Folios of Unstable Geometry

The Folios of Unstable Geometry are a class of archival document whose physical dimensions, mass, and internal angles are not constant between two observations. A folio measured at 31 by 44 centimetres on a Monday morning may present as 29 by 41 by Monday afternoon, and rather more often as both simultaneously during the intervening night. The class is recognised by the Bureau of Ambivalent Geometry under provisional heading BG-114 and is distinguished from the Möbius Folios chiefly by the fact that a Möbius Folio is unstable in a manner that can be predicted, whereas an unstable folio is unstable in a manner that cannot.

Handling of the class has never been performed manually. The Kinetic Page-Turner was conceived for this purpose, and its principal schematic was recorded under KI-7821α; that the Turners have never left the drawing stage has not prevented the class from being discussed at length in three separate Proceedings.

Physical behaviour

An unstable folio is stable while unobserved and becomes unstable at the moment of measurement, which has led the Custodians of Static Geometry to argue that no unstable folio has ever in fact existed and that the archive is describing a clerical habit. The Bureau's position, set out in its response of 14 Frost, is that the matter is settled by the sheets themselves, which persist in the stacks whether or not anyone opens them.

Measurements taken by Fourth Librarian of Ephemeral Geometry over the winter of the long inventory suggest three recurring states, though the Bureau disputes the third:

• Folded — the folio occupies less area than its contents require, with no loss of legibility.
• Spreading — the folio enlarges until it meets an obstruction, usually shelving, sometimes a reader.
• Recurrent — the folio returns to a prior dimension it has already used, carrying marginalia acquired in the interval.

Readers are asked not to stack unstable folios on unstable folios. This is the only prohibition in the class's handling record and the only one that has ever been enforced.

The folding incident of Floor 45

In the third week of Frost, a folio from the Unindexed Folios of Floor 45 was observed to fold along a crease that did not previously exist and could not subsequently be located. The fold propagated through eleven adjacent documents before a junior clerk, Aurel Stave, closed the reading room door. Stave's report notes that the propagation ceased at the door frame, that the door frame has since measured two centimetres narrower each year, and that he was not asked to file a second report.

"The crease was not in the paper. The paper was in the crease. I have written this sentence four times and it will not improve."

— Aurel Stave, incident report 45-F/3, appended note

The Bureau treats the incident as a containment success. The Custodians treat it as evidence that unstable geometry is contagious, which they regard as an argument for their own jurisdiction rather than against it.

Jurisdictional dispute

The Third Concordance distinguishes the purview of the Custodians of Static Geometry from that of the Bureau of Ambivalent Geometry, but does so by describing what each office may not touch, and the two lists overlap in a passage that has been read three ways since the Concordance's fourth amendment. The Doctrine of Unstable Foundations is cited by both offices and has been annotated by neither, on the grounds that annotation would constitute a claim.

The dispute acquired its present shape in the matter of the Winter Recension, when the Custodians sealed a cabinet of unstable folios on the authority of the Third Concordance and the Bureau unsealed it on the authority of the same document, citing a different annex. Both offices agree the folios were not disturbed. They disagree about which of them did not disturb them.

Relation to other unstable holdings

Unstable folios are frequently confused with Recursive Folios, which contain instructions for their own cataloguing, and with Negative Folios, whose creation is underpinned by the Principle of Recursive Authenticity. The distinctions are technical and are not observed in the reading rooms. A folio whose own catalogue entry describes it as an unstable folio is, by the Bureau's reckoning, both classes at once and should be referred to the Warden of Perilous Folios, who holds Proceedings Vol. 781 under restricted access and has declined to clarify the point.

The Geometry of Unmade Decisions is sometimes named as a fourth class. It is not a class of document; it is a condition of the stacks, and the Bureau has asked that it stop being named in folio discussions.

Cataloguing practice

An unstable folio is catalogued at the dimension it held when first accessioned, with a note reading dimensions provisional, and thereafter at the discretion of the cataloguer. The result is a catalogue in which the same folio appears at 31 by 44 centimetres in one hand and 29 by 41 in another, neither entry marked as superseding the other, both correct.

The Kinetic Page-Turner schematic was itself recorded on an unstable folio, which is why KI-7821α exists in four mutually inconsistent versions and why the resonance event of 4.7 seconds cannot be reconstructed from any one of them. The Office of Schematics has ruled that the four versions be treated as a single drawing viewed from four angles, none of which is perpendicular to the page.

Accession of new unstable folios was suspended by administrative note in the year of the long inventory and has not been resumed. The suspension is recorded, as is customary, on the folio it concerns.