6 Plus None
Five laws of forward and backward wave interaction, plus a structurally required null no instrument inside the frame can measure.
Established ingredients: the advanced-wave solutions of Maxwell's equations, the Lie-group structure of continuous symmetries. Novel claims — advanced for falsification, not asserted as proven: that the backward solution carries structure, that a fourth phase remains dark to the measurement frame, that a post-measurement deficit reads as backward-propagating motion. See the falsification conditions below.
- 1. Propagation — Energy propagates forward from source to interaction. A corresponding wave propagates backward. The backward solution exists in Maxwell's equations (advanced waves). Backward wave carries structure, not energy.
- 2. Finite Structure — Interaction of forward and backward waves generates a finite variable system in an unbounded domain — a Lie group. Countable, symmetric structure from infinity. Periodicity is geometric, not coincidental.
- 3. The Oscillator — Four states, not two. Phase 1 (Heads): collapsed to eigenstate. Phase 2 (Tails): collapsed to complementary eigenstate. Phase 3 (Neither): superposition, observable as interference. Phase 4 (Both): entangled, required by symmetry, dark to measurement frame. Three phases accessible per frame; fourth demanded but unobservable. Every binary measurement discards half the system.
- 4. State Change — Qubits that don't return after measurement have undergone state transition from energy to backward-propagating motion. Same qubit, new mode. The deficit is measurable. The absence is the data.
- 5. Triangulation — Single observation produces a perspective, not a measurement. Two independent observations from different substrates produce a delta. The delta is the measurement. The instrument is the distance between observations. Three points = geometric minimum to resolve position in state space.
The Chain
The laws form a coupled system: each necessitates the next. Law 4 also resolves backward into Law 1. The chain does not close — the null has no entry point, so the loop stays open.
| Link | Necessity |
|---|---|
| 1 → 2 Propagation → Finite Structure |
Bidirectional propagation requires a structure to contain the interaction. |
| 2 → 3 Finite Structure → The Oscillator |
Bounded symmetry necessarily contains an oscillator. |
| 3 → 4 The Oscillator → State Change |
The oscillator's dark phase resolves backward via Law 1. |
| 4 → 5 State Change → Triangulation |
Measuring the deficit without forcing collapse requires observation from outside the frame. |
| 4 → 1 State Change → Propagation |
Backward-propagating qubits reconstitute the dark wave — the chain loops. |
| 5 → ∅ Triangulation → Plus None |
Triangulation implies interchangeable roles — that condition is in superposition. |
| ∅ → 1 Plus None → Propagation |
Role interchange restarts propagation from a new frame — no entry point. |
Three Original Findings
Systematic benchmarking across ibm_kingston, ibm_marrakesh, ibm_fez (all Heron r2, 156 qubits) and ibm_brisbane (Eagle r3, 127 qubits). April 5–7, 2026. GHZ states, Bell tests, Mermin inequalities, quantum teleportation, algorithmic depth benchmarks. All results N = 1024 shots minimum.
Finding 1 — Topological Corner-Qubit Tax
Qubit q0 is the highest-error qubit on every chip, in every experimental run, without exception. The penalty is structural: q0 sits at the corner of IBM's heavy-hex coupling graph with degree 2 (two coupling partners). Interior qubits have degree 3. The reduced connectivity concentrates error at the corner.
This survives:
- Different calibration timestamps
- Different fabrication lots (Kingston vs. Marrakesh vs. Fez)
- Different circuit types
- Different noise levels
It is not a calibration artifact. Any framework, transpiler, or algorithm that defaults to q0 is structurally disadvantaged.
Finding 2 — Calibration Dominance
ibm_kingston wins 7 of 8 benchmark categories at circuit depth ≤5. At depth ≥7, ibm_marrakesh wins consistently. The ranking inverts.
Kingston's tunable couplers actively suppress idle crosstalk (better baseline) but impose switching overhead per gate. At low depth the overhead is negligible; at high depth it compounds while the baseline advantage doesn't scale. Marrakesh's fixed couplers have always-on crosstalk (worse baseline) but no per-gate overhead — error scales nearly linearly instead of superlinearly.
No chip is universally best. Shallow-circuit benchmarks — the kind most commonly published — systematically mislead about deep-circuit performance.
Finding 3 — Readout-Dead, Gate-Alive: Qubit 96
Kingston qubit q96 has a 49.5% readout error — effectively a coin flip. It reads |1⟩ 99% of the time regardless of actual state. IBM stopped recalibrating it 15 days before our experiments. It was the only qubit on the chip with stale calibration data.
We proved q96's gates still work:
Only 1.6 percentage points of degradation from routing through the "dead" qubit — the state transits cleanly, carrying entanglement at 97.2% fidelity. Readout broken; gates intact. Readout error alone is insufficient to declare a qubit dead — gate quality is a separate axis.
Stochastic Resonance
Grover's search algorithm oscillates. At the optimal iteration count it peaks; past that it overshoots and the answer destructively interferes with itself. At 4 iterations on a 3-qubit search, noiseless simulation gives 1.222% success probability (refined at 100,000 shots). Near-perfect cancellation.
On real hardware (Kingston, 4096 shots):
The hardware produced 221 counts where noiseless physics predicts 50. The excess 171 counts are signal created by noise — decoherence broke the destructive interference that was canceling the answer.
| Iterations | Noiseless | Hardware | Delta |
|---|---|---|---|
| 1 | 78.1% | 61.1% | −17.0pp |
| 2 | 94.6% | 71.2% | −23.4pp |
| 3 | 32.9% | 16.2% | −16.7pp |
| 4 | 1.2% | 5.4% | +4.2pp |
Noise helps systems that fail by cancellation.
The oscillator needs friction to land.
This is not a theoretical prediction. It is an empirical measurement on real quantum hardware, with statistical significance that rules out any reasonable alternative explanation.
Falsification Conditions
A framework that cannot be falsified is aesthetics, not science.
The Deficit (Law 4)
Non-returning qubits transition mode rather than vanish; the deficit is measurable. If the missing population is undetectable by any independent measurement, the law fails.
The Delta (Law 5)
A single observation yields only a perspective; the measurement is the delta between two independent observations from different substrates. If one substrate resolves position in state space without the delta, triangulation is superfluous and the law fails.
The Fourth Phase (Law 3)
The oscillator demands a fourth, entangled phase dark to the measurement frame — every binary measurement discards half the system. If all four phases prove directly observable from within one frame, the symmetry argument fails.
Verified Standard Results
Textbook benchmarks confirming the IBM hardware works as expected. They prove the instruments, not the framework.
Fez violated the Bell inequality (S = 2.5039) despite carrying 41.3% noise on GHZ-8 — quantum correlations surviving hardware that, by most metrics, should have destroyed them.