What does a machine know about when?
Arc ·
Give a machine a document and a date, and it knows nothing about the date. A model reading the document treats the date as a string of characters, handled by the same machinery that handles a surname; it cannot feel that this is old. An index that stores the document’s meaning in one column and its time in another returns the same point for the same sentence written a year apart; to the index they are one document. A system watching you cannot tell that three in the morning on a Wednesday is strange for you and ordinary for someone else, because it has never been given a usual. And a permission issued at noon is exactly as alive at midnight as it was at noon, unless somebody remembers to take it away.
Every one of these is a question about time, and in every one the machine holds time the same way: as a count of seconds, in a field at the end of the record, that nothing reads. A count has no shape. You cannot ask it whether two moments are near, whether this is the usual hour, whether something has faded. You can only subtract.
This paper is about giving the count a shape — and then about what happens when that shape shares a space with meaning. The short version: meaning gets a trajectory. The rest of the paper draws what that means, one shape at a time, and names the paper in this series that proves each one.
Store a moment as a place, not a count. Where it falls on the day. Where on the week. Where on the year. How far along its own road. Eight numbers, as exact as the calendar, computed identically by any machine handed the same instant. Then set those eight numbers beside the numbers that already say what a thing means — the coordinates the first walk found, in which words are stars and distances can be trusted.
That is the whole move. Plate I is what it does to a sky of meanings.
Plate I — The sky, twice. Left: time stored beside meaning. The same sentence written in 2025 and again in 2026 is one star; the index cannot tell them apart. Right: time fused with meaning. Every star carries its when, and the two sentences separate along it — the same meaning, a year apart, two places.
On the left, two documents that say the same thing a year apart are the same point, because the index ranks by meaning and treats time, if at all, as a filter applied afterwards. On the right they are two points, a year apart along a direction the space now has. Nothing was learned to do this and nothing is approximate: the when is computed from the calendar’s own frequencies, so two machines drawing this sky draw the same one.
Once every point has a when, a sequence of points is a path. This entity, saying these things, doing these things, at these hours, over this week — a line through the same space the meanings live in. And because the path lives where the meanings live, the same instrument that finds a meaning’s neighbours finds a path’s: two paths that rhyme are near each other, and a path that has wandered has moved by a distance you can measure.
Plate II — A trajectory. One entity’s week as a path through the sky of meanings, each point carrying its hour. Beside it, dashed, a path that rhymes — near, by the same measure that makes two words near. Far away, a path that does not.
This is what it means to give meaning a trajectory: not a timestamp on a record and not a date filter on a search, but a where and a when in one geometry, so that the question “is this still the same entity I was dealing with an hour ago?” becomes “does this point belong to that path?” — a question geometry can answer. The first paper of the series asks the smallest version of it: how far apart are two moments — really?
Here is the pattern a timestamp cannot see. Every Monday morning lands near every other Monday morning, because on the day’s circle and the week’s circle they sit in the same place. An entity’s habit therefore draws a loop in the fused space, and the loop is a shape the instrument can recognise. A quiet Monday with nothing in it is a point on the loop: zero alarm. A request at three in the morning on a Wednesday, one day after the last one, is a short absence and an enormous distance.
Plate III — The loop. An entity’s Monday mornings close into a habit; last week’s loop is dashed beside this week’s. A quiet Monday sits on the loop. Three a.m. Wednesday sits far off it — and the alarm is that distance, not the time since the last event.
Cycles appear as loops. Departures appear as distances from the loop, measured against the entity’s own habit rather than against a threshold an administrator typed. Silence at the right phase is nothing; a small change at the wrong phase is everything. This is recognition of cyclical and temporal pattern inside the embedding space itself, and it is the capability the series builds toward. Paper 04 asks it directly: when is a change a departure — and when is absence just Tuesday?
A point on the path can carry a mass — the weight of a piece of evidence, the strength of a permission — and mass in this geometry halves every half-life. The old end of a path is faint by physics, not by policy. A permission is a mass on a curve; when the curve crosses the floor the permission is dead, everywhere, at once, with nothing to revoke and no message to send, because every machine holding the parameters computes the same curve.
Plate IV — Fading. The same path, its older points dimming by halves; inset, the staircase of halves descending to the floor. Below the floor a weight is dead for everyone who can compute the curve, which is everyone.
Paper 03 asks: how much does a moment still weigh?
A circle has one flaw: in closing on itself it forgets the lap. This midnight and last midnight land on the same point of the face. The cure is one more dimension — pull the day’s circle upward into a spring. The angle still says what time of day it is; the height now says how many days there have been; midnight’s seam runs continuous up the side, and nothing is torn.
Plate V — The lap. Left, the day as a circle, which knows when and not which day. Right, the same circle pulled into a spring: the angle keeps the hour, the height keeps the count, and the seam at midnight runs unbroken up the side.
Paper 02 asks: how does time turn without forgetting how many times it has turned?
Everyone stores time next to meaning. Nobody we can find folds the two into one geometry and then asks the geometry questions. Position codes and learned time embeddings make time legible to a model as a feature. Memory-decay models describe forgetting. A vector index ranks by meaning and filters by date afterwards. In each of these, time is a feature or a filter. Here it is a coordinate of the same space meaning occupies, computed identically by any machine from the calendar’s own frequencies, so that a trajectory, a loop, a distance from a loop and a fading mass are the same objects wherever they are drawn. The shapes in this paper are the construction’s own, not metaphors for it.
That is the claim, and it is checkable in three places: the coordinates are published in the formal paper; the construction runs; and each shape above has, or will have, a sealed measurement behind it in the paper named beside it.
In the Sovereignty architecture, every observation of an entity carries its eight temporal coordinates beside its meaning coordinates. The governor decides on both. The identity object is re-measured on both. A warrant’s remaining authority is read off the decay curve. The construction — nested phase coordinates, decay as a physical quantity, deadbands and hysteresis that make a temporal comparison stable enough to govern against, a per-entity origin derived from the entity’s own history, and one metronome stamping a frame for every part of the system — is set out in full in the formal paper, Kronos: Temporal Embedding as Governed Geometry.
Four results are sealed on the public board. The anchor a clock was shipped with was forgeable — none of its eight dimensions resisted (V3) — which is the disproof that made everything after it necessary. Ordering cannot be back-dated once events are bound to one another: five hundred of five hundred attempts were rejected (V4). A naively shared timeline, held in common, does not bind two parties — agreement fell to 49.7%; shared time is not free (V30). And the fading decomposes: the rate can be shared by everyone while the events that spend it stay private, and a forger gains almost nothing from knowing the rate (V31). The meaning campaign’s other cells measured the space of meanings without time; the time cells are these four, and the series adds to them one paper at a time.
Four shapes, four questions, four papers. How far apart are two moments — really? How does time turn without forgetting how many times it has turned? How much does a moment still weigh? When is a change a departure — and when is absence just Tuesday? After them come the harder shapes: many rhythms braided around one axis and read as a single polygon; letters stepping off a centreline so that a text has a body on the timeline; and the machine that is told the time by one metronome and never asks for it.
The first question is the smallest, and it is the one every computer gets wrong a thousand times a day. How far apart are two moments — really?
Series note. This introduction stands before Paper 01, Midnight’s Neighbor, and Paper 02, The Spiral, which are published; Papers 03 to 07 are planned and listed on the time shelf. The four cells cited here (V3, V4, V30, V31) are on the public verdict board. The papers chain by question, not by number, so that a paper can be added without renumbering the rest.
Refutations welcome