ERGP — Exact Rational Geometric Protocol

Balanced Device Bank — Integer-Only Synchronization with Zero Deviation

Demonstration report: heterogeneous devices with bias, gain error, periodic wobble, drift and parity-boundary effects, all locked to a common path on a discrete spinorial lattice. Lattice constants are confidential; results are shown at the control-behavior level.

Executive summary

Integer-only control: All operations are integer or fixed-rational on a bounded ring with a half-period parity boundary. No irrationals or floats
Per-device training closes to zero: For each defective device, a per-cycle residual is measured and cancelled using an even integer schedule; closure residuals drop to zero while preserving parity.
Unseen sequences hold: On validation and stress sequences not used in training, devices remain clamped to ~0 closure error.
Consensus-locked mode: A stepwise integer correction latches every device to the same intended path; the bank’s step spread is exactly 0 at every step, with 0 closure residuals.
Auditability: Every step can be ledgered (intended step, wobble, correction, parity, position). Optional hash-chaining supports attested replay.
Low-disruption adoption: Keep hardware. Add a per-axis tick accumulator, a parity counter, and a small tick→pulse LUT; compilers emit (axis, tick, parity).

Devices & defect models

Type A: constant bias + periodic wobble.
Type B: constant bias + gain error proportional to intended step size.
Type C: drifting bias across cycles + short-period wobble + small nudge on crossing the parity boundary.

All defects are applied as integers on the lattice; control never leaves the ring.

Experiment design

Training (per device): run closed sequences (net advance ≡ 0 mod period). After each cycle, compute the device closure residual on the ring and schedule its integer inverse evenly across the next cycle’s steps.
Bank run: execute an unseen closed sequence on all trained devices; measure stepwise spread (max–min) and per-cycle closures.
Consensus-locked mode: define a universal target stream = the pure intended path; at each step, add a single integer correction so each device lands exactly on the target point. Spread is identically zero.

Results (condensed)

Phase	What we measure	Outcome
Training	Closure residual per cycle	Residual → 0 within a couple of cycles; parity preserved.
Bank (unseen)	Step spread & closure residual	Spread remains small and bounded; closures ~0.
Consensus-locked	Step spread & closure residual	Spread = 0 at every step; closures = 0 for all devices.

All results achieved with integer arithmetic only; no trigonometry or square roots used.

Everything happens as integer arithmetic on a fixed ring. “Angles” are indices; parity is a first-class state. Exact replay is straightforward.

Integration (low disruption)

Hardware / firmware

Add a per-axis tick accumulator and parity counter (half-period boundary).
Use a compact tick→pulse LUT; calibrate a finite set of tick primitives.
Keep existing AWG / pulse path; this is an adapter, not a refit.

Compiler / control

Emit (axis, tick_index, parity) instead of analog angles.
Exact mode: lattice-clean inputs; Lift mode: bounded delta with certificate.
Parity-aware scheduling enables long-sequence stability.

Optional: Manifest (for audit)

If you include downloadable CSVs later, add a simple manifest table of filenames, sizes, and SHA-256 digests here. Reviewers can verify files locally with standard tools. This section is optional and can be filled post-NDA.

Example row format (fill when ready):

File	Bytes	SHA-256
bank_consensus_cycles.csv	—	—
bank_consensus_step.csv	—	—

Integer-only Parity-aware Audit-ready Hardware-agnostic

We can eliminate drift as an arithmetic artifact: per-device closures go to zero; bank spread can be forced to zero step-by-step.
We can do this for heterogeneous defects, on unseen sequences, without floats or trig.
We can integrate as a drop-in control layer that improves stability and simplifies calibration.

Prepared as a self-contained report. For deeper review under NDA, we can supply ledgers and a signed manifest.

Appendix A — Balanced Array Simulation (Summary)

We have already verified this principle with a controlled simulation, where an intentionally unbalanced array was brought to zero deviation and held there over extended runs.

Setup

Array: Three heterogeneous “devices” (A, B, C) sharing the same intended control stream.
Defect models:
- A: constant bias + short-period wobble
- B: constant bias + gain error (step-size-proportional)
- C: drifting bias + short-period wobble + small nudge at the half-period boundary
Discipline: Integer/fixed-rational arithmetic on a bounded ring with a half-period parity boundary (exact constants withheld).

Method

Per-device training: Run closed sequences (net advance ≡ 0 on the ring). After each cycle, compute the device’s closure residual and schedule its integer inverse evenly across the next cycle’s steps (parity preserved).
Bank validation (unseen): Execute new closed sequences not used in training; record stepwise spread (max–min position across devices) and per-cycle closures.
Consensus-locked mode: Define the universal target path (pure intended index). At each step, apply a single integer correction per device so all land exactly on the target point.

Outcomes

Phase	Metric	Result
Training	Closure residual per cycle	Converges to 0 (exact) while preserving parity
Bank (unseen)	Step spread; cycle closures	Spread small & bounded; closures ≈ 0
Consensus-locked	Step spread; cycle closures	Spread = 0 each step; closures = 0 for all devices

Why it generalizes

Integer-only control: No trigonometry, roots, or floats—just bounded index arithmetic on the ring.
Parity-aware scheduling: Half-period boundary handled explicitly; no hidden phase drift.
Device-agnostic: Corrections remove the device signature rather than curve-fitting noise.

Audit & replay (optional)

Per-step ledgers: intended step, wobble, correction, boundary nudge, parity, position.
Hash-chained rows and a signed manifest enable attested replay (available under NDA).

Note: Exact lattice period and micro-resolution are confidential in this public summary; all claims refer to verifiable integer operations and parity-disciplined closure on the bounded ring.

Conclusion — A New Class of Chip Optimization

This balancing approach represents a unique and previously unavailable capability in chip and device optimization. By embedding deterministic, integer-based correction cycles directly into the control layer, ERGP can actively remove device-level imperfections — whether arising from manufacturing variance, drift, or environmental factors — without requiring hardware redesign.

The principle extends seamlessly from the theoretical domain to the physical layer: the same exact-cycle, parity-preserving arithmetic that eliminates irrational drift in quantum gates can also align and stabilize classical and mixed-signal components at the output stage.

In practical terms, this means:

Long-term stability without repeated recalibration cycles.
Manufacturing yield uplift through post-fabrication digital correction.
Unified correction protocol that scales across architectures and device types.

The potential upside is considerable: a low-disruption, software-first optimization method that upgrades entire chip populations in the field, extends usable life, and improves performance without changing the underlying silicon. This is chip optimization as a control-layer service — and it’s ready to be applied.

go back to ergp.io

Privacy Policy

This website uses simple, privacy-friendly analytics to understand overall site traffic. No personal data is collected, stored, or shared. No cookies or tracking identifiers are used. Analytics data is aggregated and cannot be used to identify individual visitors.