What survives a
change of coordinates?
Two memories live in the phase differences around a graph’s loops. Scramble every vertex’s phase, rewrite one detail, and interrogate the paths. Does the answer survive? What is the price?
01 / Write the history
Each channel stores a tiny binary world; the phase around each face encodes the bit. Select a cell to interrogate or change it.
An overwrite is a physical edit to edge bytes, not an invisible change to a target image. The compensated write may touch several edges to protect neighboring loops.
02 / Read without the original
Memory answers are decoded from edge phases only. Direct indexed bits appear below as the deliberately stronger baseline.
03 / Inspect the transport
Oriented edges are colored by their stored uint8 phase. The selected face shows its two competing paths: turquoise (top/right) and amber (left/bottom).
Choose a cell above to see its oriented edges.
04 / Poke the interrogation policy
Allocate the same 196 paired measurements among 98 cells. Uniform repeats each cell twice. Adaptive observes all once, then asks about the least confident remaining cells. No labels are used during allocation.
Finite-storage accounting
| Store | Payload | Exact read |
|---|---|---|
| Phase graph, A+B | 224 bytes | 2 paths |
| Bit-indexed table | 13 bytes | 1 bit lookup |
| Original source images | 98 bits (binary) | direct |
No information-theoretic or compression advantage is claimed. The point is the behavior of remote, gauge-invariant measurements.
05 / Frozen pilot receipts
Mean of 100 seeded trials per condition. Under common-mode phase disturbance (σ=1.5 rad), the paired two-route measurement cancels shared disturbances exactly. Independent shot noise (σ=0.85, heterogeneous per cell) is a separate test.
Error bars are trial-level standard errors. Each trial contains 98 correlated facts, which are not treated as 98 independent runs.
Raw 100-trial JSON · Measurement contract06 / What this did not prove
Loop holonomy is a known invariant. A graph that stores two binary images in 224 bytes does not beat a 13-byte bitset. Scrambling the gauge is a restricted, mathematically designed change of coordinates—not an arbitrary physical perturbation.
The useful test is narrower: does relational encoding support stable updates and useful interrogation when local edge values themselves cannot be trusted as absolute coordinates?
Under a vertex coordinate rephasing α, every oriented edge φᵤᵥ becomes φᵤᵥ + αᵥ − αᵤ. Every closed loop retains its phase.
To explore beyond this mathematical control, the next gate needs an experience-trained writer and interrogation policy that beats conventional memory on unforeseen structured questions with matched storage and compute.