Keep the record through the next operation
Effective Repeated Position Records with Retained Entropy and Calibrated Reset
A finite protocol writes 44 earlier archive labels into separate receivers and controls their retention through later operations and calibrated resets.
Jeremy Rodgers · Independent Researcher · 9 October 2026
9 October 2026 manuscript
The argument
Records that survive the operations that follow
A physical record must keep identifying its earlier event while the rest of the apparatus continues to operate. This construction reads successive digits of an actual retained archive into different receiver positions and follows every receiver through the remaining schedule.
Each cycle has four jobs: expose an archive digit, load its sign, copy that sign into a receiver, and restore the scratch wave. A compact smooth baker, a scalar loader, a coherent copying gate, and a positive Ermakov reset perform these jobs. Used reset coordinates stay in the apparatus and retain the quantum correlations transferred to them. One original law governs the whole history.
For a complete entrance law bounded by ten times its wave-density reference, the stated 10,000-unit model schedule gives a joint failure bound below 0.0000002641 for 44 records. That event includes every receiver’s assigned region from copying through the final time. Further sections develop finite calibration and a separate approximate reset tolerant of a specified constant spring-gain error.
Build the reversible reader
The smooth compact map reproduces the baker’s affine action on controlled regions. Its inverse exposes the archive digits in the correct order.
Read the argument →Write an earlier actual event
The coherent Gaussian comparison retains interference and phase information. Complete-current estimates connect the receiver’s region to the scratch coordinate’s earlier entry sign.
Read the argument →Restore the scratch and keep its correlations
A positive scalar pulse exchanges wave factors with a reset mode already in the bank. Its arbitrary-input formula shows exactly where the used scratch correlations are stored.
Read the argument →Check the whole schedule
The read, load, copy, and reset modules are assembled with the later holding costs. The numerical example is a joint guarantee for all 44 complete record histories.
Read the argument →Price finite control errors
The calibration criterion includes local current errors, moving boundaries, actual archive motion between pulses, and guard losses.
Read the argument →This paper supplies a finite repeated-record mechanism for actual archive digits. P1 supplies a separate one-use preparation and instrument result; its readiness can enter only with the correct full-bank conditioning. P3 studies the complete flow needed to interpret currents as histories, while P4 develops coherent-current estimates for source-coupled models.
The complete paper
Follow the full argument.
Every section, proof and appendix, with linked equations and the complete bibliography.
- OpeningAbstract and publication identity
- Section 1The question: a record of an earlier actual event
Complete laws, currents and errors · Established methods and inherited work
- Section 2A compact stock-preserving baker module
Smooth rounded squares with an area clock · What the first-flow-derivative estimate controls
- Section 3The scalar Hamiltonian and complete current
- Section 4The original law, fine archive and retained information
Where the information goes · A cap-free fixed-dimensional preparation variant
- Section 5Reading a retained archive into different receivers
An exact sign-preserving scalar loader
- Section 6A smooth scalar gate which copies the entry sign
The coherent Gaussian comparison · Localized forcing and the shifted energy graph · From the complete current to the receiver's own record
- Section 7Exact reset with its correlations retained
- Section 8Earlier receivers during every later operation
- Section 9One complete protocol and its joint error budget
- Section 10What reset preserves: full laws and exact counterexamples
Exact reset on an uncertainty interval · Idle curvature is a different error
- Section 11Calibration in the complete current and record history
A local current bound with a quadratic remainder · Active stock energy and actual archive motion
- Section 12An approximate reset uniform over an actual spring-gain interval
Finite resources and the limits of this tolerance
- Section 13Conclusion
Research support and AI assistance. · Collaboration.
- Appendix AA distinct retained-symbolic-history calibration
Full inverse branches with finite overlap errors
- OpeningBibliography