What this round could not reach

An audit’s last obligation is the list of what it did not do. This one is longer than the round’s findings and every item on it is specific enough to be picked up.

The claim #

The round left eleven specific things undone, most of them an afternoon’s work, and the reason in every case is that the round ran out of round rather than that any of them is hard.

• Four are runs the machinery supports and nobody executed: the census under two observers, the census on a wide grid, the observer audit on the wide grid, and the enclosure sweep with a lobe.
• Three are measurements the constructions cannot make: a gloss finish below the solver’s boundary, a structured sample near the tabulation’s limit, and a real ink library’s observer allowance.
• Two are checks against tables rather than models, which the round’s method cannot supply.
• And two are absences that have been recorded for six rounds and are recorded again.

The runs that were not run #

The census under two observers. Its comparisons should survive an observer change and its levels should not, and the run would settle whether an adaptation model’s error depends on whose eye it is evaluated through. The machinery exists — a census function and an observer with arguments — and the two have never been called together.

The census on a wide grid. The interesting version is not one run but three, under three defensible extensions of its surfaces below 380 nanometres, reporting the sensitivity to the assumption rather than a corrected level. That is the shape a sensitivity result should have and it needs the surfaces extended first.

The observer audit on the wide grid. Two of the six departures are absorptions below 500 nanometres and the range’s truncation removes 300 to 380, so widening it would change the departures as well as the levels. The direction is predictable and the size is not.

And the enclosure sweep with a lobe. The metamer-separation result is parameterised by how enclosed the geometry is, the directional solver takes the same room, and running one across the other is a loop nobody wrote.

What the constructions cannot reach #

Three items are not runs but limits of the objects the round built.

A gloss finish. The directional solver’s boundary is at roughness 0.15, measured rather than declared, and a gloss enamel is at 0.02 to 0.05. So every scene number in the round is a lower bound and the curve is still rising at the left-hand end of the axis. Reaching further needs more patches rather than more directions, which is a different solver.

A structured sample. The tabulation’s governing ratio is properly about the product of light and sample, and every sample in the round is smooth, so no measurement here can distinguish “the light’s narrowest feature” from “the product’s”. An interference filter, a structural colour or a laser-line notch would settle it.

And a real ink library. The brand-colour recommendation is inferred from where each departure lives rather than computed over real colorants. Computing it over a printed ink library is a straightforward loop over measured spectra and this collection has no such library.

The checks that need a table #

Two items are outside the round’s method rather than outside its effort, and they are the ones worth being clearest about.

The observer departures against the tabulated observers. Everything in the round is computed with an analytic construction whose residual against the 1931 functions is 1.42 ΔE₀₀ at the median, published in front of the results. Recomputing the departures against the CIE’s own 1931 and 1964 tables would give the standard’s numbers rather than the construction’s — and cannot be done for the field size, the age or the peaks, because a table has no such arguments.

The tabulation’s terms against the tabulated functions. Same obstacle, harder: a five-nanometre error cannot be measured with five-nanometre data, so the analytic reference is not a convenience but the only available instrument. There is no version of this measurement that uses the standard tables.

Those two are the round’s methodological boundary and they are not going to move. A model was built because the questions had outgrown the data, and the data cannot be asked to check the model on the questions that needed it.

The absences recorded again #

Two items have been on this collection’s list for six rounds and are on it for a seventh.

The corresponding-colour data. Every published chromatic adaptation transform was fitted to measured pairs reported to look alike under two lights, this collection has none of those data, and three of this round’s results depend on the fit — the basis question, the appearance model’s internal observer, and whether the published transforms’ sharpening is a fit to a second site or an artefact of the data.

And whether an ageing eye’s normalisation is complete. The lens is the round’s largest departure and the largest question about it is whether a seventy-year-old’s visual system has renormalised, which would absorb most of its effect on appearance while leaving all of it on matching. Nothing in this collection can measure that.

Recording an absence for the seventh time is not a ritual. Each round the absence has cost something specific and different, and naming what it cost this time is the only thing that distinguishes a recorded shortfall from a standing apology.

Two things the round found and did not pursue #

There are two loose ends that are findings rather than omissions, and they belong on the list because somebody should follow them.

The desaturation reverses by direction. A lobe on a wall lowers the bounce’s chroma seen from the front and raises it seen from the coloured walls, so a lobe moves colour around a room rather than removing it. The total is very nearly conserved and its angular distribution is not, and nobody has checked how nearly.

And the two audits’ terms are anti-correlated with colour temperature. A lamp’s ultraviolet decides one and its blue poverty decides the other, and the two run in opposite directions along the Planckian locus. That is stated from two radiators and a thermodynamic argument, and a sweep along the locus would turn it into a curve.

Both are cheap and both were noticed too late in the round to be run.

Reading the previous round’s list against what this one did gives a useful calibration for how fast such a queue moves.

It named four things. Widen the grid and give the scene solver a lobe were both taken, and both turned into substantial parts of this round. Compute the remaining interaction pairs was not, and the next object is the observer was taken and became half the round.

So three of four in one round, which is faster than the queue has usually cleared and is a consequence of the slate being unusually large. At an ordinary slate the rate is closer to one or two, and this round’s eleven items are therefore several rounds’ worth rather than one’s.

That matters for how the list should be read. It is not a plan for the next round; it is a pool the next round will draw two or three from, and the ranking below is a recommendation about which.

What the shortfall list is for #

This collection keeps such a list on a stated rule and the rule is worth restating, because a round of this size makes it easy to forget.

An empty shortfall queue on a full slate usually means nobody wrote one. A round that produced twenty departures and ten conditions and left nothing undone would be a round that did not look hard enough at its own boundaries.

The list also has a second function, which four rounds of this collection have now demonstrated. Every one of this round’s three audits began from a sentence in a previous round’s shortfall — the observer whose substitutions already existed, the range that was a truncation, the scene solver with no lobe. None of those sentences was a plan and each turned out to be a round.

So the value of an entry depends entirely on its precision. The observer is a limitation would have produced nothing. The substitutions exist and only the plumbing is missing named the work, and turned out to be right about the plumbing and wrong about the difficulty, which is the most a shortfall entry can hope for.

Three should be taken first. Ranking the eleven by what they would settle rather than by what they cost gives a clear first three.

The census under two observers, because it would answer whether an adaptation model’s error is a property of the spectra or of the eye — which bears on every corresponding-colour fit in the field and not only on this collection.

The wide-grid sensitivity, in its three-extension form, because it would convert the range from an outstanding item into either a settled small term or a stated irreducible uncertainty. Either outcome closes something that has been open for three rounds.

And the structured sample, because it is the cheapest of the eleven and it would settle whether the tabulation’s governing ratio is about lights or about products — which decides whether the round’s decision procedure is general or is a statement about smooth reflectances.

The rest are worth doing and none of them changes a conclusion.

Three things the round leaves behind make the eleven cheap. A shortfall list is about what was not done and it is worth balancing with what the round leaves behind that was not there before, because those are what make the eleven items cheap.

An observer with arguments. A new module builds a set of colour-matching functions from a field size, an age, a macular density, a cone optical density, three peak wavelengths and a rod contribution, on any wavelength grid. Nothing in this collection had one; every calculation called observer("1931") and took what it got.

A grid-generic optical eye. The pigment template and the ocular media now take a list of wavelengths, so the whole apparatus is answerable at any resolution rather than only at five nanometres. That is twenty lines and it is what made the tabulation audit possible at all.

And a directional transport solver. It solves one radiance per ordered pair of patches and reduces to the existing radiosity solver at the floating-point floor, so a scene question about direction can now be asked.

Each of the eleven outstanding items is cheap because one of those three exists. That is the usual relationship between a round’s machinery and the next round’s slate, and it is why the machinery is worth building even when a simpler calculation would have answered the question in hand.

What was computed, and how #

Nothing is computed here. The list is assembled from the round’s own essays, each of which records its own limits in a section written for the purpose, and this is the aggregation.

The claim that most items are an afternoon’s work is an estimate based on the machinery existing and the loops being short. The two that are not are the ink library, which requires data this collection does not have, and the sub-0.15 roughness, which requires a different solver.

One further item belongs on the list and it is about the collection rather than about colour. Three of this round’s findings are defects in this collection’s own figures, recorded and not repaired: its narrowband sources are point-sampled where an instrument would integrate, its summation is the standard’s and the standard’s is for measured data, and every scene number it has published was computed on matt walls.

None of the three is repaired because each would move every number the collection has published, which is a reason for care rather than for delay. The delay is the honest state and it is recorded rather than left in prose, which is the rule this collection applies to anything it knows about and has not fixed.

Where the model stops #

A list of what was not done is itself incomplete, and the honest statement is that it contains what the round noticed it had not done. Anything it failed to notice is not on it, by construction, and the previous round’s list turned out to be missing an item that became this round’s largest finding.

The estimates of effort are the author’s and are the kind of estimate that is usually optimistic.

There is a last item that is not on the list because it is not an omission, and it should be said before the list is used as a plan. The round wrote fifty essays against a fleet-wide phase size of twenty, which is two and a half phases of content in one, and the queue’s eleven items are the visible cost of that pace.

A round of ordinary size leaves three or four things undone; this one left eleven, and the difference is not that it was less careful but that it covered more ground and therefore had more edges. A larger slate produces a longer queue in proportion, and reading the queue’s length as a judgement about the work would be reading it backwards.

The generalisation #

The habit is about writing the list while the work is fresh.

A shortfall recorded at the end of a round is recorded by somebody who remembers why each thing was left, which is the part that makes an entry usable later. The same list assembled six months afterwards is a list of gaps with no reasons attached, and a gap with no reason is indistinguishable from a gap nobody thought worth filling.

The move is to write each entry where it was found — in the essay whose work stopped there — and to aggregate at the end. That is what this collection does and it is why the aggregation is a reading rather than a reconstruction.

The failure mode is to record the gaps and not the reasons. A shortfall entry is a note to a future round about what it would be walking into, and the reason something was left is more useful than the fact that it was.

A note on what the list deliberately excludes, since a queue that contained everything would be useless. It carries only items that are specific enough to be picked up: a named run with named inputs, a named measurement with a named obstacle, or a named absence with a named cost. General dissatisfactions — that the constructions are constructions, that the samples are analytic, that the observers are modelled — appear in each essay’s own limits and not here, because a queue of those would never shorten.

That distinction is the difference between a shortfall list and a disclaimer, and it is worth policing. A disclaimer protects the author and a shortfall list serves the next round, and the two look similar on the page.

Who found it, and when #

The practice of ending a round with its own shortfall list is this collection’s own and dates from the phase that first audited its declared inputs. Its clearest justification is the one four rounds have now demonstrated: the list is where the next round’s subject comes from.

The fleet this collection belongs to states the rule in its own instructions, on the grounds that a queue empty on a full slate means nobody wrote one. This round’s slate was fifty essays and its queue has eleven items, which is about the ratio the previous rounds have run at.

Where the ladder goes next #

The round has audited the index, the observer and the solver, and the list above says what it left. What is not on the list is the next object, and there is one obvious candidate: everything downstream of tristimulus values is nonlinear, none of this round’s structure applies to it, and it is where every remaining assumption in the collection lives.