FL-HEAVY Pursuit: Membership Census + Scale (FL-H1 / FL-H2)
Date: 2026-08-09
Script: scripts/investigations/s3_geometry/fl_heavy_membership_scale_census.py
JSON: scripts/investigations/s3_geometry/data/fl_heavy_membership_scale_census.json
Priors: flavour_heavy_lobe_reframe.md · G₂ dictionary · FLAV-RES · FL-O1 · GS-E1 · Q1b card
Tags:
[E] ·
[E data] ·
[E meta] ·
[M] ·
[O] ·
[F]
0. Ontology (L0)
Quark = SM-equivalent name for a lobe / multipole channel of a geometric seat — not a CPT primitive. This probe never packages free \((c,b,t)\) onto \(e_i\).
1. FL-H1 — Membership census
1.1 PDG sector counts (export labels only)
| Sector | all_with_mass (n=334) |
|--------|----------------------------------:|
| other | 112 |
| charm | 78 |
| bottom | 63 |
| strange | 42 |
| light_strange_mix | 22 |
| light | 17 |
1.2 Ground multiplet anchors (MeV)
| Anchor | mean mass | native note |
|--------|----------:|-------------|
| light_pseudoscalar | 137.27 | T(2,2)-class / light multipole |
| light_nucleon | 938.92 | proxy — use N(939) mass constants |
| strange_kaon | 495.64 | lattice/G2 light 3 structure |
| charm_D | 1867.25 | OPEN native seat |
| charm_Ds | 1968.35 | OPEN native seat |
| charm_Lc | 2286.46 | OPEN native seat |
| charmonium | 3040.50 | OPEN — dual-seat heavy? |
| bottom_B | 5279.56 | OPEN native seat |
| bottom_Bs | 5366.93 | OPEN native seat |
| bottom_Lb | 5619.57 | OPEN native seat |
| bottomonium | 9460.40 | OPEN — dual-seat heavy? |
1.3 Native bank coverage
| Bank | Heavy open-charm/beauty? | Tag |
|------|--------------------------|-----|
| Octonion/Gaussian 102 census |
No (0/102; S-only strange) |
[E coverage] |
| Q1b multiplet card |
No (e + T(2,3) hadronic candidate) |
[E coverage] |
| Explicit T(p,q) seats (e,p,n,π,N
) | No heavy | [E] |
| Lattice field D in census | Not charm (integer lattice feature) | [E honesty] |
1.4 Native seat membership table
| Seat | Identity | SM export | Lobe / status |
|------|----------|-----------|---------------|
| T(1,1) | e± | lepton | single-wind Hopf |
| T(2,3) | p / hadronic | light baryon | p=2 |
| T(3,2) | n | light baryon | p=3 multipole |
| T(2,2) | π-class | light meson | link |
| T(2,7) | N(2190)-class | light baryon | high-q |
| lattice (w1,w2) | K / strange towers | strange | G2 3 structure |
| — | D / Ds / Lc | charm | NO native seat
[O] |
| — | B / Bs / Lb | bottom | NO native seat
[O] |
| — | J/ψ / Υ | heavyonium | NO native seat
[O] |
Finding H1 [E]: Lab heavy
hadrons are catalogued;
no native CPT multiplet membership for open-charm/beauty is present in current banks. The residual is a
membership gap, not a missing \(e_i=c\) assignment.
2. FL-H2 — Scale probes
2.1 Banked generation scales (leptons / geometry)
| Scale | Value |
|-------|------:|
| \(m_\mu/m_e\) | 206.7683 |
| \(m_\tau/m_e\) | 3477.2283 |
| \(3/(2\alpha)\) | 205.5540 |
| Route E \(m_1/m_e\) | 206.5540 |
| Route E \(m_2/m_e\) | 3495.4180 |
| LEAD-5 \(E_0\) | 59.3383 |
GS-E1 already marks
quark generations out of scope for Route E.
2.2 Heavy hadron ratios (export sector)
| Ratio | Value |
|-------|------:|
| m_D / m_p | 1.9901 |
| m_D / m_K | 3.7823 |
| m_D / m_pi | 13.3786 |
| m_B / m_p | 5.6269 |
| m_B / m_D | 2.8274 |
| m_Lc / m_p | 2.4369 |
| m_Lb / m_Lc | 2.4578 |
| m_Jpsi / m_p | 3.3006 |
| m_Ups / m_Jpsi | 3.0548 |
2.3 Match board (±10%)
No ground heavy ratio matches Route E / \(3/(2\alpha)\) / LEAD-5 within 10%.
Finding H2a [E]: Open-charm/beauty ground masses sit at
O(2–6)× nucleon, not on the lepton Willmore ladder.
Finding H2b [M]: Within the heavy sector, \(m_B/m_D \approx 2.83\) and \(m_\Upsilon/m_{J/\psi} \approx 3.05\) are
O(1) steps — a generation-
like spacing observation, not a derivation and not free \(c,b,t\).
3. Integrity board
| Claim | Tag |
|-------|-----|
| Quark = SM lobe/channel label | [E meta] |
| PDG open-charm/beauty hadrons exist in lab catalogue | [E data] |
| Octonion 102 census includes open charm/bottom | [F coverage — absent] |
| Q1b multiplet card has heavy seats | [F coverage — absent] |
| Native T(p,q) for D/B/Lc/Lb |
[O] missing |
| Lobe multipole of light n/p as free c,b,t | [F as method] |
| e_i → (c,b,t) basis packaging | [CLOSED F] |
| Route E Willmore ladder for heavy hadrons | [F as that claim] / out of scope |
| O(1) B/D and Υ/Jψ mass steps | [M observation] |
| FL-HEAVY residual after census |
[O] membership still open |
| CKM from this census | [F if claimed] |
4. Verdict
1.
FL-H1 [E]: Heavy hadron sectors exist in PDG;
native membership is empty in octonion census, Q1b card, and explicit \(T(p,q)\) bank.
2.
FL-H2 [E/M]: Scale is
not Route E lepton ladder; O(1) charm→bottom steps are observed only.
3.
Not claimed: free \(c,b,t\) on \(e_i\); CKM; zero-param heavy zoo.
4.
Residual FL-HEAVY remains [O]: need a
new native multiplet object (or geometric membership rule) for heavy hadron seats — still lobe/seat language, not quark primitives.
Next forks (honest)
| Fork | Content |
|------|---------|
|
A | Build / import lattice assignments for open-charm/beauty hadrons (extend census) |
|
B | Dual-seat / multi-knot packaging for heavyonium (\(J/\psi\), \(\Upsilon\)) as composite seats |
|
C | Park FL-HEAVY until a new geometric membership principle appears |
|
Do not | Reopen \(e_i\to(c,b,t)\); fit CKM; force Route E onto hadrons |
One-liner: Heavy flavour in CPT is an open hadron multiplet membership problem; the lab charm/bottom sectors are not yet seats in the native bank, and their masses are not lepton-ladder generations.
Related bank
| Doc | Role |
|-----|------|
|
flavour_heavy_lobe_reframe.md | L0 ontology |
|
g2_e7_quark_basis_dictionary_results.md | light G₂ freeze |
|
lattice_knot_flavour_evidence.md | prior: no charm/bottom lattice rule |
|
a_geom_gap2_gs_e1_route_e_activation_results.md | Route E lepton-only |
|
fl_o1_flavour_assignment_results.md | lattice→multiplet wall |
Changelog
| Date | Change |
|------|--------|
| 2026-08-09 | FL-H1/H2 census: membership empty for heavy; scale not Route E |