Unknot–Energy Correspondence: Causal Closure as the Origin of 4D Spacetime and Photon Properties

### Abstract We propose a framework in which energy is identified with a closed 1D causal loop (an unknot) and 4D spacetime is the minimum geometry supporting stable topological interaction between such loops and non-trivial knots (candidate matter structures). The speed of light c is treated as the structural ratio δ x/δ t of fundamental projection units. Photon helicity is identified with the framing number (±1) of the loop's stable 3D embedding, whose boundary structure is a Hopf link — unifying the "photon as unknot" and "photon as Hopf link" pictures as two views of the same framed object. Photon energy follows $E = hc/C$ with zero rest mass. Quantization of C yields a hard photon energy ceiling Eₘₐₓ ≈ 2.56×10¹⁹ GeV and a stochastic discrete-redshift mechanism producing cumulative spectral broadening σE/E ~ 1/√N. Both are several orders of magnitude beyond current observational reach; we present them as principled falsification targets rather than near-term tests.