformation links. Your extension pattern is explicitly represented.
Formulas
10,273
Relations
16,095
Families
10,308
Family Relations
25,366
Generated
10,267
Bound
1–4 octaves
Messiaen Mode 1 (Whole Tone)
formula:2x6@12
(W)x6
span 12 semitones (1 oct), motif 1, LT 2
Messiaen Mode 2 (Octatonic)
formula:1-2x4@12
(H W)x4
span 12 semitones (1 oct), motif 2, LT 3
Messiaen Mode 3
formula:1-1-2x3@12
(H H W)x3
span 12 semitones (1 oct), motif 3, LT 4
Extended Mode 3 Over Four Octaves
formula:3-3-5-5x3@48
(T T P4 P4)x3
span 48 semitones (4 oct), motif 4, LT 4
Integrity Snapshot
No issues detected in the latest build.
Retrieval Preview
Hybrid retrieval combines lexical matching, dense similarity, and graph distance over the unified library.
Diminished Augmented
0.780
concept:chords/diminished-augmented
Matches on: tension, symmetry (1.00 L / 0.66 S / 0.00 G)
Half-Diminished and Diminished Seventh Chords
0.771
concept:chords/half-diminished-diminished
Matches on: tension, symmetry (1.00 L / 0.63 S / 0.00 G)
Augmented-Major Seventh Chord
0.585
concept:chords/augmented-major-seventh
Matches on: symmetry (0.70 L / 0.58 S / 0.00 G)
Messiaen Mode 1 (Whole Tone)
0.577
formula:2x6@12
Matches on: symmetry (0.61 L / 0.69 S / 0.00 G)
Messiaen Mode 3
0.567
formula:1-1-2x3@12
Matches on: symmetry (0.61 L / 0.66 S / 0.00 G)
Unified API
Pull summary or full graph from the API, then use search for tooling, ranking experiments, and concept-model training loops.
/api/unified/api/unified?full=1/api/unified/search?q=ligeti/api/unified/recommend?q=nocturne/api/unified/similar?id=track:catalog/keep-running/api/unified/concepts/api/unified/formulas?q=TTP4P4/api/unified/formulas?parse=(TTP4P4)x3/api/unified/formulas/address?index=42/api/unified/formulas?view=families/api/unified/formulas/family-label/api/unified/formulas/ml/api/unified/formulas/math/api/unified/formulas/deep-math/api/unified/concepts/label?conceptId=.../research/formula-lab