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Author SHA1 Message Date
Alexander Whitestone
74365aec0c feat: track NH broadband install lifecycle (#533)
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2026-04-22 00:45:55 -04:00
5 changed files with 257 additions and 221 deletions

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@@ -1,8 +1,8 @@
# NH Broadband Install Packet
**Packet ID:** nh-bb-20260415-113232
**Generated:** 2026-04-15T11:32:32.781304+00:00
**Status:** pending_scheduling_call
**Packet ID:** nh-bb-20260417-154500
**Generated:** 2026-04-17T15:45:00Z
**Status:** scheduled_install
## Contact
@@ -15,14 +15,46 @@
- 123 Example Lane
- Concord, NH 03301
## Desired Plan
## Availability
residential-fiber
- **Status:** available
- **Checked at:** 2026-04-17T15:45:00Z
- **Exact address confirmed:** yes
- **Notes:** Online availability lookup showed fiber service available at the exact cabin address.
## Pricing + Plan Recommendation
- **Recommended plan:** 1Gbps fiber
- **Monthly cost:** $79.95
- **Install fee:** $99.00
- **Notes:** 1Gbps chosen over 100Mbps because remote work + AI fleet uploads justify the higher tier.
## Installation Appointment
- **Scheduled:** yes
- **Date:** 2026-04-24
- **Window:** 08:00-12:00
- **Confirmation #: NHB-2026-0417**
## Installer Access Notes
- **Installer can reach cabin:** yes
- **Driveway note:** Driveway is gravel but passable for contractor van; call 30 minutes before arrival if mud is present.
- **Site contact:** 603-555-0142
## Payment
- **Method:** credit_card
- **First month due:** $79.95
- **Install fee due:** $99.00
- **Notes:** Card on file approved for first month plus install fee.
## Call Log
- **2026-04-15T14:30:00Z** — no_answer
- Called 1-800-NHBB-INFO, ring-out after 45s
- **2026-04-17T15:45:00Z** — scheduled
- Confirmed exact-address availability, selected 1Gbps, booked morning install window, and recorded confirmation number NHB-2026-0417.
## Appointment Checklist
@@ -34,4 +66,3 @@ residential-fiber
- [ ] Prepare site: clear path to ONT install location
- [ ] Post-install: run speed test (fast.com / speedtest.net)
- [ ] Log final speeds and appointment outcome

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@@ -11,10 +11,44 @@ service:
desired_plan: residential-fiber
availability:
status: available
checked_at: "2026-04-17T15:45:00Z"
exact_address_confirmed: true
notes: "Online availability lookup showed fiber service available at the exact cabin address."
pricing:
recommended_plan: 1Gbps fiber
monthly_cost_usd: 79.95
install_fee_usd: 99.0
notes: "1Gbps chosen over 100Mbps because remote work + AI fleet uploads justify the higher tier."
appointment:
scheduled: true
date: "2026-04-24"
window: "08:00-12:00"
confirmation_number: "NHB-2026-0417"
installer_access:
installer_can_reach_cabin: true
driveway_note: "Driveway is gravel but passable for contractor van; call 30 minutes before arrival if mud is present."
site_contact: "603-555-0142"
payment:
method: credit_card
first_month_due_usd: 79.95
install_fee_due_usd: 99.0
notes: "Card on file approved for first month plus install fee."
call_log:
- timestamp: "2026-04-15T14:30:00Z"
outcome: no_answer
notes: "Called 1-800-NHBB-INFO, ring-out after 45s"
- timestamp: "2026-04-17T15:45:00Z"
outcome: scheduled
notes: "Confirmed exact-address availability, selected 1Gbps, booked morning install window, and recorded confirmation number NHB-2026-0417."
speed_test: {}
checklist:
- "Confirm exact-address availability via NH Broadband online lookup"

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@@ -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 3040 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 (√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."*

View File

@@ -11,36 +11,74 @@ from typing import Any
import yaml
DEFAULT_CHECKLIST = [
"Confirm exact-address availability via NH Broadband online lookup",
"Call NH Broadband scheduling line (1-800-NHBB-INFO)",
"Select appointment window (morning/afternoon)",
"Confirm payment method (credit card / ACH)",
"Receive appointment confirmation number",
"Prepare site: clear path to ONT install location",
"Post-install: run speed test (fast.com / speedtest.net)",
"Log final speeds and appointment outcome",
]
def load_request(path: str | Path) -> dict[str, Any]:
data = yaml.safe_load(Path(path).read_text()) or {}
data.setdefault("contact", {})
data.setdefault("service", {})
data.setdefault("call_log", [])
data.setdefault("checklist", [])
data.setdefault("checklist", list(DEFAULT_CHECKLIST))
data.setdefault("availability", {})
data.setdefault("pricing", {})
data.setdefault("appointment", {})
data.setdefault("installer_access", {})
data.setdefault("payment", {})
data.setdefault("speed_test", {})
return data
def validate_request(data: dict[str, Any]) -> None:
contact = data.get("contact", {})
for field in ("name", "phone"):
if not contact.get(field, "").strip():
if not str(contact.get(field, "")).strip():
raise ValueError(f"contact.{field} is required")
service = data.get("service", {})
for field in ("address", "city", "state"):
if not service.get(field, "").strip():
if not str(service.get(field, "")).strip():
raise ValueError(f"service.{field} is required")
if not data.get("checklist"):
raise ValueError("checklist must contain at least one item")
def derive_status(data: dict[str, Any]) -> str:
availability = data.get("availability", {})
appointment = data.get("appointment", {})
speed_test = data.get("speed_test", {})
if str(availability.get("status", "")).strip().lower() == "unavailable":
return "blocked_unavailable"
if speed_test.get("tested_at") and speed_test.get("download_mbps") and speed_test.get("upload_mbps"):
return "post_install_verified"
if appointment.get("scheduled"):
return "scheduled_install"
return "pending_scheduling_call"
def build_packet(data: dict[str, Any]) -> dict[str, Any]:
validate_request(data)
contact = data["contact"]
service = data["service"]
availability = data.get("availability", {})
pricing = data.get("pricing", {})
appointment = data.get("appointment", {})
installer_access = data.get("installer_access", {})
payment = data.get("payment", {})
speed_test = data.get("speed_test", {})
return {
packet = {
"packet_id": f"nh-bb-{datetime.now(timezone.utc).strftime('%Y%m%d-%H%M%S')}",
"generated_utc": datetime.now(timezone.utc).isoformat(),
"contact": {
@@ -55,20 +93,76 @@ def build_packet(data: dict[str, Any]) -> dict[str, Any]:
"zip": service.get("zip", ""),
},
"desired_plan": data.get("desired_plan", "residential-fiber"),
"availability": {
"status": availability.get("status", "unknown"),
"checked_at": availability.get("checked_at", ""),
"notes": availability.get("notes", ""),
"exact_address_confirmed": bool(availability.get("exact_address_confirmed", False)),
},
"pricing": {
"recommended_plan": pricing.get("recommended_plan", data.get("desired_plan", "residential-fiber")),
"monthly_cost_usd": pricing.get("monthly_cost_usd"),
"install_fee_usd": pricing.get("install_fee_usd"),
"notes": pricing.get("notes", ""),
},
"appointment": {
"scheduled": bool(appointment.get("scheduled", False)),
"date": appointment.get("date", ""),
"window": appointment.get("window", ""),
"confirmation_number": appointment.get("confirmation_number", ""),
},
"installer_access": {
"installer_can_reach_cabin": bool(installer_access.get("installer_can_reach_cabin", False)),
"driveway_note": installer_access.get("driveway_note", ""),
"site_contact": installer_access.get("site_contact", contact["phone"]),
},
"payment": {
"method": payment.get("method", ""),
"first_month_due_usd": payment.get("first_month_due_usd"),
"install_fee_due_usd": payment.get("install_fee_due_usd"),
"notes": payment.get("notes", ""),
},
"speed_test": {
"tested_at": speed_test.get("tested_at", ""),
"download_mbps": speed_test.get("download_mbps"),
"upload_mbps": speed_test.get("upload_mbps"),
"provider": speed_test.get("provider", ""),
},
"call_log": data.get("call_log", []),
"checklist": [
{"item": item, "done": False} if isinstance(item, str) else item
for item in data["checklist"]
],
"status": "pending_scheduling_call",
}
packet["status"] = derive_status(packet)
return packet
def _money(value: Any) -> str:
if value in (None, ""):
return "n/a"
try:
return f"${float(value):.2f}"
except (TypeError, ValueError):
return str(value)
def _bool_label(value: bool) -> str:
return "yes" if value else "no"
def render_markdown(packet: dict[str, Any], data: dict[str, Any]) -> str:
contact = packet["contact"]
addr = packet["service_address"]
availability = packet["availability"]
pricing = packet["pricing"]
appointment = packet["appointment"]
installer_access = packet["installer_access"]
payment = packet["payment"]
speed_test = packet["speed_test"]
lines = [
f"# NH Broadband Install Packet",
"# NH Broadband Install Packet",
"",
f"**Packet ID:** {packet['packet_id']}",
f"**Generated:** {packet['generated_utc']}",
@@ -85,13 +179,44 @@ def render_markdown(packet: dict[str, Any], data: dict[str, Any]) -> str:
f"- {addr['address']}",
f"- {addr['city']}, {addr['state']} {addr['zip']}",
"",
f"## Desired Plan",
"## Availability",
"",
f"{packet['desired_plan']}",
f"- **Status:** {availability['status']}",
f"- **Checked at:** {availability['checked_at'] or 'pending'}",
f"- **Exact address confirmed:** {_bool_label(availability['exact_address_confirmed'])}",
f"- **Notes:** {availability['notes'] or 'pending live lookup'}",
"",
"## Pricing + Plan Recommendation",
"",
f"- **Recommended plan:** {pricing['recommended_plan']}",
f"- **Monthly cost:** {_money(pricing['monthly_cost_usd'])}",
f"- **Install fee:** {_money(pricing['install_fee_usd'])}",
f"- **Notes:** {pricing['notes'] or 'confirm on scheduling call'}",
"",
"## Installation Appointment",
"",
f"- **Scheduled:** {_bool_label(appointment['scheduled'])}",
f"- **Date:** {appointment['date'] or 'pending'}",
f"- **Window:** {appointment['window'] or 'pending'}",
f"- **Confirmation #: {appointment['confirmation_number'] or 'pending'}**",
"",
"## Installer Access Notes",
"",
f"- **Installer can reach cabin:** {_bool_label(installer_access['installer_can_reach_cabin'])}",
f"- **Driveway note:** {installer_access['driveway_note'] or 'pending'}",
f"- **Site contact:** {installer_access['site_contact'] or contact['phone']}",
"",
"## Payment",
"",
f"- **Method:** {payment['method'] or 'pending'}",
f"- **First month due:** {_money(payment['first_month_due_usd'])}",
f"- **Install fee due:** {_money(payment['install_fee_due_usd'])}",
f"- **Notes:** {payment['notes'] or 'confirm on scheduling call'}",
"",
"## Call Log",
"",
]
if packet["call_log"]:
for entry in packet["call_log"]:
ts = entry.get("timestamp", "n/a")
@@ -112,6 +237,17 @@ def render_markdown(packet: dict[str, Any], data: dict[str, Any]) -> str:
mark = "x" if item.get("done") else " "
lines.append(f"- [{mark}] {item['item']}")
if speed_test.get("tested_at") or speed_test.get("download_mbps") or speed_test.get("upload_mbps"):
lines.extend([
"",
"## Post-install Speed Test",
"",
f"- **Tested at:** {speed_test['tested_at'] or 'pending'}",
f"- **Download:** {speed_test['download_mbps'] or 'pending'} Mbps",
f"- **Upload:** {speed_test['upload_mbps'] or 'pending'} Mbps",
f"- **Provider:** {speed_test['provider'] or 'pending'}",
])
lines.append("")
return "\n".join(lines)

View File

@@ -32,11 +32,45 @@ def test_load_and_build_packet() -> None:
assert packet["contact"]["name"] == "Timmy Operator"
assert packet["service_address"]["city"] == "Concord"
assert packet["service_address"]["state"] == "NH"
assert packet["status"] == "pending_scheduling_call"
assert packet["availability"]["status"] == "available"
assert packet["appointment"]["scheduled"] is True
assert packet["pricing"]["monthly_cost_usd"] == 79.95
assert packet["installer_access"]["installer_can_reach_cabin"] is True
assert packet["payment"]["method"] == "credit_card"
assert packet["status"] == "scheduled_install"
assert len(packet["checklist"]) == 8
assert packet["checklist"][0]["done"] is False
def test_build_packet_marks_blocked_when_availability_fails() -> None:
data = load_request("docs/nh-broadband-install-request.example.yaml")
data["availability"] = {
"status": "unavailable",
"checked_at": "2026-04-17T16:00:00Z",
"notes": "Address lookup returned no fiber service.",
}
data["appointment"] = {}
data["speed_test"] = {}
packet = build_packet(data)
assert packet["status"] == "blocked_unavailable"
def test_build_packet_marks_post_install_verified_when_speed_test_present() -> None:
data = load_request("docs/nh-broadband-install-request.example.yaml")
data["speed_test"] = {
"tested_at": "2026-05-01T18:30:00Z",
"download_mbps": 942.6,
"upload_mbps": 881.4,
"provider": "fast.com",
}
packet = build_packet(data)
assert packet["status"] == "post_install_verified"
def test_validate_rejects_missing_contact_name() -> None:
data = {
"contact": {"name": "", "phone": "555"},
@@ -86,6 +120,11 @@ def test_render_markdown_contains_key_sections() -> None:
assert "# NH Broadband Install Packet" in md
assert "## Contact" in md
assert "## Service Address" in md
assert "## Availability" in md
assert "## Pricing + Plan Recommendation" in md
assert "## Installation Appointment" in md
assert "## Installer Access Notes" in md
assert "## Payment" in md
assert "## Call Log" in md
assert "## Appointment Checklist" in md
assert "Concord" in md
@@ -97,6 +136,8 @@ def test_render_markdown_shows_checklist_items() -> None:
packet = build_packet(data)
md = render_markdown(packet, data)
assert "- [ ] Confirm exact-address availability" in md
assert "Installer can reach cabin" in md
assert "- **Confirmation #: NHB-2026-0417**" in md
def test_example_yaml_is_valid() -> None: