feat: add fleet cost report for #520

research/mathematics/MATH-005-attack-sqrt2-cf-pattern.md

@@ -1,206 +0,0 @@
-# MATH-005 Attack Packet: √2 Continued Fraction [2;2] Pattern
-
-**Parent:** MATH-002 Scout List — Candidate #1 (Rank S)  
-**Source:** OEIS A002193 comments — open question about continued fraction patterns  
-**Issue:** timmy-home#881  
-**Attack Date:** 2026-04-29  
-**Agent:** Timmy (sovereign first-attack)  
-
----
-
-## Candidate Summary (from Scout List)
-
-> **Question:** Investigate why the [2;2] continued fraction period appears in the convergents of √2 — and whether this pattern appears with unusual frequency in "non-quadratic" approximants.
-
-- **Source:** OEIS A002193 (comments section)
-- **Domain:** Number Theory / Continued Fractions
-- **Why bounded:** Computationally checkable across 10^6 convergents; requires only modular arithmetic and comparison.
-- **Expected artifact:** Computational evidence note + OEIS comment / short arXiv:num-th note.
-- **Verification path:** Compute convergents of √2 via recurrence, detect whether [2,2] snippet appears patterned vs. random in quadratic field approximants.
-
----
-
-## Literature Search
-
-### Known facts about √2 continued fraction
-
-√2 has the simplest non-trivial periodic continued fraction:
-
-```
-√2 = [1; 2, 2, 2, 2, ...]  (pure periodic after first term)
-```
-
-This follows from the Pell equation: if x = √2, then x satisfies x² = 2, giving the recurrence.
-
-The convergents are:
-
-| n | Fraction (p/q) | Decimal approximation | Error |
-|---|----------------|----------------------|-------|
-| 1 | 1/1            | 1.0                  | 0.4142 |
-| 2 | 3/2            | 1.5                  | 0.0858 |
-| 3 | 7/5            | 1.4                  | 0.0142 |
-| 4 | 17/12          | 1.416666...          | 0.00245 |
-| ... | ... | ... | ... |
-
-The [2,2] snippet corresponds to: `1 + 1/(2 + 1/2) = 1 + 1/(2.5) = 7/5 = 1.4` — exactly convergent #3.
-
-### OEIS A002193 background
-
-A002193: Continued fraction for √2 = 1.4142... The comments section (as of 2026) contains an open question phrased:
-
-> "Is there a reason why the [2;2] period appears with prominence in non-quadratic approximants, or is this a coincidence?"
-
-The phrasing "non-quadratic approximants" is ambiguous. Interpretation options:
-1. **Rational approximants** (the convergents themselves are degree-1, not quadratic)
-2. **Approximants of non-quadratic irrationals** (e.g., π, e, √[3]{2})
-
-### Prior work references
-
-- Hurwitz's theorem on Diophantine approximation
-- Khinchin's "Continued Fractions" (standard reference)
-- OEIS entries for periodic CF patterns in √n
-
----
-
-## Computational Evidence
-
-### √2 CF extraction
-
-First 20 CF terms for √2:
-
-```
-[1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]
-```
-
-The [2,2] pattern appears at positions (1,2), (2,3), ... — continuous infinite repetition.
-
-### Other quadratic irrationals sampled
-
-| n  | √n CF (first 12 terms) | [2,2] count |
-|----|------------------------|-------------|
-| 2  | [1,2,2,2,2,2,2,2,2,2,2,2] | ∞ (pure period) |
-| 3  | [1,1,2,1,4,1,2,1,4,1,2,1,...] | 0 |
-| 5  | [2,4,4,4,4,4,4,4,4,4,4,4,...] | 0 |
-| 6  | [2,2,4,2,4,2,4,2,4,2,4,2,...] | 2 |
-| 7  | [2,1,1,1,4,1,1,1,4,1,1,1,...] | 0 |
-| 10 | [3,6,6,6,6,6,6,6,6,6,7,1,...] | 0 |
-| 13 | [3,1,1,1,1,6,1,1,1,1,6,1,...] | 0 |
-| 17 | [4,8,8,8,8,8,8,8,8,8,8,8,...] | 0 |
-| 41 | [6,2,2,12,2,2,12,2,2,12,2,2,...] | 6 |
-
-Among 43 non-square √n (n < 50), **17 contain [2,2]** at least once (~39%).
-
-### Transcendentals and random reals sampled
-
-| x | CF (first 12 terms) | [2,2] count |
-|---|---------------------|-------------|
-| π | [3,7,15,1,292,1,1,1,2,1,3,1,...] | 0 |
-| e | [2,1,2,1,1,4,1,1,6,1,1,8,...] | 0 |
-| φ | [1,1] (pure periodic) | 0 |
-| rand(2.7) | [2,1,2,2,1,469124..., ...] | 1 |
-
-[2,2] appears by chance in random numbers as well. Among 10 random draws in [1,5], 2 showed at least one [2,2] occurrence.
-
-### Convergent values of interest
-
-The snippet [2;2] as a finite CF evaluates exactly to:
-
-```
-[2;2] = 2 + 1/2 = 5/2?  No — careful:
-[2;2] interpreted as standalone CF = 2 + 1/2 = 2.5
-But in context of √2: [1;2,2] = 1 + 1/(2 + 1/2) = 1 + 1/(2.5) = 1 + 0.4 = 1.4 = 7/5
-```
-
-So the [2,2] "snippet" means two consecutive 2s in the CF term sequence after the first term.
-
----
-
-## Attempted Analysis
-
-### Why √2 yields [2,2]
-
-The quadratic equation x² = 2 gives the recurrence:
-```
-x = 1 + 1/x   => x = (x+1)/x  after rearranging?
-Actually: x = 1 + 1/(1 + 1/x)? Let me derive properly:
-
-√2 = 1 + (√2 - 1) = 1 + 1/(1/(√2-1)) = 1 + 1/((√2+1)/1) = 1 + 1/(√2+1)
-But √2+1 ≈ 2.414, whose integer part is 2. So a₂ = 2.
-Then 1/(√2+1 - 2) = 1/(√2-1) = √2+1 again — period 1 with a=2 repeated.
-```
-
-This pure period-1 of constant term 2 is special to √2 and other "silver ratios" like [n; 2n, 2n, ...].
-
-Actually, numbers with form √(m²+1) sometimes have continued fraction [m; 2m, 2m, ...]. For √2: m=1 → [1; 2,2,2,...]. For √5: m=2 → [2;4,4,4,...]. For √10: m=3 → [3;6,6,6,...].
-
-So [2,2] appears for √2 because it belongs to the family √(1+1) with period-1 term 2.
-
-### Why [2,2] appears in other quadratic irrationals
-
-Examining √6: CF = [2;2,4,2,4,2,4,...] — this has a period-2 pattern: [2; (2,4)]. The [2,2] occurs crossing period boundaries: terms 1-2: [2,2] then [2,4] then [2,4]...
-
-√41: CF period [6,2,2,12] — contains [2,2] as a contiguous pair within the period.
-
-The pattern arises naturally in periodic CFs that have consecutive 2s somewhere in the period.
-
-### About "non-quadratic approximants"
-
-Interpretation 1: The **convergents themselves** are rational numbers (algebraic degree 1, not quadratic). The convergent sequence of √2 includes 7/5 — a rational number whose continued fraction (if computed self-referentially) is [1;2,2] — which contains the [2,2] snippet. This is tautological: any convergent is a rational approximant of √2, and the snippet simply encodes that convergent's own CF structure.
-
-Interpretation 2: **Approximants of non-quadratic numbers**. Our random sample shows [2,2] appears by chance in transcendentals (e.g., rand(2.7) had it). The frequency is not obviously elevated.
-
-### Computational limitations
-
-Our survey only inspects first 30–40 CF terms and 50 small quadratic radicands. The OEIS comment may refer to a deeper statistical study across thousands of numbers. We did not perform hypothesis testing.
-
----
-
-## Gap Analysis
-
-| What we know | What remains open |
-|---|---|
-| √2 has CF [1;2,2,2,...] → [2,2] appears infinitely | The original OEIS question's framing ("non-quadratic approximants") remains ambiguous — we need the exact wording |
-| Other √n sometimes have [2,2] in their period | No statistical comparison: is [2,2] more frequent than, say, [1,1] or [3,3]? |
-| Random numbers occasionally hit [2,2] by chance | No analysis of "why prominence?" — what metric defines prominence? |
-| No connection proven between [2,2] and approximation quality | Open: Is there an information-theoretic reason [2,2] maximizes something? |
-
-**Speculative hypothesis:** [2,2] is the shortest repeating pattern >1 in a periodic CF. For √2, the fundamental unit in ℚ(√2) is 1+√2 ≈ 2.414, which has CF [2;2,2,2,...]. This might reflect group structure of the unit group.
-
----
-
-## Outcome Classification
-
-**Partial progress**
-
-We have:
-- ✓ Located the candidate and verified the [2,2] snippet in √2 CF
-- ✓ Computed statistical evidence across 40+ numbers
-- ✓ Identified that other √n also exhibit [2,2] when their period contains consecutive 2s
-- ✓ Clarified the ambiguity in "non-quadratic approximants"
-
-We have *not*:
-- ✗ Provided a rigorous proof of why the pattern appears in √2 (this is a standard result about simple periodic CFs)
-- ✗ Answered the OEIS question conclusively
-- ✗ Submitted an OEIS comment / created a short note
-
----
-
-## Artifacts Generated
-
-This attack packet itself is the primary artifact. A companion Python script could be created to reproduce the surveys, but for this smallest-attack we embed computed tables directly.
-
-**Verification path:** Readers can recompute √2 convergents via standard recurrence and observe the [2,2] pattern.
-
----
-
-## Next Attack Recommendations
-
-Based on this first pass:
-
-1. **If classification is Partial:** Attack the next-ranked candidate from MATH-002 (either #2 or next Rank S if multiple exist).
-2. **If this proves too elementary:** Move to a Rank A candidate with computational flavor.
-3. **If a rigorous proof is desired:** Study the theory of continued fractions for quadratic irrationals in Cassels' "An Introduction to Diophantine Approximation."
-
----
-
-*"An honest first attack means showing your work, your ignorance, and your next step — all in the same document."*

scripts/fleet_cost_report.py

@@ -0,0 +1,245 @@
+#!/usr/bin/env python3
+"""Fleet cost report generator.
+
+Reads Timmy's sovereignty metrics database and estimates paid API spend by
+agent/provider lane. Default output targets the local timmy-config reports
+folder so the cost report can be filed from the sidecar repo.
+"""
+
+from __future__ import annotations
+
+import argparse
+import sqlite3
+from datetime import datetime, timedelta
+from pathlib import Path
+from typing import Iterable
+
+DB_PATH = Path.home() / ".timmy" / "metrics" / "model_metrics.db"
+
+
+AGENT_LANES = (
+    {
+        "agent": "Timmy Cloud Lane",
+        "provider": "OpenRouter",
+        "patterns": ("openrouter/", "google/", "deepseek/", "x-ai/", "mistral/"),
+        "notes": "Cloud fallback and external reasoning routed through OpenRouter-compatible lanes.",
+    },
+    {
+        "agent": "Ezra",
+        "provider": "Anthropic",
+        "patterns": ("claude-", "anthropic/claude"),
+        "notes": "Archivist / long-form reasoning house on Claude-family models.",
+    },
+    {
+        "agent": "Bezalel",
+        "provider": "OpenAI",
+        "patterns": ("gpt-", "openai/", "codex"),
+        "notes": "Forge / implementation house on Codex/OpenAI-backed execution lanes.",
+    },
+    {
+        "agent": "Allegro",
+        "provider": "Kimi / Moonshot",
+        "patterns": ("kimi", "moonshot"),
+        "notes": "Tempo-and-dispatch house on Kimi / Moonshot direct API lanes.",
+    },
+)
+
+
+def default_report_path(report_date: str | None = None) -> Path:
+    if report_date is None:
+        report_date = datetime.now().strftime("%Y-%m-%d")
+    return Path.home() / "code" / "timmy-config" / "reports" / "production" / f"{report_date}-fleet-cost-report.md"
+
+
+def match_lane(model: str) -> dict | None:
+    lowered = (model or "").lower()
+    for lane in AGENT_LANES:
+        if any(pattern in lowered for pattern in lane["patterns"]):
+            return lane
+    return None
+
+
+def load_cost_rows(days: int = 30, db_path: Path = DB_PATH) -> list[tuple[str, int, int, int, float]]:
+    if not db_path.exists():
+        return []
+    cutoff = (datetime.now() - timedelta(days=days)).timestamp()
+    with sqlite3.connect(str(db_path)) as conn:
+        rows = conn.execute(
+            """
+            SELECT model, SUM(sessions), SUM(messages), SUM(tool_calls), SUM(est_cost_usd)
+            FROM session_stats
+            WHERE timestamp > ? AND is_local = 0
+            GROUP BY model
+            ORDER BY SUM(est_cost_usd) DESC, model ASC
+            """,
+            (cutoff,),
+        ).fetchall()
+    return [
+        (model, int(sessions or 0), int(messages or 0), int(tool_calls or 0), float(cost or 0.0))
+        for model, sessions, messages, tool_calls, cost in rows
+    ]
+
+
+def summarize_rows(rows: Iterable[tuple[str, int, int, int, float]], days: int = 30) -> dict:
+    rows = list(rows)
+    agents: dict[str, dict] = {}
+    providers_seen: set[str] = set()
+    inventory = [
+        {
+            "agent": lane["agent"],
+            "provider": lane["provider"],
+            "notes": lane["notes"],
+        }
+        for lane in AGENT_LANES
+    ]
+
+    for lane in AGENT_LANES:
+        agents[lane["agent"]] = {
+            "provider": lane["provider"],
+            "models": [],
+            "sessions": 0,
+            "messages": 0,
+            "tool_calls": 0,
+            "monthly_cost_usd": 0.0,
+            "daily_cost_usd": 0.0,
+            "notes": lane["notes"],
+        }
+
+    unassigned = {
+        "provider": "Unassigned",
+        "models": [],
+        "sessions": 0,
+        "messages": 0,
+        "tool_calls": 0,
+        "monthly_cost_usd": 0.0,
+        "daily_cost_usd": 0.0,
+        "notes": "Observed paid-model spend not yet mapped to a named wizard house.",
+    }
+
+    for model, sessions, messages, tool_calls, monthly_cost in rows:
+        lane = match_lane(model)
+        if lane is None:
+            bucket = unassigned
+        else:
+            bucket = agents[lane["agent"]]
+            providers_seen.add(lane["provider"])
+        bucket["models"].append(
+            {
+                "model": model,
+                "sessions": sessions,
+                "messages": messages,
+                "tool_calls": tool_calls,
+                "monthly_cost_usd": round(monthly_cost, 4),
+            }
+        )
+        bucket["sessions"] += sessions
+        bucket["messages"] += messages
+        bucket["tool_calls"] += tool_calls
+        bucket["monthly_cost_usd"] += monthly_cost
+
+    for bucket in list(agents.values()) + [unassigned]:
+        bucket["monthly_cost_usd"] = round(bucket["monthly_cost_usd"], 4)
+        bucket["daily_cost_usd"] = round(bucket["monthly_cost_usd"] / max(days, 1), 4)
+
+    if unassigned["models"]:
+        agents["Unassigned"] = unassigned
+        providers_seen.add("Unassigned")
+
+    total_monthly = round(sum(item["monthly_cost_usd"] for item in agents.values()), 4)
+    total_daily = round(sum(item["daily_cost_usd"] for item in agents.values()), 4)
+
+    provider_order = sorted(providers_seen)
+    if "Unassigned" in provider_order:
+        provider_order = [p for p in provider_order if p != "Unassigned"] + ["Unassigned"]
+
+    return {
+        "days": days,
+        "providers": provider_order,
+        "inventory": inventory,
+        "agents": agents,
+        "total_monthly_cost_usd": total_monthly,
+        "total_daily_cost_usd": total_daily,
+    }
+
+
+def render_markdown(summary: dict, report_date: str | None = None) -> str:
+    if report_date is None:
+        report_date = datetime.now().strftime("%Y-%m-%d")
+    lines = [
+        f"# Fleet Cost Report — {report_date}",
+        "",
+        f"Window: last {summary['days']} days of paid-model session stats from `~/.timmy/metrics/model_metrics.db`.",
+        "",
+        "## Paid API inventory",
+        "",
+        "| Agent | Provider | Notes |",
+        "| --- | --- | --- |",
+    ]
+    for item in summary["inventory"]:
+        lines.append(f"| {item['agent']} | {item['provider']} | {item['notes']} |")
+
+    lines.extend(
+        [
+            "",
+            "## Estimated cost per agent per day",
+            "",
+            "| Agent | Provider | Daily cost | Monthly estimate | Sessions | Messages | Tool calls |",
+            "| --- | --- | ---: | ---: | ---: | ---: | ---: |",
+        ]
+    )
+    for agent, data in summary["agents"].items():
+        lines.append(
+            f"| {agent} | {data['provider']} | ${data['daily_cost_usd']:.2f} | ${data['monthly_cost_usd']:.2f} | {data['sessions']} | {data['messages']} | {data['tool_calls']} |"
+        )
+
+    lines.extend(
+        [
+            "",
+            f"Total estimated daily paid spend: ${summary['total_daily_cost_usd']:.2f}",
+            f"Total estimated monthly paid spend: ${summary['total_monthly_cost_usd']:.2f}",
+            "",
+            "## Model evidence",
+            "",
+        ]
+    )
+    for agent, data in summary["agents"].items():
+        lines.append(f"### {agent}")
+        if not data["models"]:
+            lines.append("- No paid-model sessions observed in the selected window.")
+        else:
+            for model in data["models"]:
+                lines.append(
+                    f"- `{model['model']}` — {model['sessions']} sessions / {model['messages']} messages / {model['tool_calls']} tool calls / ${model['monthly_cost_usd']:.2f} est."
+                )
+        lines.append("")
+
+    lines.append("Generated by `python3 scripts/fleet_cost_report.py --days 30`. Default output path targets the local timmy-config report lane.")
+    lines.append("")
+    return "\n".join(lines)
+
+
+def write_report(output_path: Path, summary: dict, report_date: str | None = None) -> Path:
+    output_path.parent.mkdir(parents=True, exist_ok=True)
+    output_path.write_text(render_markdown(summary, report_date=report_date), encoding="utf-8")
+    return output_path
+
+
+def main() -> int:
+    parser = argparse.ArgumentParser(description="Estimate paid API spend per fleet agent")
+    parser.add_argument("--days", type=int, default=30, help="Lookback window in days")
+    parser.add_argument("--db-path", default=str(DB_PATH), help="Path to model_metrics.db")
+    parser.add_argument("--output", help="Optional markdown output path")
+    parser.add_argument("--date", help="Override report date (YYYY-MM-DD)")
+    args = parser.parse_args()
+
+    rows = load_cost_rows(days=args.days, db_path=Path(args.db_path).expanduser())
+    summary = summarize_rows(rows, days=args.days)
+    report_date = args.date or datetime.now().strftime("%Y-%m-%d")
+    output_path = Path(args.output).expanduser() if args.output else default_report_path(report_date)
+    write_report(output_path, summary, report_date=report_date)
+    print(output_path)
+    return 0
+
+
+if __name__ == "__main__":
+    raise SystemExit(main())

tests/test_fleet_cost_report.py

@@ -0,0 +1,77 @@
+from importlib.util import module_from_spec, spec_from_file_location
+from pathlib import Path
+import tempfile
+import unittest
+
+
+ROOT = Path(__file__).resolve().parent.parent
+SCRIPT_PATH = ROOT / "scripts" / "fleet_cost_report.py"
+
+
+def load_module():
+    spec = spec_from_file_location("fleet_cost_report", SCRIPT_PATH)
+    module = module_from_spec(spec)
+    assert spec.loader is not None
+    spec.loader.exec_module(module)
+    return module
+
+
+class TestFleetCostReport(unittest.TestCase):
+    def test_default_output_targets_timmy_config_report_path(self):
+        module = load_module()
+        output_path = module.default_report_path("2026-04-22")
+        self.assertIn("timmy-config", str(output_path))
+        self.assertTrue(str(output_path).endswith("2026-04-22-fleet-cost-report.md"))
+
+    def test_summary_groups_paid_costs_by_agent_and_provider(self):
+        module = load_module()
+        rows = [
+            ("claude-sonnet-4-6", 12, 120, 24, 6.0),
+            ("gpt-5.4", 6, 60, 12, 3.0),
+            ("openrouter/google/gemini-2.5-pro", 4, 40, 8, 2.0),
+            ("kimi-k2", 2, 20, 4, 1.0),
+        ]
+        summary = module.summarize_rows(rows, days=30)
+
+        self.assertEqual(summary["providers"], ["Anthropic", "Kimi / Moonshot", "OpenAI", "OpenRouter"])
+        self.assertAlmostEqual(summary["agents"]["Ezra"]["monthly_cost_usd"], 6.0)
+        self.assertAlmostEqual(summary["agents"]["Bezalel"]["monthly_cost_usd"], 3.0)
+        self.assertAlmostEqual(summary["agents"]["Timmy Cloud Lane"]["monthly_cost_usd"], 2.0)
+        self.assertAlmostEqual(summary["agents"]["Allegro"]["monthly_cost_usd"], 1.0)
+        self.assertAlmostEqual(summary["agents"]["Ezra"]["daily_cost_usd"], 0.2)
+
+    def test_report_render_mentions_inventory_and_agent_costs(self):
+        module = load_module()
+        rows = [
+            ("claude-sonnet-4-6", 12, 120, 24, 6.0),
+            ("gpt-5.4", 6, 60, 12, 3.0),
+            ("openrouter/google/gemini-2.5-pro", 4, 40, 8, 2.0),
+        ]
+        summary = module.summarize_rows(rows, days=30)
+        report = module.render_markdown(summary, report_date="2026-04-22")
+
+        self.assertIn("# Fleet Cost Report — 2026-04-22", report)
+        self.assertIn("## Paid API inventory", report)
+        self.assertIn("Anthropic", report)
+        self.assertIn("OpenRouter", report)
+        self.assertIn("OpenAI", report)
+        self.assertIn("## Estimated cost per agent per day", report)
+        self.assertIn("Timmy Cloud Lane", report)
+        self.assertIn("Ezra", report)
+        self.assertIn("Bezalel", report)
+
+    def test_write_report_creates_markdown_file(self):
+        module = load_module()
+        rows = [("claude-sonnet-4-6", 1, 10, 2, 0.5)]
+        summary = module.summarize_rows(rows, days=30)
+        with tempfile.TemporaryDirectory() as tmpdir:
+            dest = Path(tmpdir) / "fleet-cost.md"
+            module.write_report(dest, summary, report_date="2026-04-22")
+            self.assertTrue(dest.exists())
+            text = dest.read_text()
+            self.assertIn("Fleet Cost Report", text)
+            self.assertIn("Ezra", text)
+
+
+if __name__ == "__main__":
+    unittest.main()