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grid2d
- 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
misc
ring Book: chapter-3-ring-baseline
Lazy Ring Jump-Over Mechanism (K2 vs K4)
ring_lazy_jump
This report establishes the baseline jump-over mechanism for lazy rings with one directed shortcut, contrasting K=2 and K=4 under exact first-passage diagnostics.…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:42 UTC
ring Book: chapter-4-shortcut-variants
Lazy Ring Shortcut Beta Scan
ring_lazy_jump_ext
This extension quantifies how shortcut strength beta reshapes first-passage bimodality on lazy rings at fixed N=100, then checks transfer by N sweeps and Monte Carlo class decomposition.…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:42 UTC
ring Book: chapter-4-shortcut-variants
Lazy Ring Shortcut Figure-1 Revision
ring_lazy_jump_ext_rev2
This revision reorganizes the lazy-shortcut extension into a publication-ready evidence flow: co-located Fig.1 overlays f(t) with window-level class bars, while threshold, window-shift/width, and MC-uncertainty analyses test robustness.…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:42 UTC
ring Book: chapter-1-core-fpt
Lazy Ring Flux Baseline
ring_lazy_flux
This report studies first-passage distributions on a lazy ring with one directed shortcut drawn from self-loop probability. It combines Chebyshev generating-function derivation, AW/FFT inversion, and flux-recursion cross-checks to show a reproducible small-p bimodal regime, while…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:42 UTC
ring Book: chapter-3-ring-baseline
Ring Valley Regime Map
ring_valley
This valley-study report analyzes a non-lazy K-neighbor ring with a one-way shortcut 6->N/2+1 under the Fig.3 peak rule. Exact AW inversion and MC validation map bimodality windows across even N and K: no bimodality for K=2 after parity-aware coarse graining, but clear windows fo…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:42 UTC
ring Book: chapter-4-shortcut-variants
Destination-Scan Valley Control
ring_valley_dst
This report fixes N=100 and K=6, then scans shortcut destination dst to control the second-peak structure of first-passage distributions.…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:42 UTC
ring Book: chapter-0-reading-guide
Ring Derivation Backbone
ring_deriv_k2
This derivation report provides the analytical backbone for ring models with one directed long-range link, including defect-free propagators, defect corrections, and first-passage generating functions.…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:42 UTC
ring Book: chapter-0-reading-guide
Two-Target Lazy Ring Mechanics
ring_two_target
This report builds an exact two-target lazy-ring framework and compares no-shortcut versus selfloop-shortcut regimes. By scanning N, K, and beta with peak/valley diagnostics, it shows how target geometry and shortcut routing jointly control the transition among unimodal, bimodal,…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:42 UTC
ring Book: chapter-6-repro-validation
1D Ring Two-Walker Encounter With Shortcut
ring_two_walker_encounter_shortcut
Robust numerical verification of appendix Eq. Exact first-encounter computation on 1D ring with directed shortcut.
Languages: en, cn
Updated: 9 Jun 2026, 21:57:42 UTC
grid2d Book: chapter-0-reading-guide
Grid2D Bimodality Baseline
grid2d_bimodality
This foundational Grid2D report establishes how biased/lazy random walks generate first-passage bimodality on a square lattice. It unifies model constraints, defect-aware propagators, AW inversion, and candidate-case scans into one auditable chain that separates genuine two-chann…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
grid2d Book: chapter-2-grid2d-family
Grid2D Reflecting-Boundary Bimodality
grid2d_reflecting_bimodality
This reflecting-boundary Grid2D report tests whether bimodality survives when periodic shortcuts are removed and all walls reflect.…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
grid2d Book: chapter-2-grid2d-family
Grid2D Blackboard Endpoint Case
grid2d_blackboard_bimodality
This blackboard-style Grid2D case studies reflecting boundaries with start and target anchored at wall endpoints. The Z/S endpoint configurations are used to test whether a visually delayed hump is a true second peak or a window-edge artifact, with diagnostics linked to channel d…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
grid2d Book: chapter-1-core-fpt
Grid2D Two-Target Double-Peak
grid2d_two_target_double_peak
This report studies two absorbing targets in 2D and maps when the total first-passage distribution develops visible double peaks.…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:42 UTC
grid2d Book: chapter-6-repro-validation
2D Two-Walker Encounter With Shortcut
grid2d_two_walker_encounter_shortcut
A robust numerical routine verifying equivalence between appendix Eq. Exact time-domain first-encounter computation for two independent walkers.
Languages: en, cn
Updated: 9 Jun 2026, 21:57:42 UTC
grid2d Book: chapter-2-grid2d-family
Grid2D Rectangle Bimodality
grid2d_rect_bimodality
This report extends Grid2D bimodality from square to rectangular domains, testing how aspect ratio, reflecting walls, and endpoint geometry reshape first-passage channels.…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
grid2d Book: chapter-6-repro-validation
Grid2D Membrane Near Target
grid2d_membrane_near_target
one-target corridor with symmetric/asymmetric semi-permeable membranes; no-corridor two-target setting with one target near the start.
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
cross Book: chapter-5-cross-model-synthesis
Cross-Model Luca Regime Map
cross_luca_regime_map
This cross-report study benchmarks full-FPT solvers under fixed-horizon fairness, comparing sparse exact recursion against Luca defect-reduced routes while keeping linear-system MFPT only as reference.…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
misc Book: chapter-6-repro-validation
Final Multitimescale FPT and Encounter Report
final_multitimescale_fpt_encounter
shows the actual spatial configuration for each selected case. The left panel in each row is the physical reflecting one-dimensional lattice: the two walker starts are marked, the reflecting walls are drawn at sites (1) and (N), and the dominant early/late encounter sites are sho…
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
grid2d Book: chapter-6-repro-validation
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.
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
grid2d Book: chapter-6-repro-validation
Grid2D One Target — Exit Timing
grid2d_one_target_exit_timing
**Status: WIP scaffold (not yet started).** Tracking: [#5] Directory layout is in place; no code, manuscript, or notes have been written.
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
grid2d Book: chapter-6-repro-validation
Grid2D One Target — Valley/Peak Budget
grid2d_one_target_valley_peak_budget
**Status: 3-page short report. code and notes still pending.**
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
grid2d Book: chapter-6-repro-validation
Grid2D One Target — Window Measures
grid2d_one_target_window_measures
**Status: WIP scaffold (not yet started).** Tracking: [#7] Directory layout is in place; no code, manuscript, or notes have been written.
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
grid2d Book: chapter-6-repro-validation
Grid2D One vs Two Target — Gating
grid2d_one_two_target_gating
**Status: WIP scaffold (not yet started).** Tracking: [#8] Directory layout is in place; no code, manuscript, or notes have been written.
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
misc Book: chapter-6-repro-validation
Exact Recursion — Method Guide
exact_recursion_method_guide
**Status: WIP scaffold (not yet started).** Tracking: [#9] Directory layout is in place; no code, manuscript, or notes have been written.
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
misc Book: chapter-6-repro-validation
Reflecting Encounter Diagonal Decomposition
encounter_reflecting_diagonal_decomp
This report runs a bounded mobility-ratio scan for the reflecting-boundary
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
misc Book: chapter-6-repro-validation
Reflecting Encounter Mean Validation
encounter_reflecting_mean_validation
This report validates the first exact-computation step for a one-dimensional
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC
grid2d Book: chapter-6-repro-validation
Grid2D Two-Target Bias-Radius Scaffold
grid2d_two_target_bias_radius
State space: rectangular grid `{0, Lx-1} x {0, Ly-1}`. Boundary rule: reflecting attempted-outside-stays. Any move that would leave
Languages: en, cn
Updated: 9 Jun 2026, 21:57:41 UTC