# Syncre: Massive-Scale Framing (Quick Note)

## Core idea

Earth “local time” is an example of a general phenomenon:

A single global moment induces a full phase field across a space, and that positional phase field can be viewed as the restriction (pullback) of a larger global phase field.

## Minimal formal package

- Ambient arena: \(M\)
- Slicing into global instants: \(M=\bigsqcup_{s\in\mathbb{R}}\Sigma_s\)
- Phase codomain: \(\mathbb{T}_P=\mathbb{R}/P\mathbb{Z}\)
- Global phase field: \(\Phi:M\to\mathbb{T}_P\)

### Coverage axiom

\[
\forall s,\quad \Phi(\Sigma_s)=\mathbb{T}_P.
\]

### Earth as pullback

Given an embedding \(i_s:\mathcal{E}\hookrightarrow\Sigma_s\), the induced local phase field is

\[
\tau_s=\Phi\circ i_s:\mathcal{E}\to\mathbb{T}_P.
\]

This makes the Earth formulas a special case: they are the pullback of \(\Phi\) to a particular embedded subsystem.

## Doorway to nonlinear time

Use a lift \(F:M\to\mathbb{R}\) with \(\Phi=F\bmod P\), then impose structural constraints on \(F\) (monotonicity along a chosen future direction, bounded rate, regularity, and holonomy consistency). This keeps the theory analyzable while allowing nonlinearity.
