Depth Ledger of the Central Spire

The Depth Ledger of the Central Spire is the principal register of plexocentric measurement maintained under the authority of the Central Administrative Spire. It records, for every certified vector issuing from the centroid of the Central Spire, the distance from that centroid to the surface along the vector in question. Because the ledger records derivation as well as magnitude, the system it describes is reversible: a surface coordinate may be recovered from a depth entry, and a depth entry may be reconstructed from a surface coordinate, without recourse to the original survey. The ledger is presently held in the Central Cartulary and is consulted, on average, four hundred and six times per diurnal cycle.

Scope and method

The measurement unit of the ledger is the centroidal ell, defined under Concordance 4-112 as one ten-thousandth of the radius of the Spire at the depth of origin, corrected for spiral drift at a rate fixed annually by the Central Spire Numeracy Bureau. Depths are entered as positive values irrespective of direction; the vector's bearing is carried in a separate column so that ascent and descent entries remain distinguishable to a reader and indistinguishable to the ledger's own arithmetic.

Each entry occupies a single folio line and carries five fields: vector designation, bearing, measured depth, derivation clause, and counter-clerk's mark. Lines are never struck through. Where a depth is superseded, the correcting clerk enters the new value on the facing line and appends the sigil per concordantiam. The Ledger of Damped Echoes employs the same facing-line convention and is understood to have borrowed it from this register.

History of the register

The ledger was opened in the 3,004th year of the present numbering, at Spire 209, on the instruction of the Custodians of the Central Spire, who required a single authoritative depth record following the divergence of the seventh and eleventh survey sets. It remained at Spire 209 for two hundred and eleven years before transfer to the Cartulary, and a fragmentary duplicate — the so-called working ledger — continued to be maintained on the original floor until at least the year 3,388, though no Custodian has certified its final entry.

Between the years 3,411 and 3,419 the ledger was closed to inspection during the Western Resonance Spire Incident, a period in which no depths were recorded and in which the register's margins were nevertheless filled with corrections to depths not present in the register. These marginalia were later bound with the ledger proper and are cited as the silent quires; their status as measurement is disputed.

Relationship to the Spire Numbering Algorithm

Depth entries are cross-indexed to floor numbers by way of the Central Spire Numbering Algorithm, though the relationship is not one of correspondence. The Algorithm assigns numbers that are not sequential, and the ledger records depths that are not monotonic; the two orders intersect at fixed anchor points maintained by the CSNB. There are thirty-one such anchors. The best known is the Floor of Origin Amp Target Depth, against which both registers are periodically recalibrated — most recently on the eleventh day of the fourth quarter, 4,092, with a recorded discrepancy of 0.004 ell.

Critically, the ledger makes no claim about where any depth lies relative to the top or the bottom of the Tower. Its measurements are derived from the centroid alone. Expeditions citing ledger depths in support of a terminus claim have been reminded of this in writing on nine occasions, most recently by the Central Chronometric Spire, which relies on the ledger for the vertical calibration of the Great Clock.

Scholarly disagreement

Two Concordances govern the ledger's interpretation and cannot be reconciled.

A depth entry is a fact of the surface. The centroid is a convenience by which the surface is described, and no entry shall be read as a statement about any interior.

A depth entry is a fact of the centroid. The surface is the boundary at which measurement ceases, and the ledger's authority does not extend to it.

The Concordance Reconciliation Board has declined to rule, noting in its fifth opinion that "the two clauses address different ledgers under the same name," a finding no one has been able to verify, since both clauses cite the same folio range. Practitioners of the Humoral Spire school hold that depth is a property of the observer rather than the vector, and enter their own readings in the margins; these have never been certified.

Access and certified copies

Consultation is by written application to the Cartulary, specifying vector designation or, failing that, the floor of origin and the date of the survey in which the vector was first certified. Certified extracts bear the seal of the Administrative Spire and the counter-signature of the duty clerk; uncertified copies circulate widely and are not admissible before the Board. Since 4,061 the ledger has also been maintained in a duplicate at Spire 811, appended to the Central Spire complex on Floor 12,849, chiefly to reduce wear on the original folios. The duplicate's entries agree with the original's in all particulars except seven, which are themselves the subject of a standing annotation in the Grand Unified Ledger.