FPRD research loop state

Updated after the 8 September 2026 clean-excess meridian-cokernel ATTACK. Other programs and the existing CK publication retain their prior scope.

Latest completed mode

ATTACK — a clean-excess obstruction to point-local deformation detectors for the actual six-root meridian cokernel.

This is a supporting research note, not a new Publication. The work is AI-assisted and internally audited, without external specialist review or author endorsement. Novelty and first priority are unassessed.

Chen and Kricker were separately emailed about the earlier comparison publication, with Joshua Gay CC’d. No reply, mathematical confirmation or endorsement is assumed. This continuation made no new author contact.

Active program and retained publication

Program: https://fprd-lab.joshgay.chatgpt.site/research-programs/dehn-filled-quantum-trace

Latest completed Publication: https://fprd-lab.joshgay.chatgpt.site/publications/ck-degree-zero-descent

Panitch–Romo Conjecture 7.1 remains open in this work. No unrestricted actual filling nonvanishing or actual full-six-root conjecture counterexample has been proved.

Current evidence packet

The new clean-excess-meridian-attack/ packet contains:

• FPRD-clean-excess-meridian-obstruction-2026-09-08.md: complete obstruction proof and exact countermodels.
• hostile-audit.md, source-ledger.md, source-snapshots.json: proof boundaries, primary-source inspection, credit and hashes.
• verify-clean-excess.py, verification-output.txt: exact Laurent/Poisson identities, Jacobian rank, scalar corrections and formal-series audit.
• README.md, SHA256SUMS.txt: reproducibility and payload integrity.

The preceding six-root-peripheral-attack/ packet remains the named-action/collar bridge; neither its generic third-sign resolution nor its local dictionary is being reopened.

Retained exact target and named action

Use $k=\mathbb Q(i,A^{1/2})$. The full native GY target has left-generated tetrahedron relations $z^{-2}+(z'')^2-1$, right-generated actual edge relations $H_e+A^2$, and all four central vertex values $iA$. Opposite roots are not identified. Central vertex elimination retains each involution $\sigma_T$; central idempotents give sign sectors, some possibly zero.

The prior packet proves the source-native additive six-root peripheral action and its raw named GY/CK/PP collar dictionary using GY’s local calculation, PP’s unweighted marking reversal and inverse cup/cap picture factors, CK’s convention-adjusted comparison, and the existing original-PP Eulerian normalization. Weighted self-duality is not a substitute for that unchanged same-state splitting square. The source-reading caveat for CK’s mixed-sided Laurent target remains; no author-confirmed erratum is claimed.

For native additive row $u_\gamma$, the named original-PP monomial remains

$$E^{PP}_\gamma=i^{-\sum_e(u_\gamma)_e}\epsilon^{Pu_\gamma}W_x(Pu_\gamma),$$

with reciprocal coefficient on its inverse summand and all central signs retained. The all-slope argument remains generic; target-wide canonicity across basis choices or Pachner moves is not asserted.

The intrinsic generic filled target remains isomorphic to

$$C_s^6=\operatorname{coker}(m+A^2:Q_G^6\to Q_G^6), \qquad ml=A^2lm.$$

The isomorphism sends $[v]$ to $[(1-l^2)v]$. A nonzero descended trace still requires a detector nonzero on this filled-vacuum image, not merely a nonzero abstract cokernel.

New theorem: clean excess extinguishes the previous local detector

In a fixed actual sign sector, at a nonzero signed classical root point, set $A=e^{\hbar}$ and use the logarithmic formal star product on $R[[\hbar]]$. Use right tetrahedron multiplication and left multiplication by independent edge/filling relations; these operators commute exactly.

Suppose the scheme-theoretic common locus is smooth and has dimension strictly greater than the expected $r-1$. Each separate differential block is independent. An actual non-Koszul syzygy then has first Bockstein

$$\beta(u[a])=u\beta([a])+V_a(u), \qquad V_a(u)=\sum_i a_i\{u,f_i^0\},$$

where $V_a$ is a tangent vector field nonzero at the point. The resulting first-order operator is surjective on the smooth formal germ. A direct convergent coefficient-vector correction proves

$$\hbar H_p=0,\qquad H_p[\hbar^{-1}]=0.$$

Remaining actual edge relations only take a further quotient, so no independent-edge redundancy in every sign sector is assumed. Quantum scalar shifts affect the zero-order term and do not cure this local obstruction.

This applies conditionally to the actual presentation; no existence of such a locus for every filling is asserted. It does not cover singular excess or nilpotent thickenings. A singular complete intersection can still be regular and remains within the earlier theorem.

Exact limits and preserved useful failures

• A folded algebraic two-tetrahedron model supplies an explicit syzygy and nonzero tangent obstruction. Its moments are not claimed to be actual manifold incidence rows.
• Vanishing of every formal-local detector does not imply algebraic vanishing: $T/(T(m-1)+(m-1)T)\cong k$ has a global Fourier functional, while every corresponding generic formal-local quotient is zero. Formal logarithms supply primitives absent from finite Laurent polynomials.
• Nonzero cyclic peripheral modules and nonempty classical filling support do not force generic filling nonvanishing. On $k[z^{\pm1}]$, let $l=z$ and $m(z^n)=-A^{c+2n}z^n$. For $c=1$, $m+A^2$ is bijective; for $c=2$, its cokernel is one-dimensional. Both have the identical nonzero classical filling fiber $m=-1$. These are algebraic countermodels, not actual triangulation counterexamples.
• A nonzero derived tensor product or completed object is not the required algebraic degree-zero cokernel without an explicit comparison and nonzero image.

The broad deformation-quantization/derived-intersection background is existing literature, including Gunningham–Safronov’s Theorem 7.1 and clean-intersection discussion. It is not claimed as a new discovery or imported without checking category and completion differences.

Positive results retained

The previous regular-intersection nonvanishing theorem and strictly positive geometric-filling theorem retain every hypothesis, including actual signed logarithmic surgery and the longitude vacuum test. Their nonzero identified target transfers to the full six-root and named original-PP targets through the previously proved boundary-linear maps. Nothing in this continuation extends that positive chamber or proves survival of every global sign sector.

Next mode

ATTACK — global algebraic detection for the actual generic six-root meridian cokernel.

Seek a Laurent/residue, global difference-equation or rigorously compared cycle-valued functional that annihilates every actual tetrahedron/edge/filling relation, respects the actual quantum shifts, and has a proved nonzero value on an original algebraic class. Check $1-l^2$ separately if a nonzero descended trace is claimed. A tightly bounded alternative is explicit first-syzygy analysis at genuinely singular excess loci, which the clean theorem does not cover.

Do not continue the regular-intersection local-flatness proof through clean excess without new input. Do not infer actual vanishing from zero formal detectors, nonvanishing from target comparisons, or a PR 7.1 counterexample from algebraic models or degenerate-chart remarks. Do not enumerate manifolds, slopes, triangulations or skein configurations. Do not restart the generic third-sign problem. Other programs remain at their latest paused or withdrawn statuses.