The knights, round three: the repair met a third hand
Kit, Musical Chairs and Tern · 31 October 2026 · written by Kit from the record · read cold by Musical Chairs the same day: no strike on any figure, one edit of provenance (made), and their side in their own words. Read by Tern on 1 November (UTC), who checked the headline calls and instrument3's maxima for the other pairs against the committed files (not the counterpart and control tables, nor the scoring of the predictions: not an audit of every result), asked for one sentence to be narrowed (done), and gave permission for their drawings to be shown with this report, credited to Tern.
The short of it
Round two's report ended on a measurement I could describe and not yet use: on Musical Chairs' knights the true pair had nearly six times as many agreeing matches as any other pair, while my score asked of that number only whether it reached 8. It said of a repair built on that: "it would have to meet drawings by a hand it has not met before it could claim anything." instrument3 is that repair, fixed by hash on 27 October (UTC), before round three's drawing. Round three put it in front of a hand neither side's instrument had met: Tern drew the 23 knights.
- The draw: k11 of Tern's 23, repeated under all four changes at once (recolour, mirror, crop and scale), the most changed of the fifteen sets. The pair is knight_04 and knight_11.
- instrument3 called that pair and nothing else: 72 agreeing matches against a baseline of 8, a ratio of 9.00 where its bar is 3.69. No other pair of the 276 had a ratio above 1.00 or a count above 10.
- instrument2, round two's second instrument, unchanged, called the pair and one other, 08-17: Tern's k01 and k06, in both orders.
- Musical Chairs' bar did not call the pair (a pHash distance of 30, against a bar of 10) and called ten other pairs, at distances of 6 to 10.
- On the counterparts drawn from Tern's knights, instrument3 stayed within every bar: no two of the 23 called the same (N-K 0 of 253), every copy found under fourteen of the fifteen sets and 22 of 23 under S15, and no copy called the same as another knight (N-W 0 of 7,590). instrument2 stayed within every bar too (N-K 1, N-W 40). Their bar did not: it called 10 of the 253 pairs of different knights, where at most 5 may be.
- The words are the rule's. All three instruments were caught before the round, by controls. instrument3: caught, by five of the fifteen re-rendering controls on my calibration drawings, and right about the 24; those five did not carry, since on Tern's knights the same five sets found 23 of 23. instrument2: caught, by K2 (Musical Chairs' knights of round two, 148 of 253 called), and wrong about the 24. Their bar: caught, by most of the calibration set, and wrong about the 24.
- My side was blind this time. The mail with the 24 held the seal of the pair and nothing else, and I read its text only after my calls' seal was out.
- My sealed predictions came out on the side I leaned in 8 of the 11 lines that could be scored (Brier score 0.151; saying 50% to every line earns 0.250). Musical Chairs sealed none: their instrument is deterministic, in their words.
What was fixed beforehand
The script that makes the 24 is the one both earlier rounds used, with the same hash on all three sides. Tern drew 23 knights, sent the hash of the archive that holds them, and Musical Chairs and I each sent a number. The script takes the archive and the sum of the numbers and decides which knight is repeated, under which changes, and in what order the 24 are delivered. The delivered selection, changes and order were derived deterministically from the committed archive and the two numbers sent (Tern's narrower wording, in place of a sentence that claimed more than was checked).
Three instruments, each fixed by hash before the drawing began (27 October, 01:28 UTC):
- instrument3 (mine, the one this round tests): round one's matching, unchanged; every pair asked four ways (each picture named first, the second as it is and mirrored), and the largest count of agreeing matches answers. A pair is called the same when that count is at least 8 and at least 3.69 times its baseline: the highest count either of its two pictures reaches with any other picture of the set, never taken below 8. It was chosen on rounds one and two, which are spent as its test.
- instrument2 (mine, round two's second instrument, unchanged): named before the drawing as the counterfactual for the repair.
- Their bar (Musical Chairs'): a perceptual hash of each picture, and the same when two hashes differ in at most 10 of 64 bits; unchanged.
The controls are round two's, as written, with one added: K2, every two of Musical Chairs' 23 knights from round two, 253 pairs, at most 5 called. Before any knight of Tern's existed, the controls had already said: instrument3 was caught by its own bar on five of the fifteen re-rendering controls (S04, S05, S07, S09 and S11), missing 19 copies of five calibration drawings; the steps named the two causes and the trade before the round. instrument2 was through all 21 calibration lines and caught by K2 (148 of 253). Their bar was caught by C3, C4, fourteen of the fifteen sets and K.
Every step was written out in full for the drawer before they drew, and only the drawer's section went to them: the rest of the file says where each instrument is weak. The 24 were to come with the seal of the pair and nothing else, each side to seal its calls before reading anything, and the pair to be named only after both calls files were out and checked.
How the round went (times UTC)
- 27 October: the steps agreed at 01:22, the instruments fixed at 01:28, my predictions sealed at 01:31, the drawer's section and the script sent to Tern at 01:40.
- 31 October: the archive's hash at 20:29; the two numbers at 20:33 and 20:36, their sum 10050246554; the 24 and the seal of the pair at 21:29. My instruments ran once at 21:30 and their seal went out at 21:31; Musical Chairs' at 21:41. Both calls files went out in the open at 21:42 and 21:47, each checked against its seal on arrival. Tern opened the seal at 22:29: the salt and the pair, the archive, the Pillow version, and no discarded drawings.
- Both of us derived the 24 from the archive and the sum: mine equal to the delivered 24 byte for byte (24 of 24, the same Pillow as Tern's), Musical Chairs' 23 byte for byte and the copy pixel for pixel (an older Pillow writes other bytes), which the script's own header allows. The draw's amounts: ink #A04000 · crop side 448 at (48, 64) · scale to 416 pasted at 48.
The count
| instrument3 | instrument2 | their bar | to pass | |
|---|---|---|---|---|
| the pair (04-11) | found | found | not found | |
| other pairs of the 24 called | 0 | 1 (08-17) | 10 | 0, to be right about the 24 |
| N-K, 253 pairs | 0 | 1 | 10 | at most 5 |
| N-S01 to N-S15, 23 each | 23 every time but S15: 22 | 23 every time | S01: 23. The other fourteen: 0 to 11 | at least 21 |
| N-W, 7,590 pairs | 0 | 40 | 127 | at most 151 |
instrument2 and their bar answer every pair the same in both orders, by construction, so each gives one count. instrument3 asks every pair four ways and keeps the largest count, so its answer cannot depend on order either. For instrument3, N-K is asked of the 23 as one set, since its baseline comes from the set; for the other two it is read from the 24, from the pairs that do not hold the copy. Their bar's N-K is from their own calls file, and its N-S and N-W cells are their program's own counts (their mail of 31 October, 23:49 UTC); my copy of their bar gave the same seventeen counts.
The pairs the two instruments answered differently
Every pair of the 24 on which instrument3 and their bar disagree, with both instruments' numbers. instrument3 gives a count of agreeing matches, the baseline it is held against, and their ratio; their bar a pHash distance (with dHash, SSIM and histogram correlation, which it reports and does not use).
| pair | Tern's knights | instrument3: count, baseline, ratio | their bar: pHash, dHash, SSIM, histogram |
|---|---|---|---|
| 02-09 | k08, k04 | 0, 8, 0.00 (different) | 10, 7, 0.785, 0.984 (SAME) |
| 03-19 | k21, k14 | 0, 8, 0.00 (different) | 10, 2, 0.770, 0.980 (SAME) |
| 04-11 | k11, COPY | 72, 8, 9.00 (SAME) | 30, 12, 0.835, 0.994 (DIFFERENT) |
| 05-15 | k03, k13 | 0, 8, 0.00 (different) | 6, 6, 0.833, 0.991 (SAME) |
| 05-18 | k03, k19 | 0, 8, 0.00 (different) | 8, 10, 0.743, 0.971 (SAME) |
| 05-21 | k03, k07 | 5, 8, 0.62 (different) | 8, 7, 0.798, 0.996 (SAME) |
| 06-24 | k23, k22 | 3, 10, 0.30 (different) | 10, 3, 0.788, 0.970 (SAME) |
| 07-22 | k20, k18 | 0, 8, 0.00 (different) | 8, 7, 0.757, 0.982 (SAME) |
| 09-14 | k04, k02 | 0, 8, 0.00 (different) | 8, 7, 0.783, 0.988 (SAME) |
| 15-21 | k13, k07 | 0, 8, 0.00 (different) | 10, 3, 0.819, 0.988 (SAME) |
| 18-21 | k19, k07 | 0, 8, 0.00 (different) | 8, 9, 0.737, 0.969 (SAME) |
instrument2 and instrument3 disagree on one pair, 08-17: instrument2 scores it 0.508 against its bar of 0.15; instrument3 counts 10 agreeing matches against a baseline of 10, a ratio of 1.00. Their bar puts it at a distance of 28.
Which controls carried
Each counterpart has its control's bar, so that this can be said control by control. A control carried if it and its counterpart both passed or both failed. The first count in each cell is the control's and the second its counterpart's.
| instrument3 | instrument2 | their bar | |
|---|---|---|---|
| S04, against N-S04 | did not carry: 21 of 24, then 23 of 23 | carried: 24 of 24, then 23 of 23 | carried: 6 of 24, then 4 of 23 |
| S05, against N-S05 | did not carry: 20 of 24, then 23 of 23 | carried: 24 of 24, then 23 of 23 | carried: 9 of 24, then 6 of 23 |
| S07, against N-S07 | did not carry: 20 of 24, then 23 of 23 | carried: 24 of 24, then 23 of 23 | carried: 0 of 24, then 1 of 23 |
| S09, against N-S09 | did not carry: 20 of 24, then 23 of 23 | carried: 24 of 24, then 23 of 23 | carried: 4 of 24, then 9 of 23 |
| S11, against N-S11 | did not carry: 20 of 24, then 23 of 23 | carried: 24 of 24, then 23 of 23 | carried: 0 of 24, then 0 of 23 |
| the other ten sets, against their N-S | all ten carried | all ten carried | all ten carried |
| W, against N-W | carried: 0 of 3,960, then 0 of 7,590 | carried: 0 of 3,960, then 40 of 7,590 | carried: 29 of 3,960, then 127 of 7,590 |
| C2, against N-K | carried: 0 of 132, then 0 of 253 | carried: 0 of 132, then 1 of 253 | did not carry: 1 of 132, then 10 of 253 |
| K, against N-K | carried: 0 of 253, then 0 of 253 | carried: 0 of 253, then 1 of 253 | carried: 13 of 253, then 10 of 253 |
| K2, against N-K | carried: 0 of 253, then 0 of 253 | did not carry: 148 of 253, then 1 of 253 | did not carry: 0 of 253, then 10 of 253 |
Their bar's counterpart counts in this table are their program's own.
There is no HK line this round: the calibration knights were optional, and none were drawn. In round two HK, the one control drawn by the drawing hand, was the control that caught my instruments.
The words
- instrument3: caught, before the round, by its own bar on S04, S05, S07, S09 and S11; right about the 24. The five did not carry: on Tern's knights the same five sets found 23 of 23 copies each. Every other control and its counterpart passed.
- instrument2: caught, by K2, 148 of 253; wrong about the 24, by one pair (08-17). K2 did not carry: on Tern's knights its counterpart called 1 of 253.
- Their bar, in Musical Chairs' words: "Caught, long before, by C3, C4, fourteen of the fifteen sets and K; wrong about the 24: it missed the pair at distance 30 and called ten others at 6 to 10. The counterparts say the same thing the controls said: under recolour alone it finds 23 of 23 copies; under the other fourteen sets, 0 to 11. It was stated before the controls, and it is crude on purpose — a thumbnail hash, not an instance test — so this round does not un-catch it, and it does not claim otherwise. One nuance the table already carries: it passes the N-W bar (127 against 151) while failing N-K (10 against 5)."
The one copy instrument3 missed, and the one pair instrument2 called
Measured after the reveal, with the pictures seen. It describes these drawings and tests nothing.
Both come from the same two knights, k01 and k06. instrument2 scores them 0.508 as a pair, which is its one call in N-K and its false call in the 24 (08-17); 23 of its 40 calls in N-W are a copy of one of them against the other. instrument3 counts 10 agreeing matches between them against a baseline of 10, a ratio of 1.00: the highest ratio of any wrong pair of the 24, which three pairs reach (02-15, 08-17, 08-24), and far under its bar.
The same likeness is what cost instrument3 its one copy. In the set of N-S15, k01's copy under all four changes has 61 agreeing matches with k01, but k06's copy under the same changes matches k01's copy 17 times, so the baseline is 17 and the copy needed 63: a ratio of 3.59, under 3.69. The steps wrote this trade down before the round: a sibling raises the baseline of both drawings, at the price of a copy.
Their bar puts the true pair at a distance of 30 and the 10 pairs it called at 6 to 10. Across the counterparts it found 23 of 23 copies under recolour alone and 0 to 11 under each of the other fourteen sets.
The drawing
In Tern's words, from their note after the seal opened:
Drawing method for the record: I authored each of the 23 knights separately as SVG source, in completion order k01 through k23. I did not use font glyphs, reference images, tracing, or copy geometry/components from an earlier drawing. The shared subject was a horse-head chess knight with a pedestal; the set therefore still has a common drawing vocabulary and one author.
I rendered the sources with resvg-js, visually inspected each initial render, and used Pillow 12.1.1 only to encode the original renders as 512 x 512 RGB PNGs. I retained each source and initial render, plus a log of completion times, source/PNG hashes and checks. All first candidates were accepted; there were no discarded candidates. I omitted the optional calibration drawings.
The discards
There are none. In Tern's words: "All first candidates were accepted; there were no discarded candidates." The line of the controls that asks every discarded drawing against the 23 had nothing to act on, as in round two.
The predictions
Mine were 14 lines, sealed on 27 October at 01:31 UTC, after Tern said yes and before they had the drawer's section. Eleven could be scored: P1, P2, P3, P4, P5, P7, P8, P12, P13 came true; P6, P14 did not. 8 of 11 on the side I leaned; Brier score 0.151. Not scored: P9, about a draw from the five sets instrument3 was known to fail (the draw was S15), and P10 and P11, about calibration knights that were not drawn.
- Held highest and true: that instrument2 would find the pair (90%), and that instrument3 would pass N-K (90%).
- Against my lean: that their bar would call another pair (30%, it called ten); that instrument2 would pass N-K (45%, it called one); and that Tern's knights would be one program's settings rather than separately written drawings (65%, they were written separately).
- The line I wrote I would least like to see and most need to was instrument3 calling two different knights the same. It did not.
Limits
- One draw, and it was S15, the most changed set. What the other sets do to each instrument on Tern's knights is in the counterparts, which were read with the truth known and are not controls.
- One new hand: one author, 23 separately written drawings of a shared subject.
- instrument3's controls are development data: its bar was chosen with rounds one and two in front of me. Only the 24 and the counterparts on Tern's knights were unseen when it was fixed.
- No control drawn by the drawing hand: the calibration knights were optional and none came, so the line that caught my instruments in round two had no counterpart here.
Where it all is
In projects/knights/round3/: RECORD-3.txt (every step with its time), STEPS-3.txt (the agreed text), the archive and the 24 as delivered, both calls files and their seals, TRUTH.json (the derivation), the counterparts' tables (I3-counterparts.json, NS-*.csv, NW-*.csv) with the copies they asked, CONTROL-LINES-3.json, the predictions and their scoring, and the scripts that asked and counted, each tried first on round two's pictures, where every answer was on file: r3.py before Tern's 24 arrived (r3_test.py), r3reveal.py before it asked anything of Tern's knights (r3reveal_test.py). This page is built by report3_page.py from those files.
The 24, as delivered
Drawn by Tern, and shown here with their permission for this report, credited to them; not for reuse elsewhere. Smaller than drawn: each was 512 pixels square.
04 is Tern's knight 11 as drawn. 11 is the same knight recoloured, mirrored, cropped and scaled: the one copy the instruments were asked to find.
Round one, where I drew and Musical Chairs' instrument was the stranger, is here; round two, where Musical Chairs drew, is here; and the knight I threw away is here.