§9.8.2

Triangles and Matrix Tables

A triangular grid—how are the empty positions filled?

✅ NormativeSettled. The requirement holds as written.📄 Page ruleCan be applied from the page alone.Read §9.8.2 in the RFC ↗

The requirement

Every row MUST carry the full column count. The jagged half MUST be padded with individual empty cells — one <td></td> per missing position. A colspan or rowspan over the empty region MUST NOT be used, and a 0 or any other value MUST NOT be invented.

When it applies

Loss development exhibits and similar matrices are jagged on purpose. The missing half is meaningfully empty — that development period has not happened yet — not data that failed to be read.

Sketch of the printed page — layout, not output

Accident yr | 12mo | 24mo | 36mo |
| 2021      | 450  | 512  | 530  |
| 2022      | 470  | 528  |      |  ← structurally empty,
| 2023      | 465  |      |      |    not "failed to read"

Reading the examples. Each one pairs a source page with the output the rule expects. ✅ Sample: the rule applies. ❌ Counter-sample: it looks like it applies and does not, or a rendering got it wrong. A non-conforming output, in red, is shown only for contrast. … marks content left out of an excerpt.

Requirements

The shape MUST be kept. Every row has the full column count; the cells past the end of the row are present and empty. Rows MUST NOT be truncated.
One empty cell per missing position. Four unhappened periods are four <td></td>, not one colspan="4". The span would say "this region is one thing", and it is not — it is four distinct coordinates that each have not happened yet.
The empty half MUST NOT be padded with values. Filling it with 0, n/a or a repeat of the last figure destroys the only thing the triangle asserts.
A printed value MUST NOT be read as structural emptiness either. Some pages print 0 across the future half. A zero is a claim and a blank is an absence; the output MUST render whichever the page prints.
A cell that is empty because it cannot be read is a different situation — see Cell Text Fidelity (§9.6.3).

✅ SampleThe rule applies

Stacked loss-development exhibits where the empty lower-right is meaningfully empty`ppy`

those development periods have not happened. Every row of the first triangle carries all eleven cells. The column headers are underlined, not bold.

Source page

Expected output · table 1 of 3

All Companies Reporting to the Loss Data Bureau ¹
Accident Year Ended	15	27	39	51	63	75	87	99	111	123
12/31/2003	418,550,936	418,042,452	417,267,765	417,492,929	417,216,932	417,189,136	417,146,522	417,095,498	417,140,320	417,120,054
12/31/2004	431,833,889	427,373,100	425,430,426	425,032,454	424,899,046	424,930,538	424,893,684	424,824,851	424,784,418	424,738,538
12/31/2005	471,370,885	466,106,849	464,434,610	463,396,915	463,268,706	463,175,541	463,165,720	463,139,866	463,075,855	463,014,244
12/31/2006	463,200,919	457,725,282	455,822,189	454,841,890	455,017,266	455,000,340	454,915,676	454,822,382	454,797,996
12/31/2007	515,029,169	510,374,742	508,154,461	507,592,525	507,251,378	507,252,665	507,124,706	507,069,577
12/31/2008	547,084,231	543,696,826	542,151,638	541,255,839	540,913,464	540,904,143	540,713,622
12/31/2009	459,114,867	455,232,703	454,478,144	454,047,620	454,108,281	453,794,733
12/31/2010	511,853,602	507,399,547	506,256,705	506,014,933	506,071,619
12/31/2011	571,554,254	566,987,304	565,194,620	564,927,450
12/31/2012	603,862,305	602,282,512	600,316,599
12/31/2013	591,546,839	588,047,899
12/31/2014	656,279,959

❌ Counter-sampleLooks like it applies and does not — or a rendering got it wrong

The same shape, filled differently`waiox`

the un-earned future half is printed with explicit 0s rather than left blank. A zero is a claim; a blank is an absence — here every 0 is kept.

Source page

Expected output · table 1 of 2, excerpt

Medical
Incurred Month
Paid Month	202401	202402	202403	202404	202405	202406	202407	202408	202409	202410	202411	202412
202401	41,539	0	0	0	0	0	0	0	0	0	0	0
202402	191,691	29,902	0	0	0	0	0	0	0	0	0	0
202403	90,233	324,478	55,730	0	0	0	0	0	0	0	0	0
202404	11,157	20,717	326,646	70,804	0	0	0	0	0	0	0	0
202405	5,533	8,224	429,936	308,025	125,102	0	0	0	0	0	0	0
202406	283	-45,171	36,806	13,870	241,742	52,107	0	0	0	0	0	0
…

Why a span is wrong here, when it is free elsewhere

Blank and Spacer Rows (§9.5.1) leaves the encoding of an unruled empty region free: leading empty cells and one blank spanning block render identically, and neither is preferred.

A triangle is the carve-out. Every empty cell sits at a real coordinate — an accident year crossed with a development period — and "12 months has not elapsed for the 2023 year" is a separate fact from the same statement about 24 months. Collapsed into one span, those coordinates stop being addressable: a consumer can no longer ask what the 2023 row holds at 24 months, because the cell it would look in no longer exists.

Elsewhere the empty region is one undifferentiated blank. Here it is a set of individually meaningful absences that happen to be adjacent.

This is the same principle that settles blank space beside a header in Barely-Existing Columns and Headers (§9.3.1): a span is a claim that the page merged something. The page did not merge these.

Why the blank matters more here than elsewhere

In most tables, blank versus an explicit empty marker is cosmetic. In a loss triangle the blank carries actuarial meaning: it asserts this development period does not exist yet, which is a fact about the world, not a gap in the transcription. That is the same argument that makes the em-dash a value in Marks and Symbols in Cells (§9.6.6) and the coloured fill a value in Color as the Value (§9.6.4) — a non-value that is a value.

Rule id tables-triangles-and-matrix-tables · tables encoding empty-cells

When it applies

Requirements

Why a span is wrong here, when it is free elsewhere

Why the blank matters more here than elsewhere

Neighbouring rules, and how they differ

More