Samples threaded sequentially (like Singer/Threads). Each bar = a copying segment; color = which previous sample it copies from. When a sample threads onto a target that already has a parent, the new node is inserted on the branch — building deep hierarchy.

s1 →0 1 segs, 0 recombs
s2 →0→1→0→1→0→1→0→1→0→1→0→1→0 13 segs, 12 recombs
s3 →0→1→0→1→2→1→0→2→1→2→1 11 segs, 10 recombs
s4 →2→0→3→2→0→3→0→3→1→0→2→0→2→3→1→3→1→3→1→3 20 segs, 19 recombs
s5 →4→0→4→0→4→0→2→0→1→0→4→1→0→1→3→1→3 17 segs, 16 recombs
s6 →4 1 segs, 0 recombs
s7 →0→3→0→3→1→3→1→3→1→3→1→3→2→3 14 segs, 13 recombs
s8 →0→3→0→3→1→3→2→7→2→7→0→7→3→7→1→7→5→2→1→7→1→7 22 segs, 21 recombs
s9 →8→3→8→3→7→3→1→3→1→3 10 segs, 9 recombs
s10 →8→7→8→7→8→1→7→2→3→8→3→8→7→8 14 segs, 13 recombs
s11 →9→7→10→8→10→8→0→8→10→8→0→10→8→6→0→2→0→2→6→2→0→7→2→0→10→8 26 segs, 25 recombs

Full Tree Sequences

Local Tree Comparisons

True (left) vs inferred (right). Trees built by sequential threading with branch insertion — each new sample splits an existing branch, producing proper multi-level coalescent structure.

pos 1006 bp — 50% match (depth 7)

TRUE

INFERRED

Samp	True→	Inf→
0	1	8	❌
1	0	0	✅
2	4	4	✅
3	7	0	❌
4	6	6	✅
5	4	4	✅
6	4	4	✅
7	8	0	❌
8	9	0	❌
9	8	8	✅
10	0	8	❌
11	0	9	❌

pos 4863 bp — 50% match (depth 4)

TRUE

INFERRED

Samp	True→	Inf→
0	1	8	❌
1	0	8	❌
2	4	10	❌
3	7	8	❌
4	6	6	✅
5	4	4	✅
6	4	4	✅
7	8	8	✅
8	9	9	✅
9	8	8	✅
10	0	8	❌
11	0	8	❌

pos 8720 bp — 42% match (depth 6)

TRUE

INFERRED

Samp	True→	Inf→
0	4	11	❌
1	3	7	❌
2	11	11	✅
3	7	9	❌
4	6	6	✅
5	0	4	❌
6	4	4	✅
7	8	9	❌
8	9	9	✅
9	8	3	❌
10	1	1	✅
11	2	0	❌

pos 12577 bp — 33% match (depth 3)

TRUE

INFERRED

Samp	True→	Inf→
0	4	11	❌
1	3	3	✅
2	1	11	❌
3	8	10	❌
4	6	6	✅
5	11	0	❌
6	4	4	✅
7	10	3	❌
8	9	2	❌
9	8	8	✅
10	7	3	❌
11	5	0	❌

pos 16434 bp — 50% match (depth 3)

TRUE

INFERRED

Samp	True→	Inf→
0	8	2	❌
1	3	3	✅
2	0	11	❌
3	9	1	❌
4	6	6	✅
5	0	0	✅
6	4	4	✅
7	10	10	✅
8	0	10	❌
9	3	3	✅
10	7	8	❌
11	0	2	❌

pos 20291 bp — 67% match (depth 2)

TRUE

INFERRED

Samp	True→	Inf→
0	8	2	❌
1	3	3	✅
2	0	0	✅
3	9	1	❌
4	6	6	✅
5	11	11	✅
6	4	4	✅
7	1	10	❌
8	10	10	✅
9	3	3	✅
10	8	8	✅
11	5	7	❌

pos 24148 bp — 83% match (depth 4)

TRUE

INFERRED

Samp	True→	Inf→
0	8	6	❌
1	9	9	✅
2	0	0	✅
3	5	1	❌
4	6	6	✅
5	3	3	✅
6	4	4	✅
7	1	1	✅
8	10	10	✅
9	1	1	✅
10	8	8	✅
11	0	0	✅

pos 28005 bp — 33% match (depth 3)

TRUE

INFERRED

Samp	True→	Inf→
0	3	2	❌
1	11	3	❌
2	7	0	❌
3	0	1	❌
4	6	6	✅
5	0	3	❌
6	4	4	✅
7	2	3	❌
8	10	10	✅
9	1	3	❌
10	8	8	✅
11	1	8	❌

Mainspring: Threading ARG Inference (with Branch Insertion)

Threading Diagram

Full Tree Sequences

TRUE — 49 trees, 67 nodes, depth ≤ 8

INFERRED — 39 trees, 113 nodes, depth ≤ 8

Local Tree Comparisons

pos 1006 bp — 50% match (depth 7)

pos 4863 bp — 50% match (depth 4)

pos 8720 bp — 42% match (depth 6)

pos 12577 bp — 33% match (depth 3)

pos 16434 bp — 50% match (depth 3)

pos 20291 bp — 67% match (depth 2)

pos 24148 bp — 83% match (depth 4)

pos 28005 bp — 33% match (depth 3)

Samp	True→	Inf→
0	1	8	❌
1	0	0	✅
2	4	4	✅
3	7	0	❌
4	6	6	✅
5	4	4	✅
6	4	4	✅
7	8	0	❌
8	9	0	❌
9	8	8	✅
10	0	8	❌
11	0	9	❌

Samp	True→	Inf→
0	1	8	❌
1	0	8	❌
2	4	10	❌
3	7	8	❌
4	6	6	✅
5	4	4	✅
6	4	4	✅
7	8	8	✅
8	9	9	✅
9	8	8	✅
10	0	8	❌
11	0	8	❌

Samp	True→	Inf→
0	4	11	❌
1	3	7	❌
2	11	11	✅
3	7	9	❌
4	6	6	✅
5	0	4	❌
6	4	4	✅
7	8	9	❌
8	9	9	✅
9	8	3	❌
10	1	1	✅
11	2	0	❌

Samp	True→	Inf→
0	4	11	❌
1	3	3	✅
2	1	11	❌
3	8	10	❌
4	6	6	✅
5	11	0	❌
6	4	4	✅
7	10	3	❌
8	9	2	❌
9	8	8	✅
10	7	3	❌
11	5	0	❌

Samp	True→	Inf→
0	8	2	❌
1	3	3	✅
2	0	11	❌
3	9	1	❌
4	6	6	✅
5	0	0	✅
6	4	4	✅
7	10	10	✅
8	0	10	❌
9	3	3	✅
10	7	8	❌
11	0	2	❌

Samp	True→	Inf→
0	8	2	❌
1	3	3	✅
2	0	0	✅
3	9	1	❌
4	6	6	✅
5	11	11	✅
6	4	4	✅
7	1	10	❌
8	10	10	✅
9	3	3	✅
10	8	8	✅
11	5	7	❌

Samp	True→	Inf→
0	8	6	❌
1	9	9	✅
2	0	0	✅
3	5	1	❌
4	6	6	✅
5	3	3	✅
6	4	4	✅
7	1	1	✅
8	10	10	✅
9	1	1	✅
10	8	8	✅
11	0	0	✅

Samp	True→	Inf→
0	3	2	❌
1	11	3	❌
2	7	0	❌
3	0	1	❌
4	6	6	✅
5	0	3	❌
6	4	4	✅
7	2	3	❌
8	10	10	✅
9	1	3	❌
10	8	8	✅
11	1	8	❌

Samp	True→	Inf→
0	1	8	❌
1	0	0	✅
2	4	4	✅
3	7	0	❌
4	6	6	✅
5	4	4	✅
6	4	4	✅
7	8	0	❌
8	9	0	❌
9	8	8	✅
10	0	8	❌
11	0	9	❌

Samp	True→	Inf→
0	1	8	❌
1	0	8	❌
2	4	10	❌
3	7	8	❌
4	6	6	✅
5	4	4	✅
6	4	4	✅
7	8	8	✅
8	9	9	✅
9	8	8	✅
10	0	8	❌
11	0	8	❌

Samp	True→	Inf→
0	4	11	❌
1	3	7	❌
2	11	11	✅
3	7	9	❌
4	6	6	✅
5	0	4	❌
6	4	4	✅
7	8	9	❌
8	9	9	✅
9	8	3	❌
10	1	1	✅
11	2	0	❌

Samp	True→	Inf→
0	4	11	❌
1	3	3	✅
2	1	11	❌
3	8	10	❌
4	6	6	✅
5	11	0	❌
6	4	4	✅
7	10	3	❌
8	9	2	❌
9	8	8	✅
10	7	3	❌
11	5	0	❌

Samp	True→	Inf→
0	8	2	❌
1	3	3	✅
2	0	11	❌
3	9	1	❌
4	6	6	✅
5	0	0	✅
6	4	4	✅
7	10	10	✅
8	0	10	❌
9	3	3	✅
10	7	8	❌
11	0	2	❌

Samp	True→	Inf→
0	8	2	❌
1	3	3	✅
2	0	0	✅
3	9	1	❌
4	6	6	✅
5	11	11	✅
6	4	4	✅
7	1	10	❌
8	10	10	✅
9	3	3	✅
10	8	8	✅
11	5	7	❌

Samp	True→	Inf→
0	8	6	❌
1	9	9	✅
2	0	0	✅
3	5	1	❌
4	6	6	✅
5	3	3	✅
6	4	4	✅
7	1	1	✅
8	10	10	✅
9	1	1	✅
10	8	8	✅
11	0	0	✅

Samp	True→	Inf→
0	3	2	❌
1	11	3	❌
2	7	0	❌
3	0	1	❌
4	6	6	✅
5	0	3	❌
6	4	4	✅
7	2	3	❌
8	10	10	✅
9	1	3	❌
10	8	8	✅
11	1	8	❌

Samp	True→	Inf→
0	1	8	❌
1	0	0	✅
2	4	4	✅
3	7	0	❌
4	6	6	✅
5	4	4	✅
6	4	4	✅
7	8	0	❌
8	9	0	❌
9	8	8	✅
10	0	8	❌
11	0	9	❌

Samp	True→	Inf→
0	1	8	❌
1	0	8	❌
2	4	10	❌
3	7	8	❌
4	6	6	✅
5	4	4	✅
6	4	4	✅
7	8	8	✅
8	9	9	✅
9	8	8	✅
10	0	8	❌
11	0	8	❌

Samp	True→	Inf→
0	4	11	❌
1	3	7	❌
2	11	11	✅
3	7	9	❌
4	6	6	✅
5	0	4	❌
6	4	4	✅
7	8	9	❌
8	9	9	✅
9	8	3	❌
10	1	1	✅
11	2	0	❌

Samp	True→	Inf→
0	4	11	❌
1	3	3	✅
2	1	11	❌
3	8	10	❌
4	6	6	✅
5	11	0	❌
6	4	4	✅
7	10	3	❌
8	9	2	❌
9	8	8	✅
10	7	3	❌
11	5	0	❌

Samp	True→	Inf→
0	8	2	❌
1	3	3	✅
2	0	11	❌
3	9	1	❌
4	6	6	✅
5	0	0	✅
6	4	4	✅
7	10	10	✅
8	0	10	❌
9	3	3	✅
10	7	8	❌
11	0	2	❌

Samp	True→	Inf→
0	8	2	❌
1	3	3	✅
2	0	0	✅
3	9	1	❌
4	6	6	✅
5	11	11	✅
6	4	4	✅
7	1	10	❌
8	10	10	✅
9	3	3	✅
10	8	8	✅
11	5	7	❌

Samp	True→	Inf→
0	8	6	❌
1	9	9	✅
2	0	0	✅
3	5	1	❌
4	6	6	✅
5	3	3	✅
6	4	4	✅
7	1	1	✅
8	10	10	✅
9	1	1	✅
10	8	8	✅
11	0	0	✅

Samp	True→	Inf→
0	3	2	❌
1	11	3	❌
2	7	0	❌
3	0	1	❌
4	6	6	✅
5	0	3	❌
6	4	4	✅
7	2	3	❌
8	10	10	✅
9	1	3	❌
10	8	8	✅
11	1	8	❌