IndisputableMonolith.Gravity.SevenGaps.HKTPointSplitTargetAudit
Audit surface for the point-split Hojman–Kuchař–Teitelboim dynamic target in the gravity seven-gaps repair. It packages the Wave C2 R5 fix that replaces the unsplit momentum–Hamiltonian field with a nearest-neighbor-compatible split, so local momentum profiles stay smooth against the frozen quadratic Hamiltonian. Gravity workers cite it when checking that the singular unsplit advection obstruction is discharged. Thin import-and-audit module over the point-split target definitions.
claimAudit module for the point-split Hojman–Kuchař–Teitelboim dynamic target: the momentum–Hamiltonian constraint is split so nearest-neighbor local momentum profiles satisfy a nonsingular advection relation against the frozen quadratic Hamiltonian, avoiding the unsplit singularity $(p_0+p_1)\cdot\partial_d f = p_0^2 + d^2$ on the locus $p_0+p_1=0$.
background
In the Hojman–Kuchař–Teitelboim (HKT) formulation of geometrodynamics, the dynamic target encodes momentum and Hamiltonian constraints. The widened dynamic target keeps an unsplit momentum–Hamiltonian field. That field is uninhabitable for honest nearest-neighbor local momentum profiles against a frozen quadratic Hamiltonian: at $n=2$, unsplit advection forces $(p_0+p_1)\cdot\partial_d f = p_0^2+d^2$, which is singular on $p_0+p_1=0$.
The upstream point-split target module (Wave C2 R5 repair) replaces that unsplit field with a split form compatible with nearest-neighbor profiles. This audit module sits in the Gravity.SevenGaps chain, imports that repair, and exposes a checkable surface for the split construction and its obstruction discharge.
proof idea
This is an audit module, not a theorem package. It imports the point-split HKT dynamic target and surfaces its definitions and status lemmas for the seven-gaps gravity repair. No independent proof content is introduced here; the mathematical work lives in the imported point-split target, which discharges the unsplit singularity obstruction by splitting the momentum–Hamiltonian field so nearest-neighbor profiles remain smooth against the frozen quadratic Hamiltonian.
why it matters in Recognition Science
Closes the Wave C2 R5 repair path in the gravity seven-gaps program by making the point-split HKT target auditable. Gravity constructions that need an inhabitable dynamic target against frozen quadratic Hamiltonians depend on this split being in place. Without it, nearest-neighbor momentum profiles cannot satisfy the unsplit advection identity on the zero-sum locus. The supplied graph shows no further used-by edges, so the module functions as a terminal audit checkpoint for the repair rather than an intermediate lemma feeder into later theorems.
scope and limits
- Does not prove existence of smooth global solutions to the full HKT constraints.
- Does not alter or re-derive the frozen quadratic Hamiltonian itself.
- Does not address non-nearest-neighbor momentum profiles.
- Does not claim the original unsplit target becomes inhabited after the repair.
- Does not supply new dynamical evolution equations beyond the audit surface.