synchronization_mechanism
plain-language theorem explainer
Recognition Science defines the synchronization mechanism as the enumerated list of four statements on global 8-tick phase initialization and J-cost coherence. Cosmologists working within the Recognition framework would cite it when presenting an alternative to inflation for CMB uniformity. The definition is a direct list construction that assembles descriptive strings from the universal tick and phase primitives.
Claim. The synchronization mechanism is the list of strings: ``Ledger initialization sets global 8-tick phase'', ``All events are timestamped relative to universal clock'', ``Coherence is maintained by J-cost consistency'', ``Homogeneity is the low-cost configuration'', where the 8-tick phase takes values $kπ/4$ for $k=0,…,7$ and J-cost is the derived cost of a multiplicative recognizer.
background
The module COS-004 addresses the horizon problem: the CMB is uniform to 1 part in 10⁵, yet standard Big Bang cosmology leaves distant regions causally disconnected. Recognition Science supplies a complementary account via the universal 8-tick clock. Upstream, tick is the fundamental RS time quantum τ₀ = 1, phase(k) = kπ/4 for k in Fin 8 supplies the discrete phases, and cost extracts the J-cost of any recognition event or multiplicative recognizer. The 8-tick octave (period 2³) therefore supplies a global synchronization that does not rely on light-speed signals.
proof idea
The definition is a direct enumeration of four descriptive strings. It assembles the list without invoking tactics or lemmas beyond the imported constants for tick and phase.
why it matters
The declaration supplies the concrete RS-native account of homogeneity for the horizon problem (COS-004). It rests on the eight-tick octave (T7) and the J-cost minimization principle that favors homogeneous configurations. No downstream theorems are recorded, so the definition stands as the interface between the ledger primitives and the cosmological claim that phase coherence enforces uniformity without inflation.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.