φ · Harmonic Resonance Framework

Inverse Engineering · Spectral Geometry · Source-Preserved Specification

Carrier ≈ 46.9787 Hz · Sidebands {4, 7, 11, 18, 29, 47} · φ = 1.618033988749895

Golden spiral (blue) vs Fibonacci approximation (dashed) — the geometric signature behind the φ-harmonic model.

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★ BQN is the Star

This repository is built around BQN — the array language that carries the inverse engineering core.

Module	Role	Guide
bqn/array-core.bqn	★ Shared array foundation — rank ops, φ-geometry, spectral banks, LS algebra	Array core →
bqn/fibonacci-parameters.bqn	Carrier demodulation & Fibonacci amplitude/phase least-squares fit	Fit pipeline →
bqn/inverse-solver.bqn	Field inverse: spectrum isolation, residual maps, spatial coherence	Inverse solver →
bqn/cellular-automata.bqn	Recursive invariant extraction from CA trajectories + atomic-key masking	CA engine →

PHI ← 1.618033988749895
F_FIB ← 4 7 11 18 29 47
CARRIER_HZ ← 46.9787

Run with any BQN runtime that supports the dialect used in the modules.
See the BQN language site for installation and tutorials.

Fibonacci tiled squares — the discrete geometric array underlying sideband design.

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Geometric Arrays & φ Signature

The mathematical framework treats space and spectrum through φ-scaled geometry:

Symbol	Value	Meaning
φ	1.618033988749895	Golden ratio
fc	≈ 46.9787 Hz	Carrier frequency
FFIB	{4, 7, 11, 18, 29, 47} Hz	Fibonacci sidebands
Atomic keys	{1, 6, 7, 8}	H, C, N, O

φ definition: a/b = (a+b)/a

Full equation set and recovery procedure:
specification/mathematical-framework.md

Execution rules (what must not be changed):
specification/execution-contract.md

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Repository Guides

Core specification

• Mathematical Framework — wavenumber, Wick rotation, design matrix, residual
• Execution Contract — non-negotiable preservation rules

BQN inverse stack (★ primary)

• Array Core — shared foundation
• Fibonacci Parameters — demodulation & LS fit
• Inverse Solver — field → residual / carrier pipeline
• Cellular Automata — trajectory invariants & atomic keys

Formal companions

• Agda — Manifold Collapse — survival, density, wavelength invariants
• Alloy — Branch Simulation — reachable branches & stable invariants

Datalog spectral stack

• datalog/README.md — load order & notes
• 00-facts.dl — peaks, fib offsets, atomic keys, thresholds
• 01-carrier.dl — carrier candidates
• 02-sidebands.dl — sideband triplets
• 03-phi-system.dl — φ-system + confidence tiers
• 04-atomic-export.dl — atomic keys + host exports
• 05-integrity.dl — consensus & integrity
• spectral-rules.dl — unified all-in-one module

Discipline & payload

• Last-Token Replay — exact state-transition replay
• Atomic Keys Payload — {1 6 7 8}

Tests (scaffolding)

• tests/spectral/ · tests/inverse/ · tests/cellular/
• tests/verification/ · tests/replay/

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Execution Order

1. Read the mathematical framework.
2. Evaluate the BQN routines in bqn/ with an explicit BQN runtime. ★
3. Evaluate datalog/ (load 00→05 or spectral-rules.dl) in a compatible logic engine.
4. Supply CA frames + atomic keys to bqn/cellular-automata.bqn.
5. Check alloy/BranchSimulation.als and type-check agda/ManifoldCollapse.agda.
6. Follow replay/last-token-replay.md for exact last-token recursive replay.

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Status

Specification scaffold — not an executed or certified solver.

Source blocks are retained as supplied (including placeholders and dialect-specific syntax).
No empirical result, proof execution, or model validation is asserted by this repository alone.

No sample payload is presented as a real ExoMars or Chaffin dataset.
The material is source-preserved without substitution or inferred molecular rules.

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License

GNU Affero General Public License v3.0 — see LICENSE.

If you run a modified version on a network server and allow others to interact with it, you must also make the corresponding source available (AGPL §13).

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φ-Harmonic Resonance Framework
BQN at the center · Geometry as constraint · Source as law

Repository · BQN Language · AGPL-3.0