Independent correctness audit

Physical premise (IDWT): Physical spacetime has infinitely many ordinary spatial dimensions plus time. Matter occupies up to ten spatial dimensions; all remaining spatial directions are unbound for every particle. Depth counts a pattern's bound spatial involvement within that space. “Observed” and “unobserved” describe an observer's access, not different kinds of dimension. Older projective and nested-geometry calculations below retain their additional hypotheses; they do not establish a separate physical manifold or compactified direction. See spatial meaning and mathematical scope.

Summary: Independent recurrence refinement exposes false numerical acceptance, while scope corrections separate valid conditional geometry and conservation tests from physical identification.

Verdict and scope

Not everything was correct. There are valid conditional constructions and reproducible diagnostics, but the periodic-continuation acceptance and several physical-inference statements exceeded their evidence. This audit corrects those statements rather than counting earlier successful script exits as proof of the full theory.

The audit inspected the core module statements and recent orbit, response, geometry, mass-operator, and conservation calculations. The initial sweep ran 57 existing diagnostic scripts, excluding the two expensive continuation searches, and all exited successfully. Independent checks then reintegrated saved continuation candidates and found the failure below. The mass-spectrum program also reproduces its stated fixed-index depth sequence. These are finite checks, not an end-to-end independent proof of every theorem in the historical archive. Earlier research notes not individually rederived remain historical records with their existing correction links.

After the corrections, a fresh suite run completed 58 diagnostic scripts, including the new independent audit, with no failing exit status. The saved suite report contains every script's output, exit status, timing, interpreter version, and the two explicit continuation-search exclusions. The independent audit performed 84 checks and classified all three archived candidates as not accepted. The mass-spectrum program also passed its stated checks. These finite numerical checks are not mathematical proof.

Corrections with explicit witnesses

1. Periodic continuation was accepted at inadequate integration accuracy. The three archived candidates at $h=0.0064,0.0096,0.0128$ have refined closure errors $2.41423,7.43896,5.31450$ times $10^{-6}$, respectively, rather than the reported sub-$10^{-6}$ values. Their Casimirs are correct. The optimizer's residual was not a reliable independent error estimate. See Cylindrical petal continuation for pinned states, numerical settings, and the withdrawn acceptance claim.

2. The fully cylindrical centre had a removable implementation singularity. At $h=1$, the coefficient of the old Coulomb potential vanishes, but the implementation still evaluated that potential at $q=0$. The corrected code omits the discarded term and returns $V(0)=-3/(2a)$ and zero central force. This fixes an endpoint evaluation; it does not remove the actual Coulomb singularity when $h<1$.

3. Projection does not establish a smeared physical electron. The delta-distribution calculation and experimental distinction are in Electron detection and shape. An additional normalization mistake is corrected in Bound within, free without: a uniform probability density normalized in a fibre box of volume $V$ gives an overlap proportional to $1/V$, not an automatically volume-independent coupling. A cylindrical field and a normalized uniform wavefunction are different objects; the action must specify which is intended.

4. A frozen-route ligand minimum is not full molecular stability. The positive ligand Hessians are meaningful for the specified frozen route, fixed centre, and fixed planes. The regular tetrahedral snapshot has nonzero transverse force in that energy and relaxes to a disphenoid. At nuclear radius $0.6$, overlapping profiles are still assigned point-centre repulsion, so those entries are hybrid-model controls. See Cylindrical molecular shape stability.

5. Configurable electron mass had inconsistent factors. The completed kinetic energy is $|p-m_e\lambda Cs|^2/(2m_e)$. The reciprocal executable previously used the unit-mass factors even when $m_e$ changed. Corrected velocity, force, and source equations now pass independent Hamiltonian-derivative and conservation checks at $m_e=0.7,1,2.3$, including nonaligned nuclear planes. The original unit-mass trajectory is unchanged. See Reciprocal cylindrical molecule.

   The continued orbit occupies an invariant four-coordinate subspace of the six-coordinate model. Random-state checks verify the exact embedding of its $h=0$ field, including zero inactive derivatives, to roundoff. It therefore is not an independent dimension witness. This does not reassign the electron: depth six remains the working mass-formula input. Also, a generic skew $C$ need not obey $C^2=-c^2I_6$, whereas an orthogonal their symmetry groups are related. See Sector geometry premise audit.

6. Several module summaries omitted necessary premises. Base-coordinate locality does not force a rank-one contact operator: band-compressed identity remains identity, whereas a specified point evaluation can be rank one. The occupied-ray and normalization assumptions are now explicit in the self-contact module. See Contact-kernel audit. A generation-blind charged-current vertex is identity in a common basis, but its mass-basis matrix is $U_{u,L}^\dagger U_{d,L}$; obtaining identity there additionally requires aligned left mass bases. The CKM module now says so. The coherent CPd submanifold is also distinguished from the full projectivization of the cumulative mode bundle.

7. Energy preference and representation realization were overstated. A positive lock-energy coefficient is not dynamical capture: for $H=V(s)$, $\dot s=\{s,V(s)\}=0$. A small observer-space motional magnetic estimate does not prove that additional curvature supplies the missing lock. Constructing a group action with the desired generator does not derive its physical electromagnetic current. The visualization prose now makes these distinctions without changing its petal rendering. The photon module also states that spatial polarization and normal propagation are premises of its orthogonality theorem, not consequences of dimensional counting alone.

What survives and what comes next

The exact representation algebra, specified analytic orbit constructions, fixed-source chart, and checked conservative equations remain useful. They are positive mathematical results for defined models. Known unstable and rejected branches must remain in the record.

The September 7 audit recommended correction and independent closure tests of the fixed-Casimir cylindrical candidates, followed by moving-nucleus recurrence and perturbation stability. This is a historical recommendation; the excerpt does not establish whether those tasks were subsequently completed. The active September 28 research target is the physical mass operator, its canonically normalized spatial source map and frequency selection. A common action and measurement law connecting spatial patterns, reciprocal response and detections remains necessary for physical identification. Neither chain can substitute for the other.

Reproduction

From the repository root (use a fresh report filename for a new run):

OPENBLAS_NUM_THREADS=1 python3 -B experiments/independent_audit_checks.py
OPENBLAS_NUM_THREADS=1 python3 -B experiments/reciprocal_cylindrical_molecule_checks.py
OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python3 -B experiments/run_checks.py --skip-continuation --jobs 3 --report experiments/results/audit-2026-09-07/reproduction-suite.json
python3 -B experiments/idwt-v2.py
python3 -B scripts/validate-kb.py

The independent script consumes archived states without re-fitting them and regenerates its report. Its successful diagnostic checks and the candidates' computed acceptance fields are separate: passing the audit does not mean the orbit candidates passed. Integration-failure negative controls reject failed, partial, and nonfinite trajectories. Full long-run continuation has not been rerun as part of this independent saved-state test.