SONIFICATION — ETQ-303 and D4 Triality Research

This repository contains two related but separately versioned research lines:

• ETQ-303 v3.0.1 — the current documentation/publication release for the exact ETQ-303 protocol. The canonical runtime contract and deterministic outputs remain v3.0.0.
• D4-TIA — exact D4 triality covariants, an exact S3 symmetry harness, and a symbolic sonification profile built on top of them.

They share D4 triality context, but the D4-TIA work does not change ETQ-101 or ETQ-303 protocol identity.

The short version

ETQ-303:

ETQ-101 v2 selected states
        × independent 3-state fibre
                → 303 exact tensor states
                → one exact 303-step traversal
                → deterministic event document
                → JSON / CSV / symbolic MIDI

D4-TIA:

published 15-generator D4 covariant basis
        → exact symbolic covariants
        → exact S3 action and equivariance checks
        → exact six-position evaluations
        → symbolic MIDI contour

The repository is designed so that the mathematics, the event data, and the receiver choices remain distinguishable.

ETQ-303 in plain language

The ETQ-303 runtime contract is v3.0.0. The v3.0.1 repository release only clarifies its documentation and publication material; it does not change the runtime contract, state indexing, event generation, or deterministic outputs.

The protocol extends the preserved 101-state ETQ-101 model with an independent three-state factor:

$$\mathcal H_{303}=\mathcal H_{101}\otimes\mathbb C^3.$$

That gives exactly $101\times3=303$ basis-indexed states.

The support step advances both indices:

(j,a) → (j+1 mod 101, a+1 mod 3)

Because 101 and 3 are coprime, one traversal visits all 303 tensor addresses exactly once before returning to the start.

303 means algebraic states here. It does not mean 303 physical dimensions or 303 distinct E8 roots.

The canonical ETQ output is an event document. JSON, CSV, and MIDI are deterministic receiver formats built from that document.

See the ETQ-303 event protocol for the full construction.

D4 triality bridge

The repository also checks that the four-coordinate ETQ triality matrix matches the D4/F4 convention used by Kazuhiro Sakai:

$$A=w_Sw_T, \qquad W(F_4)/W(D_4)\cong S_3.$$

That is a literature alignment. It does not mean Sakai's papers derive ETQ's state selector, qutrit factor, SCL stencil, or sonification choices.

See the D4/F4 triality reference bridge.

D4-TIA: from published algebra to sound

The D4-TIA work is split into three layers.

1. Exact covariant algebra

D4-TIA-COV v0.1.0 constructs the published 15-generator basis directly with exact rational arithmetic.

It verifies the covariants, their grading, and the cubic syzygy. No floating-point algebra is used.

Verify it with:

npm run verify:d4-tia-cov

See D4-TIA-COV.

2. Exact symmetry and equivariance

D4-TIA-S3-EQUIV v0.1.0 builds the six-element D4/F4 triality quotient and matches it to six canonical representatives of

$$SL_2(\mathbb Z)/\Gamma(2)\cong S_3.$$

For all 15 covariants and all six representatives, the repository verifies the exact transformation law

$$\Psi(\alpha';u,v)=\Psi(\alpha;u',v').$$

That is 90 exact symbolic equivariance checks.

Verify it with:

npm run verify:d4-tia-s3

See D4-TIA-S3-EQUIV.

3. Evaluated-covariant sonification

D4-TIA-15 v2.0.0 evaluates the 15 exact covariants across the six quotient positions and maps their exact within-generator value ordering into a small MIDI pitch contour.

The fixed evaluation probe is:

(a0,a1,a2,b0,b1,b2,b3) = (1,2,3,4,5,6,7)
(u,v) = (1,0)

This produces:

15 generators × 6 orbit positions = 90 symbolic events

The coefficient probe and pitch mapping are authored sonification choices. The exact algebra and symmetry checks are separate from those choices.

For the five order-zero invariants, the receiver requires the same:

• exact value;
• MIDI note;
• MIDI channel;
• velocity; and
• duration

at every orbit position.

So the invariant rows remain invariant at the symbolic MIDI-control level. Their playback time changes because the six orbit positions are presented in sequence.

Verify and build v2 with:

npm run verify:d4-tia-v2
npm run build:d4-tia-v2

See D4-TIA-15 v2.

The preserved v1 grading-only profile is documented at D4-TIA-15 v1.

Quick verification

Node.js 20 or newer:

npm test
npm run verify

The full verifier checks:

D4-TIA-COV
→ D4-TIA-S3-EQUIV
→ D4-TIA-15 v2
→ preserved D4-TIA-15 v1
→ ETQ-303 runtime v3.0.0
→ preserved ETQ-101 v2 and v1

Build the main root bundles with:

npm run build:v3
npm run build:d4-tia-v2

Runtime/export artifact policy

The root runtime/export bundle commands — npm run build:v3, npm run build:d4-tia, and npm run build:d4-tia-v2 — persist only:

.json
.csv
.mid

That allowlist applies to generated runtime/export artifacts, not normal repository or publication files. For example, npm run build:paper may produce archival PDF and checksum files.

Rendered audio generation is permanently prohibited in root ETQ runtime/export workflows. Root code must not create PCM or sampled-audio buffers even transiently — in memory, temporary files, caches, logs, snapshots, fixtures, playback paths, or analysis steps — and must not encode or emit WAV or any other rendered-audio format.

The separate APP/ and sonification/ directories are independent audio laboratories. They may render audio, but those features must not be imported into, called from, or used to bypass the root ETQ runtime/export policy.

ETQ-303 artifacts

npm run build:v3 writes a deterministic bundle containing the canonical contract, event document, graph data, observation receipt, symbolic MIDI, and manifest.

The exact file list and provenance rules are documented in the ETQ-303 event protocol.

No tempo or hertz value is canonical.

D4-TIA v2 artifacts

npm run build:d4-tia-v2 writes:

contract.json
evaluations.json
events.json
events.csv
events.mid
manifest.json

evaluations.json keeps the exact 15-by-6 covariant evaluation matrix separate from the 90-event receiver document.

Scientific boundary

This repository makes exact mathematical and deterministic software claims about the constructions it implements.

It does not claim:

• physical spacetime dimensions from algebraic dimension;
• 303 distinct E8 roots;
• a unique pitch system implied by E8 or D4 invariant theory;
• physical qutrit hardware;
• canonical tempo, tuning, timbre, or loudness;
• empirical validation from symbolic MIDI alone.

Where a mapping is authored rather than mathematically forced, the documentation says so.

Documentation

• ETQ-303 exact event protocol
• D4/F4 triality reference bridge
• D4-TIA-COV exact covariant engine
• D4-TIA-S3-EQUIV symmetry harness
• D4-TIA-15 v2 evaluated-covariant sonification
• D4-TIA-15 v1 grading-only sonification
• ETQ claim boundaries
• ETQ v2 to v3 migration
• ETQ-101 v2 mathematical model
• Implementation roadmap
• Formal ETQ-303 v3.0.1 paper

Archived releases

• ETQ-101 v2.0.0 — DOI 10.5281/zenodo.21432511
• ETQ-303 v3.0.0 — DOI 10.5281/zenodo.21455181
• ETQ-303 v3.0.1 documentation/publication release — DOI 10.5281/zenodo.21494678
• D4-TIA v2.0.0 — DOI 10.5281/zenodo.22831753

D4-TIA v2.0.0 archives the frozen D4-TIA-COV v0.1.0, D4-TIA-S3-EQUIV v0.1.0, and D4-TIA-15 v2.0.0 research line. The immutable implementation tag d4-tia-v2.0.0 points to commit 7aa6df165d0ad70297365dbf0d69072634ed4314. Publication/citation metadata was finalized afterward on the documentation line without changing the frozen D4-TIA runtime identity or deterministic commitments. D4-TIA remains separately versioned from the preserved ETQ runtime contracts.

Creator and licence

Created by Trent Slade / QSOL-IMC.

Licensed under the Mozilla Public License 2.0. Preserve the copyright and licence notices. Use CITATION.cff for ETQ-303 citation metadata and CITATION-D4-TIA.cff for the archived D4-TIA v2.0.0 release.