Spire Model

The Spire Model is the collective designation for the family of theoretical constructs by which the Librarians describe the interior arrangement, load distribution, and administrative behaviour of the Tower's vertical structure. Although the term entered general use only in the eleventh recension of the Third Concordance, the model it names is considerably older, and it remains the only framework in which the Tower's floors are treated simultaneously as architecture and as a filing problem. There are four recognized formulations — the Structural, the Stack, the Descending, and the Petitionary — and scholarly opinion has never settled which of them describes the building and which describes the Librarians' hopes for it.

Origin and the stack formulation

The earliest attested use is found in the Third Concordance, which devotes its opening annex to what its drafters called the "non-Euclidean stack": the observation that a floor may be farther from its neighbour above than from a floor nine thousand levels distant, and that this distance cannot be expressed in spans, paces, or any measure the Metrological Spire is willing to certify. The Concordance's drafters proposed that floors be treated not as storeys but as leaves of a single volume, bound in an order that the reader's passage through them does not alter.

This formulation survives almost unchanged in the Stack Model proper, which holds that vertical adjacency is a matter of call number rather than elevation. Under the Stack Model, the question "what lies above Floor 70,203?" has no answer; the correct query is "what is shelved after it?" The Alban Resonance Model was documented on that floor and its filing position has since been disputed twice.

The structural formulation and the load question

The Structural Spire Model addresses load. It is maintained chiefly by the Office of Vertical Reconciliation, which holds that the Tower's fabric is supported not by its walls but by the aggregate weight of its holdings, and that the removal of any volume from its assigned position produces a measurable though usually harmless settling of the floors above it. The office's returns for the winter of 4,411 — a season in which some sixty thousand volumes were sent for rebinding — record eleven days of "prolonged settlement" on the upper intramural stacks, during which the third spiral stair admitted no traffic before the tenth bell. The office has requested that rebinding be scheduled by intake rather than by need ever since.

The Central Spire, whose centralized model was deviated from during the Sultanate period, is treated in the Structural Model as a load anomaly rather than a support: the Central Spire bears nothing, and is retained in the calculations because its removal would change them.

The Descending Model

The Descending Spire Model, favoured by the Clerks of the Interior Spire, inverts the Stack formulation: the Tower is not built upward from a base but parcelled downward from a single unlocatable floor, and every staircase is best understood as a corridor of increasingly grudging permission. The clerks cite the Third Concordance's description of the stack as evidence for, not against, their reading, on the grounds that a volume is read from its front matter, wherever the binder has placed it. The disagreement between the Descending and Stack readings has been before the Concordance three times and has been referred onward each time.

The Petitionary Model and the Model IV affiliation

The fourth formulation, the Petitionary Spire Model, is the most recent and the least architectural. It holds that the Tower's vertical order is maintained by the volume of petitions seeking to move within it, and that floors exist wherever sufficient petitions have accumulated to require one. Its principal instrument is Model IV, the current version of the Tower's standard petition-reading apparatus, whose Sentient Scribe scans incoming petitions and extracts citations for the Priority-by-Obscurity Model of queue formation. The Vect Resonance Model, formalized by the Bureau of Coincidental Resonance, classifies the resulting damping into Coincidental, Procedural, and Material classes, and the Petitionary Model adopts all three without alteration.

The Temporal Recursion Model endorsed by the Central Registry of Precedents conflicts with this arrangement at the point of precedence, and the competing Priority-by-Obscurity Model of Queue Formation predicts that the Spire Model's more obscure annexes will come to govern its better-read ones. Clerks of the Petitionary school regard this as a forecast; the Structural school regards it as a complaint.

Criticisms and the record of disagreement

The most persistent objection is that no single Spire Model has ever predicted a floor's arrival, only its admissibility. In a memorandum of the eleventh session, a clerk of the Vertical Reconciliation office — named in the register only as Vell, of the seventh intake — recorded that she had applied all four formulations to a petition concerning a stairwell on Floor 44,006 and obtained four different floors, none of them the one she was standing on. The memorandum was not answered. It was, however, annexed.

"The model is not required to tell us where we are. It is required to tell us why we cannot leave."

— Third Concordance, Annex 11, marginal note

Since Vell's memorandum, the practice has been to run the Structural and Petitionary readings in parallel and to assign the floor indicated by whichever model requires fewer rebindings. The Static Congestion Model is consulted where queues have formed, and the Static Congestion Model of Queue Formation where they have formed twice. Model VII's White Noise Generator is not consulted, on the ground that the Spire Model is settled enough without it.

Maintenance

The Spire Model is recalculated in full only when a Concordance is amended, and not before the next bell. Clerks are asked not to lean on the load-bearing volumes, and no petition may be filed on a landing.