3624 — Aspect's Six-Rung Tester Admits Exactly the Rank-Four Relative Connection Attack
Superseded by Entry 3627. This entry correctly identified the four raw (B)-coordinates but failed Aspect's non-alias gate because it did not first quotient regular triangular gauge. Explicit endpoint two-torsion makes the intrinsic rational de Rham extension quotient zero.
Hard-to-vary claim
Applying Aspect's current six-rung machinery to the deck-odd marked-relative infinity architecture isolates an exact four-dimensional unresolved kernel.
In endpoint-first ordering, the relative connection has typed form
where (A_K) is the rank-two odd endpoint block, (A_E) is the rank-two elliptic block, and
is the only unresolved extension block.
The existing endpoint, reciprocal-chart, and deck tests have observation rank zero on these four coordinates. Aspect's falsifier compiler therefore requires exactly four mixed-derivative interventions.
Six-rung result
Rung one: realization
The source object is the deck-completed marked-relative elliptic system with the sign-weighted physical finite-part covector, derived in Entries 3607--3618.
Rung two: existing tester
The current exact gates establish:
- failure of ordinary (H^1) factorization;
- source tangential normalization;
- cancellation of endpoint derivative divergences;
- reciprocal-chart cocycle closure;
- deck-character completion.
These gates fix the diagonal and transition data but do not observe (B).
Rung three: falsifier compiler
The declared mutation carrier is
The current observation kernel has dimension four. Four dual mixed-derivative rows raise the diagnostic rank to four and close this declared kernel.
Rungs four and five: ontology and admission
All eight ontology mutations were classified:
Admitted:
- endpoint port creation;
- ordinary-versus-relative support refinement;
- the rank-four deck-odd arity lift;
- elliptic-to-endpoint cross-coordinate composition.
Rejected:
- nonlinear functions of the existing covector as aliases;
- probe-dependent adaptation without source provenance;
- a new (mathcal Q) or endpoint singular-support label;
- an unconstructed fresh predicate.
The extension attack is admitted because it has source provenance, a typed term, a separating split-versus-nonsplit target, the relative Gauss--Manin constructor, non-alias evidence, and a bounded four-coordinate test.
Rung six: portfolio
Exactly one computation has independent gain:
Derive the complete rank-four odd marked-relative connection and measure the four entries of (B).
Repeating endpoint tails, reciprocal-chart checks, or deck-character censuses has zero new quotient gain and is suppressed as alias work.
Scope boundary
The four-dimensional closure is relative to the frozen two-endpoint, two-sheet marked-relative object. Additional source-derived denominator marks may enlarge the hostile language. Aspect's open-world rule remains active.
Verification
- scoped checker:
research/benincasa/checkers/check_infinity_relative_aspect_six_rung.py; - packet:
research/benincasa/results/infinity-relative-aspect-six-rung.json; - Aspect regression checkers:
check_four_rung_tower.py,check_five_rung_tower.py,check_six_rung_tower.py.
All scoped and upstream gates passed.
Allocator claim: seqclaim-9ffebd282eb9bdba674a99b7.