Construct element gonols and test molecular affixiation

.gitignore

@@ -0,0 +1,2 @@
+__pycache__/
+.skill-lib/

research/epac/README.md

@@ -5,3 +5,38 @@ Reserved for **energy particle affixiation coupling**.
 Status: `hmmm` — no source repository exists yet. This directory carries no doctrine
 until a canonical `The-Interdependency/epac` source is created and pinned in
 `STACK_MANIFEST.md`.
+
+## Current content
+
+- [`subatomic/subatomic-affixiation-baseline.md`](subatomic/subatomic-affixiation-baseline.md) —
+  provisional research candidate: hydrogen → helium baseline and the lithium/carbon
+  construction form over current METAPAT affixiation semantics and UCNS carrier identity.
+  Status: CROSS-DOMAIN-HYPOTHESIS / proposed. Not org canon.
+- [`epac_public_gonol.py`](epac_public_gonol.py) — EPAC Public Gonol constructor
+  on the UCNS carrier. Not the EDCM text-domain constructor.
+- [`docs/arity.md`](docs/arity.md) — arity is declared dimensional coupling,
+  not ambient dimension count. Charged oriented couplings plus degree are the
+  three-dimensional structure.
+- [`docs/preregistration-molecular-geometry-from-element-gonols.md`](docs/preregistration-molecular-geometry-from-element-gonols.md) —
+  provisional candidate: Z=1–18 element gonols from atomic structure only, then
+  affixiation of H₂, H₂O, NH₃, CH₄, CO₂ through unpaired valence electrons,
+  declared dimensional couplings, and UCNS Möbius observation. Known chemistry
+  is sealed until after construction.
+
+## Usage
+
+From this directory:
+
+```bash
+PYTHONPATH=".:../ucns/src" python3 -m unittest discover -s tests -q
+```
+
+Do not open `data/sealed_known_molecular_geometry.json` during construction.
+After construction:
+
+```bash
+PYTHONPATH=".:../ucns/src" python3 - <<'PY'
+from epac_comparison import compare_after_construction
+print(compare_after_construction()["standings"])
+PY
+```

research/epac/data/periodic_table_z1_18.json

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+{
+  "schema": "epac.periodic-table-atomic-structure",
+  "version": "v1",
+  "scope": "Z=1-18 ground-state atomic structure for element-gonol construction",
+  "source": "established main-group ground-state electron configurations and typical hydride valences; not a molecular-shape table",
+  "excludes": [
+    "bond-angle",
+    "shape-class",
+    "hybridization-as-shape"
+  ],
+  "elements": [
+    {"Z": 1, "symbol": "H", "period": 1, "group": 1, "electron_configuration": "1s1", "valence_electrons": 1, "typical_valence": 1},
+    {"Z": 2, "symbol": "He", "period": 1, "group": 18, "electron_configuration": "1s2", "valence_electrons": 2, "typical_valence": 0},
+    {"Z": 3, "symbol": "Li", "period": 2, "group": 1, "electron_configuration": "1s2.2s1", "valence_electrons": 1, "typical_valence": 1},
+    {"Z": 4, "symbol": "Be", "period": 2, "group": 2, "electron_configuration": "1s2.2s2", "valence_electrons": 2, "typical_valence": 2},
+    {"Z": 5, "symbol": "B", "period": 2, "group": 13, "electron_configuration": "1s2.2s2.2p1", "valence_electrons": 3, "typical_valence": 3},
+    {"Z": 6, "symbol": "C", "period": 2, "group": 14, "electron_configuration": "1s2.2s2.2p2", "valence_electrons": 4, "typical_valence": 4},
+    {"Z": 7, "symbol": "N", "period": 2, "group": 15, "electron_configuration": "1s2.2s2.2p3", "valence_electrons": 5, "typical_valence": 3},
+    {"Z": 8, "symbol": "O", "period": 2, "group": 16, "electron_configuration": "1s2.2s2.2p4", "valence_electrons": 6, "typical_valence": 2},
+    {"Z": 9, "symbol": "F", "period": 2, "group": 17, "electron_configuration": "1s2.2s2.2p5", "valence_electrons": 7, "typical_valence": 1},
+    {"Z": 10, "symbol": "Ne", "period": 2, "group": 18, "electron_configuration": "1s2.2s2.2p6", "valence_electrons": 8, "typical_valence": 0},
+    {"Z": 11, "symbol": "Na", "period": 3, "group": 1, "electron_configuration": "[Ne].3s1", "valence_electrons": 1, "typical_valence": 1},
+    {"Z": 12, "symbol": "Mg", "period": 3, "group": 2, "electron_configuration": "[Ne].3s2", "valence_electrons": 2, "typical_valence": 2},
+    {"Z": 13, "symbol": "Al", "period": 3, "group": 13, "electron_configuration": "[Ne].3s2.3p1", "valence_electrons": 3, "typical_valence": 3},
+    {"Z": 14, "symbol": "Si", "period": 3, "group": 14, "electron_configuration": "[Ne].3s2.3p2", "valence_electrons": 4, "typical_valence": 4},
+    {"Z": 15, "symbol": "P", "period": 3, "group": 15, "electron_configuration": "[Ne].3s2.3p3", "valence_electrons": 5, "typical_valence": 3},
+    {"Z": 16, "symbol": "S", "period": 3, "group": 16, "electron_configuration": "[Ne].3s2.3p4", "valence_electrons": 6, "typical_valence": 2},
+    {"Z": 17, "symbol": "Cl", "period": 3, "group": 17, "electron_configuration": "[Ne].3s2.3p5", "valence_electrons": 7, "typical_valence": 1},
+    {"Z": 18, "symbol": "Ar", "period": 3, "group": 18, "electron_configuration": "[Ne].3s2.3p6", "valence_electrons": 8, "typical_valence": 0}
+  ]
+}

research/epac/data/sealed_known_molecular_geometry.json

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+{
+  "schema": "epac.sealed-known-molecular-geometry",
+  "version": "v1",
+  "opened_only_after_construction": true,
+  "molecules": {
+    "H2": {"atom_count": 2, "known_shape": "linear"},
+    "H2O": {"atom_count": 3, "known_shape": "bent"},
+    "NH3": {"atom_count": 4, "known_shape": "trigonal-pyramidal"},
+    "CH4": {"atom_count": 5, "known_shape": "tetrahedral"},
+    "CO2": {"atom_count": 3, "known_shape": "linear"}
+  }
+}

research/epac/docs/arity.md

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+# Dimensional arity
+
+Status: **CROSS-DOMAIN-HYPOTHESIS / provisional**. Not org canon.
+
+Dimension tells where. Arity tells what intersects at once. Degree tells how a
+dimension is incident on declared couplings.
+
+```text
+(z, x) ≠ (x, z)
+(x, z) and (y, z) ↛ (x, y, z)   without an explicit proof
+
+every physical instance of x has its own (z, x_i)
+every physical instance of y has its own (z, y_j)
+```
+
+A second atom occurrence is a second instance. `(z, x_0)` does not cover `x_1`.
+`(x_i, z)` does not satisfy `(z, x_i)`. Letters and chemical-symbol
+abbreviations are nomenclature, not physics, and are not these instances.
+
+Precursors: each proton and each neutron is a closed gonol. The nucleus is
+their affixiation. Neutrons couple to protons as `(proton_j, neutron_i)` with
+slot charges `(+1, 0)`. Proton-proton and neutron-neutron are not inferred.
+Hydrogen-1 is one proton and no neutrons.
+
+At atomic scale the hub is that closed nucleus and every electron instance has
+its own `(nucleus, electron_i)` with slot charges `(Z, -1)`. Molecular scale
+does not reopen nucleons or electrons: water remains `(O#2, H#0)` and
+`(O#2, H#1)`.
+
+Degree is required. For ambient `{x,y,z}` with couplings `(z,x)` and `(z,y)`:
+
+```text
+deg(z) = 2 at slot 0
+deg(x) = 1 at slot 1
+deg(y) = 1 at slot 1
+```
+
+That incidence structure is the geometry of two binary couplings sharing `z`.
+It is not a ternary coupling and not `(x,y)`.
+
+Charge state rides on each coupling from the math already present: per-slot
+dimension charges (nuclear `Z` when the axis is an atom) and Möbius `ε` at
+`t=0`. `(z,x)` with charges `(q_z, q_x, ε)` is not `(x,z)` with
+`(q_x, q_z, ε)`. The three-dimensional structure **is** that combination —
+oriented couplings, each arity's charge state, and degree. Two charged
+arity-2 couplings on a degree-2 hub already occupy three participating axes.
+It still does not declare `(x,y,z)`.
+
+Representing that 3 takes 4 dimensions: a quaternion
+`(ε, q_z, q_x, q_y)`. The extra coordinate is the scalar, Möbius `ε`, already
+in the math. It is not a fourth ambient axis, not Minkowski time, and not a
+Hamilton-product proof of `(x,y,z)`. `ij = k` does not install a coupling.
+Helium's nucleus plus two electrons is one local 3 in 4-representation;
+the letters `H` and `e` are not those axes. A single binary (H₂, hydrogen
+atom) is not a 3 and has no quaternion.
+
+Construction is `epac.public_gonol` on the UCNS Public Gonol carrier, not
+`edcm.gonol`.
+
+Overlap of members is not a proof. Forbidden inference rules include
+`overlap-closure`, `permutation-identity`, and `ambient-power-set`.
+
+See `epac_dimensional_arity.py`. After construction, `epac_comparison.py` reads
+that 3-structure against sealed known chemistry. Sealed shape names stay out
+of construction.

research/epac/docs/preregistration-molecular-geometry-from-element-gonols.md

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+# Preregistration: molecular geometry from element gonols
+
+- Status: **CROSS-DOMAIN-HYPOTHESIS / provisional research candidate**
+- Owner of record: `The-Interdependency/stack` → `research/epac/`
+- Constructor: `epac.public_gonol` on the pinned UCNS Public Gonol carrier.
+  Not `edcm.gonol`.
+- Comparison policy is frozen **before** construction. Known molecular-shape
+  labels are sealed and may be opened only by the comparison step.
+
+## Domain claims
+
+| Surface form | Term id | Claiming domain | Claimed sense | Excluded |
+|---|---|---|---|---|
+| element gonol | `epac.periodic.element_gonol` | epac candidate | closed gonol of one periodic-table element carrying Z, ground-state electron configuration, and typical main-group valence | molecular shape, bond angle, hybridization |
+| valence arity | `epac.periodic.typical_valence` | epac candidate | main-group hydride valence from the periodic table (group-derived) | VSEPR domain count as a shape rule |
+| affixiation | `metapat.affixiation_harmonics.affixiation` | METAPAT | identity-preserving higher-order relation | UCNS topology selection |
+| UCNS coupling | `ucns.native-mobius-root-loop` | UCNS | established 360° frame flip / 720° restore | invented 3-space arrangement |
+| molecular gonol | `epac.molecular.affixiated_whole` | epac candidate | closed recursive gonol of element-gonol participants | known chemistry shape names |
+| predicted geometry | `epac.molecular.construction_invariants` | epac candidate | atom count, center valence, slot occupancy, Möbius frame sequence | sealed comparison labels |
+
+Collision check: physics/chemistry own empirical molecular shapes. This candidate
+does not claim those senses during construction. Resolution: **clear** (separate
+scopes) until comparison.
+
+## Frozen pipeline
+
+```text
+proton gonols (charge +1) and neutron gonols (charge 0)
+  -> nucleus = affixiation of those nucleons; (proton_j, neutron_i)
+  -> every electron instance: (nucleus, electron_i) with charges (Z, -1)
+  -> close that atomic 3-structure inside the element gonol
+  -> unpaired-valence attachment sites
+  -> declared oriented (center, ligand_i) couplings with per-slot Z and Möbius ε
+  -> molecular three-dimensional structure = those atom-instance couplings + charge states + degree
+  -> each local 3 represented in 4 quaternion components (scalar ε plus the three axis charges)
+  -> molecular Public Gonol (closed atoms remain atomic participants)
+  -> construction invariants
+  -> (only then) compare to sealed known chemistry
+```
+
+## Inputs allowed in construction
+
+- atomic number Z, default isotope A
+- each proton instance and each neutron instance of that isotope (counts must match Z and A−Z)
+- every electron: n, l, m_l, m_s, shell, subshell
+- hydrogenic angular identity Y_l^m, radial node count n-l-1
+- Slater atomic Z_eff and hydrogenic Rydberg energy -Z_eff²/n²
+- unpaired valence electrons from Hund filling
+- atomic s→p promotion in the same n when more unpaired sites are required
+- caller-supplied stoichiometric formula (element counts only)
+
+## Inputs forbidden in construction
+
+- bond angles
+- VSEPR shape names
+- hybridization labels used as shape
+- any sealed comparison filename contents
+
+## UCNS coupling candidate
+
+Only the implemented Möbius root loop is applied:
+
+```text
+(t, ε) ~ (t + n, (-1)^n ε)
+t = 0, 1, 2
+```
+
+Public Gonol positions, when supplied, are identity coordinates. Position
+operations remain `hmmm`. No spherical equal-spacing rule is added.
+
+## Molecules in this run
+
+`H2`, `H2O`, `NH3`, `CH4`, `CO2`
+
+## Comparison policy (frozen)
+
+Opened only after molecular gonols exist:
+
+1. Construction source and receipts must not contain the sealed shape labels.
+2. Record construction invariants per formula.
+3. Open `data/sealed_known_molecular_geometry.json`.
+4. Ask whether the constructed three-dimensional structure distinguishes
+   formulas that chemistry distinguishes by shape.
+5. Compare four signatures: charged oriented couplings plus degree (the
+   3-structure already in the math); arity/degree topology without charge;
+   UCNS Möbius coupling; atomic unpaired (l, m_l) plus ligand shell content;
+   against a matched-information control of formula symbols only.
+   Do not import sealed shape names into construction.
+
+## Terminal standings for the hmmm question
+
+The question: does gonol geometry predict molecular shape, or merely reproduce
+information already present in the inputs?
+
+- `SURVIVED` as prediction — only if the charged 3-structure is invariant
+  inside each sealed shape class, distinguishes different sealed classes, and
+  is not the matched-information control.
+- `FALSIFIED` as prediction — if the 3-structure splits a sealed class, or
+  collapses classes chemistry splits, or if distinguishing power is already
+  present in valence+stoichiometry.
+- `UNRESOLVED` — if the readout is incomplete.
+- None of these standings select canon.
+
+## hmmm
+
+- Public Gonol function operations beyond carrier identity
+- whether a later UCNS 3-space coupling exists that is not VSEPR imported
+- expansion of the element table beyond Z=1–18
+- epac still has no canonical source repository