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GMU ANALYTICAL · INDEX PROOF · DR099

Rule 2 Case 2b First Empty Blue — Analytical Coordinate Proof (DR099)

DR099 pairs Rule 2 Case 2b First Empty Blue (Continuing column row r = d_{k-m} + 1 stepping one row past reference) with Analytical Modality (Formal Index Notation): learners verify Cell (k-m, r) is empty while cell (k-m, r-1) above it is populated, master Rule 2 Case 2b First Empty Cell Past Reference returning Blue (≠), and eliminate marking red when an active streak first outgrows the reference column by 1 row.

Drill Reference ID
DR099
Big Road Streaks
10 Cols
Big Eye Boy Total
20 Marks
Small Road Total
17 Dots
Engine-Verified Scoreboard · 24 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road B B P P P B B B B P P B P P P P B P B B P P
Big Eye Boy = ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = = ≠ ≠ = ≠ ≠ = ≠
Small Road = ≠ = ≠ = ≠ ≠ = ≠ = ≠ = ≠ ≠ ≠ ≠ =
Cockroach Pig = = ≠ = = = = ≠ = = ≠ ≠ =

DR099 drill board (BBPPPBBBBPPBPPPPBPBBPPTP): 10 Big Road columns, 20 Big Eye Boy, 17 Small Road, and 13 Cockroach Pig marks.

Big Road B is Banker, P is Player Roads under it Red (=): repeating Blue (≠): breaking
Step-by-Step Mark Proofs (Rule 1 & Rule 2)
Big Eye Boy · Mark #1

This bead is at Row 2. Column 1 has a bead at Row 2 too → red (=).

  1. Column 2 goes down to Row 2, so use Rule 2: look 1 column back, at Column 1.
  2. Column 1 has a bead at Row 2 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Small Road · Mark #5

This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=).

  1. Column 4 goes down to Row 2, so use Rule 2: look 2 columns back, at Column 2.
  2. Column 2 has a bead at Row 2 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 2 stopped exactly one row above this bead.

Cockroach Pig · Mark #1

This bead is at Row 2. Column 1 has a bead at Row 2 too → red (=).

  1. Column 4 goes down to Row 2, so use Rule 2: look 3 columns back, at Column 1.
  2. Column 1 has a bead at Row 2 too → red (=).

Common table reading watchout: Thinking "no bead at this row" means blue. It is blue only when Column 1 stopped exactly one row above this bead.

Verified Reference Data

Key Facts & Table Specifications

DR099 Target Coordinate
Rule 2 Case 2b First Empty Blue

Continuing column row r = d_{k-m} + 1 stepping one row past reference

DR099 Rule Classification
Analytical Coordinate Proof

Rule 2 Case 2b First Empty Cell Past Reference returning Blue (≠)

DR099 Depth Comparison
10 Big Road Cols

Cell (k-m, r) is empty while cell (k-m, r-1) above it is populated

DR099 Misconception Focus
Diagnostic Check

Marking red when an active streak first outgrows the reference column by 1 row

DR099 GMU Modality Goal
Analytical Modality (Formal Index Notation)

Detect the exact row where an active streak breaks one cell past d_{k-m} by writing out (k, r) and (k-m, r) coordinates to prove the derived output

DR099 · Coordinate & Rule Specification

DR099 Rule 2 Case 2b First Empty Blue: Analytical Coordinate Proof Walkthrough

Inside Analytical Modality (Formal Index Notation) (DR099), exercise Rule 2 Case 2b First Empty Blue targets Rule 2 Case 2b First Empty Cell Past Reference returning Blue (≠) while writing out (k, r) and (k-m, r) coordinates to prove the derived output produces 20 Big Eye Boy marks over BBPPPBBBB.

Within DR099, Analytical Modality (Formal Index Notation) highlights the primary mark: This bead is at Row 2. Column 1 has a bead at Row 2 too → red (=). Across 17 Small Road and 13 Cockroach Pig entries, Cell (k-m, r) is empty while cell (k-m, r-1) above it is populated remains transparent.

Table DR099: Rule 2 Case 2b First Empty Blue specification under Analytical Coordinate Proof.
DR099 Drill DimensionCoordinate / RuleGMU Modality Action
DR099 Matrix CoordinateContinuing column row r = d_{k-m} + 1 stepping one row past referenceAnalytical Modality (Formal Index Notation)
DR099 Rule & DepthRule 2 Case 2b First Empty Cell Past Reference returning Blue (≠)Cell (k-m, r) is empty while cell (k-m, r-1) above it is populated
DR099 Diagnostic TargetMarking red when an active streak first outgrows the reference column by 1 rowDetect the exact row where an active streak breaks one cell past d_{k-m}
  • DR099 Step 1: Locate Continuing column row r = d_{k-m} + 1 stepping one row past reference across the 10 columns of BBPPPBBBBPPB.
  • DR099 Step 2: Verify Cell (k-m, r) is empty while cell (k-m, r-1) above it is populated under Rule 2 Case 2b First Empty Cell Past Reference returning Blue (≠).
  • DR099 Step 3: Answer "What are the exact 1-based and 0-based indices for the active comparison?" via writing out (k, r) and (k-m, r) coordinates to prove the derived output.
DR099 · Analytical Modality (Formal Index Notation)

DR099 Misconception Diagnostic & Secondary Road Audit

Multi-road audit DR099 (Rule 2 Case 2b First Empty Blue) shows: This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=). Grounded in Analytical Modality (Formal Index Notation), readers verify Continuing column row r = d_{k-m} + 1 stepping one row past reference across 10 Big Road columns.

Table Reality Check

Myth vs. Truth

MythIn DR099 (Rule 2 Case 2b First Empty Blue), marking red when an active streak first outgrows the reference column by 1 row or reading red/blue derived marks as Banker/Player outcomes.
TruthRule 2 Case 2b First Empty Cell Past Reference returning Blue (≠) evaluates Cell (k-m, r) is empty while cell (k-m, r-1) above it is populated; derived road colors reflect structural symmetry only and never alter independent shoe probabilities.
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  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
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