Level 1 of 3 · the shared message. This section is identical in every repository of this system.
This is one deterministic compositional instrument and the living history that produced it. It began as a loudspeaker's ground state — uniform 4π radiation into a room, a fixed 6.02 dB budget apportioned across a cabinet's dimensions and summing to a constant — and that single structure, forced by physics rather than chosen at a whiteboard, became the simplex, the Higgins operator, composition monitoring (MC‑4 / EITT), the deterministic CN‑TT engine, the 3ⁿ confidence index, and finally a verification network where any node checks any other. Each step was forced by the one before it.
Who it is for. This is an expert system, and these repositories are its expert onboarding. The qualifier is the data itself: if you have a composition — parts of a whole tracked in order, within a shared budget — you already have the need, and this is the instrument for it. If your data isn't a composition of many parts within a budgeted whole, then with respect this isn't the right tool for you — and we'd rather say so kindly up front than waste your time; other methods are better suited to that, and we hope they serve you well. The work is told, shown, and offered for reproduction — not advertised.
Safety before power. This is not merely a powerful compositional system — it is one in which safety is dominant and absolute. The operator holds the last breaker (LOOP‑001 / SAFE‑001): full automation is never possible, at any scale the operator chooses. Coherence is offered, never imposed — observe‑don't‑impose, operator‑gated, distributed, auditable — and capability is admitted only behind governance. The discipline is the point: a system that may be trusted with something larger must first refuse to overclaim about itself.
Read the whole arc, source to network → ARC_OF_DISCOVERY.md.
Level 2 of 3 · the other half exists.
This is one cross‑brain split across sibling repositories that reference and check each other:
- HUF — Higgins‑Unity‑Framework — you are here — the governance, lineage, and development history.
- Hˢ — higgins‑decomposition — the live deterministic instrument (the math).
- RWA — Rogue‑Wave‑Audio — the headwater, where the ground state and diffraction were first measured.
Two‑repo map and the cross‑repo resolver: CROSS_BRAIN.md.
Level 3 of 3 · what this one is.
HUF (Higgins Unity Framework) is the experimental origin, governance layer, and development history — where the ideas (EITT, MC‑4, the cross‑AI collective) were discovered and stress‑tested before they matured into the Hˢ instrument. It is kept whole on purpose: lose nothing. Everything below this line is that record.
▶ The instrument HUF governs is Hˢ kinematics — the matured deterministic engine for reading any composition in motion, with the guards, the determinism receipt, the traceability chain, and the data‑is‑the‑star (49/51) governance (
huf-gov/THE_DATA_IS_THE_STAR.md) that all of this exists to protect. If you have a composition to analyse, start atIS_Hs_RIGHT_FOR_YOU.mdin the Higgins Decomposition (Hˢ) repository: whether Hˢ fits your data, what it does at your D, and how an AI assistant can run it — under the governance HUF provides.
Why three. Three statements — what the system is, that a sibling exists, and which one you are reading — let any reader, human or machine, confirm both their position and the system's status. It is the same rule the instrument runs on: one perspective is a point, two a line, three a plane; three is the minimum to locate, not merely detect. Machines: each repo's entry point is its
AI_ASSIST.jsonand fast‑refresh JSON; the resolver inCROSS_BRAIN.mdkeeps every cross‑repo path valid standalone.
Role in the arc of discovery — read this first. HUF is the experimental origin, governance layer, and development history of what became Hˢ (Higgins Decomposition) — the current, deterministic compositional instrument. The wide‑ranging exploration in this repo (EITT, MC‑4, the cross‑AI collective, the geochemistry/energy/chemistry studies) is where the ideas were discovered and stress‑tested; they matured into the Hˢ engine (CNT → CNQ → CN‑TT v4). This repository is the support / lineage / history; the active instrument and its engine live in the higgins‑decomposition (Hˢ) repo. It is kept whole on purpose — the past is the strength and the future; lose nothing. New here? Start with
AI_ASSIST.jsonandRELATIONSHIP_TO_Hs.md.
An independent research project in Compositional Data Analysis (CoDa) and entropy-invariant monitoring on the simplex. This is a scientific research repository — not a game engine, not a Unity plugin, not a software library.
Author: Peter Higgins, Rogue Wave Audio, Markham, Ontario, Canada
EITT — a key point of contact, divided influence. The Entropy-Invariant Time Transformer: Shannon entropy of compositional time series is empirically near-invariant under geometric-mean decimation — measured at 0.18% variation across a 341:1 compression ratio (validated across energy systems, chemistry [500,000 data points], hardware reliability, climate, and 40,666 igneous rocks). Its influence is deliberately divided: minor inside the deterministic engine (one diagnostic, eitt_bench_test, among many — nothing load-bearing rests on it), and major as two things — the temporal face of the framework's central thesis (the timescale is intrinsic; the time-domain twin of the acoustic ground state) and the falsifiable open problem HUF offers the compositional-data-analysis community (measured, not proven — can it be derived from Aitchison geometry?). Full positioning: science/eitt/EITT_THE_PLACE_IT_HOLDS.md.
Disciplines: Compositional Data Analysis, Shannon entropy, Aitchison geometry, simplex monitoring, quantum information correspondence, energy transition analysis.
Conference: CoDaWork 2026, Coimbra, Portugal (June 2026). Abstract page 25.
Phase status (2026-04-17): Phase 1 (CoDaWork 2026 submission content) marked STABLE. Phase 2 (EITT hardening for broader adoption) ACTIVE. April 2026 — Geochemistry extension. EITT validated on 40,666 real igneous rocks (Ball 2022 + AGDB3 Alaska), 8 major oxides, 37/39 TAS classification types pass. Foidite sole anomaly (deep mantle phase chaos). Gold Standard Working Example: complete 10-step Higgins Decomposition chain with pedagogical commentary from 5 analytical viewpoints (23-page PDF, 11 plots). New top-level codawork2026/ folder consolidates all deliverables. See ai-refresh/PHASE_MARKERS.json and codawork2026/README.md.
Lineage: The framework's engineering DNA traces to Rogue Wave Audio's DADC-DADI-ADAC loudspeaker diffraction correction chain (Dec 2024–Nov 2025), then through the Higgins Operator H₁ (Feb 2026), to HUF/EITT. The compositional structure was discovered empirically in acoustic engineering before it was formalized mathematically. Engineering sibling: Rogue Wave Audio. See ai-refresh/MASTER_LINEAGE.json for the full arc, briefings/THE_LINEAGE.md for the founding narrative, and science/coda-monitoring/ORIGIN_BRIDGE_DADC_TO_MC4.md for the technical bridge. Principle: The past is our strength and our future.
HUF proposes that composition — the internal proportional balance of a system's parts — can be monitored as a primary observable alongside magnitude, identity, and trend. The instrument reads. The human expert decides. The loop stays open.
The framework builds on Aitchison (1982/1986) simplex geometry and Shannon (1948) entropy, applying them to longitudinal monitoring of any system where parts share a conserved whole: energy grids, chemical mixtures, drive fleets, financial portfolios, wetland ecosystems.
EITT's influence within HUF is deliberately divided. In the deterministic engine it is one diagnostic among many (eitt_bench_test); nothing load-bearing depends on it. As a result it is the framework's primary point of contact with the compositional-data-analysis community — a measured, still-unproven invariance offered as a shared open problem — and the temporal statement of the framework's central thesis (the time-domain twin of the acoustic ground state). Full positioning: science/eitt/EITT_THE_PLACE_IT_HOLDS.md.
Shannon entropy appears empirically near-invariant under geometric-mean block decimation of compositional time series. This is not a theorem — it is an empirical observation awaiting formal proof.
Measured: 0.18% variation across a 341:1 compression ratio (daily to annual European electricity compositions, 8 carriers, 4089 trading days). Confirmed independently on EMBER monthly generation data (6 countries, mean 1.02%, all below 2%) and NGFS Phase 4 climate scenarios (35 scenarios, all below 5%).
April 2026 — Chemistry extension. EITT tested on 500,000 chemical mixture data points (CheMixHub benchmark, 7 datasets). Four diagnostic lenses applied simultaneously (Shannon, Jensen-corrected, Renyi q=2, Aitchison norm). Interior compositions pass at 54-82%. Boundary compositions reveal simplex curvature effects. First empirical decomposition: approximately 50% of the invariance comes from Aitchison geometry, approximately 50% from temporal autocorrelation.
This produced three new frameworks:
| Framework | What It Does | Document |
|---|---|---|
| EITT Findings | Raw science. Four-lens results, failure taxonomy, multi-modal simplex | science/eitt/ |
| HUF-IDX | Development index. What residuals mean. Domain distance from ground zero | science/eitt/ |
| PRISM | Operational layer. Ranked resource allocation targets from residual analysis | science/eitt/ |
Posture: We found this empirically. We can't prove it. Can you?
| Category | Name | Question | Status |
|---|---|---|---|
| MC-1 | Magnitude Monitoring | How much? | Universally deployed |
| MC-2 | Identity Monitoring | Who or what? | Universally deployed |
| MC-3 | Trend Monitoring | Which direction? | Universally deployed |
| MC-4 | Composition Monitoring | What is the balance? | Proposed (HUF) |
HUF/
├── codawork2026/ # ★ CODAWORK 2026 — COMPLETE PACKAGE ★
│ ├── presentation/ # Talk PPTX + submitted abstract
│ ├── journals/ # All formal PDF documents (11 PDFs)
│ ├── experiments/ # Builders, Working Example, plots
│ ├── reproducibility/ # HIGGINS_REPRODUCIBILITY_PACKAGE.json v5.0
│ ├── primers/ # 4 researcher briefings
│ ├── preparation/ # Q&A prep, conversation guide
│ ├── extended/ # Extended results, handouts, bridge docs
│ ├── science/ # Key supporting science docs
│ └── data/ # EMBER, gold/silver, geochemistry, NGFS
│
├── ai-refresh/ # AI STARTS HERE — fast context loading
│ ├── HUF_FAST_REFRESH.json # All canonical values, single file
│ ├── HUF_INTEGRITY_MANIFEST.json # Hash verification, drift patterns
│ └── huf_spec_v2.0.json # Complete framework specification
│
├── science/ # All scientific work by subject
│ ├── reference/ # Core reference (9 docs, ~105 min)
│ ├── core/ # EITT maths, formulas, user handbook
│ ├── methodology/ # Governance scale, confidence index
│ ├── chemistry/ # CheMixHub results, HUF-IDX, PRISM
│ ├── quantum/ # HUF-QIT: 9 isomorphisms, Bell test
│ ├── eitt/ # EITT evidence: 4 proofs, adversarial
│ ├── coda-monitoring/ # Perturbation drift detection protocol
│ ├── spectral/ # Frequency-domain analysis
│ ├── loudspeaker-analogy/ # Origin: crossover networks as CoDa
│ ├── wetlands/ # Ramsar Convention monitoring
│ └── governance/ # 201-country ranking outputs
│
├── huf-gov/ # Active governance
│ ├── governance/ # Standards, protocols, kill tests
│ ├── science/ # Monitoring taxonomy, ontology
│ └── evidence/ # Case studies (energy, backblaze, etc.)
│
├── tools/ # Everything runnable
│ ├── interactive/ # ★ LIVE HTML TOOLS — open in browser ★
│ │ ├── EXP-19_Interactive_Simulator.html
│ │ ├── EXP16_Interactive_Simulator.html
│ │ ├── EXP-19_Fourier_Conjugate_Preservation_Theorem.html
│ │ └── HUF_Spectrum_Analyzer_Universal.html
│ ├── pipeline/ # EITT pipeline, preparsers, scripts
│ ├── diagnostics/ # Validators, dashboards, UML diagrams
│ ├── spectrum-analyzer/ # HUF Spectrum Analyzer (all versions)
│ └── shared/ # Build utilities, styles, glossary
│
├── drafts/ # Conference materials, papers, proposals
│ ├── codawork-2026/ # CoDaWork 2026, Coimbra
│ │ ├── presentation/ # Main talk slide deck
│ │ ├── primers/ # 4 personalized researcher primers
│ │ ├── preparation/ # Q&A prep, conversation guide
│ │ └── extended/ # Extended results, EITT handout
│ ├── papers/ # Paper submissions (7 venues)
│ ├── proposals/ # Unified proposal, integration briefs
│ └── books/ # Book-length QIT treatments
│
├── briefings/ # Session briefings & AI handoffs
│
├── data/ # Datasets by domain
│ ├── backblaze/ # Hard drive failure data
│ ├── energy/ # EMBER/OWID energy data
│ ├── ember/ # EMBER processed results
│ ├── ngfs/ # NGFS Phase 4 scenarios
│ ├── codawork-samples/ # Reproducible CoDaWork samples
│ ├── eitt-lab/ # EITT lab package
│ └── toronto/ # TTC transit data
│
├── dormant/ # Paused branches — sleeping, not dead
│ ├── pre-coda-metrics/ # Pre-CoDa metric formulations
│ ├── early-governance/ # Multi-AI collective experiments
│ ├── planck-case/ # Planck sky map analysis
│ ├── peterson-outreach/ # Peterson letters (paused)
│ ├── hagf/ # Adaptive governance (superseded)
│ └── deceptive-drift/ # Arithmetic hiding composition changes
│
└── archive/ # Superseded work — what failed speaks loudest
Download any HTML file and open in a browser. No installation required. Everything runs locally.
| Tool | What It Does | Try It |
|---|---|---|
| Hˢ Simplex Scope | Real-time Fourier conjugate pair decomposition. 12 pairs, all 12 pipeline steps visualised simultaneously. See self-conjugate preservation in action. | EXP-19_Interactive_Simulator.html |
| Spring-Mass Force Decomposition | Damped oscillator decomposed into KE/PE/Damping carriers. Watch chaos detection at carrier zero-crossings. EITT entropy panel. 3D helix. | EXP16_Interactive_Simulator.html |
| Fourier Conjugate Preservation Theorem | Mathematical proof visualisation. 3 theorems + 1 corollary. Interactive step-through of the formal proof. | EXP-19_Fourier_Conjugate_Preservation_Theorem.html |
| Spectrum Analyzer | Universal JSON reader. Drop any Hˢ pipeline output and get 5 readings: Source, Calibration, Complexity, Velocity, Peak. | HUF_Spectrum_Analyzer_Universal.html |
All tools use the Hˢ symbol (H-superscript-S = Higgins Decomposition on the Simplex) and the current 12-step pipeline v1.0 with HVLD vertex lock diagnostic.
15/15 experiments classified NATURAL across 12 physical domains (Acoustics, Astrophysics, Commodities, Energy, Force, Geochemistry, Gravity, Materials, Matter, Nuclear, Particle, QCD). Pipeline v1.0 with 35 transcendental constants, 13 Fourier conjugate pairs, 4 input guards. Tightest match: EXP-03 Nuclear SEMF locks to 1/(π^e) at δ = 5.87 × 10⁻⁶ — six millionths.
Key documents:
- Character Analysis — 30+ page cornerstone specification (DUT exploded diagnostic, state machine, adversarial robustness, theorems, disclosures)
- EXP-03 Precision Inference Paper — Standalone paper on the nuclear SEMF result
- Release Validation — Full sweep results for all 15 experiments
Start here: Read ai-refresh/HUF_FAST_REFRESH.json first. It contains every canonical name, number, formula, and structural rule. If anything elsewhere disagrees with FAST_REFRESH, the FAST_REFRESH wins. Then verify with ai-refresh/HUF_INTEGRITY_MANIFEST.json. Then read INDEX.json for the full file map.
Context aggregator: Run python build_context.py --mode seed to generate a single paste-ready text file containing the full AI seed layer. Modes: seed (~9k tokens), science (~232k tokens), full (~346k tokens).
Known drift traps: EITT is "Entropy-Invariant Time Transformer" (never Ternary). Japan drift flag is 2013-2014 (never 2011-2012). Germany is 2023-2024/2024-2025 (never 2011). UK has three specific values (2.98, 3.23, 3.26), never "approximately 3".
| Time | What | Where |
|---|---|---|
| 5 min | The cylinder problem and fuel gauge — one-page HUF | science/reference/ |
| 105 min | Reference Collection — 9 documents, full learning path | science/reference/INDEX.md |
| 15 min | User Handbook — fast summary + guided links | science/core/HUF_USER_HANDBOOK.md |
| 20 min | Chemistry results (the new frontier) | science/chemistry/ |
| 30 min | The kill test — 19 documented failure modes | huf-gov/governance/ |
| 10 min | Quantum correspondence (advanced) | science/quantum/ |
| 23 pp | Gold Standard Working Example — step-by-step decomposition chain | codawork2026/journals/HIGGINS_Working_Example.pdf |
| — | CoDaWork 2026 complete package — everything for Coimbra | codawork2026/ |
If you want to break it, the kill test is where to start.
- Composition can be monitored directly, not only as a statistical correction.
- In some systems, structural change appears in ratio-state before magnitude-based indicators visibly fail.
- This can be tested across any domain where a conserved whole divides into meaningful parts.
- New simplex mathematics. The foundations are Aitchison (1982), Shannon (1948), Stevens (1946), Amari (1985).
- Universal validity. Cross-domain validity must be earned domain by domain.
- That every compositional change is harmful, actionable, or predictive.
- That HUF replaces domain expertise, causal explanation, or policy judgment.
- That autonomous intervention is justified on compositional readings alone.
Nothing dies here — only goes dormant. The dormant/ folder preserves paused work with documented reasons and conditions for reawakening. The archive/ folder holds superseded and rejected approaches as reference for what was tried and why. What failed always speaks louder.
Standard: RWA-001 (Rogue Wave Audio Corporate Reference)
Protocol: HUF-GOV. Measure, report, file. No intervention on the data.
Multi-AI Review: All core findings subjected to adversarial review by Claude, ChatGPT, Grok, Gemini, and Copilot.
MIT. See LICENSE.
See CITATION.cff.
Peter Higgins | Rogue Wave Audio | PeterHiggins@RogueWaveAudio.com
Repository: github.com/PeterHiggins19/Higgins-Unity-Framework
A fully maintained list. The science here stands on the work of others; we cite it extensively, as both respect and protection. When the framework adopts a new method, or a member of the community engages the work, add it here — and in the identical block carried by the sibling repositories.
This instrument is built on standard compositional tools, and it exists in dialogue with the people who created and steward them. With gratitude to the CoDa Association and the organisers, scientific committee, and hosts of CoDaWork 2026 (Coimbra, Portugal, 1–5 June 2026; co-hosted with the Sociedade Portuguesa de Geologia), whose welcome made this work's first compositional presentation possible — and to the community members who welcomed, questioned, and strengthened it:
- Conference chairs & hosts: Juan José Egozcue (chair of the committee that accepted the work), Teresa Albuquerque (conference co-chair and host).
- Foundational scholars whose work the instrument stands on: Vera Pawlowsky-Glahn, Juan José Egozcue, Raimon Tolosana-Delgado, Karel Hron, Antonella Buccianti, Gregory B. Gloor, Javier Palarea-Albaladejo.
- Colleagues who welcomed and challenged the work: Paul-Gauthier Noé, Patricia Genius Serra, Christine Thomas-Agnan, Dot Dumuid, Kamila Fačevicová, Gianna Serafina Monti, Rui Santos.
- Fellow presenters whose work runs alongside this one: Narayana & Chotirmall (microbiome time series), Ascari & Fiori (energy-mix clustering), Kanjiradan & Veetil (compositional health series), Vega Baquero & Santolino (compositional finance).
Particular thanks to Juan José Egozcue and Vera Pawlowsky-Glahn for their written discussion of this work and their subcompositional-coherence results, which directly informed it.
The instrument reads. The expert decides. These are the experts.
Compositional data analysis.
- Aitchison, J. (1982). The statistical analysis of compositional data. Journal of the Royal Statistical Society, Series B, 44(2), 139–177.
- Aitchison, J. (1986). The Statistical Analysis of Compositional Data. London: Chapman & Hall.
- Pawlowsky-Glahn, V., & Egozcue, J. J. (2001). Geometric approach to statistical analysis on the simplex. Stochastic Environmental Research and Risk Assessment, 15, 384–398.
- Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G., & Barceló-Vidal, C. (2003). Isometric logratio transformations for compositional data analysis. Mathematical Geology, 35(3), 279–300.
- Egozcue, J. J., & Pawlowsky-Glahn, V. (2005). Groups of parts and their balances in compositional data analysis. Mathematical Geology, 37(7), 795–828.
- Pawlowsky-Glahn, V., Egozcue, J. J., & Tolosana-Delgado, R. (2015). Modeling and Analysis of Compositional Data. Chichester: John Wiley & Sons.
- Egozcue, J. J., & Pawlowsky-Glahn, V. (2023). Subcompositional coherence and proportionality. SORT — Statistics and Operations Research Transactions.
- Martín-Fernández, J. A., Barceló-Vidal, C., & Pawlowsky-Glahn, V. (2003). Dealing with zeros and missing values in compositional data sets. Mathematical Geology, 35(3), 253–278.
- Palarea-Albaladejo, J., & Martín-Fernández, J. A. (2015). zCompositions: R package for the imputation of left-censored compositional data. Chemometrics and Intelligent Laboratory Systems, 143, 85–96.
- Filzmoser, P., Hron, K., & Templ, M. (2018). Applied Compositional Data Analysis. Cham: Springer.
- Greenacre, M. (2018). Compositional Data Analysis in Practice. Boca Raton: Chapman & Hall/CRC.
- Gloor, G. B., Macklaim, J. M., Pawlowsky-Glahn, V., & Egozcue, J. J. (2017). Microbiome datasets are compositional: and this is not optional. Frontiers in Microbiology, 8, 2224.
Information theory & geometry.
- Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27, 379–423 & 623–656.
- Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103(2684), 677–680.
- Amari, S. (1985). Differential-Geometrical Methods in Statistics. New York: Springer.
Acoustic & mathematical lineage (the DADC origin).
- Strutt, J. W. (Lord Rayleigh) (1896). The Theory of Sound (2nd ed.). London: Macmillan.
- Sommerfeld, A. (1896). Mathematische Theorie der Diffraction. Mathematische Annalen, 47, 317–374.
- Olson, H. F. (1957). Acoustical Engineering. Princeton: Van Nostrand.
- Vanderkooy, J. (1991). A simple theory of cabinet edge diffraction. Journal of the Audio Engineering Society, 39(12), 923–933.
- Linkwitz, S. H. (1976). Active crossover networks for noncoincident drivers. Journal of the Audio Engineering Society, 24(1), 2–8.
- Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae, 3, 133–181.
- Gershgorin, S. A. (1931). Über die Abgrenzung der Eigenwerte einer Matrix. Izvestiya Akademii Nauk SSSR.
How to cite this work: see CITATION.cff. AI assistance is used per HUF-STD-001; research design, mathematical content, and scientific responsibility remain with the named author.