---
slug: phase_synchronization
name: Phase Synchronization
one_liner: "When two or more oscillators with initially different phases are coupled, they can spontaneously adjust until their phases lock into a fixed relationship — a coupling-driven convergence of rhythm (not amplitude) above a critical coupling strength, out of which collective tempo can emerge."
type: prime
schema_version: 2
status: density_v2_draft
categories: [structural, physical, biological]
origin_domain: nonlinear_dynamics
alternate_origin_domains: [physics, neuroscience, chronobiology, complex_systems]
aliases: [entrainment, frequency_locking, phase_locking, mutual_synchronization, collective_synchronization, kuramoto_coupling]
related: []
solution_archetypes: []
review_flags:
- "OPERATOR-DERIVED (op-03 temporalization, flavor 3b) — the DYNAMIC prime obtained by temporalizing the static coupling relation into the rhythm-locking process it can produce: two or more oscillators, initially out of phase, coupled until their phases converge to a fixed relationship without their amplitudes changing. Reached from `teleconnection` and `tempo_mismatch` in the op-03 sweep; convergence ×2. Discovered 2026-07-03. MODERATE hold (verified absent from corpus; established scientific name — Kuramoto 1975; entrainment, frequency/phase locking). STATUS: HOLD pending owner keep/cut with the resonance/coupling screens."
- "Created 2026-07-03; STUB ONLY (frontmatter + Core Idea + Notes). SI/SF/similarity are PROPOSER ESTIMATES pending triangulation. Body sections (Structural Signature onward) NOT written."
- "Phase-C action: re-similarity-check vs `coupling` (the enabling influence relation), `oscillation` (the units being synchronized), `resonance` (amplitude response at a matched frequency — argue the distinction), and any collective-behavior / emergence prime; confirm it is the genuine rhythm-locking dynamic and not a restatement of `coupling` or `resonance`; draw a subsumption/relation edge `coupling` → `phase_synchronization` and a boundary note vs `resonance` at incorporation; decide whether entrainment (external driver) and mutual synchronization (peer coupling) are one prime or two (note both under one head); write a v1 draft and sync the one_liner across v1/v2 per CLAUDE.md before merge."
substrate_independence:
  composite_substrate_independence: 4
  domain_breadth: 5
  structural_abstraction: 4
  transfer_evidence: 5
  reasoning: 'The bare structure — a set of oscillators with initially different phases, coupled so that above a critical coupling strength their phases converge to a fixed relationship (in-phase, anti-phase, or constant offset) while amplitudes are left untouched — is a genuinely substrate-neutral dynamical form. It recurs across radically unlike substrates: mechanical (Huygens'' coupled pendulum clocks, power-grid generators locking), biological (fireflies flashing in unison, cardiac pacemaker cells, circadian entrainment to the light cycle, neural oscillation binding), and social (applause converging to a beat). These are structurally-unlike siblings sharing only the abstract coupled-oscillator engine, so domain_breadth scores 5 and transfer_evidence 5 (the Kuramoto model is the canonical cross-domain formalism). Structural abstraction is 4 because the core is a pure statement about phase dynamics under coupling — no physical substance required — but stays just short of 5 because it still presupposes the notion of an "oscillator" with a well-defined phase, a mild structural precondition rather than a fully bare relation.'
similarity_to_nearest_existing_prime:
  slug: coupling
  similarity: 0.58
structural_framed:
  label: structural
  aggregate: 0.33
  criteria: {vocab_travels: 0.75, evaluative_weight: 0.15, institutional_origin: 0.1, human_practice_bound: 0.15, import_vs_recognize: 0.35}
  rationale: 'Reads structural. The core claim — coupled oscillators whose phases converge to a fixed relationship above a critical coupling strength, with amplitudes unchanged — is recognized rather than imported, and travels cleanly from clocks to fireflies to neurons to power grids without carrying any single domain''s vocabulary. The frame residue is very light: "oscillator," "phase," and "coupling" are structural terms, not evaluative or institution-bound ones, so evaluative_weight and institutional_origin sit near the floor. Slightly higher import_vs_recognize than a fully bare relation because the notion of a phase-bearing oscillator is a modest structural precondition. Comparable framing to its neighbors `coupling`, `oscillation`, and `resonance`.'
phase_b_passes_completed: []
---
# Phase Synchronization

## Core Idea

Phase synchronization is a *dynamic* consequence of coupling: when two or more oscillators that start with different phases (or frequencies) are coupled, they can spontaneously adjust until their phases lock into a fixed relationship — in-phase, anti-phase, or a constant offset — *without any change in their amplitudes*. The static prime `coupling` says only that the units influence each other; phase synchronization names what that influence *does over time* when the units are oscillators — it drives the temporal alignment of their rhythms. The load-bearing anatomy is threefold: (1) convergence of *phase*, not magnitude — the oscillators end up beating together while their individual amplitudes are left untouched; (2) a *critical coupling strength* — below it the units drift independently, above it they lock, so synchronization is a threshold phenomenon rather than a gradual one; and (3) the possibility of a *collective rhythm* emerging from many coupled units, a shared tempo that no unit imposed and none owns.

The feature present here but absent in the static `coupling` relation is precisely the *temporal locking*: coupling is a standing fact about mutual influence, whereas phase synchronization is the process by which that influence resolves initially-mismatched rhythms into a common one. It is also distinct from `resonance`: resonance is an *amplitude* response — a driven oscillator swells when forced near its natural frequency — whereas phase synchronization is *phase* alignment among *mutually coupled* oscillators, with amplitudes held roughly fixed. The two are easily conflated because both involve frequency matching, but the discriminating claim is the variable that converges: resonance amplifies magnitude at a matched frequency; synchronization aligns phase across coupled units. The canonical formalism is the Kuramoto model, which shows how a population of oscillators with distributed natural frequencies, coupled all-to-all, undergoes a sharp transition to collective synchronization once coupling exceeds a critical value.

Read structurally, the same coupled-oscillator shape appears across genuinely unlike substrates. In *mechanics*, Huygens' two pendulum clocks on a shared beam settle into anti-phase swinging, and generators on a power grid lock to a common electrical frequency. In *biology*, fireflies flash in unison, cardiac pacemaker cells fire together, circadian clocks *entrain* to the external light cycle, and neural populations bind by locking their oscillations. In *social* settings, scattered applause can converge into a rhythmic clap. Across all of these the shared abstract engine is identical — oscillators, initially out of phase, coupled until their phases converge above a critical strength — and the substrates are so unlike (clocks, insects, heart cells, grids, crowds) that the genus is plainly the bare dynamical structure, not any one domain's physics.

## Notes

**Provenance.** Produced by operator 03 (temporalization), flavor 3b, as the *dynamic* prime obtained by temporalizing the static `coupling` relation into the rhythm-locking process it can produce among oscillators. Reached from `teleconnection` and `tempo_mismatch` in the op-03 temporalization sweep; convergence ×2. Surfaced 2026-07-03. Established scientific construct: the Kuramoto model (Kuramoto 1975) of collective synchronization; entrainment; frequency/phase locking. Classic instances span Huygens' coupled pendulum clocks, fireflies flashing in unison, circadian entrainment to the light cycle, cardiac pacemaker cells, applause synchronizing, power-grid generator locking, and neural oscillation binding — a highly substrate-neutral spread. Verified absent from the corpus. Manifest: MODERATE hold.

**For owner evaluation (keep/cut).** The case FOR is strong: phase synchronization is a *canonical, named scientific construct* (Kuramoto; entrainment), verified absent, with a clean and vivid anatomy — phase convergence + critical coupling + emergent collective rhythm — and genuinely unlike siblings (clocks, fireflies, neurons, circadian, grids). It fills a real gap: the corpus already carries `coupling`, `oscillation`, and `resonance`, but not the specific dynamic of *phase-locking among coupled oscillators*. The RISKS Kurt should weigh: (1) **overlap with `resonance`** — these are distinct: resonance is *amplitude* amplification at a matched frequency (a driven single oscillator responding), whereas phase synchronization is *phase* alignment among *mutually coupled* oscillators with amplitudes held fixed; the discriminating variable is what converges (magnitude vs. phase). (2) **overlap with `coupling`** — coupling is the enabling *influence relation*; phase synchronization is a specific dynamic *consequence* it can produce, so they should relate by subsumption, not merge. (3) **one prime or two** — entrainment (a driven oscillator locking to an *external* driver, e.g. circadian to light) versus mutual synchronization (peers converging by symmetric coupling, e.g. fireflies) — the proposer recommends noting *both* under one head, since they share the phase-convergence-above-critical-coupling anatomy and differ only in the coupling topology (asymmetric driver vs. symmetric peers). Sharp keep/cut question: *is "phase-locking of coupled oscillators" a distinct prime, or is it just `coupling` (or `resonance`) applied to oscillators?* — the proposer's answer is that the phase-convergence dynamic with a critical threshold and emergent collective tempo is a feature neither `coupling` (a static relation) nor `resonance` (an amplitude response) names.

**At incorporation.** Re-run similarity against `coupling` (the enabling relation / nearest existing prime), `oscillation` (the units being synchronized), `resonance` (the amplitude-response contrast — screen explicitly for confusion), and any collective-behavior / emergence prime to confirm no collapse. If kept: draw a subsumption/relation edge `coupling` → `phase_synchronization` (influence relation → the rhythm-locking dynamic it can produce) and a composition/relation edge from `oscillation` into `phase_synchronization` (the units), and add a missing-edge note stating the boundary vs. `resonance` (phase alignment of coupled oscillators, not amplitude response at a matched frequency) explicitly. Decide whether entrainment and mutual synchronization live as one head or two. Write a v1 draft and sync the one_liner across v1 and v2 per CLAUDE.md before merge.
