Model
Model summary placeholder for grid2d_one_target_base.
grid2d_one_target_base
Grid2D One Target — Base
**Status: WIP scaffold (not yet started).** Tracking: [#4] This is the **mother report** for the `grid2d_one_target_*` sub-series. It defines the shared problem setup, notation, and conventions used by the four sibling reports listed below.
Book PositionReading PathConnected ReportsNarrative Arc PositionVerifiable ClaimsInteractive FiguresMathematical LogicFormula LibraryNarrative NotesAppendix & Assets
Updated: 9 Jun 2026, 21:57:41 UTC
Method
Method summary placeholder for grid2d_one_target_base.
Result
Result summary placeholder for grid2d_one_target_base.
Book Position
This report is part of the chapterized mainline. Use chapter links to keep continuity instead of reading reports in isolation.
Primary chapter Chapter 6: Reproducibility & Validation
Also appears in chapter-6-repro-validation
Reading Path
- Scan key findings first to decide whether this report is relevant.
- Use the interactive panel to test parameter and shape sensitivity.
- Then read the mathematical chain and formula library for derivation details.
Key Findings
- `grid2d_one_target_exit_timing` — exit-timing distribution
- `grid2d_one_target_window_measures` — fixed-window measures (mass, percentile, tail)
- `grid2d_one_two_target_gating` — gating effect of adding a second target (uses base + extends)
- **Problem setup**: single absorbing target on a finite 2D-grid; choose between reflecting / periodic boundary; start position protocol; T grid convention.
- **Notation**: target placement $\mathbf{x}^\star$, start $\mathbf{x}_0$, FPT $\tau$, lattice constants, time discretisation.
Connected Reports
This report sits inside a shared chain. Use links below to move upstream/downstream and across model families.
Track Continuity
- Previous: Grid2D Membrane Near Target
- Next: Grid2D One Target — Exit Timing
Same-Group Links
- Grid2D Membrane Near Target
adjacent in trackFirst-passage distribution
- Grid2D One Target — Exit Timing
adjacent in trackFirst-passage distribution
- Grid2D One Target — Valley/Peak Budget
First-passage distribution
- Grid2D One Target — Window Measures
First-passage distribution
Cross-Group Bridges
- Cross-Model Luca Regime Map
First-passage distribution
- Reflecting Encounter Diagonal Decomposition
First-passage distribution
- Reflecting Encounter Mean Validation
First-passage distribution
- Exact Recursion — Method Guide
First-passage distribution
Narrative Arc Position
This report appears in one or more global arcs. Use these checkpoints to keep reading continuity across pages.
grid2d progression
grid2d track links 13 reports into one continuous argument.
Checkpoints: 13 Claims: 63
Open arc sequence
- Grid2D Bimodality Baseline
- Grid2D Reflecting-Boundary Bimodality
- Grid2D Blackboard Endpoint Case
- Grid2D Two-Target Double-Peak
- 2D Two-Walker Encounter With Shortcut
- Grid2D Rectangle Bimodality
- Grid2D Membrane Near Target
- Grid2D One Target — Base
- Grid2D One Target — Exit Timing
- Grid2D One Target — Valley/Peak Budget
- Grid2D One Target — Window Measures
- Grid2D One vs Two Target — Gating
- Grid2D Two-Target Bias-Radius Scaffold
Grid and ring mechanisms converge into cross-report synthesis.
Global storyline that connects all report families from mechanism to synthesis.
Checkpoints: 27 Claims: 130
Open arc sequence
- Lazy Ring Jump-Over Mechanism (K2 vs K4)
- Lazy Ring Shortcut Beta Scan
- Lazy Ring Shortcut Figure-1 Revision
- Lazy Ring Flux Baseline
- Ring Valley Regime Map
- Destination-Scan Valley Control
- Ring Derivation Backbone
- Two-Target Lazy Ring Mechanics
- 1D Ring Two-Walker Encounter With Shortcut
- Grid2D Bimodality Baseline
- Grid2D Reflecting-Boundary Bimodality
- Grid2D Blackboard Endpoint Case
- Grid2D Two-Target Double-Peak
- 2D Two-Walker Encounter With Shortcut
- Grid2D Rectangle Bimodality
- Grid2D Membrane Near Target
- Grid2D One Target — Base
- Grid2D One Target — Exit Timing
- Grid2D One Target — Valley/Peak Budget
- Grid2D One Target — Window Measures
- Grid2D One vs Two Target — Gating
- Grid2D Two-Target Bias-Radius Scaffold
- Cross-Model Luca Regime Map
- Final Multitimescale FPT and Encounter Report
- Exact Recursion — Method Guide
- Reflecting Encounter Diagonal Decomposition
- Reflecting Encounter Mean Validation
Verifiable Claims
Claims below are tied to explicit evidence paths so each statement can be audited.
Report Objective
Result summary placeholder for grid2d_one_target_base.
Verification Steps
- Read the key claims and their evidence references first.
- Verify at least one equation card and one dataset panel against source paths.
- Cross-check this report with upstream/downstream linked reports.
MODEL
model grid2d_one_target_base-c1
Model summary placeholder for grid2d_one_target_base.
Evidence trail
source_documentresearch/reports/grid2d_one_target_baseSource-backed model claim in Grid2D One Target — Base: Model summary placeholder for grid2d_one_target_base.
Linked reports Reflecting Encounter Diagonal DecompositionReflecting Encounter Mean ValidationExact Recursion — Method GuideGrid2D One Target — Exit Timing
METHOD
method grid2d_one_target_base-c2
Method summary placeholder for grid2d_one_target_base.
Evidence trail
dataset/data/v1/reports/grid2d_one_target_base/series/asset-size-profile.jsonMechanism dataset for Grid2D One Target — Base: asset-size-profile
Linked reports Reflecting Encounter Diagonal DecompositionReflecting Encounter Mean ValidationExact Recursion — Method GuideGrid2D One Target — Exit Timing
RESULT
result grid2d_one_target_base-c3
Result summary placeholder for grid2d_one_target_base.
Evidence trail
dataset/data/v1/reports/grid2d_one_target_base/series/asset-size-profile.jsonMechanism dataset for Grid2D One Target — Base: asset-size-profile
Linked reports Reflecting Encounter Diagonal DecompositionReflecting Encounter Mean ValidationExact Recursion — Method GuideGrid2D One Target — Exit Timing
FINDING
finding grid2d_one_target_base-c4
grid2d_one_target_exit_timing — exit-timing distribution.
Evidence trail
source_documentresearch/reports/grid2d_one_target_basegrid2d_one_target_exit_timing — exit-timing distribution.
section_summaryresearch/reports/grid2d_one_target_baseOverview: grid2d_one_target_exit_timing — exit-timing distribution.
math_blockresearch/reports/grid2d_one_target_baseFinding formula context in Grid2D One Target — Base: grid2d_one_target_exit_timing — exit-timing distribution.
dataset/data/v1/reports/grid2d_one_target_base/series/asset-size-profile.jsonMechanism dataset for Grid2D One Target — Base: asset-size-profile
Linked reports Grid2D One Target — Exit TimingGrid2D Reflecting-Boundary Bimodality
finding grid2d_one_target_base-c5
grid2d_one_target_window_measures — fixed-window measures (mass, percentile, tail).
Evidence trail
source_documentresearch/reports/grid2d_one_target_basegrid2d_one_target_window_measures — fixed-window measures (mass, percentile, tail).
section_summaryresearch/reports/grid2d_one_target_baseOverview: grid2d_one_target_window_measures — fixed-window measures (mass, percentile, tail).
math_blockresearch/reports/grid2d_one_target_baseFinding formula context in Grid2D One Target — Base: grid2d_one_target_window_measures — fixed-window measures (mass, percentile, tail).
dataset/data/v1/reports/grid2d_one_target_base/series/asset-size-profile.jsonMechanism dataset for Grid2D One Target — Base: asset-size-profile
Linked reports Grid2D One Target — Window MeasuresLazy Ring Shortcut Beta ScanGrid2D Blackboard Endpoint Case
Interactive Dataset
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Mathematical Logic Chain
From model assumptions to interpretation in a short, ordered chain.
Distribution Setup
Defines first-passage probability objects used by later diagnostics.
Fallback
Mathematical Principles
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Fallback EN
Formula source
research/reports/grid2d_one_target_base
Narrative Sections
Cleaned chapter summaries are shown first; low-value placeholders are hidden.
Overview
Overview: this section connects Grid2D One Target Base assumptions to measurable observables, verification commands, and downstream chapter claims.
Source
research/reports/grid2d_one_target_base
Reproducibility Commands
Open command list
python3 scripts/reportctl.py build --report grid2d_one_target_base --lang enpython3 scripts/reportctl.py translation-qcpython3 scripts/reportctl.py web-build --mode changed --skip-npm-ci
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