Flavour Residuals Ledger (FLAV-RES)
Isospin · excited \(J^P\) · single formula · PMNS — integrity freeze after FL-O1
CPT Framework — Flavour Date: 2026-07-28 Status: BANKED LEDGER Priors:fl_o1_residuals_o1_o7_closeout_results.md · paper_8d_membership_flavour.md ·
octonion_flavour_knowledge_arc.md · paper_spin_parity_topology.md ·
er_o4_op_classes_slice0_results.md · neutrino_residual_nu_geo_results.md ·
visibility_gates_residual_ledger.md
Script: scripts/investigations/s3_geometry/flavour_residuals_ledger.py
Tags: [E] · [M] · [O] · [F] · [P]
0. One-line stance
Flavour structure is largely frozen; FL-HEAVY heavy multiplet membership is PARKED after H1–H6; gap-survey #5 items are honest parks — not unexamined holes. Applications use operational multiplet tagging; barcode, free \(c,b,t\) on \(e_i\), excited \(J^P\), and PMNS are not sold as theorems.Ontology lead (2026-07-29): flavour as confinement-boundary residual (isospin = physical 3-face; Y/S = bulk/extra) — same stack as Pathway B Clifford BC —
flavour_as_confinement_boundary_residual.md [M]. Does not close spectrum parks.
Heavy reframe + park (2026-08-09): “Heavy quark packaging \((c,b,t)\)” demoted. Quarks = SM-equivalent lobe / multipole channels. Residual FL-HEAVY = multiplet membership + scale — PARKED (native empty; lattice seeds provisional; dual binding fail). Core v2.15 §1d.3 · hub doctrine v1.0.3. Reopen only with new native object.
| Wall (survey #5) | Status |
|------------------|--------|
| Isospin | Architecture closed [E]; pure-lattice I [F] |
| Excited \(J^P\) | Explicit GAP [O]; ground rule [E anchors] |
| Single multiplet formula | Path exhausted [E meta] |
| PMNS / \(\nu\) spectrum | Open no-invent [O]; Op slots [E] |
| FL-HEAVY heavy membership | PARKED [O] after H1–H6 |
1. Settled structure (do not re-litigate)
| ID | Claim | Tag | |----|-------|-----| | FL1 | G2 ⊃ SU(3) flavour triplet slot (Günaydin–Gürsey) | [E] · octonion arc | | FL1b | Preferred G₂ dictionary: e₄ fixed; P→3⊕3̄→(u,d,s)⊕antiquarks; GMN Q | [E structure] ·g2_e7_quark_basis_dictionary_results.md |
| FL1c | Bijection e₁…e₇ → (u,d,s,c,b,t) / eᵢ=single quark | [CLOSED F] · same |
| FL1d | Quark = SM-equivalent lobe/channel label — not CPT primitive | [E meta] · flavour_heavy_lobe_reframe.md |
| FL-HEAVY | Heavy residual = multiplet membership + scale (not G₂ store of \(c,b,t\)); H1–H6 banked; PARK | [O parked] · reframe · H6 fl_heavy_binding_geometry_results.md |
| FL-H1 | PDG charm/bottom hadrons exist; native T(p,q)/102-census/Q1b membership empty | [E coverage] · same |
| FL-H2 | Heavy mass ratios ≠ Route E lepton ladder; B/D∼2.83, Υ/Jψ∼3.05 O(1) | [E/M] · same |
| FL-H3A | Nearest Hopf lattice seeds for D/B/… empty + often competitive; density weakens high-mass score | [E/M] · fl_heavy_lattice_dual_seat_results.md |
| FL-H3B | Dual-seat \(2M_{\mathrm{open}}\) fails (binding ∼0.6–1.1 GeV); geometric dual toys only | [E / M toy] · same |
| FL-H4 | Large competitive clouds; S6=empty∩gcd1∩≤0.5% provisional seed package | [E/M] · fl_heavy_selection_tower_results.md |
| FL-H5 | Towers not tight on seed; mass-annulus closer-than-wrong only | [E honesty] · same |
| FL-H6 | Dual/multi-seat binding: GeV Δ real; lattice dual pkgs + L1c + vector dual all fail; PARK | [E/F park] · fl_heavy_binding_geometry_results.md |
| FL2 | I3 = physical Lz in preferred Stab(e4) frame | [E] · preferred basis |
| FL3 | Isospin structure = rotation in physical space; Y/S into extra | [E] · flavour map |
| FL4 | Least-squares 2×2 Cartan→(I3,Y) as prediction | [F] · tautology |
| FL5 | Full-census lattice (w1,w2) → multiplet barcode | [F] · FL-O1 / MF |
| FL6 | Lattice NN inheritance as tower glue | [F] · MF16 / O7 |
| FL7 | Multiplet S ladder (transport + GMN) | [E] · FL-O1 |
| FL8 | Ground R3/R4 → multiplet → G2 (I,Y,S) | [E/M] · structure rules |
| FL9 | Operational (M,J,I)→multiplet→S applications path | [M] · FL-O1 default |
| FL10 | O1 single algebraic formula path | [F_exhausted] · O1 closeout |
| FL11 | Pure lattice → I without multiplet ID | [F] · O3 |
| FL12 | Strange multiplet (p,q) in FL geometry | [E_structure_ER] · O6→ER-O3 |
| FL13 | Ground J^P: gcd=1 → 1/2+; gcd>1 → 0-; p=0 special | [E_anchors] · spin-parity paper |
| FL14 | Op_e/μ/τ three residual bookkeeping slots | [E_ledger] · ER-O4 |
| FL15 | PMNS / Δm² invented from topology | [F_if_claimed] · ER-O4 |
| FL16 | VIS dual gates / partner Δ category split | [E_M] · VIS-GATE ledger |
2. Isospin
| Layer | Content | Tag | |-------|---------|-----| | Structure | \(I_3 = L_z\) physical rotation; preferred Stab(\(e_4\)) frame | [E] | | Multiplet \(I\) | G2 weight after multiplet identity | [E] architecture (O3) | | Pure lattice \(\to I\) | Barcode abandoned | [F] | | Lab \(I\) in applications | Spectroscopy multiplet classifier | [M] operational | | Absolute u/d/s cosmic orientation | Beyond isospin frame | [O] prior (O5) | Finding FR1: Isospin is not “missing geometry” — it is closed as architecture and open only as absolute orientation / pure-lattice fantasy (killed).3. Spin–parity
3.1 Ground rule [E anchors]
\[ \gcd(p,q)=1 \Rightarrow J^P=\tfrac12^{+},\qquad \gcd(p,q)>1 \Rightarrow J^P=0^{-},\qquad p=0 \Rightarrow \text{spin-}\tfrac12\text{ special (neutrino)} \] | Anchor | \(T(p,q)\) | Pred | Meas | |--------|-----------|------|------| | \(e\) | (1,1) | \(1/2^+\) | \(1/2^+\) | | \(p\) | (2,3) | \(1/2^+\) | \(1/2^+\) | | \(n\) | (3,2) | \(1/2^+\) | \(1/2^+\) | | \(\pi\) | (2,2) | \(0^-\) | \(0^-\) | | \(\nu\) | (0,2) | special \(1/2\) | special | Cold: 5/5 anchors PASS (this script).3.2 Excited spectrum [O] GAP
| Class | Why bare \((p,q)\) fails | |-------|-------------------------| | \(\Delta(1232)\,3/2^+\) | Orbital / spin excitation not in ground knot | | Vector mesons \(1^-\) | Same link class as \(0^-\) ground | | \(N^\,1/2^-\), \(3/2^-\) | Parity / \(L\) not in bare \((p,q)\) | | Tensors \(2^+\) | Higher orbital | Finding FR2: Ground rule is a real PASS test; excited \(J^P\) is a named programme residual, not a silent failure.4. Single multiplet formula
| Claim | Tag | |-------|-----| | Universal \((w_1,w_2)\to\) multiplet algebra | PATH EXHAUSTED [E meta] (O1) | | Piecewise R3 ground structure rules | [M] tool retained | | Full-census barcode | [F] | Finding FR3: Do not re-open single-formula barcode hunting under a new name.5. PMNS / residual classes / \(\nu\) spectrum
| Item | Tag | |------|-----| | Op\(_e,\mu,\tau\) ledger slots | [E] structure (ER-O4) | | Generation match at charged-lepton vertex | [E] lab bookkeeping | | PMNS matrix elements | [O] — do not invent | | \(\Delta m^2\), mass eigenstates \(\nu_{1,2,3}\) | [O] | | Op class = mass eigenstate without mixing | [F if claimed] | | Absolute \(m_\nu\) | Parked after NU-GEO | Finding FR4: Mixing is honestly open; bookkeeping is not a spectrum law.6. Cold tests this pass
| ID | Test | Outcome | Tag | |----|------|---------|-----| | T1_GROUND_JP | Ground-state J^P rule on anchors | PASS_ALL | [E] | | | gcd rule reproduces e,p,n,pi,nu special | | | | T2_EXCITED_JP | Bare (p,q) ground rule on excited J^P labels | GAP_CONFIRMED | [O_E] | | | Ground rule systematically fails excited spectrum — orbital L not in bare knot [paper_spin_parity] | | | | T3_I_ARCH | Geometric I after multiplet ID vs pure lattice I | ARCHITECTURE_CLOSED | [E] | | | I = G2 multiplet weight after multiplet identity; pure (w1,w2)→I barcode abandoned [O3 freeze] | | | | T3b_I3_LZ | I3 as physical Lz in Stab(e4) | STRUCTURE_E | [E] | | | Isospin quantisation axis locked by preferred Cartan / knot angular momentum [octonion arc] | | | | T3c_LAB_I | Lab multiplet I without geometry | OPERATIONAL_M | [M] | | | Applications may use spectroscopic I as multiplet classifier [flavour_push4]; not pure-lattice mint | | | | T4_SINGLE_FORMULA | Universal algebraic multiplet formula from (w1,w2) | PATH_EXHAUSTED | [E_meta] | | | O1 closeout: full-census single map below baseline; piecewise R3 is ground tool | | | | T5_PMNS | PMNS matrix / Delta m^2 from geometry | OPEN_NO_INVENT | [O] | | | ER-O4 freezes Op slots only; mass eigenstates and mixing not derived; NU-GEO parks absolute m_nu | | | | T5b_OP_NE_MASS | Op_e/μ/τ identified with nu_1,2,3 without mixing law | F_IF_CLAIMED | [F] | | | Ledger books Op by charged lepton at vertex; mass basis needs PMNS [ER-O4] | | | | T6_OPS_PATH | Default flavour applications path | BANKED_DEFAULT | [M_E] | | | Use multiplet-first or (M,J,I)→multiplet→G2 weight→S; ground seeds R3 when lattice available | | | | T7_SIGMA_ISLAND | Sigma- lattice island (Hopf,10,14) under R3 | PARKED_PARTIAL | [M] | | | O2 documented miss; not 100% charge-state complete; operational ID accepted | | | | T8_VIS_PARTNER | Partner Δ and dual gates as flavour membership | CROSS_LINK_ONLY | [E_M] | | | VIS-GATE: Δ post-dual; dual occupancy not lattice barcode; use without category merge | | |7. How to use flavour now
| Task | Path | |------|------| | Ground multiplet seed | R3/R4 structure when lattice key available | | Strangeness \(S\) | Multiplet ID → transport/GMN ladder [E] | | Excitations / towers | Operational \((M,J,I)\to\) multiplet [M] — not lattice NN | | Reactions / strange topology | ER-O3 Layer-B seeds — no hyperon mass \(pq\) | | Dual Free/Hopf occupancy | VIS-GATE environment — not multiplet barcode | | Neutrino residual | H-ν ontology + seesaw shape; no PMNS fit |8. Remaining deep parks only
| ID | Residual | Tag | |----|----------|-----| | FR-O1 | Excited \(J^P\) / orbital \(L\) law | [O] | | FR-O2 | PMNS + \(\Delta m^2\) | [O] | | FR-O3 | Absolute u/d/s cosmic orientation | [O] | | FR-O4 | Tilt \(k=1\) as derived law (not construction) | [O] | | FR-O5 | \(\Sigma^-\) island polish | [M] partial | | FR-O6 | Partner \(\Delta\) first principles (VIS cross-link) | [O/M] | | FR-O7 | FL-HEAVY heavy multiplet membership + scale (H1–H6 banked; park) | [O parked] |9. Explicit rejects
| Claim | Tag | |-------|-----| | Lattice barcode of every PDG multiplet | [F] | | Excited \(J^P\) from bare \((p,q)\) alone | [F if claimed] | | Single universal multiplet formula already derived | [F] | | PMNS fitted and sold as topology theorem | [F if claimed] | | Op\(_\ell = \nu_i\) without mixing | [F if claimed] | | Least-squares quark \((I_3,Y)\) as prediction | [F] tautology |10. Findings register
| ID | Finding | Tag | |----|---------|-----| | FR1 | Isospin: structure [E] (I3=Lz preferred frame; I as G2 weight post multiplet); pure-lattice I closed-null. | [E] | | FR2 | Ground J^P rule passes anchors [E]; excited J^P remains explicit GAP (orbital L) [O]. | [E_O] | | FR3 | Single multiplet formula path exhausted [E meta]; piecewise R3 stands for grounds. | [E_meta] | | FR4 | PMNS/spectrum not derived; Op bookkeeping ≠ mass eigenstates [E discipline / O]. | [E_O] | | FR5 | Applications default operational multiplet tagging [M]; barcode hunt stays dead [F]. | [E_M] | | FR6 | Gap-survey #5 walls are mostly parked residuals, not unexamined gaps — ledger freezes status. | [E_meta] | | FR7 | Deep parks only: excited JP law; PMNS; absolute u/d/s orientation; O4 tilt law; Sigma- island polish. | [O] | | FR8 | FL-HEAVY H1–H6: PDG hadrons real; native empty; S6 provisional; dual binding GeV but no geometric dual close — PARK. | [E_O park] |11. One-line
FLAV-RES: structure frozen, barcode dead, ground \(J^P\) real, excited \(J^P\) and PMNS honestly open — use operational multiplet path; do not invent spectrum laws.
End of FLAV-RES residual ledger (2026-07-28).*