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DephazEAudi0

This is not analysis. This is the processing itself.
What you hear is what you see.  •  No lookahead  •  No memory  •  Zero latency

What DephazEAudi0 is

DephazEAudi0 is a Dephaze projection-dynamics audio core.
It is not defined by its wrapper (Python / Android / native / host), but by a single invariant processing law that can be embedded anywhere.

It does not treat sound as an “amplitude over time” object. It treats each sample as a projection event (Ψₙ), evaluated against a symmetry reference (Ω₀) inside a Φ³-structured topology.

  • Core claim: audio is processed as projection state, not as a time-function.
  • Consequence: no envelope logic, no attack/release time constants, no predictive staging is required.
  • Result: coherent behavior emerges from topology + invariants, not from time-based heuristics.

Scale-invariant magnitude domain (10⁻⁵⁵ → 10⁵⁵)

In classical audio pipelines, the numeric corridor is narrow (typically normalized around ±1.0), and stability is enforced by thresholds, clipping rules, and gain staging.

DephazEAudi0 explicitly runs in a scale-invariant projection domain: extremely small fluctuations and extremely large excursions coexist inside the same operational space without switching logic.

Magnitude domain: 10⁻⁵⁵ ←────────────── Ψ ───────────────→ 10⁵⁵ • micro-structure and near-zero detail • full-scale waveform energy • mathematically large transient excursions All are handled by the same invariant rule.

This is not “just normalization”. The engine uses a log-geometry mapping so that magnitude becomes a stable coordinate in Φ³ topology.

So values are never “too small” or “too large” — only nearer or farther from the Ω₀ symmetry manifold.

One minimal form of the mapping

One compact way to express the scale operation (illustrative form):

Let Φ ≈ 1.618..., so Φ³ ≈ 4.236... Given raw sample x: μ(x) = sgn(x) · log_{Φ³}( 1 + |x| ) • preserves ordering • expands micro-detail near zero • compresses dominance at large magnitudes • keeps the domain bounded and aperiodic
Why it matters
  • No thresholds: because magnitude is a coordinate, not a danger zone.
  • No limiter logic: because excursions are mapped geometrically, not clipped.
  • Single law across scales: micro and macro remain coherent under the same Ξ regulation.

Why Φ³

Φ³ is used as the topology scale because it avoids short-cycle closure.
In audio terms: it suppresses stable repeating numerical loops that create “digital ringing artifacts”. In Dephaze terms: Φ³ corresponds to the minimal high-instability but still coherent spiral order.

Φ ≈ 1.6180339887... Φ³ ≈ 4.2360679... Φ³ behavior (in this context): • non-repeating (aperiodic) update cadence • bounded stability (no runaway) • topology that naturally relaxes toward symmetry

Axiomatic alignment with Dephaze

DephazEAudi0 is the Dephaze axioms expressed in audio. Not “inspired by” — directly mapped.

AXIOM_0 — TIMELESS_DUALITY

  • Reality = Ω₀ ⊗ Ψ → Ω₀ is the invariant symmetry reference; Ψₙ is the current sample-event state.
  • Processing measures deviation from Ω₀ and relaxes Ψₙ accordingly — Ω₀ itself remains invariant.

AXIOM_1 — PROJECTION_ONTOLOGY

  • Ψ = Φ³[Ω₀ → Imago] → each sample is evaluated as a projection in Φ³ topology.
  • “Time” is the sampling sequence, not a required processing dimension.

AXIOM_2 — GENERATION vs PATTERN

  • Ξ = φ³ / φ⁻³ → regulation targets coherence ratio, not level or band-energy heuristics.
  • φ³ acts as generative geometry; φ⁻³ is the measurable trace. The engine keeps their balance critical.

AXIOM_4 — SELF_REGULATION

  • Instead of attack/release loops, DephazEAudi0 performs instantaneous relaxation toward Ξ ≈ 1.
  • This is why coherent behavior can exist without lookahead or memory as a conceptual requirement.

Core processing model (sample-event form)

Each PCM sample is treated as a self-contained event with a deterministic projection map:

Given input sample xₙ: 1) Embed: xₙ → Ψₙ (Φ³-geometry embedding) 2) Measure: Δₙ = dist(Ψₙ, Ω₀) + curvature(Ψₙ vs Ω₀) 3) Regulate: Ψ'ₙ = Relax(Ψₙ, Ω₀; Ξ-control) 4) Project out:yₙ = Π(Ψ'ₙ) (audible-domain projection)
  • No lookahead: regulation is local relaxation, not future optimization.
  • No memory: coherence is enforced by topology + Ξ, not time smoothing.
  • Wrappers differ: Python/Android/host differ in I/O and UI only — core is invariant.

Closing

DephazEAudi0 works because the axioms are structurally correct.
Not as a claim — as an operational consequence: the core produces stable, coherent behavior using the minimal projection law, without needing time-based heuristics as the engine.

This page is informational: it documents the engine’s internal logic and its axiom-consistent structure.