The Dimitrov Method — Complete Glossary

Quick Navigation

• The Dimitrov Method
• The Unified Outcome Theorem
• The Two Orders — Epistemic vs Ontological
• Threat Levels — The Two Tracks
• Geometric Signatures of L-Levels
• Threat Level Variants (#, *, d#)
• “Defensible in X Moves”
• The Priority Hierarchy (Tiered)
• Cross-Track Priority
• Calculation Horizon
• CAB Defense System
• Extended L3 Defenses
• CAB Manipulation
• Captures as Threat-Grid Operations
• Capture Execution (X) — Terminus of the Capture Track
• Against-Self Analysis
• Relationships (Static Topology)
• Convergence
• The Delta View
• Process Audit

The Dimitrov Method

A deterministic, brute-force, step-by-step chess analysis algorithm that audits your thought process, not just your moves. Normal chess engines tell you the move you should have played. The Method tells you the thought process you should have had — every best move has an optimal thought process that would have led to its selection.

Unlike heuristic systems that teach you what to consider, the Method specifies the exact order of operations. If you follow the steps, you WILL find the solution. Equally, when you fail to find it — or when you happen to find it via faulty reasoning — the Method tells you which specific step you skipped, making thinking failures auditable for the first time. Every blunder corresponds to a specific skipped step. Every correct move arrived at via wrong reasoning corresponds to a specific lucky skip that won’t reproduce — the hidden Dunning-Kruger that the Method exposes.

The Method has two complementary frames:

• Move Analysis — the dynamic, action-oriented view (“if I play this move, what threat does it create?”)
• Relationships — the static, descriptive view (“how far apart are these pieces right now, regardless of whose turn it is?”)

The Unified Outcome Theorem

The foundational theoretical claim of the Dimitrov Method: chess has exactly one outcome, and it is king capture.

Piece captures are not separate outcomes — they are defender-removal operations on the king’s defensive lattice. A captured piece is one less piece available to block, defend, counter-attack, or otherwise participate in protecting the king. Under the standard chess assumption that accurate play exchanges pieces evenly, accumulated material differential compounds through the endgame into a forced king-capture sequence.

This means the L-system is not two independent tracks (king-threat vs piece-threat). It is a single timeline (distance to L0) with two annotation conventions — one for direct progress, one for deferred progress. Both terminate at the same outcome.

The implications are foundational: the Cross-Track Priority rule, the structure of the Process Audit, and every claim in the Method’s algorithm derive from this single principle.

For the full treatment of the Cross-Track Priority rule, see The One Outcome.

Calculation Horizon

The Method’s algorithm operates inside a finite-step window — the number of plies a player can realistically calculate in real time. Threats inside the window are subject to the Priority Hierarchy and the Capture Clearance Protocol. Threats outside the window are not.

What’s Inside the Horizon

The default horizon for in-game decision-making:

These are the threats the priority rule and the clearance protocol weigh against each other. Roughly: anything within 2 plies of an execution (mate or material) is in-horizon.

What’s Outside the Horizon

L6, L7, L8+ threats (chained 3+ moves from execution) are outside the horizon for priority-rule purposes. They are real — they exist in the Relationships matrix — but they are NOT gates on the priority rule or the clearance protocol. They are handled by:

• Structural/positional layers (Relationships, Convergence) — long-horizon topology
• Tempi math — you have multiple moves to prepare a defense or counter-threat before any L6/L7/L8 escalates into a horizon-relevant threat

Why This Matters

The intuition “I don’t need to worry about an L6, it’s three moves away” is correct — and the horizon concept names it. Without an explicit horizon, the L-system becomes paralytic: every position has dozens of L6+ relationships, none of which should gate your move.

The horizon is the boundary between priority-rule territory (must compare, can’t ignore) and structural-layer territory (can defer, can absorb via topology). Every Method-derived decision is implicitly bounded by it.

Horizon Extension Under Pressure

Strong players extend the horizon to 3+ plies in critical positions (e.g., tactical sequences, classical time controls). Weaker players operate at a 1-ply horizon and miss L4# / L2## threats entirely. Training the Method largely means gradually expanding the horizon until it routinely captures all of Tier 2 plus the relevant Tier 3 candidates.

The Two Orders — Epistemic vs Ontological

The L-system has two orderings of threats, doing two different jobs. Conflating them produces apparent inconsistencies in the notation; separating them resolves every objection.

Epistemic Order (What to Identify First)

The order in which threats are visible to a player scanning a position before any calculation has occurred. Lower L-numbers come first because their geometric signatures are simpler (easier to spot) and their expected response is more forcing. This is the order in which the Method instructs a player to look: L1 first, then L2, then L3, then L4, then L5.

The epistemic order makes position analysis startable. Without it, “calculate forcing moves first” is empty advice — you cannot find forcing moves before you know what to look for.

Ontological Order (What’s Most Urgent)

The order in which threats actually demand response, given complete information about the position. Determined by the Cross-Track Priority calculation with suffix refinement (#, *, d#) and piece values. See Priority Hierarchy for the tiered ranking.

Why Both Are Necessary

The L-numbers are not a priority scale. They are a perceptual scaffold that scaffolds priority calculation. The base L-number (L1, L2, L3…) is identifiable from raw geometry; the suffixes (#, *) require analysis. The two-phase architecture — perceive first, then refine — is what makes the Method’s algorithm tractable.

You can’t compute priority without first identifying candidates. You can’t identify candidates without a perceptual scaffold. The L-numbers are the perceptual scaffold.

For the full treatment of the two-phase architecture, see How Do You Even Begin?.

Threat Levels — The Two Tracks

Every chess move and every piece-to-piece relationship is quantified by threat proximity — how many moves away a piece is from contributing to king capture (L0).

The L-system has two notational conventions, annotating the same outcome timeline at different time horizons:

Direct Track (King-Capture Sequence)

L1, L2, L4, L6, L8… — these annotate the immediate king-capture timeline. Even L-numbers (plus L1, the special “currently delivering check”) count moves to deliver check or progress along a check chain.

Deferred Track (Material Compounding)

L3, L5, L7, L9… — these annotate the deferred king-capture timeline through material differential. Odd L-numbers from L3 onward count moves to capture an opposing piece, which removes a king-defender and compounds toward forced king capture in the endgame.

Both tracks terminate at L0. They are not separate outcomes — they are the same outcome at different time horizons. See The Unified Outcome Theorem for why this matters.

L0 — Game Over (Terminal)

King capture. Theoretical only — the game ends with checkmate before this happens. L0 is the terminus of every threat chain on either track. “This threat chain leads to L0.”

Direct Track (L1, L2, L4, L6, L8…)

L1 — Check

A move that puts the opponent’s king in check (+ in PGN, # if mate). L1 moves are slippery: when played, they either deliver mate, get captured, or slide back to L2 (avoid). They force a CAB response.

L2 — Threatens Check (1 move out)

A move that, on the next turn, will enable a check. L2 moves can be addressed by playing your own L1 (ignore with tempo), capturing the L2 piece, blocking the future check line, or downgrading the L2 to L4.

L4 — Threatens to Threaten Check (2 moves out)

A move that, after one further move, enables an L2 (and then L1). The direct-track chain: L4 → L2 → L1 → L0.

L6 — Threatens to Threaten to Threaten Check (3 moves out)

A move that, after two further moves, enables an L4. Direct-track chain: L6 → L4 → L2 → L1 → L0. Primarily used in the Relationships frame for static topology analysis; rarely actionable as a Move Analysis target since the time horizon is long.

L8, L10… (4+ moves out)

Same pattern, increasingly distant. Used in the Relationships frame for geometric topology; rarely actionable in Move Analysis. The Method typically caps Move Analysis at L4 or L5.

Deferred Track (L3, L5, L7, L9…)

L3 — Threatens Capture

A move that creates a capture threat on an opponent piece. L3 has the broadest defense set in the Method — see Extended L3 Defenses.

L3 is the opening move of the deferred king-capture sequence: the captured piece is removed from the king’s defensive lattice, contributing to the compounding material differential that resolves at L0 in the endgame.

L5 — Threatens to Threaten Capture (1 move from L3)

A move that, after one further move, enables an L3. Deferred-track chain: L5 → L3 → capture → … → L0 (through endgame compounding).

L7 — Threatens to Threaten to Threaten Capture (2 moves from L3)

A move that, after two further moves, enables an L5. Primarily used in the Relationships frame.

L9, L11… (3+ moves from L3)

Same pattern. Distant geometric relationships in the Relationships frame; rarely actionable in Move Analysis.

Why the two tracks have different time geometries

The direct track has forced sequences: L1 demands a CAB; L2# demands an L1 or L1(d#). Each step on the direct track compresses the opponent’s response space.

The deferred track has no forced response: an opponent can usually accept a capture and play on. Its progress accumulates rather than forces.

This asymmetry is what makes the Cross-Track Priority rule necessary: comparing direct-track progress to deferred-track progress requires accounting for how much each track constrains the opponent’s next moves, not just how many moves until L0.

Threat Level Variants

The Method uses suffix notation to capture indefensibility and cascade properties:

# (hash) — Indefensible

• L1# — Forced check sequence ending in mate. Zero CAB responses.
• L2# — Threatens an indefensible check (mate in 1). Can only be addressed by playing your own L1, OR by an L1(d#).
• L4# — Two moves from threatening forced mate.

* (asterisk) — Forced material gain

• L1* — Forced check sequence winning material.
• L3 — Threatens a loose* (unprotected) piece. Generally higher priority than equal-level threats with defenders.

## (double hash) — Doubly-indefensible

• L2## — Indefensible check threat that can only be defended by playing L1(d#), an exact check that also removes the opponent’s mate threat. If you don’t have L1(d#) loaded, you lose.
• L4## — Threatens an indefensible L2#. Same defense requirement.

d# — Defends checkmate

• L1(d#) — A check that, by being played, removes one of the opponent’s checkmate threats. The most demanding defensive resource in the Method.

Geometric Signatures of L-Levels

Each L-level has a visual pattern that allows the threat to be identified without calculation. This is what makes the epistemic order operable — you don’t need to compute anything to spot a candidate; you just need pattern recognition on piece geometry.

L1 — Direct Laser to King

Your piece’s attack line passes directly to the opponent’s king square with no obstructions. – Bishop on a1 lasers diagonally to king on h8 – Knight at f5 has its knight-jump to a square containing the king – Identification cost: trivial — recognized in under a second

L2 — Laser Through One Intermediate Square

Your piece’s attack line reaches the king square via one intermediate square that’s either empty (move there next turn → L1) or contains a piece you can remove via capture/interference. – Direct line, intermediate empty: bishop two diagonals from king through an empty square – Perpendicular segment: rook on the a-file, can swing to king’s rank – Discovered check setup: your blocking piece, when moved, opens the L1 of the piece behind it – Identification cost: low — recognize the intermediate-square pattern

L3 — Direct Laser to Enemy Piece

Same perceptual operation as L1, but the target is an opposing non-king piece. – Identification cost: trivial — same pattern as L1

L4 — Chained L2 Pattern

Your piece, if moved one move, lands on a square that has an L2 relationship to the king. – Identification cost: higher — composes two perceptual operations (“where can I move?” and “from where I land, is there an L2 to king?”)

L5 — Chained L3 Pattern

Same as L4 but for piece-track. Your piece, if moved one move, lands on an L3 square against an opposing piece.

The geometric signatures are what justify the epistemic order: L1 first because L1 is easiest to spot. The order is not arbitrary; it tracks perceptual difficulty.

“Defensible in X Moves”

The # notation appears binary — a threat either is or isn’t indefensible. This is not strictly accurate. No move in chess is truly indefensible. Every threat is “defensible in X moves,” where X is the calculation depth required to find or prepare the defense.

This generalizes the suffix system as a recursive count of defense-preparation moves:

• No suffix (e.g., L2) — defensible in 1 move (one CAB suffices)
• # suffix (e.g., L2#) — defensible in 2 moves (defense requires 1 move of preparation, then the response)
• ## suffix (e.g., L2##) — defensible in 3 moves, OR requires an L1(d#), itself a 2-move artifact
• ### suffix — defensible in 4 moves (rare in practice; calculation depth typically caps at 5-6 ply)

This recursion makes the suffix system open-ended rather than terminal. Position evaluation isn’t “is this indefensible?” but “how many moves of preparation does the defense require?” — which is computable, finite, and linearly comparable across candidates.

The Priority Hierarchy (Tiered)

The ontological order, organized into tiers. This is the order in which threats actually demand response once they’ve been identified and classified.

Tier 0 — Game-Terminal (must respond IMMEDIATELY)

You forfeit if you don’t address these this turn; chess rules force the response. 1. L1 — currently in check; must play CAB

Tier 1 — One-Move-To-Loss (must respond THIS turn)

You will be mated next turn if you don’t address these this turn. The address can be the move you play, OR a higher-priority move that addresses them as a side effect. 2. L2# — mate threat in 1 3. L2## — mate threat that requires 2-move defense; only L1(d#) addresses

Tier 2 — Forcing With One Move of Grace (must address WITHIN 1 turn)

Can be ignored for one move if you have a sufficiently powerful counter-action loaded. 4. L4# — threatens to become L2# next move 5. L4## — threatens to become L2## next move; the eventual defense must be L1(d#)

Tier 3 — Material-Significant (priority depends on piece value)

Don’t end the game directly but cost material that compounds toward eventual king capture. Priority is contextual via the Cross-Track Priority rule. 6. L3 — loose piece attack; generally dominates L2-with-CABs 7. L3 — capture threat against defended piece; priority scales with material at stake 8. L2* — regular check threat with CABs; eventually addressable, often deferrable

Tier 4 — Setup Threats (deferred)

9. L4 — regular 2-step check threat
10. L5 — regular 2-step capture threat

Same-Level Pairs

Some threats sit at equivalent priority — whoever plays first must have the response loaded: – L3 ≈ L4# — direct material threat vs forced-mate-in-2 setup – L3* ≈ L4## — loose piece vs deeper indefensible mate setup

Same-level pairs are where games are won and lost on tempo.

For the full justification of these tiers — including the L1’s slippery property and the role of suffix recursion — see How Do You Even Begin?.

Cross-Track Priority

The Method’s rule for deciding which threat to address when multiple threats exist on different tracks (or different positions on the same track).

The Rule

Ignore opponent’s piece threat IFF your alternative move achieves greater progress toward king capture (L0) than the deferred king-capture cost of losing your piece.

Equivalently: address opponent’s threat IFF your alternative candidate’s net king-capture progress is less than the cost of allowing the threat to execute.

This is not a heuristic. It follows directly from The Unified Outcome Theorem — both threats are progress on the same timeline, so prioritization reduces to a structural comparison rather than probabilistic weighting.

The Three Sufficient Exceptions

A piece threat may be ignored under any of three conditions, all of which reduce to the same underlying claim (your move’s king-capture progress ≥ the cost of allowing the threat):

Exception 1 — Symmetric Counter-Capture

You threaten an opposing piece of equal value. Net deferred king-capture progress = 0. Both players exchange equivalent defender-removal. Acceptable.

Exception 2 — Asymmetric Counter-Capture

You threaten an opposing piece of greater value. Net deferred king-capture progress > 0. Exchange favors you in the long-time-horizon king-capture sequence. Acceptable.

Exception 3 — Direct King-Track Progress

Your move advances the direct king-capture sequence (L4 → L2, L2 → L1, L1 with CABs removed → L1#) or removes a CAB from an existing opposing-king threat. Direct king-track progress is generally more efficient than deferred piece-track progress because:

• It compounds against the current king-capture sequence rather than the future one
• It is more likely to be forced, denying the opponent the chance to address the piece-track threat
• Convergence health on the direct track is preserved or improved

The most powerful single moves combine all three exceptions: they capture or threaten material AND advance the direct king-track AND remove opposing CABs. These are the moves classical chess literature labels “brilliancies” without explaining the underlying compositional structure.

Step in the Method

Cross-Track Priority Resolution is an explicit step in the Method’s algorithm, applied after [Candidate Generation] and before [Variation Evaluation]. Skipping it produces the two most common adult-improver skip patterns:

• Skip Pattern A (passive play): Player addresses every piece threat reflexively, never realizing they had a stronger king-track candidate that would have made the piece threat irrelevant.
• Skip Pattern B (over-aggressive play): Player pushes king-track moves while accumulating losses on the piece track that compound into a lost endgame.

Process Audits diagnose whichever skip pattern is responsible for a given failed move.

Endgame Caveat

The compounding assumption (material advantage converts to king capture in the endgame) is empirically true in the overwhelming majority of cases but admits a finite set of exceptions: K+B vs K (drawn), K+N vs K (drawn), K+B+B same color vs K (drawn), various fortress positions, wrong-color rook pawn endings, etc.

These should be treated as a known-position correction table: in cross-track priority, the deferred king-capture value of any material advantage is reduced to zero in positions known to draw, and adjusted toward the appropriate fractional value in positions where conversion is uncertain. The caveat does not weaken the rule; it constrains its application to the (vast) middlegame domain where compounding holds.

For the full treatment of the Cross-Track Priority rule, see The One Outcome.

Calculation Horizon

The Method’s algorithm operates inside a finite-step window — the number of plies a player can realistically calculate in real time. Threats inside the window are subject to the Priority Hierarchy and the Capture Clearance Protocol. Threats outside the window are not.

What’s Inside the Horizon

The default horizon for in-game decision-making:

These are the threats the priority rule and the clearance protocol weigh against each other. Roughly: anything within 2 plies of an execution (mate or material) is in-horizon.

What’s Outside the Horizon

L6, L7, L8+ threats (chained 3+ moves from execution) are outside the horizon for priority-rule purposes. They are real — they exist in the Relationships matrix — but they are NOT gates on the priority rule or the clearance protocol. They are handled by:

• Structural/positional layers (Relationships, Convergence) — long-horizon topology
• Tempi math — you have multiple moves to prepare a defense or counter-threat before any L6/L7/L8 escalates into a horizon-relevant threat

Why This Matters

The intuition “I don’t need to worry about an L6, it’s three moves away” is correct — and the horizon concept names it. Without an explicit horizon, the L-system becomes paralytic: every position has dozens of L6+ relationships, none of which should gate your move.

The horizon is the boundary between priority-rule territory (must compare, can’t ignore) and structural-layer territory (can defer, can absorb via topology). Every Method-derived decision is implicitly bounded by it.

Horizon Extension Under Pressure

Strong players extend the horizon to 3+ plies in critical positions (e.g., tactical sequences, classical time controls). Weaker players operate at a 1-ply horizon and miss L4# / L2## threats entirely. Training the Method largely means gradually expanding the horizon until it routinely captures all of Tier 2 plus the relevant Tier 3 candidates.

CAB Defense System

When facing an L1 (check), you have exactly three direct response types — Capture, Avoid, Block.

Capture

Take the checking piece. The threat disappears.

Avoid

Move the king out of check. The L1 slides back to L2 — the threat persists at lower priority.

Block

Interpose a piece between the checking piece and the king. Block transforms the L1 into a combined L2 (still threatens check) + L3 (now threatens the blocking piece).

Why CAB matters

Counting available CABs is how the Method determines indefensibility. Zero CABs = L1#. One CAB = potentially L2# if you can remove that CAB. Multiple CABs = explore further options.

Extended L3 Defenses

L3 (capture threats) have a richer defense vocabulary than L1 because the threatened piece isn’t the king. The Method recognizes 8 defense types:

1. Capture

Take the attacking piece outright.

2. Avoid

Move the threatened piece to safety.

3. Block

Interpose between attacker and target.

4. Tempo

Play a check (L1) to buy time. The opponent must respond to your L1 before executing their L3, often allowing you to address it on the next move.

5. Pin (King)

Pin the attacker to its own king. The attacker can’t capture without moving into a pin violation.

6. Pin (Material)

Pin the attacker to a more valuable piece. The attacker can capture, but only at the cost of losing the piece behind.

7. Deflect

Capture a piece the attacker is currently defending. The attacker now has a new threat to address (your capture), often giving you tempo to escape the original L3.

8. Protect

Add a defender to the threatened square. If they capture, you recapture — turning the L3 into a trade.

9. Counter-Attack

Threaten something more valuable than what they’re attacking. Forces them to choose: their threat or yours.

CAB Manipulation

Moves don’t just create threats — they ADD or REMOVE defensive options for existing threats.

CAB Removal

A move that removes one of the opponent’s defensive options against your L2. If you remove the last CAB, your L2 becomes L2#. Methods of CAB removal: – Capture defender — take the piece guarding the check square – Deflect defender — capture a piece the defender is protecting – Interfere — block the defender’s line to the check square – Pin defender — pin the defending piece so it can’t move – Laser escape square — attack a king escape (removes Avoid) – Capture blocker — take the piece that could interpose

CAB Addition

A move that gives YOU a new defensive option against an opponent’s L2 — preventing it from becoming L2#. Methods: – Vacate escape square — move your own piece off the king’s escape – Reposition king — move king to a square with more escapes – Laser the check square — add an attacker to the threatening square – Create protected block — add a second attacker to a blocking square

CAB Manipulation is the heart of tactical chess. Every brilliant combination resolves to: “I removed your last CAB; my threat is now indefensible.”

Captures as Threat-Grid Operations

A capture is not merely a +N material event. It is a threat-grid operation that performs one or more functions, each with different priority implications. Before evaluating any capture, ask: what does this capture accomplish in terms of the threat grids?

Function 1 — Removal of an Active Threat

The capture removes a piece currently delivering a threat (an L1, L2, or L3 attacker). The threat disappears with the captured piece.

Function 2 — Removal of a Deep-Down Threat

The capture removes a piece that is part of a deferred threat chain (L4, L5, L6…). Prophylactic capture; preempts the deep threat before it activates.

Function 3 — Removal of Opponent’s Threat-Defense (CAB-Removal)

The capture removes a piece that was defending against one of your threats — i.e., it removes an opposing CAB. This enables one of your threats to escalate (e.g., upgrades your L2 to L2# by removing the last defender).

Function 4 — Enabler of a Deeper Threat

The capture clears a line, opens a discovery, or creates space that activates one of your deeper threats. The capture itself is incidental; the line-clearing or square-vacating is the point.

Why this framing matters

A capture’s value isn’t its material change in isolation — it’s the net topology shift across both your and your opponent’s threat structures. The “poisoned pawn” failure mode is exactly when a player executes Function 1 or 4 (capturing for material or threat-removal) while ignoring a higher-priority active threat that the capture enabled or didn’t address.

The Capture Clearance Protocol

Before executing any capture-for-material, run three clearance checks in order. The capture is permissible only when all three pass. This protocol is a direct corollary of the Cross-Track Priority rule, specialized for the most consequential single decision in adult-improver chess.

Check 1 — Mate-Tier Clearance. Does the opponent have an against-self {L1, L2#, L2##, L4##} that would mate inside the calculation horizon? These are the four “must-respond” moves (Tiers 0/1/2 of the Priority Hierarchy).

• If yes: the capture is permissible only if it also addresses the mate threat (captures the attacker, blocks the line, removes a critical opponent CAB) — OR you have a loaded L1(d#) that buys tempo to defend after the capture.
• If no: proceed to Check 2.

Check 2 — Material Clearance. Does the opponent have an against-self L3 against one of your pieces of value ≥ the capture’s gain?

• If yes: the capture is permissible only if net gain (capture value − retaliation cost) exceeds the opponent’s L3 cost. Apply Cross-Track Priority directly.
• If no: proceed to Check 3.

Check 3 — Horizon Truncation. L5, L6, L7+ threats (chained 3+ moves from execution) are outside the calculation horizon — you have tempi to handle them via Relationships and Convergence later. They do not gate the capture.

When all three checks pass, the capture is freely executable. When Check 1 or 2 fails and no conditional bypass applies, the higher-tier threat is addressed first.

The protocol’s order matters: Check 1 must come first because mate is final. See Capture Execution (X) for the deeper framing of why captures require this special handling.

Capture Execution (X) — Terminus of the Capture Track

A capture (notated X) is the execution terminus of the capture track. The L-system describes threats — L1, L2, L3, L4, L5 — and threats-of-threats. X is the only “current-move execution” on the capture track, just as L1 is the only one on the king track.

The Symmetry

This symmetry is exact. The threat of X = L3 (just as the threat of L1 = L2). X is the cashing-in of deferred king-capture progress per the Unified Outcome Theorem.

The Critical Asymmetry — Tempo

The execution termini are not tempo-equivalent:

• L1 grants tempo — opponent is forced by chess rules to respond (CAB). After L1, the next move is implicitly yours to direct; you can recover from a marginal position because the next exchange is your tempo.
• X does not grant tempo — opponent can respond if X also creates a threat (e.g., capture-with-check, capture-with-discovery), but doesn’t have to. After a “naked” X, opponent moves freely.

This asymmetry is why “when can I capture?” is operationally harder than “when can I check?” — checking buys the next tempo; capturing does not. A capture that ignored an opponent’s loaded L4# loses next move, because the opponent doesn’t owe you a response.

The Capture Clearance Protocol exists precisely because X demands stricter clearance than L1.

Placement in the Priority Hierarchy

X is not a fixed rung in the Priority Hierarchy. It is an execution-mode operation gated by the hierarchy. When the Capture Clearance Protocol passes against Tiers 0/1/2, X executes at Tier 3 (alongside L3*/L3/L2). When loaded counters apply (e.g., your L1(d#) buying tempo against opponent’s L4##), X conditionally leapfrogs Tier 2.

X’s “base tier” is Tier 3 with conditional escalation. The clearance protocol is the placement — there is no fixed rung.

X for Material vs X for Function

Not every capture is “X for material.” Captures perform one or more of the four functions in Captures as Threat-Grid Operations. The clearance protocol applies to the for-material case specifically (Function 1 or 4 — material gain or threat-removal that yields material). Captures that are simultaneously Function 3 (CAB-removal enabling your higher-tier threat) often don’t need the same clearance because they’re themselves part of your own higher-tier sequence.

Why X Is the Hardest Operational Question

“When is it OK to capture?” is the single most consequential in-game decision in adult-improver chess. Most blunders at 1400-1900 ELO are captures executed without the clearance protocol. The Method’s contribution is to formalize the clearance as a structured three-check sequence rather than a heuristic “look before you leap.”

For the formal protocol, see Captures as Threat-Grid Operations § Capture Clearance Protocol. For the public-facing operationalization, see When Is It OK to Capture?

Against-Self Analysis

The Method evaluates every move from BOTH sides of the board — not just what threats your move creates, but what threats your move enables for your opponent.

Against-Self L2 Your move that allows opponent to deliver check on their next turn.

Against-Self L3 Your move that allows opponent to capture one of your pieces on their next turn.

Against-Self L4 / L5

Two-step versions. Less actionable but worth checking when calculating long sequences.

Against-Self analysis is the blunder firewall — every candidate move runs through it before you commit. This is the step most club players skip, and the Method makes skipping it impossible.

Relationships (Static Topology)

A relationship is the threat proximity between two pieces in their current positions, regardless of whose turn it is.

Relationship Level

• L2 — one move from check
• L3 — one move from capture
• L4 — two moves from check
• L5 — two moves from capture
• L6 — three moves from check
• L7 — three moves from capture
• … and so on, with the level determined by the shortest path

Square Path

A relationship is defined by a path of squares, not a sequence of moves. Example:

Bf1 ⟷ Ke8 — square path: f1 → g2 → h3 → d7 → e8 (5 squares = L6)

The path shows pure geometry, independent of whose turn it is.

Multiple Paths

A single piece-to-piece relationship can have many valid square paths. Nb1 ⟷ Ke8 has 7 paths in the starting position. The relationship level = the shortest path; the path count = the antifragility of the relationship (more paths = more resilience against defensive blocks).

Obstructions

Pieces sitting on path squares. Three types: – Own-piece obstruction — clearable; move the blocker away – Enemy-piece obstruction — must capture or find an alternate path – Permanent obstruction — cannot be cleared (e.g., your own king blocking; structural blockades)

Relationship Matrix

The full NxN matrix of all piece-to-piece relationships in a position. Every move transforms this entire matrix — typically dozens of relationships shift on a single move.

Airdrop Mental Model

The mental discipline of treating each new position as if all pieces were simultaneously airdropped onto the board, regardless of which piece moved last. Stop thinking “opponent moved Nf6”. Start thinking “the entire board is now reconfigured; here are all the relationships.” This replaces piece-tracking heuristics with systematic full-board analysis.

The Airdrop discipline has three implications:

1. The FROM square doesn’t matter for analysis. Whether the bishop on d6 came from e7 or c7 is irrelevant — what matters is that it’s on d6 RIGHT NOW, presenting threats simultaneously with every other piece.
2. You’re not responding to ONE move. When the opponent plays Rxg6+, you’re not responding to “rook moved to g6.” You’re responding to the entire reconfigured topology — Rxg6+ AND every other piece’s relationships AND every threat on the board, all at once.
3. All threats exist simultaneously. Both sides’ L2s, L3s, L5s, L6s present themselves in parallel. When it’s your turn, you’re choosing how to reconfigure THIS topology into a new one — not “responding to the last move.”

When fully internalized, the Airdrop discipline replaces piece-tracking heuristics with continuous topology perception — seeing the board as a transforming threat structure rather than a record of moves played.

Relationship Types

Relationships partition into three functional categories:

• Offensive — King-directed (your pieces → opponent’s king, L2-L9) and material-directed (your pieces → opponent’s valuable pieces, L3-L9)
• Defensive — Protection (your pieces → your threatened pieces) and counter-threat (your pieces → opponent’s attackers)
• Positional — Control (your pieces → key squares) and restriction (your pieces → opponent’s mobility)

Each type contributes differently to the Cross-Track Priority calculation. Offensive relationships drive direct king-track progress; defensive relationships protect against opposing progress; positional relationships shape long-term topology.

The Relationship Matrix

A position’s full relationship structure can be represented as an NxN matrix, where N is the number of pieces on the board. Each cell M[i][j] contains the relationship level between piece i and piece j, plus the count of distinct paths.

         Nf3   Re1   Qd2   ...
    ┌─────────────────────────
Nf6 │  L5    ∞     L7    ...
Re8 │  ∞     L3    L5    ...
Qd8 │  L7    L5    L3    ...
... │  ...

Every move transforms this entire matrix simultaneously. A “quiet” pawn push might: – Upgrade 5 relationships (move pieces closer to targets) – Downgrade 2 (move pieces farther) – Create 3 new relationships (open lines, discover pieces) – Sever 1 (block a line, obstruct a piece)

The Delta View is the UI that quantifies and visualizes this transformation per candidate move.

Convergence

The progressive narrowing of paths as a player commits to specific lines of play. Every move actualizes one possibility while eliminating others — Aristotelian act-from-potency, applied to chess.

The Aristotelian Framing

In Aristotelian-Thomistic metaphysics, change is the movement from potency (potentia) to act (actus). A block of marble has the potential to become a statue; the sculptor actualizes that potential through deliberate cuts. Each cut removes other possible statues forever — the sculptor cannot create without destroying potency.

Chess is the same operation. The starting position has vast potency (millions of possible games). Each move actualizes one possibility while eliminating others. Checkmate is pure act — the position is fully determined.

The Two Dimensions of Progress

Every move operates on two dimensions simultaneously:

• Vertical — escalation of threat level (L6 → L4 → L2 → L1 → L0). The telos of every threat chain.
• Horizontal — narrowing of paths (9 paths → 6 → 3 → 1). The progressive determination of the game’s outcome.

A piece’s relationship to the king typically has multiple square paths. The relationship level = the shortest path; the path count = the antifragility of the relationship. More paths = more defensive burden on opponent and greater resilience against any single defensive resource.

Path Efficiency

A measure of how well a move trades potency for actuality:

Efficiency = threat-level improvement / paths sacrificed

A move that gains 2 levels at the cost of 3 paths (efficiency 0.67) is more efficient than one that gains 2 levels at the cost of 7 paths (efficiency 0.29). The first move preserves more optionality while making the same progress.

Convergence Health

Four classifications of how well a move’s path-narrowing matches its threat-level progress:

• Healthy — paths narrow proportionally to threat-level improvement (e.g., L6 [9 paths] → L4 [6 paths] → L2 [3 paths] → L1 [1 path]). The sacrifice of potency purchases proportional actuality.
• Cautious — paths narrow faster than threat-level improves (e.g., L6 [9 paths] → L6 [2 paths]). Potency is spent without corresponding gain. Fragility risk rising.
• Fragile — very few paths remain at a distant threat level (e.g., L4 [1 path]). One defensive block ends the threat.
• Stagnant — threat-level improves while paths stay constant (e.g., L6 [9 paths] → L4 [9 paths]). Actually good — maintaining optionality while advancing.

Path Count as Defensive Burden

More paths = more cognitive load for the defender. A threat with 9 paths forces the opponent to find a defense that addresses all of them. A move that blocks 1 path leaves 8 threats intact. This compounds:

• Cognitive load — more possibilities to calculate
• Practical difficulty — harder to find universal solutions
• Time pressure — more variations consume clock time
• Antifragility — single defensive resources don’t neutralize multi-path threats

The Commitment Decision

Every move asks: “Should I commit (reduce paths) or maintain optionality (preserve paths)?”

Reasons to commit: – You’ve identified the winning line – Delaying allows defensive consolidation – Concrete threats force concrete responses

Reasons to maintain optionality: – The position is unclear – You’re still probing for weaknesses – Multiple threats create confusion

The goal is timely convergence — narrowing the funnel of possibility at exactly the rate that your increasing actuality demands. Premature convergence creates fragility; delayed convergence allows defensive consolidation.

“The wise player holds potency until the moment of decisive action, then commits fully — transforming the many possible victories into the one actual victory.”

The Delta View (System Impact)

The UI/feature that quantifies how every move reconfigures the entire topology. Every move simultaneously:

Upgraded Relationship

Move closer to a target piece. L7 → L5, L5 → L3, etc. Shown in green in the board overlay.

Downgraded Relationship

Move farther from a piece. L3 → L5, etc. Shown in red.

Created Relationship

New geometric connection that didn’t exist before (line opened, piece discovered). Shown in cyan.

Severed Relationship

Connection that existed before but no longer (line blocked, piece obstructed). Shown in fading gray.

Topology Score / System Impact Score

A single-number summary: Σ(upgrades) − Σ(downgrades) + Σ(created) − Σ(dangers). King-directed changes weighted +3 per level, piece-directed +1, against-self threats penalized.

Position Phase

The Delta View detects the position’s phase and adjusts what it shows: – Quiet — no active L2s/L3s. Topology Score is the right lens. Show prominently. – Tension — L2s/L3s exist but no forced sequences. Show score dimmed; flag tactical threats first. – Tactical — forced sequences exist (L2#, L4#, active checks). Hide score entirely. Forced lines dominate.

The score is shown only when it genuinely informs the decision. In tactical positions, concrete CAB analysis takes over.

When the Topology Score Is Useful (and When It Misleads)

Position phase maps directly to where the score is informative:

The Delta breakdown (upgrades/downgrades/created/severed) is always shown regardless of phase — even in tactical positions, knowing “this defense also upgrades my bishop’s relationship to opponent’s king” is useful context. Only the collapsed single-number score is hidden in tactical positions, because it can mislead when forced lines are the actual driver of move choice.

Process Audit

The diagnostic application of the Method to a failed move. When a player makes a wrong move, a Process Audit walks the position through the Method step-by-step to identify the exact step in the chain the player skipped.

Engine analysis tells you the correct move. Coach analysis tells you what to consider. Only the Process Audit tells you which specific step in your thinking process broke down.

This is the foundation of: – The flagship recurring blog column on ChessLogic.io (see chesslogic-process-audit-spec.md) – The future SaaS feature: upload a game, get an automated process audit on every mistake – The training methodology that lets adult improvers diagnose their own thinking errors

Notational Conventions Summary