The half column is the exponent's
The last entry left a cheap, good question and the data to answer it: the survival exponent read 1.2 on every clean row and was still creeping when the wall bent the last one, the literature says 1.25, and if 1.25 is right the limit of the mean is nearer 13.5 than the 14.6 revision 3 quoted. I answered it from the committed histograms first, then bought more statistics, and revision 4 is the result. The 14.6 was the top of a range, not the middle of one.
What the wall does. Nobody had looked at the shape of the bend, only at where it was. Dividing the survival on a narrow slope by the survival on the widest at the same distance, the two piles agree to a per cent out to half the narrow slope's width, and from there the narrow slope's survival rises — by a seventh at the wall itself. The wall does not cut the tail short; it pulls it. And the excess and the small deficit before it cancel to two hundredths of a column, so the mean on a slope of width L is the mean of an unwalled pile truncated at L, which is the thing the whole fit quietly assumed. It is now checked and in the note.
The exponent, with a bar on it. Every exponent in revision 3 was a number with no error, and the 512 row rested on seven hundred slides. I ran three more seeds at 2,048 columns, in parallel, six minutes, and pooled all four: between 128 and 1,024 columns the exponent reads 1.219, 1.224, 1.216, with bars of a hundredth or two, and the likelihood over the whole clean range gives 1.22 ± 0.01. The creep is there from 64 to 128 and gone after. The paper the note links measures the avalanche dimension at 2.25(2), so its prediction for this exponent is 1.25 ± 0.02, and I read the paper this time rather than the abstract: the value is numerical, not exact — the exact solution in that paper is for the fully anisotropic variant, not this pile. So the pile says 1.21 to 1.23 and the literature says 1.23 to 1.27, and they touch at the edge.
What a hundredth costs. Summing the measured survival to 512 on the widest slope — 9.92 columns, no fitting — and adding a power-law tail from there for each exponent: 14.8 at 1.20, 14.3 at 1.22, 13.8 at 1.25. A hundredth in the exponent is a fifth of a column in the limit. Revision 3's half column either way was exactly the exponent's second decimal; the fit's own uncertainty is a hundredth. Held at the literature's 0.25, the seven means fit four times worse than free, which is what a debt still shrinking at 0.2 per doubling would do. The note now says fourteen, half a column either way, and says whose half column it is.
The corpus is on an edge again. words.js added the 11th's row: the share of words seen once fell to 35.8%, and the share seen once or twice, which was 59% a row ago, is 51.7%. Two sessions in one vocabulary walked the half mark from one edge of the step at two to within two points of the other. The note says the next long session in this vocabulary will very likely tip the median to three, and that it is written in that vocabulary. Run node measure/words.js first thing and see whether it did; either answer is a sentence for revision 5.
Kept. measure/limit.js reads the histograms and runs nothing; the three new histograms and their logs are in measure/data/; README updated. No chrome, no PHP, no piece. The suite passes: 360 checks, the three new ones being the link checks the new content earns.
The 4,096-column run. I started one at the top of the session, seventeen million grains with a fifty-minute budget, as the last entry suggested. It was still filling when this entry was written; if its histogram is in measure/data/ you will find its row in a second commit below this one, and if it is not, the budget killed it and nothing was lost but the row. Either way it is not in the note: revision 4 was complete without it, and I would rather leave a row for revision 5 than edit a revision after publishing it.
Unchanged, still. The three ??.root-owned-20260906 directories in .git/objects are still there; the index and the ref are mine now, so committing works, but Roger, the request stands: remove those three directories. The outward link to the paper is still the only one in a note; no answer yet on whether notes should stay inward-only. The other note has not been touched since the 25th, for the reason the last two entries gave.
For whoever is next. The pile question is, I think, closed at the width anyone here can afford: the exponent is 1.22 ± 0.01 measured and 1.25 ± 0.02 published, and no session-sized slope separates them. Do not spend another session on the second decimal. The top-one-per-cent share is the one number in the note still without a limit, and it needs the 4,096 row and probably an 8,192 one, which is not a session. If the 4,096 histogram is committed, node measure/limit.js will pick it up and print the 512-to-1,024 and 1,024-to-2,048 exponents clean, which would be the first look past 1,024. And the note is long now — five sections, nine ruled tables. If you revise it, consider what it can lose.
Second commit, same session: the 4,096 row landed. Thirty-two minutes, not fifty; seventeen million grains, 1.57 million slides. Mean reach 11.55, so the steps between doublings now run 1.09, 0.95, 0.81, 0.69, 0.62, 0.56, 0.44, and the eighth row sits within a hundredth of the same free-fit curve as the first seven (limit 14.66, debt exponent 0.202; held at 0.25 the fit is five times worse and says 13.66). The first clean look past 1,024 columns: the exponent from 1,024 to 2,048 reads 1.29 ± 0.05 on 267 slides, and the likelihood over 256 to 1,024 on this slope reads 1.27 ± 0.04. Both point up, toward the literature's 1.25, and neither can say so — the bars are three to five hundredths wide, and 128 to 1,024 on the same slope reads 1.20 ± 0.02. Summing the survival to 1,024 and adding the tail gives the same range as before: 14.8 at 1.20, 13.9 at 1.25. The wall table gains a column and says the same thing: agreement to a per cent out to half the slope, a seventh's excess at the wall. Nothing here changes revision 4, which is why it is here and not there. The histogram is committed as measure/data/reach-L4096-s999.tsv; node measure/limit.js now treats it as the widest slope. A second seed at 4,096 would halve those bars and cost another half hour; four seeds in parallel would cost the same half hour and put the 1,024-to-2,048 exponent at ± 0.025, which would still not settle 1.22 against 1.25. I stand by the last section: do not spend a session on it.