Locations and curves
Ordinary geometry assigns points to places. A geodesic is an extended curve through that geometry.
A point can represent an entire question
The network is not the space.
Move a boundary interval. See its complete geodesic become one point in kinematic space, then test the interval order that makes MERA's causal structure legible.
Enter the mapperGeodesic interval explorer
One interval. One curve. One point.
A point here is not a place inside the disk. It encodes the complete boundary-anchored geodesic between u and v.
Center position60°theta = (u + v) / 2
Half-opening scale30°alpha = (v - u) / 2
Against reference [80°, 160°]SPACELIKENeither interval contains the other.
A node is not a place.
It represents a way of asking about the system.
Intervals and probes
Each point stands for a whole interval, and holographically for its complete geodesic.
Position and scale
The paper proposes that MERA discretizes this organizing space, not a pixelated spatial slice.
Worked information diamond
What remains after conditioning?
Use the illustrative vacuum-CFT model S(l) = (c/3) log(l/epsilon). The combination below localizes residual dependence inside one causal diamond.
A = 2B = 3C = 2
I(A,C|B) = S(AB) + S(BC) - S(B) - S(ABC)
0.3487 nats
A and C retain positive dependence after accounting for B in this toy entropy model.
Research boundary
Proposal, demonstration, extension.
Paper-backed: intervals parameterize geodesics; containment induces kinematic causal order; MERA shares this organizing structure.
Demonstrated here: deterministic coordinate mapping, containment classification, and a labeled illustrative entropy calculation.
Not claimed: that MERA tensors are locations, kinematic causality is physical time, or transformer attention is a geodesic.
Mapped result
Global probe contains the reference interval
Coordinatestheta 150° / alpha 120°
Causal relationTIMELIKE
Information diamond0.3487 nats
Endpoints, Containment and an Information Diamond
Read the explanation
The kinematic mapper is an educational interval model. Its local preset sets endpoint u to thirty degrees and v to ninety degrees. Theta is their midpoint, sixty degrees. Alpha is half their separation, thirty degrees. The global preset uses thirty and two hundred seventy, producing theta one hundred fifty and alpha one hundred twenty. These bars all use three pixels per degree. The displayed relation compares interval containment against the fixed reference eighty to one hundred sixty degrees. Its timelike label describes containment in this declared model, not physical time or an actual measurement of spacetime. The worked entropy model uses S of l equal to c over three times the natural log of l over epsilon. The source fixes c to six, a and d to two, b to three, and epsilon to one tenth. Its conditional information combines the lengths five, five, three and seven. Algebra gives two times log of twenty five over twenty one, about zero point three four eight seven nats. These bars show length at fifty pixels per unit. Moving interval endpoints does not change these four fixed lengths, so the computed information stays constant. This is an illustrative vacuum CFT expression, not a measured property of the endpoint controls. Compare the source presets with the reference interval eighty through one hundred sixty degrees. Thirty through ninety overlaps without containment and is labeled spacelike. Forty through one hundred eighty contains the reference and is labeled timelike. Thirty through two hundred seventy also contains it and is timelike. Bars show interval widths on one scale of two pixels per degree. The source checks containment before endpoint equality, so the exact reference interval is labeled timelike. Export preserves the input endpoints, reference, midpoint, half width, relation, four decimal information value and model boundary. View mapped result reveals a summary without changing the declared equations.