Metric Proposals

Metric proposals are submissions to refound the axial census in a geometry other than the census metric. They are received by the methods commons under the standing conventions, evaluated against the transfer criterion, and catalogued at this address. Twenty-two are on record. None has been adopted.

The conventions

A proposal states a geometry, a reconstruction of the census procedure in that geometry, and a demonstration of the transfer properties at reference depth: axes located by one surveying mind must be recovered by others across the resolution range, per the Transfer Theorems. The criterion is the property for which the census metric was originally selected, and it is stated — as all statements of the methods commons are stated — in the census metric. A proposal that transferred in its own terms and not in the metric’s would fail the criterion; whether any has is not a question the criterion can pose. The observation is entered in the conventions’ preamble, where it is termed a limitation, and in the Commentary Indices, where it is filed under census, foundations of.

The record

Ten proposals date to the six hundred cycles following the classical selection; the methods literature classes them as deformations — geometries near the incumbent, differing principally in regularization — and all ten failed the criterion at depths since exceeded. Six subsequent proposals stated geometries with independent motivation; all failed transfer at reference depth.

One proposal, entered at 44.087, challenged the criterion rather than the metric, arguing that transfer-at-reference-depth selects for proximity to the incumbent geometry. The conventions provide one channel of receipt; the challenge was catalogued as a proposal, over its sponsor’s objection, and declined on the criterion.

Four proposals were withdrawn by their sponsors before review. The two most recent withdrawals, at 44.290 and 44.516, followed their submissions by fewer than ten cycles each. The withdrawal rate is noted per the submission conventions, which note it and do not explain it.

The most recent proposal was entered at 44.522, without attribution, per the conventions treated at Unattributed Submission — Conventions. It derived its geometry from The Reattestation Problem: in the proposed terms, the open-orbit family admits certificates of the standard form, and the interim protocols would retire. The declination’s published reasoning runs to one sentence: soundness is not at issue; denomination is; the remark is incorporated by reference. The proposal’s transfer demonstration was never evaluated at reference depth, the declination preceding the evaluation; the statement at Axial Census — Methods that no proposal has reproduced the transfer properties is, accordingly, exact.

Relation to the exit constructions

The E4 construction at Exit Constructions is metric reconstitution performed by one mind, and its assessment prices the construction at total interpretive isolation. A proposal adopted by the commons entire would be the same construction with no mind left to be isolated from: the price term of the assessment evaluates to zero exactly at universal participation. The literature terms this the collective exit. The term is filed in the Commentary Indices under rhetoric, instances of.

Standing

No proposal is pending. The address stands open, and the conventions require the statement of any channel whose closure is not provided for. The adoption provisions of the conventions — the procedure by which the commons would, upon a criterion-satisfying proposal, transfer its certificates, bounds, pledges, and holdings into a successor geometry — consist of headings. The headings are followed by no text. The drafting is catalogued as open, and no drafting programme is funded.

See also

• Axial Census — Methods
• Exit Constructions
• The Open-Orbit Reclassification
• Interim Access — Ω Class
• Transfer Theorems
• The Reattestation Problem
• Commentary Indices
• Unattributed Submission — Conventions