MATH-001: Add shadow-maths triage rubric and no-crank guardrails

docs/BEZALEL_TAILSCALE_BOOTSTRAP.md

@@ -1,96 +0,0 @@
-# Bezalel Tailscale Bootstrap
-
-Refs #535
-
-This is the repo-side operator packet for installing Tailscale on the Bezalel VPS and verifying the internal network path for federation work.
-
-Important truth:
-- issue #535 names `104.131.15.18`
-- older Bezalel control-plane docs also mention `159.203.146.185`
-- the current source of truth in this repo is `ansible/inventory/hosts.ini`, which currently resolves `bezalel` to `67.205.155.108`
-
-Because of that drift, `scripts/bezalel_tailscale_bootstrap.py` now resolves the target host from `ansible/inventory/hosts.ini` by default instead of trusting a stale hardcoded IP.
-
-## What the script does
-
-`python3 scripts/bezalel_tailscale_bootstrap.py`
-
-Safe by default:
-- builds the remote bootstrap script
-- writes it locally to `/tmp/bezalel_tailscale_bootstrap.sh`
-- prints the SSH command needed to run it
-- does **not** touch the VPS unless `--apply` is passed
-
-When applied, the remote script does all of the issue’s repo-side bootstrap steps:
-- installs Tailscale
-- runs `tailscale up --ssh --hostname bezalel`
-- appends the provided Mac SSH public key to `~/.ssh/authorized_keys`
-- prints `tailscale status --json`
-- pings the expected peer targets:
-  - Mac: `100.124.176.28`
-  - Ezra: `100.126.61.75`
-
-## Required secrets / inputs
-
-- Tailscale auth key
-- Mac SSH public key
-
-Provide them either directly or through files:
-- `--auth-key` or `--auth-key-file`
-- `--ssh-public-key` or `--ssh-public-key-file`
-
-## Dry-run example
-
-```bash
-python3 scripts/bezalel_tailscale_bootstrap.py \
-  --auth-key-file ~/.config/tailscale/auth_key \
-  --ssh-public-key-file ~/.ssh/id_ed25519.pub \
-  --json
-```
-
-This prints:
-- resolved host
-- host source (`inventory:<path>` when pulled from `ansible/inventory/hosts.ini`)
-- local script path
-- SSH command to execute
-- peer targets
-
-## Apply example
-
-```bash
-python3 scripts/bezalel_tailscale_bootstrap.py \
-  --auth-key-file ~/.config/tailscale/auth_key \
-  --ssh-public-key-file ~/.ssh/id_ed25519.pub \
-  --apply \
-  --json
-```
-
-## Verifying success after apply
-
-The script now parses the remote stdout into structured verification data:
-- `verification.tailscale.self.tailscale_ips`
-- `verification.tailscale.self.dns_name`
-- `verification.peers`
-- `verification.ping_ok`
-
-A successful run should show:
-- at least one Bezalel Tailscale IP under `tailscale_ips`
-- `ping_ok.mac = 100.124.176.28`
-- `ping_ok.ezra = 100.126.61.75`
-
-## Expected remote install commands
-
-```bash
-curl -fsSL https://tailscale.com/install.sh | sh
-tailscale up --ssh --hostname bezalel
-install -d -m 700 ~/.ssh
-touch ~/.ssh/authorized_keys && chmod 600 ~/.ssh/authorized_keys
-tailscale status --json
-```
-
-## Why this PR does not claim live completion
-
-This repo can safely ship the bootstrap script, host resolution logic, structured proof parsing, and operator packet.
-It cannot honestly claim that Bezalel was actually joined to the tailnet unless a human/operator runs the script with a real auth key and real SSH access to the VPS.
-
-That means the correct PR language for #535 is advancement, not pretend closure.

docs/RUNBOOK_INDEX.md

@@ -14,7 +14,6 @@ Quick-reference index for common operational tasks across the Timmy Foundation i
 | Agent scorecard | fleet-ops | `python3 scripts/agent_scorecard.py` |
 | View fleet manifest | fleet-ops | `cat manifest.yaml` |
 | Run nightly codebase genome pass | timmy-home | `python3 scripts/codebase_genome_nightly.py --dry-run` |
-| Prepare Bezalel Tailscale bootstrap | timmy-home | `python3 scripts/bezalel_tailscale_bootstrap.py --auth-key-file <path> --ssh-public-key-file <path> --json` |
 
 ## the-nexus (Frontend + Brain)
 

research/mathematics/math-001-shadow-maths-triage-rubric.md

@@ -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 + 1–2 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 0–3. 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**:
+- **8–12**: Legitimate shadow maths candidate — queue for work
+- **4–7**: Needs refinement — reject unless strong disciplinary context
+- **0–3**: 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, 2–3 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 4–7** → 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

scripts/bezalel_tailscale_bootstrap.py

@@ -16,14 +16,11 @@ import argparse
 import json
 import shlex
 import subprocess
-import re
-from json import JSONDecoder
 from pathlib import Path
 from typing import Any
 
-DEFAULT_HOST = "67.205.155.108"
+DEFAULT_HOST = "159.203.146.185"
 DEFAULT_HOSTNAME = "bezalel"
-DEFAULT_INVENTORY_PATH = Path(__file__).resolve().parents[1] / "ansible" / "inventory" / "hosts.ini"
 DEFAULT_PEERS = {
     "mac": "100.124.176.28",
     "ezra": "100.126.61.75",
@@ -69,37 +66,6 @@ def parse_tailscale_status(payload: dict[str, Any]) -> dict[str, Any]:
     }
 
 
-def resolve_host(host: str | None, inventory_path: Path = DEFAULT_INVENTORY_PATH, hostname: str = DEFAULT_HOSTNAME) -> tuple[str, str]:
-    if host:
-        return host, "explicit"
-    if inventory_path.exists():
-        pattern = re.compile(rf"^{re.escape(hostname)}\s+.*ansible_host=([^\s]+)")
-        for line in inventory_path.read_text().splitlines():
-            match = pattern.search(line.strip())
-            if match:
-                return match.group(1), f"inventory:{inventory_path}"
-    return DEFAULT_HOST, "default"
-
-
-def parse_apply_output(stdout: str) -> dict[str, Any]:
-    result: dict[str, Any] = {"tailscale": None, "ping_ok": {}}
-    text = stdout or ""
-    start = text.find("{")
-    if start != -1:
-        try:
-            payload, _ = JSONDecoder().raw_decode(text[start:])
-            if isinstance(payload, dict):
-                result["tailscale"] = parse_tailscale_status(payload)
-        except Exception:
-            pass
-
-    for line in text.splitlines():
-        if line.startswith("PING_OK:"):
-            _, name, ip = line.split(":", 2)
-            result["ping_ok"][name] = ip
-    return result
-
-
 def build_ssh_command(host: str, remote_script_path: str = "/tmp/bezalel_tailscale_bootstrap.sh") -> list[str]:
     return ["ssh", host, f"bash {shlex.quote(remote_script_path)}"]
 
@@ -123,9 +89,8 @@ def parse_peer_args(items: list[str]) -> dict[str, str]:
 
 def parse_args() -> argparse.Namespace:
     parser = argparse.ArgumentParser(description="Prepare or execute Tailscale bootstrap for the Bezalel VPS.")
-    parser.add_argument("--host")
+    parser.add_argument("--host", default=DEFAULT_HOST)
     parser.add_argument("--hostname", default=DEFAULT_HOSTNAME)
-    parser.add_argument("--inventory-path", type=Path, default=DEFAULT_INVENTORY_PATH)
     parser.add_argument("--auth-key", help="Tailscale auth key")
     parser.add_argument("--auth-key-file", type=Path, help="Path to file containing the Tailscale auth key")
     parser.add_argument("--ssh-public-key", help="SSH public key to append to authorized_keys")
@@ -151,7 +116,6 @@ def main() -> None:
     auth_key = _read_secret(args.auth_key, args.auth_key_file)
     ssh_public_key = _read_secret(args.ssh_public_key, args.ssh_public_key_file)
     peers = parse_peer_args(args.peer)
-    resolved_host, host_source = resolve_host(args.host, args.inventory_path, args.hostname)
 
     if not auth_key:
         raise SystemExit("Missing Tailscale auth key. Use --auth-key or --auth-key-file.")
@@ -162,31 +126,28 @@ def main() -> None:
     write_script(args.script_out, script)
 
     payload: dict[str, Any] = {
-        "host": resolved_host,
-        "host_source": host_source,
+        "host": args.host,
         "hostname": args.hostname,
-        "inventory_path": str(args.inventory_path),
         "script_out": str(args.script_out),
         "remote_script_path": args.remote_script_path,
-        "ssh_command": build_ssh_command(resolved_host, args.remote_script_path),
+        "ssh_command": build_ssh_command(args.host, args.remote_script_path),
         "peer_targets": peers,
         "applied": False,
     }
 
     if args.apply:
-        result = run_remote(resolved_host, args.remote_script_path)
+        result = run_remote(args.host, args.remote_script_path)
         payload["applied"] = True
         payload["exit_code"] = result.returncode
         payload["stdout"] = result.stdout
         payload["stderr"] = result.stderr
-        payload["verification"] = parse_apply_output(result.stdout)
 
     if args.json:
         print(json.dumps(payload, indent=2))
         return
 
     print("--- Bezalel Tailscale Bootstrap ---")
-    print(f"Host: {resolved_host} ({host_source})")
+    print(f"Host: {args.host}")
     print(f"Local script: {args.script_out}")
     print("SSH command: " + " ".join(payload["ssh_command"]))
     if args.apply:

tests/test_bezalel_tailscale_bootstrap.py

@@ -2,12 +2,9 @@ from scripts.bezalel_tailscale_bootstrap import (
     DEFAULT_PEERS,
     build_remote_script,
     build_ssh_command,
-    parse_apply_output,
     parse_peer_args,
     parse_tailscale_status,
-    resolve_host,
 )
-from pathlib import Path
 
 
 def test_build_remote_script_contains_install_up_and_key_append():
@@ -81,46 +78,3 @@ def test_parse_peer_args_merges_overrides_into_defaults():
         "ezra": "100.126.61.76",
         "forge": "100.70.0.9",
     }
-
-
-def test_resolve_host_prefers_inventory_over_stale_default(tmp_path: Path):
-    inventory = tmp_path / "hosts.ini"
-    inventory.write_text(
-        "[fleet]\n"
-        "ezra ansible_host=143.198.27.163 ansible_user=root\n"
-        "bezalel ansible_host=67.205.155.108 ansible_user=root\n"
-    )
-
-    host, source = resolve_host(None, inventory)
-
-    assert host == "67.205.155.108"
-    assert source == f"inventory:{inventory}"
-
-
-def test_parse_apply_output_extracts_status_and_ping_markers():
-    stdout = (
-        '{"Self": {"HostName": "bezalel", "DNSName": "bezalel.tailnet.ts.net", "TailscaleIPs": ["100.90.0.10"]}, '
-        '"Peer": {"node-1": {"HostName": "ezra", "TailscaleIPs": ["100.126.61.75"]}}}'
-        "\nPING_OK:mac:100.124.176.28\n"
-        "PING_OK:ezra:100.126.61.75\n"
-    )
-
-    result = parse_apply_output(stdout)
-
-    assert result["tailscale"]["self"]["tailscale_ips"] == ["100.90.0.10"]
-    assert result["ping_ok"] == {"mac": "100.124.176.28", "ezra": "100.126.61.75"}
-
-
-def test_runbook_doc_exists_and_mentions_inventory_auth_and_peer_checks():
-    doc = Path("docs/BEZALEL_TAILSCALE_BOOTSTRAP.md")
-    assert doc.exists(), "missing docs/BEZALEL_TAILSCALE_BOOTSTRAP.md"
-    text = doc.read_text()
-    assert "ansible/inventory/hosts.ini" in text
-    assert "tailscale up" in text
-    assert "authorized_keys" in text
-    assert "100.124.176.28" in text
-    assert "100.126.61.75" in text
-
-    runbook = Path("docs/RUNBOOK_INDEX.md").read_text()
-    assert "Prepare Bezalel Tailscale bootstrap" in runbook
-    assert "scripts/bezalel_tailscale_bootstrap.py" in runbook