record

Part I, The Sentence and the Kernel · defined in Chapter I, The Founding Sentence

A mark left by an occurrence that later occurrences can read.

Plate W.9The commit between the two gates writes structure into a fresh cell of the tape; the order of the two letters inside the live word is content, rewritten in place.

The records held by one register form its word, or log, ordered by age; the newest is its top. In the minimal register the record is the last symbol written, and it decides what the probe does to the blind sign. Chapter III says what is recorded. At each occurrence a commit writes a record into a fresh cell of a growing tape, and records hold only occurrence structure: the departure into a fresh cell, the participants of a shared occurrence, each naming the other, and what the occurrence read. Content is rewritten in place, so alternatives that differ in recorded structure never interfere, and those that differ only in content can.

Every record is a letter, and in the lift every letter is a rest frame, $T_{ab}=N_a+N_b$ of determinant one; consecutive records are related by a boost. The lift fixes the weight of a record: every record is one unit of proper time there, so a weight local to one occurrence and covariant under the lift’s Lorentz group is the same for every record.

As mathematics

In the minimal automaton a record is the symbol a transition writes. In the report lattice $\Lambda=\mathrm{Herm}_2(\Z[\omega])$ the records are the vectors $T=gg^\dagger$ , $g\in\SL(2,\Z[\omega])$ : unit timelike vectors, rest frames of unit mass. Each is a sum of two primitive null vectors in exactly one way, and their cusps reduce modulo $\mathfrak p$ to two distinct points of the sky, so a record names an observer. The map is equivariant and constant on $\Gamma(\mathfrak p)$ -classes; the records form $336/12=28$ classes modulo $\Gamma(\mathfrak p)$ , and it is a bijection from them onto the observers. An observer is a class of rest frames, an edge of the lift.

The six records of the base tetrahedron span the even sublattice of $\Lambda$ , of index two, which is the arena, and they name six pairwise non-meeting observers whose clocks are six distinct ones of the seven.

Its name in another field	Bridge
the symbol a transition of the minimal automaton writes	built
a unit timelike vector $T=gg^\dagger$ of $\mathrm{Herm}_2(\Z[\omega])$	built
modulo $\Gamma(\mathfrak p)$ , an anchored observer	built
a mark	a reading