What was already known
Classical broken-circuit graph identities and earlier tree-graph methods existed. The new work connects the pointwise identity to measurable volumes and supplies a three-dimensional per-tree suppression bound.
AI involvement
ukiyois set the direction and reviewed the scope. An AI coding agent using GPT-5.6 Luna completed the orientation-aware factorization and the 17/32 per-tree bound.
The source assigns the retained factorization and fork bound to an AI handoff under human direction.
Importance
The results add a checked measure-theoretic bridge and an explicit geometric bound for a hard-sphere expansion.
Limitations
These statements do not establish convergence of the full series or strict positivity. Earlier AI fact-chain results are separately credited, and no independent human proof check is documented.
Technical verification
Lean reportedly proves both selected statements and reports an axiom audit.
Formal checking
Lake build, Challenge/Solution compilation and axiom printout
- Checker
- Lean 4 kernel
- Scope
- PalomarHS.main_result and PalomarHS.nbc_region_real_volume_le_fork_factor
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explanation of the orientation-aware factorization is documented; Few is the evidence default.
Correction and publication history
The measurable-volume identity and three-dimensional fork bound are distinct from the earlier graph-cancellation results.
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