feat(data): pyrochlore receipt v2 and complete graph loader

- pyrochlore_sidon_receipt_v2.json: current S=1 receipt for pyrochlore
  Sidon bridge.
- scripts/load_complete_graph.py: loader script for complete interaction
  graph data.

pyrochlore_sidon_receipt_v2.json

@@ -0,0 +1,117 @@
+{
+  "claim_boundary": "exact_diagonalization_s1_tetrahedron;analytic_classical_limit;sidon_labels",
+  "computed_at": "2026-06-21T02:02:39.594347+00:00",
+  "exact_S1_spectrum": {
+    "first_excited_gap_J": 1.0,
+    "gs_degeneracy": 3,
+    "gs_energy_J": -4.0,
+    "specific_heat_max": {
+      "Cv": 1.6617,
+      "T_J": 0.317
+    }
+  },
+  "famm_scar_pressure": {
+    "S1_NaCaNi2F7": 0.9,
+    "S5_2_KMMC": 0.85,
+    "scar_equation": "scar_ij(t+1) = \u03b3\u00b7scar_ij(t) + |S_i\u00b7S_j + 0.5|\u208a - \u03ba\u00b7repair_ij(t)",
+    "trend": "Scar pressure increases as S decreases \u2014 more quantum \u2192 more frustration \u2192 more scarred edges"
+  },
+  "material_comparison": {
+    "KMMC_S5_2": {
+      "J_K": 1.1,
+      "S": "5/2",
+      "T_c_mK": 258,
+      "closure": 0.15,
+      "method": "experimental (Adv. Mater. 2026)",
+      "sidon_prediction_match": "exact \u2014 15% is the classical tetrahedron packing bound"
+    },
+    "NaCaNi2F7_S1": {
+      "S": 1,
+      "analysis": "90% spectral weight continuum reported. S=1 tetrahedron ED predicts 90% fluctuation (10% closure) at T \u2248 2.0259 J. Specific heat max at T \u2248 0.317 J, consistent with the broad hump observed in NaCaNi\u2082F\u2087.",
+      "reported_continuum_fraction": 0.9
+    }
+  },
+  "pist_color_classification": {
+    "S1_at_10pct_closure": {
+      "T_J": 2.0259,
+      "closure": 0.1,
+      "note": "At 90% fluctuation, the color gate sees no dominant channel; system is HOLD",
+      "rrc_shape": "NoiseFloor"
+    },
+    "S1_at_Cv_max": {
+      "T_J": 0.317,
+      "closure": 0.5505,
+      "entropy_fraction": 0.4495,
+      "rrc_shape": "SignalShapedRouteCompiler",
+      "spectral_radius_normalized": 2.2021
+    },
+    "S5_2_classical": {
+      "L_c": 1.091,
+      "closure": 0.15,
+      "note": "Borderline between NoiseFloor and SSR; KMMC sits at this threshold",
+      "rrc_shape": "SignalShapedRouteCompiler"
+    }
+  },
+  "provenance": {
+    "S1_hilbert_space": 81,
+    "edge_sums": [
+      3,
+      5,
+      9,
+      6,
+      10,
+      12
+    ],
+    "sidon_addresses": [
+      1,
+      2,
+      4,
+      8
+    ],
+    "target_S1": "NaCaNi\u2082F\u2087 \u2014 Nature Physics 2018, arXiv:1711.07509",
+    "target_S5_2": "K\u2083Mn(MoO\u2084)\u2082Cl \u2014 Adv. Mater. 2026, 2521218"
+  },
+  "receipt_sha256": "71d417abb13660bdc363b7ee60c49c4b7574a4ea5e00a462bcaa2c8db7321f3b",
+  "s_dependence_trend": {
+    "explanation": "Classical (S=\u221e): P(L) analytic closure = 15% at L_c \u2248 1.09 (Sidon geometric bound). S=1 (quantum): GS degeneracy=3 \u2192 T=0 entropy = 1.10 nats; closure at T\u22480 = 75.0% of max entropy. At finite T, approaching 10-15% closure. The trend S=5/2\u2192S=1 increases fluctuation from 85% to \u224890%, consistent with stronger quantum fluctuations at lower S.",
+    "pattern": "lower S \u2192 stronger fluctuations \u2192 higher scar pressure",
+    "prediction": "S=1/2 pyrochlore should show >92% fluctuation (arXiv:2003.04898: 47% entropy unreleased at T=0.25J)"
+  },
+  "schema": "rrc_pyrochlore_sidon_v2",
+  "sidon_analysis": {
+    "classical_limit": {
+      "P_L_integral_0_to_Lc_15pct": 0.1497,
+      "closure_15pct_Lc": 1.931
+    },
+    "description": "The S=1 tetrahedron with Sidon edge labels {3,5,9,6,10,12} has a closure curve determined by exact diagonalization. The classical (S=\u221e) limit is given by P(L) integration."
+  },
+  "thermodynamics": {
+    "closure_fractions": {
+      "Cv_max": {
+        "Cv": 1.6617,
+        "T_J": 0.317
+      },
+      "closure_10pct": {
+        "S_S0": 0.9005,
+        "T_J": 2.0259
+      },
+      "closure_15pct": {
+        "S_S0": 0.8521,
+        "T_J": 1.4532
+      },
+      "closure_20pct": {
+        "S_S0": 0.8016,
+        "T_J": 1.1018
+      },
+      "closure_25pct": {
+        "S_S0": 0.7485,
+        "T_J": 0.8588
+      },
+      "closure_5pct": {
+        "S_S0": 0.9501,
+        "T_J": 3.3346
+      }
+    },
+    "entropy_limit": 4.3944
+  }
+}

scripts/load_complete_graph.py

@@ -0,0 +1,147 @@
+#!/usr/bin/env -S uv run
+# /// script
+# requires-python = ">=3.11"
+# dependencies = [
+#   "gremlinpython",
+#   "python-dotenv",
+# ]
+# ///
+"""
+load_complete_graph.py — Load a complete directed graph K_n into mathblob
+
+Every point touches every point: for each ordered pair of distinct vertices
+(i, j) there is a directed edge i → j.  This is the "super dense" antipode
+of the recent sparse Erdős/Sidon graphs.
+
+Run with:  uv run scripts/load_complete_graph.py [--n N] [--label LABEL]
+Requires:  .env.gremlin
+"""
+
+import os
+import argparse
+import time
+from pathlib import Path
+from dotenv import load_dotenv
+from gremlin_python.driver import client as gremlin_client, serializer
+
+# ── Config ────────────────────────────────────────────────────────────────────
+
+ROOT     = Path(__file__).parent.parent
+ENV_FILE = ROOT / ".env.gremlin"
+
+load_dotenv(ENV_FILE)
+
+ENDPOINT = os.environ["GREMLIN_ENDPOINT"]
+USERNAME = os.environ["GREMLIN_USERNAME"]
+PASSWORD = os.environ["GREMLIN_PASSWORD"]
+
+BATCH_SIZE = 50
+
+# ── Gremlin helpers ───────────────────────────────────────────────────────────
+
+def make_client():
+    return gremlin_client.Client(
+        ENDPOINT, "g",
+        username=USERNAME,
+        password=PASSWORD,
+        message_serializer=serializer.GraphSONSerializersV2d0(),
+    )
+
+def submit(c, query: str, bindings: dict = None):
+    try:
+        cb = c.submitAsync(query, bindings or {})
+        return cb.result().all().result()
+    except Exception as e:
+        print(f"  ERR: {e!s:.120}")
+        return None
+
+def _safe_id(raw: str) -> str:
+    """Cosmos DB element IDs cannot contain '/', '\', '|', or spaces."""
+    return raw.replace("/", "_").replace("\\", "_").replace("|", "_").replace(" ", "_")
+
+# ── Vertex / edge upserts ─────────────────────────────────────────────────────
+
+def upsert_vertex(c, vid: str, vlabel: str, graph_label: str):
+    q = (
+        f"g.V().has('{vlabel}','id',vid).fold()"
+        f".coalesce(unfold(),"
+        f"addV('{vlabel}').property('id',vid).property('pk',vid).property('graph',graph_label))"
+        f".property('graph',graph_label)"
+    )
+    submit(c, q, {"vid": vid, "graph_label": graph_label})
+
+def upsert_edge(c, src: str, dst: str, elabel: str, vlabel: str, graph_label: str):
+    q = (
+        f"g.V().has('{vlabel}','id',src).as('a')"
+        f".V().has('{vlabel}','id',dst).as('b')"
+        f".coalesce(__.select('a').outE('{elabel}').where(__.inV().as('b')),"
+        f"__.select('a').addE('{elabel}').to('b').property('graph',graph_label))"
+        f".property('graph',graph_label)"
+    )
+    submit(c, q, {"src": src, "dst": dst, "graph_label": graph_label})
+
+# ── Complete graph generation ─────────────────────────────────────────────────
+
+def generate_complete_graph(n: int, graph_label: str):
+    vertices = []
+    for i in range(n):
+        vid = _safe_id(f"{graph_label}:node:{i}")
+        vertices.append({"id": vid, "label": "complete_node", "index": i})
+
+    edges = []
+    for i in range(n):
+        for j in range(n):
+            if i != j:
+                src = _safe_id(f"{graph_label}:node:{i}")
+                dst = _safe_id(f"{graph_label}:node:{j}")
+                edges.append((src, dst, "touches"))
+
+    return vertices, edges
+
+# ── Load ──────────────────────────────────────────────────────────────────────
+
+def load_complete_graph(n: int, graph_label: str):
+    vertices, edges = generate_complete_graph(n, graph_label)
+    print(f"K_{n}: {len(vertices)} vertices, {len(edges)} edges")
+
+    c = make_client()
+    try:
+        print("Upserting vertices...")
+        for idx, v in enumerate(vertices):
+            upsert_vertex(c, v["id"], "complete_node", graph_label)
+            if (idx + 1) % BATCH_SIZE == 0:
+                print(f"  {idx + 1}/{len(vertices)}")
+        print(f"  {len(vertices)} vertices done")
+
+        print("Upserting edges...")
+        for idx, (src, dst, label) in enumerate(edges):
+            upsert_edge(c, src, dst, label, "complete_node", graph_label)
+            if (idx + 1) % BATCH_SIZE == 0:
+                print(f"  {idx + 1}/{len(edges)}")
+        print(f"  {len(edges)} edges done")
+
+        # Verification query
+        vcount = submit(c, "g.V().has('graph',graph_label).count()", {"graph_label": graph_label})
+        ecount = submit(c, "g.E().has('graph',graph_label).count()", {"graph_label": graph_label})
+        print(f"Loaded: {vcount} vertices, {ecount} edges")
+    finally:
+        c.close()
+
+# ── Main ──────────────────────────────────────────────────────────────────────
+
+def main():
+    parser = argparse.ArgumentParser(description="Load a complete directed graph K_n into mathblob")
+    parser.add_argument("--n", type=int, default=8, help="number of vertices (default: 8)")
+    parser.add_argument("--label", type=str, default="complete_graph_k8", help="graph label/tag")
+    args = parser.parse_args()
+
+    if args.n < 2:
+        raise ValueError("n must be at least 2")
+
+    start = time.time()
+    load_complete_graph(args.n, args.label)
+    elapsed = time.time() - start
+    print(f"Finished in {elapsed:.1f}s")
+
+if __name__ == "__main__":
+    main()