OPHobserver · patch · holography

Chapter 03

The whole family.

Once you see the pattern, you see it everywhere. A "loop" in OPH is any cycle in a graph of overlapping descriptions. When the cycle fails to close, the residue is physical.

  • Aharonov–Bohm effect

    Local
    B = 0 along both electron paths.
    Loop
    Enclosed flux Φ_B shifts the interference.
    Holon
    exp(i q ∮A·dx / ℏ)

  • Berry / geometric phase

    Local
    Quantum state evolves adiabatically.
    Loop
    Slow loop in parameter space leaves a residual phase.
    Holon
    exp(i ∮ ⟨ψ|i∇|ψ⟩ · dR)

  • Foucault pendulum

    Local
    Plumb line obeys local gravity at every point.
    Loop
    Day-long latitude loop rotates the plane of swing.
    Holon
    Δθ = 2π (1 − sin λ)

  • Three-body problem

    Local
    Pairwise Newtonian forces are simple.
    Loop
    Triangle of pair-relations carries action holonomy.
    Holon
    exp(i ∮γ (p dq − H dt) / ℏ)

  • Yang–Mills / Wilson loops

    Local
    Field strength F_μν vanishes in vacuum patches.
    Loop
    Closed Wilson loop tr P exp(i ∮A) is observable.
    Holon
    tr P exp(i ∮γ A)

  • Parallel transport on a sphere

    Local
    Each step preserves the vector locally.
    Loop
    Trip around a triangle rotates the vector.
    Holon
    Δθ = (solid angle enclosed)

  • Consensus on graphs

    Local
    Each edge agrees on a shared variable.
    Loop
    Cycles can carry a constraint that no assignment satisfies.
    Holon
    cocycle obstruction in H¹

  • Distributed systems (CRDT merge)

    Local
    Each pairwise merge is well-defined.
    Loop
    Cycles of merges may diverge from the join.
    Holon
    non-commutative residual

The unification.

OPH says: there is no "gauge" trick, no "geometric phase" trick, no "chaos" trick. There is one move — repair the patch net to its quotient-normal form. Every item above is a special case.

Potentials, gauge phases, multi-body dynamics, distributed consensus — the same lesson told four ways.