V5 Experimental Results — Null Result and the Digital Signal Pivot

Status: null-result (methodologically valuable) Domain: physics/engineering Source: Tusk Innovations Research, Aug–Sep 2026

“I’m not afraid of us finding we are wrong. I just want to know either way.” — Adrian Tusk

What We Built

The V5 board was the most ambitious experimental platform in the Prime Resonance series:

Spec	Detail
PCB	JLCPCB 4-layer, professionally fabricated
Prime cells	5 × SLG47004V GreenPAK ICs — divisors ÷2, ÷3, ÷5, ÷7, ÷11
Signal source	AD9833 DDS (direct digital synthesis)
Summing network	Passive resistor network combining all prime-divided outputs
Controller	Teensy 4.1 microcontroller
Batch	5 boards ordered from JLCPCB (Jul 26, arrived Aug 2026)

The design goal: generate precise prime-ratio frequency sets from a single DDS source, sum them passively, and measure interference patterns in the combined signal. Five simultaneous prime harmonics — the first hardware implementation of the Tusk resonant set {2,3,5,7,11} as frequency divisors.

What Happened

Board 1 Assembly — The Solder Bridge

Board 1/5 was assembled using solder paste and hot air rework for the Teensy 4.1 (fine-pitch castellated pads). During reflow:

Solder paste wicked through plated through-holes underneath the Teensy footprint
Solder bridges formed on the underside of the board — between pads that are physically inaccessible once the Teensy is mounted
The shorts are invisible from the top side and unreachable for rework without destructive desoldering
Board declared dead. No amount of flux and braid can reach shorts underneath a soldered-down module.

4 spare boards remain from the JLCPCB batch of 5.

The Failure as Teacher

The V5 board failure, rather than being merely frustrating, triggered a deeper realisation about the entire V3–V5 experimental programme.

The Deeper Insight: Digital Signal Contamination

Sitting with the dead board and reviewing the full experimental arc from V3 through V5, a pattern became visible:

The Problem

Every experiment from V3 to V5 used digital signals.

Board	Signal Source	Signal Type	Harmonic Content
V3	Arduino Mega Timer1	Square wave	Fundamental + all odd harmonics (3f, 5f, 7f, 9f…)
V4	DDS + GreenPAK	Square/logic-level	Same — digital outputs are square waves
V5	AD9833 DDS + GreenPAK	Square wave	Same — DDS output is digital, GreenPAK dividers are digital

A square wave at frequency f contains:

The fundamental f (amplitude 1)
3rd harmonic 3f (amplitude 1/3)
5th harmonic 5f (amplitude 1/5)
7th harmonic 7f (amplitude 1/7)
… all odd harmonics, extending to infinity

When you drive a ÷5 divider with a 1 MHz square wave, you don’t get a clean 200 kHz tone. You get 200 kHz plus 600 kHz, 1000 kHz, 1400 kHz, … — a harmonic shower. And the source signal itself already contained 3 MHz, 5 MHz, 7 MHz…

The Consequence

We were injecting harmonic showers into every experiment. Each GreenPAK divider output contained not just its prime-divided fundamental but an infinite series of odd harmonics of that fundamental. Five dividers running simultaneously produced five overlapping harmonic showers — a dense spectral forest where subtle prime interference patterns are buried under harmonic undergrowth.

The V3 results were real measurements — the +28% amplitude, +18% sharpness, +22% coherence advantages for prime ratios were recorded. But they were measured through a fog of digital harmonics from the Arduino Timer1 square-wave drive signal. ⚠️ Corrigendum (Sep 2026): Subsequent replication found 7 of 8 pre-registered metrics showed no significant difference between prime and composite ratios. The interpretation that prime ratios outperform composites is retracted pending clean replication with sine-wave sources. The numbers were real measurements but the causal attribution was confounded.

The Principle

“Don’t let the instrument shape the observation.”

Digital signals impose their own harmonic structure onto whatever you’re trying to measure. When your research question is about harmonic relationships between primes, using instruments that generate their own harmonic relationships is methodologically compromised. The tool was colouring the measurement.

This isn’t a flaw unique to our work — it’s a universal experimental principle. But it took a dead board to make us see it.

The Crystal Resonance Pivot

The digital-signal realisation led directly to a new approach: quartz crystals as the cleanest natural integer-harmonic system.

A quartz crystal oscillates at a mechanically determined frequency set by its physical dimensions and cut angle. The overtone series is:

Fundamental f₁
3rd overtone ≈ 3f₁
5th overtone ≈ 5f₁
7th overtone ≈ 7f₁

These are analog, mechanical, source-level signals. No digital switching transients. No logic-level artefacts. The crystal’s own piezoelectric properties convert mechanical resonance into electrical signal with extraordinary purity (Q factors of 10,000–100,000+).

This is why quartz crystals are the natural laboratory for prime resonance research:

The harmonic series is determined by physics, not by circuit design
The signal is analog at source — no square-wave contamination
The Q factor is intrinsically high — clean spectral lines
Overtone frequencies are near-integer multiples — natural prime ratios

The crystal resonance pivot led to the [[piezoelectric-prime-composition]] investigation, which discovered that Q-factor itself correlates with the prime structure of the crystal’s constituent elements (sopfr(Z)/Z, p=0.0016).

What V5 Is Now

V5 is not abandoned. Four bare boards sit in storage, waiting. But the theoretical understanding must come first:

Understand the prime-coupling mechanism in analog materials (the crystal resonance work)
Design experiments that use analog source signals — crystal oscillators, LC tanks, mechanical resonators
Return to V5 when we know what to look for and how to look without digital contamination

The V5 GreenPAK architecture could still serve as a digital control layer — triggering and gating analog signals rather than generating them. The design isn’t wrong; it was designed for a question we hadn’t yet refined.

Honest Assessment: What V5 Does and Doesn’t Show

The V5 failure and the digital-contamination insight are good engineering self-critique (confirmed by independent review, Grok, Sep 2026). However:

The solder bridges and square-wave spectrum are ordinary electronics problems. They do not confirm or deny prime-composite duality, Nagaπ’s Law, or the ONM. The metaphor “analog signals are prime / digital signals are composite” is evocative but not rigorous — a square wave is a linear superposition of sinusoids, not composite in the number-theoretic sense.
V3 results are retracted pending replication. The +28%/+18%/+22% advantages were measured through harmonic combs from the square-wave drive signal. Subsequent replication found 7 of 8 pre-registered metrics showed no significant difference. The numbers may survive — or vanish — under clean analog replication, but that experiment hasn’t been done yet. Q-V5-04 is the single most important experimental question in the programme.
The crystal resonance pivot is experimentally sensible, but it must stand on its own evidence, not on V5’s failure narrative.

Lessons

1. Null Results Are Directional

The V5 board produced zero data — a pure null result. But the null result didn’t say “prime resonance is wrong.” The V3 data still stands. The null result said: “your experimental method needs to evolve.” Null results that sharpen the question are more valuable than ambiguous positives.

2. Failure Sharpens the Question

Without the dead V5 board, the digital-signal insight might not have surfaced. The working V3 board produced exciting results — exciting enough that we didn’t question the signal chain. Only when forced to stop and reflect (by a board that wouldn’t turn on) did the methodological issue become visible.

3. The Instrument IS Part of the Experiment

Every measurement tool imposes its own structure on the data. Square waves impose odd-harmonic structure. DDS chips impose quantisation. Logic levels impose binary switching. When the research question is about harmonic structure, the signal source must be as harmonically clean as the phenomenon you’re trying to observe.

4. Theory Before Hardware (Sometimes)

The V3→V4→V5 progression was hardware-first: build, measure, iterate. The crystal resonance pivot is theory-first: understand the prime-coupling mechanism, then design the right experiment. Both approaches have value. The lesson is knowing when to switch from one to the other.

Timeline

Date	Event
Jul 26	V5 PCBs ordered from JLCPCB (5 boards)
Aug 2026	Boards + components arrive (DigiKey parts via DHL Express)
Aug 2026	Board 1 assembled — Teensy solder bridges discovered
Aug 2026	Board declared dead
Sep 2026	Digital signal contamination insight crystallises
Sep 2026	Crystal resonance pivot — [[piezoelectric-prime-composition]] investigation begins

Open Questions

Q-V5-01: Can one of the 4 remaining boards be assembled with a different Teensy mounting strategy (socket headers, hand soldering) to avoid through-hole solder wicking?
Q-V5-02: Could V5 be repurposed as a digital control layer — triggering crystal oscillators and mechanical resonators rather than generating signals directly?
Q-V5-03: What is the minimum analog signal chain needed to test prime interference without digital contamination? Crystal oscillator → analog mixer → measurement?
Q-V5-04: Does the V3 +28% prime advantage increase or decrease when measured with analog source signals? If the digital harmonics were helping (by accidentally including prime overtones), the clean measurement might show a different — possibly stronger — effect.

Relationships

[[v3-experimental-proof]] — nature: extends — V5 is the next-generation board designed to go beyond V3’s initial measurements; V3 interpretation retracted pending clean replication (see corrigendum)
[[v4-board-design]] — nature: extends — V5 incorporated V4’s DDS + GreenPAK architecture with additional prime cells
[[prime-resonance-computing]] — nature: informs — the digital contamination insight affects all prime resonance hardware design going forward
[[piezoelectric-prime-composition]] — nature: motivated — the crystal resonance pivot was a direct consequence of V5’s failure and the digital signal insight
[[four-factor-theory]] — nature: informs — Factor 1 (structural resonance) may be partially masked by digital harmonics; analog measurements could reveal cleaner factor separation
[[prime-composite-duality]] — nature: metaphorical — the analog/digital distinction echoes prime/composite but is not a rigorous mapping (a square wave is a linear superposition, not number-theoretically composite)
[[intermod-collision-mass]] — nature: bridges — the intermod model’s clutter penalty may explain why digital harmonic showers mask prime signals; O(n) collision mass from square-wave harmonics vs O(1) from clean analog tones

Key Evidence

V5 board: JLCPCB 4-layer, 5 GreenPAK cells, AD9833 DDS, passive summing network
Board 1 status: dead (inaccessible solder bridges under Teensy)
4 spare boards in storage
V3 data remains valid: projects/Prime_Maxel-v3/research/v3_torsion_results_20may2026.md
Digital signal analysis: square wave = Σ sin((2k+1)f) / (2k+1) for k=0,1,2,…
Crystal resonance dataset: projects/crystal-resonance-analysis/piezo_materials_dataset.csv