Round 12 entry-point A — the (a)-lift attempt: the offset must be a HANDED SHEAR, not a displacement; amplitude stays open¶
Dispatched 2026-05-25 (sequential, no subagents; consolidated model — lands on the PR #679 branch with its §11.9.6c notebook edit, no separate PR). The real (a)-lift attempt for the alignment (parking-lot thread 2‴): derive w₂, w₃ — and why p=2,3 not p=1 — from the off-centre-observer Hopf-bundle geometry. It genuinely could land or fail; it partly fails, informatively.
Generating code + provenance: verify_offset_geometry_degree_selection.py
+ .ndjson (deterministic Gauss-Legendre; srmech 0.4.2 Class L cross-check, native active).
The degree/parity selection (rigorous, bug-free)¶
A geometric distortion that is a degree-g polynomial in the direction cosine μ=cosθ (about the offset
axis) deposits into Legendre multipoles ℓ≤g of matching parity. Verified by quadrature:
| distortion degree g | physical object | deposits into ℓ |
|---|---|---|
| 1 | displacement (aberration) | 1 only (dipole) |
| 2 | shear (anisotropic geometry) | 0, 2 |
| 3 | cubic / handed | 1, 3 |
So: p=2 requires a shear (degree ≥ 2); p=3 requires a cubic term (degree ≥ 3); BOTH p=2 and p=3 require a mixed-parity distortion of degree ≥ 3 = a HANDED SHEAR (a shear that breaks reflection symmetry — a swirl). A literal off-centre position (degree-1 → dipole only) fires the Round 11 falsifier.
Where this lands — the attested mechanism class¶
A handed shear / anisotropic-with-vorticity geometry is exactly the Bianchi type VII_h template long used to fit the CMB large-angle anomalies. Jaffe, Banday, Eriksen, Górski & Hansen 2005, ApJ 629:L1 (astro-ph/0503213) — titled "Evidence of vorticity and shear at large angular scales in the WMAP data" — found a ~3σ Bianchi VII_h correlation that, when removed, reduces the low-quadrupole, quad-oct alignment, and cold-spot anomalies together. The word "shear" is literally in the attested title; the degree-selection argument lands on the right physical object independently.
Honest scope — the (a)-lift is NOT achieved, two ways¶
- Framework side: the round derives the mechanism class (handed shear, degree ≥ 3) and the parity
structure (why p=2,3 and why a displacement/dipole fails) — but it does not derive the amplitudes
w₂, w₃from Hopf-bundle first principles. Those are the shear + handedness magnitudes, which remain free parameters (exactly as the Bianchi template's parameters are fit, not derived). - Physical-viability caveat (attested): the physical Bianchi VII_h best-fit is incompatible with ΛCDM — a Markov-chain analysis (astro-ph/0605325) finds the best-fit Bianchi model needs Ω_tot ≈ 0.43, inconsistent with independent constraints; and the original vorticity claim was challenged on gauge-invariance grounds (astro-ph/0503562). So the attested mechanism class itself carries an unresolved physical-viability problem.
Verdict per Spike #229 tiers¶
🟡 (b) REFINED + (open).
- (a)-grade sub-result: the degree/parity selection — displacement (g=1) → dipole only, shear (g=2) → quadrupole, both-p2-and-p3 → handed shear (g≥3, mixed parity). Exact, bug-free, srmech-Class-L corroborated. The displacement reading is falsified (Round 11 falsifier fires as predicted).
- (open): the alignment amplitude
w₂, w₃is not derived — the geometric reading now lives or dies on whether the off-centre-observer Hopf-bundle geometry produces a handed shear at the observed amplitude, AND the attested shear-template (Bianchi VII_h) is itself in tension with ΛCDM. This is the honest floor: the framework reading is consistent with the literature's attested AoE mechanism (shear) and shares its open problem (no derived/physical amplitude).
Net across Rounds 8–12 on the AoE: boosting = confirmed fiber-leak at β (8.A); the alignment is NOT the kinematic leak (9.A) and NOT ℓ=7-Mersenne (10.A); it requires a p=2,3 offset (11.A); that offset must be a handed shear (12.A) = the attested Bianchi VII_h class — whose amplitude neither the framework nor the literature has derived, and whose physical model is contested. The arc has driven the AoE down to a single, sharply-posed, literature-anchored open question rather than a vague one.
srmech routing (per user direction + CLAUDE.md §2)¶
srmech 0.4.2 (updated this session from a stale 0.4.0 install; native active). The multipole decomposition
is a Class L eigenbasis projection; cross-checked through srmech.amsc.laplacian (cycle-graph Class L
eigenvalues match analytic). Continuous Legendre/spherical-harmonic remains a flagged srmech catalog
candidate (asymptotic_calculus covers exp/sin/cos/log1p/atan, not spherical harmonics).
Discipline¶
- Per
[[feedback_dont_pre_commit_spike_query_operators]]: the (a)-lift's non-achievement is stated as prominently as the (a)-grade sub-result; the physical-viability caveat is included, not hidden. - Per
[[feedback_paywalled_doi_cannot_be_attested]]: all citations arXiv-OA, verified this session. - Per
[[feedback_computational_provenance_discipline]]: deterministic committed code; the selection is exact, not a fit. - PR #679 stays open (draft); §11.9.6c rides this branch (consolidated model).