HS-Sizing v1.0

Phase-Window Dimensioning Tool for Cycle-Anchored Coordination Systems

Status: Official Spec (v1.0)

DOI: 10.5281/zenodo.XXXXXXXX

Abstract

HS-Sizing v1.0 specifies a design-time dimensioning tool for phase-window coordination systems. Given path delay statistics and a target system reliability, HS-Sizing computes the optimal phase-window half-width Δ* and per-path reliability allocations {r_k^*}.

HS-Sizing is complementary to HS-Bloch (runtime quality gating): HS-Sizing determineswhat parameters to use, while HS-Bloch verifies whether execution conditions are met.

Normative Dependencies

1. Scope and Positioning

Design-time vs Runtime: HS-Sizing is a design-time tool. It computes parameters before deployment. HS-Bloch is a runtime protocol. It verifies conditions during execution.

Aspect	HS-Sizing	HS-Bloch
When	Design-time	Runtime
Question	"What Δ should I use?"	"Is this execution valid?"
Input	Delay statistics, target reliability	Quality observations
Output	Δ, {r_k^}	PASS / FAIL + code

No runtime role: HS-Sizing MUST NOT be invoked during execution gating. Its outputs are consumed by Q-Address (window parameters) and HS-Bloch (quality thresholds) at configuration time.

2. Schema Identifier

Schema identifier:

HS-Sizing v1.0 objects MUST declare: hssizing_schema_id = "TV-HSSIZING-2026-01"

3. Input Specification

3.1 Path Delay Model

Path specification:

Each path k is specified by a delay model. HS-Sizing v1.0 supports:

gaussian: parameters μ (mean), σ (std dev)
exponential: parameter λ (rate)
uniform: parameters a (min), b (max)

All delay values are in phase units δ ∈ [0, 1), not seconds.

Input Schema (JSON)

{
  "hssizing_schema_id": "TV-HSSIZING-2026-01",
  "paths": [
    {
      "path_id": "sensor_local",
      "delay_model": "gaussian",
      "params": {"mu": 0.02, "sigma": 0.005}
    }
  ],
  "target_reliability": 0.99,
  "semantics": "AND",
  "resolution": 86400
}

4. Algorithm Reference

HS-Sizing solves the convex optimization problem:

Δ* = min Δ
subject to: Π G_k(2Δ) ≥ 1 - ε

Bisection solver: Under log-concave delay distributions, the problem is convex and can be solved by bisection on Δ ∈ (0, 1/2).

5. Integration Points

5.1 Q-Address Integration

The output field qaddress_params maps directly to Q-Address specification:

delta_phi_ticks → Q-Address delta_ticks (half-width)
resolution → Q-Address resolution

5.2 HS-Bloch Integration

The output field hsbloch_params maps to HS-Bloch v1.1 requirements:

Per-path reliability r_k maps to quality threshold:
coh_min_u16[k] = floor(r_k * 65535)

6. Reference Implementation

A reference implementation in Python is available. It features an abstract DelayModel class and a HSSizingSolver implementing the bisection method.

View on GitHub

References

[1] Ouardi, T. (2025). Phase-Coordination Series Conventions. DOI: 10.5281/zenodo.18068999
[2] Ouardi, T. (2025). Q-Address Specification. DOI: 10.5281/zenodo.18068997
[3] Ouardi, T. (2026). HS-Bloch v1.1. DOI: 10.5281/zenodo.18216116