# 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 |