HS-bit Meter: A Reportable Unit and Procedure for Measuring HS° Synchronization Cost

Abstract

Release label: HS-bit Meter v1.0 (first public release). This record introduces HS-bit as a practical, reportable unit for HS° synchronization cost and specifies an HS° Consumption Meter: a measurement/reporting procedure for quantifying how much temporal/phase alignment resource is consumed during an alignment attempt. In the Quantum HS° framework, temporal (phase) alignment without an external synchronized clock is treated as a U(1)-asymmetry resource. A key operational point is that deterministic phase shifts are not the source of consumption; consumption arises from the estimation–correction loop and the residual uncertainty it leaves behind. When the measurement record is discarded (unconditioned output), residual uncertainty induces an effective phase diffusion (a mixture of shifts). In that model, HS° consumption equals entropy production: \[\Delta A_{\mathrm{HS}} = S(\rho_{\mathrm{out}})-S(\rho_{\mathrm{in}}).\] To make this usable in implementation-facing coordination stacks, the meter supports a **tick-canonical** reporting mode aligned with phase-window/ticks specifications. In a discrete residual ticks model, the consumed cost can be reported directly as: \[\Delta A_{\mathrm{HS}} = H(p),\] where \(p\) is the residual tick-error distribution. This yields a simple “meter reading” in bits (HS-bits). When only partial information is available, the meter supports conservative lower bounds via purity and via window success mass \(p_{\mathrm{succ}}\). HS-bit definition. One HS-bit is one bit of HS° resource consumption (log base 2). If logs are taken base \(e\), costs are reported in HS-nats (convertible to HS-bits by \(1/\log 2\)). Recommended reporting fields. A minimal report includes: the unit (HS-bits/HS-nats), whether the phase-diffusion (unconditioned) model applies, tick resolution \(R\) (if applicable), the phase-window definition (ticks or half-width), and either the residual distribution \(p\), purity-based bounds, and/or window success mass \(p_{\mathrm{succ}}\), plus explicit assumptions. Normative / core references (DOIs): HS° consumption v2 (entropy-production + ticks model): https://doi.org/10.5281/zenodo.18071181 Phase-Coordination Series Conventions (ticks/windows/modulo/convention_id): https://doi.org/10.5281/zenodo.18068999 Q-Address (tick-canonical macro window + micro slot): https://doi.org/10.5281/zenodo.18068997 Timeverse Security Profile (security_profile_id suites): https://doi.org/10.5281/zenodo.18069423 TAQA (execution layer reference): https://doi.org/10.5281/zenodo.18070594 DOI (this record): https://doi.org/10.5281/zenodo.18071687 Keywords: HS-bit, synchronization cost, phase alignment, asymmetry resource theory, entropy production, ticks, phase windows, reporting standard, Q-Address.

Topics & Concepts