Exploration memo
B004 Dissection, Cross-Basin Census, and Bundle Atlas
A finite-data exploration of which recorded Collatz features change together—and whether recurring bundle labels identify stable observational units.
The memo gathers three earlier passes into one note. Nothing here is a conclusion: it records what was observed about which feature flags move together, and keeps the open questions visible rather than closing them.
A stand-alone look at basin B004: its arrow rows, the exact co-change bundle attached to each row, and pairwise counts of how often two features changed together across the side observations.
The pass keeps B004's observed complexity intact instead of compressing it into a representative arrow.
A comparison of B001 / B002 / B003 / B004 done only through feature co-change: which flags move together inside the same distinct arrow row. Counts are distinct arrow-row counts, not observation weights.
The census assigns no cause. It records which flags co-change and nothing further.
A check of whether the co-change bundles that showed up are stable units or internally diverse, by measuring each exact bundle against its own delta patterns and source faces.
The unresolved point: whether any bundle can stand alone without keeping the arrow/state evidence beside it.
Census size, counted as distinct arrow rows per basin.
B001 and B004 are the primary basins. B002 and B003 were added as a small comparison check in the same format. B003 is small enough to act as a witness rather than a broad sample, and its two rows are read as a witness, not as a basis for generalisation.
Frequency and stability are reported separately. A bundle that appears in many rows is treated as frequent; it is not thereby treated as a settled unit.
Appears in 22 of 22 arrow rows across all four basins — yet it spreads across 20 distinct delta patterns. Observed everywhere, internally diverse.
Appears in 18 of 22 arrow rows across all four basins, with 17 distinct delta patterns. A repeated co-change shape whose internal variation is not small.
B001 and B004 share exactly one exact bundle string: all_features (every flag flips). The label is common to both basins.
But the source faces and the delta detail behind that label are not identical. See Shared Label, Different Rows.
Each of the frequent bundles carries many delta patterns, so the labels are coarse where it matters. Bundle strings are useful search handles; on this pass they do not stand as independent, stable observational units.
Everything labelled here as frequent is treated as frequent, not as a settled unit.
B004 on its own has 12 pair rows and 24 side observations. Every observed −4 → −3 arrow lands at the same target, S014, so target concentration is total — while the source material stays spread across seven source states.
The miss side uses six of these source states; the control side uses one (S018). Variation remains on the source side.
All observed arrows arrive here. Target concentration is total; source variation is not reduced.
| Feature | Changes in | Where |
|---|---|---|
| band | 24 / 24 | all side observations |
| remaining_K_before | 24 / 24 | all side observations |
| remaining_K_after | 24 / 24 | all side observations |
| transition_k | 12 / 24 | miss side only |
| exit_distance | 12 / 24 | miss side only |
| front | 12 / 24 | miss side only |
| residue16 | 12 / 24 | miss side only |
| residue32 | 12 / 24 | miss side only |
| chain_status | 6 / 24 | avoid → avoid_then_caught miss arrows |
← 横にスクロールできます / scroll horizontally
The miss side and the control side therefore carry different co-change patterns.
{3: 12, 8: 6, 9: 6} — the arrows mostly move as bundles rather than as isolated single-feature edits.
The largest single arrow is S018 → S014 on the control side, at 12 of 24 side observations. That size is a temptation to nominate one representative arrow, but the miss side still keeps six separate source states, so a single representative would discard observed variation. No reduction to one arrow was made.
Not much rises to “stable candidate” on this pass. The most defensible stable-looking statements are narrow and local.
band / remaining_K_before / remaining_K_after co-change in every observed side observation. That is stable inside B004, but broad rather than discriminating: the source states still separate on R values, k, exit distance, front, chain status, and residues.all_features is a coarse label: 12 rows, 12 delta patterns, 11 source faces. all_except_chain_status (Bundle A) sits at 6 rows with 5 delta patterns and is marked internally diverse.front, residue16 and residue32 never move alone, and band moving in every arrow is too broad to describe the arrows by itself. Why the changes come bundled is left open.chain_status, which moves in only part of the miss set and separates otherwise similar arrows.Input artifacts by analysis stage. Links are relative and resolve when the files sit in the same directory as this page.
all_features bundle
This page reports descriptive observations from a finite dataset. It does not claim a general mechanism or proof concerning the Collatz map.
All statements above are observations about the recorded arrow rows, feature flags, and co-change bundles in the attached files. Frequent bundles are reported as frequent, not as settled or stable units. The two B003 rows are treated as a witness and are not generalised. Bundle labels are kept together with the arrow/state rows they came from, and the open questions are left open.