Phase 81 · first physical primitive test · hardware design ready
Every result this programme owns lives in code. This is the design for the first thing that leaves the computer: a bench-scale fabric of nonlinear electronic oscillators, coupled only to their nearest neighbours, asked one narrow question. Can a locally coupled physical medium create a bounded coherent region, move it by driving only its boundary, and erase it again — without any global controller? Coupled-oscillator synchronization in hardware is established experimental work by other groups. The moving bounded C* test below is ours, and it has not been built, powered on, or measured.
HARDWARE DESIGN READY / BUILD NOT STARTED / PHYSICAL EVIDENCE: NONE
Evidence status · permanent
1 · Objective
Can a locally coupled physical medium create, move and erase a bounded coherent state, using only nearest-neighbour interaction and boundary drive?
This is a primitive test, not a test of Adjacency Theory. The programme's toy models assume a substrate in which a transient locally coherent region — C* — can be nucleated, translated and dissolved without a global controller rewriting the whole array. That assumption has never been checked against matter. Experiment 001 checks the assumption alone, in the simplest physical medium that can host it. A clean pass says an engineered analogue behaves as the models assume. It says nothing about space, distance, or the relocation of anything.
2 · Candidate states
C0
All nodes oscillating with uncorrelated phases; no persistent local phase relationship beyond the noise floor. This is the resting state of the fabric and the state it must return to after drive removal.
Measured as: R_local across every m-node window sits at the noise-floor value expected for uncorrelated phases at that window size.
C*
A spatially bounded region in which neighbouring oscillators hold a stable phase relationship, surrounded by nodes that remain in C0. Bounded is the operative word: a fabric that simply globally synchronizes has not produced C*, it has failed the test.
Measured as: R_local high inside a contiguous region of finite width w_C*, falling to the C0 floor outside it, sustained for longer than tau_form.
3 · Recommended first platform
Bench-scale programmable electronic relaxation oscillators
Relaxation oscillators are chosen because they are cheap, individually observable, tolerant of crude construction, and their coupling can be made explicitly local and adjustable. The point of the first build is not performance; it is that every node can be probed and every coupling can be trusted.
64 nodes. Smallest array that can host a bounded cluster with a genuine exterior. Full per-node instrumentation.
256 nodes. First size at which w_C* and N_active can be measured against array size rather than eyeballed.
No 3D build is attempted until the 2D array has either passed or failed the gates below. 3D changes the neighbour count and the failure modes at once, and would confound both.
4 · Coupling rules
5 · Instrumentation requirements
I1 Per-node phase, frequency and amplitude logging
R_local cannot be computed without per-node phase. Aggregate array readouts are insufficient and will be rejected in analysis.
I2 Current, voltage and power measurement per rail and, where feasible, per tile
E_transition is a headline metric. Energy claimed without measurement is not reported.
I3 Oscilloscope and multi-channel logic acquisition
Time-resolved capture of nucleation and translation events; tau_form and tau_decay come from here.
I4 Temperature logging across the array
Thermal drift changes free-running frequency and can mimic or destroy locking. Untracked thermal drift is a confound, not a result.
I5 Electronic noise floor characterisation
R_local has a nonzero expected value under pure noise at finite m. That floor must be measured before any coherence is claimed.
I6 Full control-write log
Every write to every node is timestamped and archived, so a reviewer can prove no hidden global coordination occurred. Same anti-cheat discipline as the bench protocol.
6 · Order parameter and measurable metrics
| Symbol | Metric | Definition |
|---|---|---|
| R_local | Local order parameter | R_local = |(1/m) Σ_j exp(i θ_j)| over an m-node neighbourhood window. Primary order parameter. Reported as a spatial map, never as a single array-wide number. |
| v_C* | Cluster velocity | Displacement of the C* centroid per unit time under boundary drive, in nodes per second and in metres per second. |
| w_C* | Cluster width | Spatial extent over which R_local exceeds the declared coherence threshold. Must stay bounded and must not grow with array size. |
| tau_form | Formation time | Time from drive onset to R_local crossing threshold across the intended region. |
| tau_decay | Decay time | Time from drive removal to R_local returning to the C0 noise floor. |
| E_transition | Transition energy | Measured electrical energy consumed above baseline for one create-move-erase cycle. Measured, not modelled. |
| K_lock | Locking range | Range of coupling strength and detuning over which C* is sustainable. Defines the operating window. |
| p_fail | Failure rate | Fraction of attempted cycles that fail to nucleate, fail to translate, or fail to return to C0. |
No value exists for any metric above. Nothing has been measured.
7 · Test sequence
T1 Baseline characterisation
Free-running frequency distribution, amplitude spread, noise floor, thermal drift and the R_local value expected under pure incoherence at each window size m. No coupling. Nothing else runs until this is archived.
T2 Static nucleation
Boundary drive applied to one fixed region. Does a bounded coherent cluster form at all, and does it stay bounded? Measure tau_form, w_C*, E_transition.
T3 Moving destination
The core test. Translate the drive boundary and ask whether the coherent cluster follows without the interior ever being addressed. Measure v_C*, and whether w_C* is preserved in transit.
T4 Dead-node defects
Disable 1%, 5%, 10% of nodes. Does C* route around damage, deform, or collapse? Compare against the toy-model repair expectation without assuming it transfers.
T5 Coupling disorder
Randomise coupling strengths within declared tolerance bands. Real fabrics are not uniform; a result that needs uniformity is not a result.
T6 Timing jitter
Inject drive jitter across the boundary. Establishes how much timing precision the primitive actually demands.
T7 Thermal and electronic noise
Sweep temperature and injected noise to find where the locking range closes.
T8 Barriers
Insert regions of suppressed or severed coupling. Can C* pass, go around, or is it stopped? A barrier that stops it is informative and is published either way.
T9 Speed sweep
Increase drive translation rate until the cluster fails to follow. Establishes the empirical speed ceiling of the primitive — an engineering limit of this circuit, not a statement about any physical bound.
T10 Reverse-motion shock
Abruptly reverse the drive direction. Tests for hysteresis and for residue left behind by the previous transit.
8 · Provisional pass gates · engineering targets
Reproducibility means across sessions, seeds and physical rebuilds — not across repeats of one lucky run.
No interior node may be written to during translation. The control-write log must prove it.
Return to the measured noise floor, within tau_decay, without a reset pulse.
w_C* and the count of nodes departing C0 must not grow with array size between 8 x 8 and 16 x 16.
Audited from the control-write log, not asserted in prose.
E_transition, tau_form, tau_decay and v_C* reported with uncertainties, or the run does not count.
These are PROVISIONAL ENGINEERING TARGETS. They describe what a circuit would have to do for the primitive to be considered demonstrated. They are not physics claims, they are not predictions about space, and passing all six would establish only that a small electronic fabric behaves the way our toy models assume a substrate behaves.
9 · Falsification criteria
Any one of these outcomes kills the primitive in this medium. All of them get published.
10 · Hardware ladder
H0 Simulation
DONE (TOY MODEL)Graph and oscillator simulations in code. Everything the programme currently owns sits here.
H1 Breadboard / bench electronics
NEXT — NOT STARTED8 x 8 then 16 x 16 programmable relaxation oscillators with adjustable nearest-neighbour coupling. This page is that design.
H2 Custom PCB array
NOT STARTEDTiled PCB with per-node instrumentation headers, once the breadboard has cleared or killed the gates.
H3 3D array
NOT STARTEDStacked tiles, six-neighbour coupling. Only after 2D closes.
H4 Micro / nanoscale medium
SPECULATIVECMOS oscillator arrays or spin-torque oscillator arrays as a dense medium. Listed for direction only; nothing about it is planned or funded.
11 · Literature grounding · other groups, published hardware
L1 · established experimental precedent
Programmable CMOS relaxation-oscillator arrays with arbitrary capacitive coupling have been fabricated and operated, on the order of 30 oscillators with configurable coupling between them.
Establishes: That relaxation oscillators can be built in an array, coupled through a programmable network, and driven into stable collective phase behaviour in real silicon.
Does not establish: Anything about a bounded, movable coherent region, and nothing whatsoever about Adjacency Theory.
L2 · established experimental precedent
Arrays of spin-torque nano-oscillators have been mutually synchronized, with reports of long-lived phase synchronization across up to eight coupled oscillators.
Establishes: That nanoscale nonlinear oscillators can hold mutual phase locking through local physical coupling, which is the component physics this experiment depends on.
Does not establish: A movable bounded cluster, locality of the active region under translation, or any claim of this programme's.
These precedents validate the COMPONENT PHYSICS ONLY. Coupled nonlinear oscillators synchronize in hardware — that is settled experimental work by other groups, and it is why this experiment is buildable rather than fanciful. It is not evidence for the moving bounded C* hypothesis, it is not evidence for Adjacency Theory, and no citation on this page should ever be read as support for either.
For a ten-year-old
Imagine a big grid of tiny blinking lights that each blink at their own speed. If you nudge the ones around the edge of a small patch, do the lights inside that patch start blinking together — and only that patch? Then, if you slowly move where you are nudging, does the blinking patch walk across the grid with you? And when you stop nudging, do they all go back to blinking on their own? Nobody has built ours yet. That is the whole experiment, and it is the first time we would be asking real electricity instead of a computer.
