Co-Change Bundle Exploration: B004, Cross-Basin Census, Bundle Atlas

Purpose

This is an exploration memo. It gathers three earlier passes into one readable note: first a stand-alone look at basin B004, then a cross-basin comparison of B001 / B004 / B002 / B003 done only through feature co-change, and finally a check of whether the co-change bundles that showed up are stable units or internally diverse.

Nothing here is a conclusion. The memo records what was observed about which feature flags move together, and keeps the open questions visible rather than closing them. All statements are descriptive observations from the finite dataset used here. They are not claims about a general mechanism of the Collatz map.

Input Artifacts

Analysis stage	File	Role
B004 dissection	b004_change_bundles.csv	B004 arrow rows and their exact co-change bundles
B004 dissection	b004_feature_interaction_matrix.csv	Pairwise feature co-change counts inside B004
B004 dissection	b004_exploration_README.md	Notes for the B004-only pass
Cross-basin census	cross_basin_feature_change_flags.csv	Feature-change flags for distinct arrow rows across B001 / B004 / B002 / B003
Cross-basin census	cross_basin_bundle_frequency.csv	Frequencies of exact co-change bundle strings across the four basins
Cross-basin census	cross_basin_bundle_census_README.md	Notes for the cross-basin comparison
Bundle Atlas	bundle_variation_table.csv	Bundle-level row counts and internal-variation summaries
Bundle Atlas	all_features_deep_check.csv	Row-level check of the shared all_features bundle
Bundle Atlas	bundle_cards.md	Readable cards for the observed bundle types
Bundle Atlas	bundle_atlas_README.md	Notes for the bundle internal-variation pass

1. B004-Only Observations

B004 on its own has 12 pair rows and 24 side observations. Every observed −4 to −3 arrow lands at the same target, S014, so target concentration is total while the source material stays spread across seven source states (S018, S019, S021, S023, S025, S028, S029). The miss side uses six of those source states; the control side uses one (S018).

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.

Within the 24 side observations, the co-change pattern is layered:

• band, remaining_K_before, remaining_K_after change in all 24 observations.
• transition_k, exit_distance, front, residue16, residue32 change in the 12 miss observations but not in the control ones.
• chain_status changes in only 6 observations (the avoid to avoid_then_caught miss arrows).

Observation-weighted bundle sizes are {3: 12, 8: 6, 9: 6}. The arrows mostly move as bundles rather than as isolated single-feature edits.

2. Cross-Basin Co-Change Census

The census inventories co-change only: which flags move together inside the same distinct arrow row. Counts are distinct arrow-row counts, not observation weights. Row counts are B001 = 7, B002 = 6, B003 = 2, B004 = 7. B002 and B003 were added as a small comparison check; B003 is small enough to act as a witness rather than a broad sample.

What appeared across the four basins:

• No arrow row changed a single feature alone. Single-feature-only rows: 0.
• B001 and B004 share exactly one exact bundle string: all_features (every flag flips).
• The R-core bundle (band / remaining_K_before / remaining_K_after) appears in 22 arrow rows across all 4 basins.
• The upper bundle (transition_k / exit_distance / front / residue16 / residue32) appears in 18 arrow rows across all 4 basins.
• Smaller shapes also appear: all_except_chain_status in 6 rows across B002 / B003 / B004; a compact band+R_before+R_after+transition_k+residue16+residue32 control shape in B002 / B003; a sparse R-only control row in B004; and a sparse all_except_exit_distance row in B001.

The B001/B004 contrast reads as a difference in bundle composition rather than in kind: both carry the full-feature bundle, while B004 also has a compact R-shift-only control row and B001 has a near-compact row that still moves transition_k and the residues. The census assigns no cause; it only records which flags co-change.

3. Bundle Atlas / Internal Variation

The atlas checks each exact co-change bundle against its own delta patterns and source faces, using unique_delta_pattern_count and unique_source_face_count.

• R-core: 22 rows, but 20 distinct delta patterns.
• Upper shape: 18 rows, but 17 distinct delta patterns.
• all_features exact bundle (Bundle C): 12 rows, 12 distinct delta patterns, 11 distinct source faces.
• all_except_chain_status (Bundle A): 6 rows, 5 delta patterns, marked internally diverse.
• The sparse bundles (single R-only row; the two-row compact control shape) sit at 1–2 rows and behave as sparse rather than as repeated units.

4. What Looks Like a Stable Candidate

Honestly, not much rises to "stable candidate" on this pass. The most defensible stable-looking statements are narrow and local:

• Within B004, band / remaining_K_before / remaining_K_after co-change in every observed side observation. That is stable inside B004, but it is broad rather than discriminating: the source states still separate on R values, k, exit distance, front, chain status, and residues.
• The fact that no arrow row moves a single feature alone is stable across all four basins as an observation. It says the edits are coupled; it does not say why.

Everything labelled here as frequent is treated as frequent, not as a settled unit.

5. What Looks Internally Diverse

• The R-core bundle is frequent, not stable. It appears in 22 of 22 rows, yet spreads across 20 delta patterns. Observed everywhere, internally diverse.
• The upper bundle is likewise internally diverse: 18 of 22 rows, 17 delta patterns. A repeated co-change shape, but its internal variation is not small.
• The shared all_features bundle is a coarse label. B001 and B004 both carry it, but the deep check (all_features_deep_check.csv) shows the subset is B001 rows = 6 and B004 rows = 3 with differing source and delta detail — for example B001 miss arrows land on a target face around R:32→29 with residue transitions into 0→13/0→29, while B004 miss arrows land around R:33→31 with residue transitions into 1→15/1→31. Same label, different source faces and deltas. The bundle string is shared; the underlying rows are not identical.

So the answer to "is the shared all_features bundle really the same between B001 and B004" is: they match on the label only. The row-level evidence still differs and should stay visible.

6. What Should Be Kept Unresolved

• Whether any bundle can stand alone as a next observation unit without keeping the arrow/state rows beside it. On this pass the answer leans no: bundle labels are useful search handles, but each of the frequent bundles carries many delta patterns, so the labels are coarse where it matters.
• The coupled nature of the changes. Several features (front, residue16, 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.
• The role of chain_status, which moves in only part of the miss set and separates otherwise similar arrows.
• No arrow reduction, no reuse of a B001 grouping for B004, and no broad closure claim were made. Those are deliberately still open.

7. Suggested Next Inspection

Keep arrow/state rows together with bundle rows for now; do not promote bundle rows to a stand-alone observation unit yet. If a single next handle is wanted, Bundle C (all_features) is the most useful to inspect further: it is the direct B001/B004 shared exact case and it scores as internally diverse, so it is where the gap between "shared label" and "shared rows" is easiest to examine. Any such inspection should keep the source-face and delta-pattern columns beside the bundle label, not in place of it.