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GMU ANALYTICAL · INDEX PROOF · DR089

Rule 2 Case 2a Filled Red (=) — Analytical Coordinate Proof (DR089)

DR089 pairs Rule 2 Case 2a Filled Red (=) (Continuing column row r >= 2 where reference cell (k-m, r) is occupied) with Analytical Modality (Formal Index Notation): learners verify Reference column d_{k-m} >= r so both (k-m, r) and (k-m, r-1) are filled, master Rule 2 Case 2a Populated Reference Cell returning Red (=), and eliminate checking completed column totals instead of cell occupancy at rows r and r-1.

Drill Reference ID
DR089
Big Road Streaks
8 Cols
Big Eye Boy Total
18 Marks
Small Road Total
15 Dots
Engine-Verified Scoreboard · 22 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 B P P
Big Eye Boy = ≠ ≠ = = ≠ ≠ = ≠ ≠ ≠ = = = ≠ = ≠ =
Small Road = ≠ = ≠ = ≠ ≠ = ≠ = = ≠ ≠ ≠ =
Cockroach Pig = = ≠ = = = ≠ ≠ = = ≠

DR089 drill board (BBPPPBBBBPPBPPPPTPBBPP): 8 Big Road columns, 18 Big Eye Boy, 15 Small Road, and 11 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 #3

Column 2 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

  1. Column 3 starts, so use Rule 1: compare Column 2 with Column 1, 1 column further back.
  2. Column 2 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

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 #3

Column 5 has 1 bead. Column 2 has 3 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 3 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

DR089 Target Coordinate
Rule 2 Case 2a Filled Red (=)

Continuing column row r >= 2 where reference cell (k-m, r) is occupied

DR089 Rule Classification
Analytical Coordinate Proof

Rule 2 Case 2a Populated Reference Cell returning Red (=)

DR089 Depth Comparison
8 Big Road Cols

Reference column d_{k-m} >= r so both (k-m, r) and (k-m, r-1) are filled

DR089 Misconception Focus
Diagnostic Check

Checking completed column totals instead of cell occupancy at rows r and r-1

DR089 GMU Modality Goal
Analytical Modality (Formal Index Notation)

Verify that the reference column is still occupied at current row r by writing out (k, r) and (k-m, r) coordinates to prove the derived output

DR089 · Coordinate & Rule Specification

DR089 Rule 2 Case 2a Filled Red (=): Analytical Coordinate Proof Walkthrough

Through writing out (k, r) and (k-m, r) coordinates to prove the derived output in DR089, Rule 2 Case 2a Filled Red (=) demonstrates Reference column d_{k-m} >= r so both (k-m, r) and (k-m, r-1) are filled across 8 Big Road columns and 18 derived comparisons.

During DR089 practice (GMU ANALYTICAL · INDEX PROOF), Column 2 has 3 beads. Column 1 has 2 beads. Different depth → blue (≠). Pairing 15 Small Road and 11 Cockroach Pig entries with Continuing column row r >= 2 where reference cell (k-m, r) is occupied resolves What are the exact 1-based and 0-based indices for the active comparison?

Table DR089: Rule 2 Case 2a Filled Red (=) specification under Analytical Coordinate Proof.
DR089 Drill DimensionCoordinate / RuleGMU Modality Action
DR089 Matrix CoordinateContinuing column row r >= 2 where reference cell (k-m, r) is occupiedAnalytical Modality (Formal Index Notation)
DR089 Rule & DepthRule 2 Case 2a Populated Reference Cell returning Red (=)Reference column d_{k-m} >= r so both (k-m, r) and (k-m, r-1) are filled
DR089 Diagnostic TargetChecking completed column totals instead of cell occupancy at rows r and r-1Verify that the reference column is still occupied at current row r
  • DR089 Step 1: Locate Continuing column row r >= 2 where reference cell (k-m, r) is occupied across the 8 columns of BBPPPBBBBPPB.
  • DR089 Step 2: Verify Reference column d_{k-m} >= r so both (k-m, r) and (k-m, r-1) are filled under Rule 2 Case 2a Populated Reference Cell returning Red (=).
  • DR089 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.
DR089 · Analytical Modality (Formal Index Notation)

DR089 Misconception Diagnostic & Secondary Road Audit

Further along the DR089 scoreboard (8 columns), This bead is at Row 2. Column 2 has a bead at Row 2 too → red (=). Answering "What are the exact 1-based and 0-based indices for the active comparison?" cements Rule 2 Case 2a Populated Reference Cell returning Red (=).

Table Reality Check

Myth vs. Truth

MythIn DR089 (Rule 2 Case 2a Filled Red (=)), checking completed column totals instead of cell occupancy at rows r and r-1 or reading red/blue derived marks as Banker/Player outcomes.
TruthRule 2 Case 2a Populated Reference Cell returning Red (=) evaluates Reference column d_{k-m} >= r so both (k-m, r) and (k-m, r-1) are filled; 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
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
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