Decremental Spiral System

Definition and scope

The Decremental Spiral System is the classification regime established by Clause 12 of the Third Concordance, under which a floor's number decreases in proportion to its conceptual proximity to the Central Index. It is administered by the Third Spiral Index, which holds sole jurisdiction over both the application of Decremental Spiral protocols and their suspension.

In practice the System converts an abstract judgement — how far a given floor sits, in conceptual terms, from the Central Index — into a stable integer. Because the Central Index itself has never been located, the judgement is performed by the Third Spiral Index on a case-by-case basis, and the resulting numbers are not sequential in any way anyone has been able to reconstruct. This is considered normal.

Relation to the Spiral Decimal System

The Decremental Spiral System should not be confused with the Spiral Decimal System, which assigns coordinates to individual storage chambers rather than to floors, and which was itself introduced following Concordance 11 as the successor to the Candle-Branch system. The two overlap only at Floor 9, where chamber coordinates under the Spiral Decimal System are nested inside floor numbers issued under the Decremental system. Chamber 4-2-11, for example, lies on a floor whose number has no arithmetic relationship to any of its digits.

The Linear Decimal Protocols that preceded the Spiral Decimal System had no equivalent floor-numbering component, since under that regime floors were named before they were counted. A small number of floors retain Linear-era names despite carrying Decremental numbers; the resulting dual designations are a standing nuisance to the Clerks of the Spiral.

The Central Index problem

Clause 12 presumes a single Central Index. No Concordance identifies it. The First Concordance refers to a "datum of reference" without naming a location; the Fifth Concordance describes the Central Index as "the floor from which all other floors are distant," which is circular and has been challenged repeatedly.

Two schools of thought prevail. The first, associated with the office of the Third Spiral Index, holds that the Central Index is a fixed point and that its location is simply a matter awaiting sufficient survey. The second, associated with the Scriptorium of Deferred Measures, holds that the Central Index migrates slowly and that Decremental numbers should be revised on a periodic basis. A revision cycle was proposed in the winter of the Long Recension and abandoned after three floors changed numbers twice within a single quarter.

"A floor's distance from the Index is a property of the floor; that the Index has not been found is a property of the survey."

— Third Concordance, Clause 12, Gloss A

Suspension of protocols

The Third Spiral Index may suspend Decremental Spiral protocols on a per-floor basis. Suspensions are recorded in the Register of Suspended Measures and are, in theory, temporary. Roughly one suspension in nine has been in effect for longer than the office that granted it.

A notable suspension applies to Spiral 14, where Decremental numbering was halted during a dispute over whether the floor's shafts counted as conceptual distance or merely physical adjacency. The ruling was recorded and never acted upon, and the floor currently carries a provisional number that appears in no Concordance annex.

Contested interactions

Several adjacent systems interact uneasily with Decremental numbering:

• The Oneiric Decimal System, a specialized adjunct to the Spiral Decimal System, issues floor numbers that decrease during recollection and increase during anticipation. These are not recognized by the Third Spiral Index.
• The Fifth Spiral Watercourse, a hydraulic cataloguing system, derives its pressure gradients from floor numbers and has been forced to install compensating valves on three floors whose numbers were revised mid-cycle.
• The Cerebral Canal Lock System maps infrastructural services using Spiral Decimal void addresses, which do not decrement at all, producing occasional double-occupancy of service shafts.

The Administrative Spiral Beta inquiry system reports floor numbers to querents without indicating whether they have been Decremental-issued, Linear-era, or provisional, which remains the single largest source of misrouted correspondence recorded by the Bureau of Returned Envelopes.

Editorial notes

Floor numbers under this system are conventionally written without leading zeros, though the Spiral Notation annex permits them where a floor is considered conceptually adjacent to the Index. Whether a floor may be assigned the number zero has not been settled; the question was tabled at the Third Index sitting and has not been tabled since.

Visitors are reminded that Spiral Markings on stairwells indicate shaft identity, not floor number, and that counting landings is not a recognized method of estimation.