Lethian Formula

The Lethian Formula is the algorithmic procedure by which the Vault of Precedence calculates the moment of terminal deferral for items awaiting cataloguing on Floor 111. It is not, as is sometimes supposed, a method of cataloguing; it is a method of establishing how long cataloguing may be postponed without the item's status becoming irregular. The distinction is maintained by the Iron Dicta and has been litigated at least four times.

The Formula returns a single figure — the deferral interval — expressed in days, hours and fractions of a shift. An item whose deferral interval has not yet elapsed is described as pending; one whose interval has elapsed is described as due; one whose interval has elapsed and been twice renewed is described as Lethian, a term of art that carries no reproach but appears on the item's tag in red.

Origin and attribution

The Formula is named for Clerk-Adjutant Leth, who submitted it to the Vault of Precedence in the winter of the 61st Concurrence as a solution to the backlog on the 111th floor. Leth's covering memorandum survives and is unusually short: "The items will not spoil. The record of their waiting will spoil. I propose to measure the second thing." The Vault accepted the submission and returned it with eleven amendments, of which nine concerned the spelling of the memorandum.

Leth's original weighting of the terms has not survived in use. The version now applied derives from the recension prepared by the Central Scriptorium under Third Concordance Annex 9, which reassigned the weighting of the third term without explanation. The Scriptorium has declined to explain on four occasions, each time citing the same clause of the same annex.

Structure

The Formula operates on four inputs: the item's accession mass, the depth of its storage recess, the number of prior deferrals, and a coefficient known as the cadence residue, drawn from the Ledger of Irregular Cadences as codified by the Third Concordance. The fourth input is the subject of most of the scholarly dispute; the other three are uncontroversial and are recorded on the item's tag in Formula 12-D ink, which does not fade and is therefore legible on the oldest tags in the recess.

The residue is not a measurement of the item. It is a measurement of the irregularity with which the item was entered into the Ledger, and therefore of the extent to which its own record can be trusted to describe when it began to wait. An item entered on a regular cadence has a residue of zero and defers indefinitely; an item entered irregularly has a residue greater than zero and comes due sooner. The consequence, noted without comment in the Vault's standing instructions, is that the more carefully an irregularity is recorded, the less time the record buys.

The dispute over the terminal term

Second Concordance Clause 40 fixes the terminal term at a fixed interval of forty days from accession. Third Concordance Annex 9 replaces this with a term that diminishes asymptotically, never reaching zero, so that no item is ever strictly due. The two have never been reconciled. The Vault applies the Third where the item's tag is legible and the Second where it is not, a practice it describes as "the rule of the readable tag" and which has no written authority.

"Where two Concordances speak to the same term and neither yields, the term shall be taken from the elder, unless the elder is inconvenient, in which case the matter is one for the Vault."

— Iron Dicta, Dictum 17

Clerk-Adjutant Leth objected to this in a memorandum of the 62nd Concurrence, observing that the Formula had been designed to end disputes about waiting, not to furnish new ones. The memorandum was filed, stamped, and has not been answered.

Practical application on Floor 111

Application of the Formula is performed twice daily, at the opening and closing of the shift, by two clerks who must not confer until both have recorded their figures. Divergence between the figures is resolved by a third clerk, known informally as the tie-breaker of the recess, who is selected by lot from the floor's clerical roster and whose ruling is final for the day but not for the record.

Tags are sealed with a blend specified in Formula 743-Ξ before being returned to the recess, and the sealing is witnessed. Unsealed tags are re-entered at the residue of their original accession, which is why the sealing is witnessed. The wax must not be warmed in the hand; a tag warmed in the hand and resealed is void, and the item must be re-accessioned from the beginning, a process that on Floor 111 takes between nine and fourteen days and has never been completed within the deferral interval it restarts.

Criticism and later work

The Perceptual Flattening Quotient has been proposed as a corrective to the Formula's treatment of items whose accession mass cannot be independently verified. The proposal was referred to the Vault in the 70th Concurrence and remains under reference. Eloise of the Unspooled Chain, whose Dissonance Index was developed in the 43rd Concurrence, argued that the Formula measures the patience of the archive rather than the readiness of the item, and that the two are only coincidentally related. Her objection is reproduced in full in the Vault's margin and is answered there in a single word: "Noted."

The Formula has been applied experimentally on Floor 317 and Floor 413, both times with results the Vault has classified as "consistent with the Formula, subject to local conditions." No one has asked what the local conditions were. The clerks who conducted the trials have been reassigned.