Q-Address: Macro Phase + Micro Slot

A Minimal Addressing Primitive for Cycle-Anchored Phase-Window Coordination

Status: Official Spec

DOI: 10.5281/zenodo.18068997

Abstract

This document specifies Q-Address, a minimal addressing primitive for systems that coordinate actions using cycle-anchored phase windows. The design separates (i) macro timing (cycle index and phase-window specification), and (ii) micro timing (a slot specification inside the window), enabling high-resolution local sequencing without requiring a globally shared fine-grained timestamp. For interoperability and verification, window semantics are canonically encoded using fixed-point ticks (integers), not floating-point values. Q-Address is a data format and interpretation rule; it does not define negotiation, routing, transport, or security.

Normative dependency (Conventions)

Phase-Coordination Series Conventions, Zenodo, DOI: 10.5281/zenodo.18068999. This dependency is normative for (t₀, T_cycle), cycle index, wrap-safe windows, tick encoding, and boundary semantics.

1. Scope

Principle 1.1 (Separation of concerns): Q-Address specifies what phase context an action belongs to (macro window) and how to order/offset actions inside that window (micro slot). It does not specify negotiation, routing, authentication, or transport.

2. Canonical tick semantics (normative)

Principle 2.1 (Ticks are canonical for verification): Verification/gating MUST NOT rely on floating-point comparisons. Canonical window semantics use fixed-point ticks, as defined by the Conventions document. Float fields and HS displays are derived/UI-only.

Definition 2.1 (Tick window fields):

Fix a resolution 𝑅 ∈ N (ticks per cycle). A window is encoded by integers:

resolution = 𝑅, phi_ticks ∈ {0, . . . , 𝑅 − 1}, deltaPhi_ticks ∈ {1, . . . , ⌊𝑅/2⌋ − 1}.

Definition 2.2 (Circular distance and membership in ticks):

Let 𝑎₀ := phi_ticks. For ticks 𝑎, 𝑏 ∈ {0, . . . , 𝑅 − 1} define

d_ticks(𝑎, 𝑏) := min{|𝑎 − 𝑏|, 𝑅 − |𝑎 − 𝑏|}.

Membership is:

𝑎 ∈ 𝑊 ⇔ d_ticks(𝑎, 𝑎₀) ≤ deltaPhi_ticks.

3. Q-Address object model

Definition 3.1 (Q-Address canonical fields):

A Q-Address is a tuple:

(qaddr_schema, convention_id, scope, cycle_index, resolution, phi_ticks, deltaPhi_ticks, slot, ext)

where:

qaddr_schema is a required machine-facing schema tag (this release uses TV-QADDR-2025-12),
convention_id binds (t₀, T_cycle) and tick/boundary/time policy (see Conventions),
scope identifies the logical object/action (operation id, link id, qubit id, etc.),
cycle_index ∈ Z is the intended cycle index,
resolution is 𝑅 (ticks per cycle),
phi_ticks is the window center tick,
deltaPhi_ticks is the window half-width in ticks,
slot specifies micro timing inside the window,
ext is an optional extension dictionary.

Remark 3.1: The schema tag is machine-facing and prevents silent incompatibilities; it does not need to appear in human-facing titles.

4. Micro timing: slot specification

Definition 4.1 (Slot modes):

Q-Address defines two canonical slot modes:

Index mode (order-only):
slot ≡ (mode=index, 𝑠, 𝑆), 𝑆 ≥ 1, 𝑠 ∈ {0, . . . , 𝑆 − 1}.
Offset mode (local offset; integer units):
slot ≡ (mode=offset, ref, 𝛿, unit),
where 𝛿 ∈ Z and unit is a string such as "ns" or "us".

Definition 4.2 (Offset references):

For offset slots, ref MUST be one of:

entry, center, peak.

5. Canonicalization and hashing (qid)

Definition 5.1 (qid_body canonical field set):

If qid is used, define

qid_body := (Timeverse/Q-Address, qaddr_schema, convention_id, scope, cycle_index, resolution, phi_ticks, deltaPhi_ticks, slot)

The ext dictionary SHOULD NOT be included unless explicitly versioned and frozen.

6. Serialization example (informative)

{
  "qaddr_schema": "TV-QADDR-2025-12",
  "convention_id": "phaseconv:earth;timescale=TV_MONO_NOLEAP;epoch=...;Tcycle=...;R=...;edge=inclusive",
  "scope": "link:A-B/op:ENT_ATTEMPT",
  "cycle_index": 1188,
  "resolution": 1000000000,
  "phi_ticks": 354170123,
  "deltaPhi_ticks": 833333,
  "slot": { "mode": "index", "s": 42, "S": 1024 },
  "ext": { "ttl_cycles": 0 }
}

7. Conclusion

Q-Address provides a stable, minimal representation for cycle-anchored phase-window coordination that separates macro phase context (cycle + window) from micro timing (slot). Tick-canonical encoding reduces boundary ambiguity and improves interoperability across human interfaces, AI schedulers, and hardware controllers.

References

[1] T. Ouardi, Phase-Coordination Series Conventions, Zenodo (2025). DOI: 10.5281/zenodo.18068999.