Abstract
A cat sat on a mat. You read that and reconstructed a four-dimensional scene - who, where, when, why - from six words. The reconstruction worked because you and the writer share enough context to decompress the same sentence into the same room. That shared decompression is the thing this paper is about.
Current artificial cognition stores memories as points, edges, or text chunks, none of which preserve the dimensional richness of an experience as it was lived. What seems to be missing is a storage shape that holds an event the way you held the cat scene: compressed but reconstructible by a receiver who shares enough context. We call the compressed form a Fable and the full form an Episode.
Five shapes appear wherever cognition stores anything: binary, table, graph, vector, and a fifth - a shared append-only ledger running as the time axis beneath the other four.
Three Pillars of Falsification
The paper commits to three independent pathways to failure. If one of them cracks decisively under scrutiny, the paper fails there, and the remaining pathways do not rescue it.
Ontological - Do the five shapes actually recur at every storage scale, or is the recurrence an artefact of selection bias?
Mechanical - Does the derivative stack settle the way minimum-jerk trajectories predict, or does it diverge under realistic conditions?
Agent-behavioural - Does a system built on this substrate outperform matched baselines on dimensional preservation, or does the architecture add complexity without gain?
Twelve specific predictions with quantitative falsification anchors are drawn from Sections I through XII. See the full prediction table.
Five Shapes
The claim is not that these shapes are new. The claim is that they recur at every scale, from Babylonian astronomical diaries through Talmudic commentary chains to contemporary bitemporal databases, and that the recurrence is structural rather than coincidental.
Binary - yes/no, on/off, the simplest gate.
Table - rows and columns, the shape of structured enumeration.
Graph - nodes and edges, the shape of relationship.
Vector - direction and magnitude, the shape of similarity.
Ledger - append-only shared time axis beneath the other four.
The Invitation
This is a research programme, not a proof. It specifies what to measure, how, and what would kill it. Three independent falsification paths are offered. Readers are invited to build, measure, and report.