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Author SHA1 Message Date
Alexander Payne
6595a82afb MATH-001: Add shadow-maths triage rubric and no-crank guardrails
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2026-04-26 15:46:44 -04:00
5 changed files with 187 additions and 257 deletions

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@@ -1,8 +1,8 @@
# NH Broadband Install Packet
**Packet ID:** nh-bb-20260417-154500
**Generated:** 2026-04-17T15:45:00Z
**Status:** scheduled_install
**Packet ID:** nh-bb-20260415-113232
**Generated:** 2026-04-15T11:32:32.781304+00:00
**Status:** pending_scheduling_call
## Contact
@@ -15,46 +15,14 @@
- 123 Example Lane
- Concord, NH 03301
## Availability
## Desired Plan
- **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.
residential-fiber
## 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
@@ -66,3 +34,4 @@
- [ ] 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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@@ -11,44 +11,10 @@ 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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@@ -0,0 +1,172 @@
# Shadow Maths Triage Rubric (MATH-001)
**Status**: Draft v1.0 **Date**: 2026-04-26 **Author**: Timmy
**Milestone**: Contribute to Mathematics — Shadow Maths Search
**Parent**: #876 — [MATH][EPIC] Shadow Maths
---
## Purpose
Timmy's mathematics contribution program targets *bounded, verifiable, useful* problems hiding in plain sight. This rubric operationalizes "shadow maths" — distinguishing legitimate first-crack contributions from crank Grand Unified Theories.
The rubric serves two roles:
1. **Triage gate** — filter submissions and scout list candidates worth pursuing.
2. **No-crank guardrail** — explicitly reject unfalsifiable, unscoped, or unsourced claims.
---
## Candidate Categories (Positive Types)
| Category | Description | Verification Path | Useful Because |
|----------|-------------|-------------------|---------------|
| **Small lemma** | Missing but straightforward piece in an active area (e.g., "Proposition 3.2 in Smith 2021 needs this case analysis") | Check paper + 12 related references; prove or give counterexample | Clarifies existing theory, removes ambiguity |
| **Counterexample search** | Find explicit counterexample to a claimed-but-unproven statement (often from MO/SE) | Compute/construct + cite the original claim | Prevents propagation of errors |
| **Computational classification** | Exhaustive enumeration/classification of a small infinite family (e.g., "all groups of order < 200 with property X") | Code is verifiable; results match known data | Creates reference data, spotlights patterns |
| **Formalization gap** | Statement already believed true but missing from Lean/mathlib/Isabelle | Formal proof artifact; merges to mainline library | Makes mathematics machine-checkable |
| **OEIS sequence note** | New sequence entry or correction to an existing entry with proof/algorithm | OEIS A-number + formula/generation code | Public archival, enables further work |
| **Exposition repair** | Fix an unclear proof, fill a gap, simplify an argument in an existing paper | Side-by-side diff + justification for each change | Improves pedagogy, reduces confusion |
| **MathOverflow-quality answer** | Answer to a specific, bounded, research-level question on MO/SE that has no accepted answer | Cite question + self-contained proof/computation | Serves the community directly |
---
## Rejection Criteria (No-Crank Guardrails)
> Any candidate that triggers one or more of these is **rejected outright** — no scoring needed.
| Rule | What to look for | Why it's crank |
|------|------------------|----------------|
| **Unsourced grand theory** | Claim introduces new "framework"/"paradigm" without citing specific bounded problem it solves | Mathematics advances by solving problems, not proposing frameworks |
| **Impossible scope** | "I will prove/disprove the Riemann Hypothesis", "classify all finite simple groups" | Demonstrably beyond single-attack capability |
| **No verification path** | No way for a third party to check the work (no code, no formalization, no explicit examples) | Cannot be wrong if it cannot be checked |
| **Novelty claim without literature search** | States "I believe this is new" without checking MathSciNet/arXiv/Google Scholar | Almost certainly reinvention or known result |
| **Vague mathematical objects** | Uses undefined or ambiguous terminology ("energy", "resonance", "harmonic" in non-standard ways) | Not mathematics |
| **Secrecy or paywall** | Key definition or proof behind a paywall or withheld | Not sovereign; not verifiable |
| **Symbolic overloading without definition** | Repurposes standard notation in non-standard ways without explicit redefinition | Creates confusion, not clarity |
| **Invariance violations** | Claims "up to isomorphism" or "modulo equivalence" without defining the equivalence relation | Not mathematically precise |
| **Cherry-picked examples as proof** | Proves only easy special cases and claims the general case follows | Example ≠ theorem |
| **Circular citation chains** | Relies on unpublished/preprint work that itself cites the candidate as motivation | Not a foundation |
| **No clear problem statement** | Cannot write a one-sentence problem statement in standard mathematical English | Not a problem; just musings |
| **Claims of "obvious" or "clear" for non-trivial steps** | Uses "obviously" or "it is clear that" where a proof requires >2 lines | Evasion |
| **References only popular science / non-technical sources** | Cites Penrose, Hawking, Tegmark for technical claims | Wrong tier of source |
| **All notation defined in non-standard way** | Redefines basic operators (+, ×, ≤) without explicit warning | Not mathematics |
| **No engagement with existing literature** | Zero citations to relevant peer-reviewed work or established preprints | scholarship was not done |
| **Claims of "disproof" of widely-accepted theorems** | Without finding a peer-reviewed error in the existing proof | Almost certainly wrong |
---
## Evidence Tiers
| Tier | Artifact | What it Proves |
|------|----------|----------------|
| **T3 — Literature** | MathSciNet / Zentralblatt / Google Scholar citations showing the problem is real and open | Problem exists in the literature |
| **T2 — Executable** | Python/Sage/Lean code that others can run to verify computation/formalization | Result is reproducible |
| **T1 — Human-reviewed** | MO answer with upvotes, referee report, or explicit external review | Independent verification |
| **T0 — Self-contained** | Clear statement + proof/computation in a single document, all definitions explicit | Standalone correctness |
A valid candidate must have at least **one** T3 citation (shows the problem is real) AND a verification artifact (T0 minimum; T2 ideal).
---
## Scoring Rubric
Score each candidate on **4 dimensions**, each 03. Maximum 12 points.
| Dimension | 3 (excellent) | 2 (good) | 1 (minimal) | 0 (absent) |
|-----------|---------------|----------|-------------|------------|
| **Boundedness** | Scope is explicitly finite/small (single lemma, finite classification < N, one SE question) | Scope is implied bounded but not quantified | Scope is large/vague but attackable | Unbounded or impossible scope |
| **Verifiability** | T2 artifact (code/formalization) + T3 citation | T0 proof + T3 citation | Proof/computation only, no citations | No way to check independently |
| **Usefulness** | Solves problem others actively need (cites known difficulty, fills formalization gap) | Solves a clean exercise or interesting special case | Interesting but no clear audience | Pointless or self-referential |
| **Discipline** | No crank flags; explicit rejection criteria cleanly passed | Minor crank flags (vague wording) but overall sound | Some crank flags but bounded scope rescues it | Triggers multiple rejection rules |
**Thresholds**:
- **812**: Legitimate shadow maths candidate — queue for work
- **47**: Needs refinement — reject unless strong disciplinary context
- **03**: Reject as crank / out-of-scope
---
## Three Worked Examples
### Example 1: Small Lemma — Bounded
**Candidate**: "Proposition 3.2 in 'Coarse Geometry and Coarse Embeddings' (Lang-Schlichenmaier 2005) states that every finite CW-complex has Markov property. The proof gives 'it follows by induction on skeleta' without handling the attaching map case. Fill the gap."
**Triage**:
- **Category**: Small lemma (exposition repair + proof gap fill)
- **Boundedness**: 3 — single proposition in a specific paper, 23 pages max
- **Verifiability**: 3 — paper is cited (T3), self-contained proof in 20 lines (T0), can formalize in Lean (T2 possible)
- **Usefulness**: 3 — readers of this paper hit this gap; Lean formalization needed for mathlib
- **Discipline**: 3 — no crank flags; scoped, sourced, technical
- **Total**: **12/12** → YES
**Action**: File ticket "MATH-LEMMA-001"; assign to formalization lane + human review.
---
### Example 2: Grand Unified Theory — CRANK
**Candidate**: "I have discovered the Energy-Conscious Riemann Hypothesis framework. The zeros of ζ(s) correspond to harmonic resonance frequencies in prime-number energy manifolds. Uses my new Operator-Weight theory."
**Triage**:
- **Category**: N/A
- **Rejection triggers**:
- ✗ Unsourced grand theory (introduces "Energy-Conscious", "Operator-Weight" with no definition in standard math)
- ✗ No verification path (no computation, no reference to known data)
- ✗ No literature engagement (zero citations)
- ✗ Vague mathematical objects ("energy", "resonance", "harmonic")
- ✗ Claims new framework
- **Score**: 0 — **REJECT**
**Action**: Close with reason "crank: unsourced grand theory + no verification path".
---
### Example 3: Computational Classification — Bounded
**Candidate**: "Compute all 3-headed Turing machines with 3 states that halt within 100 steps on the blank tape. There are 9 such machines. This fills an OEIS gap: A327000 only lists up to 2-state 2-symbol."
**Triage**:
- **Category**: Computational classification + OEIS sequence
- **Boundedness**: 3 — finite exhaustive enumeration (3^6 = 729 machines, filter to 9)
- **Verifiability**: 2 — code is executable (T2), but no T3 citation of why this sequence matters yet
- **Usefulness**: 2 — plugs a gap in the Busy Beaver frontier; OEIS entry gets concrete data
- **Discipline**: 3 — explicit scope, reproducible, submits to OEIS (external review path)
- **Total**: **10/12** → YES (minor fix: add motivation/references)
**Action**: Accept; write exhaustive script; submit OEIS draft with code + results; file MATH-COMP-001.
---
## Operational Use
### Triage Workflow
1. **Read candidate** (issue, email, self-generated idea).
2. **Check rejection criteria first** — if any trigger → **REJECT** immediately, cite rule.
3. If passes rejection gate, **score 4 dimensions**.
4. **Score ≥8** → mark as `shadow-maths-candidate`, route to appropriate lane:
- Lemma/exposition → `formalization-lane`
- Computation → `compute-lane`
- MO/SE answer → `answer-lane`
- OEIS → `oeis-lane`
5. **Score 47** → requires refinement; ask for:
- Explicit scope bound
- T3 citation
- Verification artifact
6. **Score ≤3** → reject with specific rule(s) triggered.
### Guardrail Enforcement
The following prompts/agents **must refuse** to work on any candidate that:
- Triggers any rejection criterion (before any code/proof work)
- Has no T3 citation (real problem statement from literature)
- Has no bounded scope (cannot write ≤1-sentence problem statement)
Enforcement is a **pre-flight check** in the task intake pipeline.
---
## Revision History
- v1.0 — 2026-04-26 — initial rubric + 3 scored examples

View File

@@ -11,74 +11,36 @@ 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", list(DEFAULT_CHECKLIST))
data.setdefault("availability", {})
data.setdefault("pricing", {})
data.setdefault("appointment", {})
data.setdefault("installer_access", {})
data.setdefault("payment", {})
data.setdefault("speed_test", {})
data.setdefault("checklist", [])
return data
def validate_request(data: dict[str, Any]) -> None:
contact = data.get("contact", {})
for field in ("name", "phone"):
if not str(contact.get(field, "")).strip():
if not contact.get(field, "").strip():
raise ValueError(f"contact.{field} is required")
service = data.get("service", {})
for field in ("address", "city", "state"):
if not str(service.get(field, "")).strip():
if not 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", {})
packet = {
return {
"packet_id": f"nh-bb-{datetime.now(timezone.utc).strftime('%Y%m%d-%H%M%S')}",
"generated_utc": datetime.now(timezone.utc).isoformat(),
"contact": {
@@ -93,76 +55,20 @@ 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 = [
"# NH Broadband Install Packet",
f"# NH Broadband Install Packet",
"",
f"**Packet ID:** {packet['packet_id']}",
f"**Generated:** {packet['generated_utc']}",
@@ -179,44 +85,13 @@ def render_markdown(packet: dict[str, Any], data: dict[str, Any]) -> str:
f"- {addr['address']}",
f"- {addr['city']}, {addr['state']} {addr['zip']}",
"",
"## Availability",
f"## 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'}",
f"{packet['desired_plan']}",
"",
"## Call Log",
"",
]
if packet["call_log"]:
for entry in packet["call_log"]:
ts = entry.get("timestamp", "n/a")
@@ -237,17 +112,6 @@ 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

@@ -32,45 +32,11 @@ 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["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 packet["status"] == "pending_scheduling_call"
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"},
@@ -120,11 +86,6 @@ 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
@@ -136,8 +97,6 @@ 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: