valley-k-small
encounter_reflecting_mean_validation

Reflecting Encounter Mean Validation

This report validates the first exact-computation step for a one-dimensional

Book PositionReading PathConnected ReportsNarrative Arc PositionVerifiable ClaimsInteractive FiguresMathematical LogicFormula LibraryNarrative NotesAppendix & Assets

Updated: 9 Jun 2026, 21:57:41 UTC

Model

Model summary placeholder for encounter_reflecting_mean_validation.

Method

Method summary placeholder for encounter_reflecting_mean_validation.

Result

Result summary placeholder for encounter_reflecting_mean_validation.

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

← Previous chapter Next chapter →

Reading Path

  1. Scan key findings first to decide whether this report is relevant.
  2. Use the interactive panel to test parameter and shape sensitivity.
  3. Then read the mathematical chain and formula library for derivation details.

Key Findings

Show remaining findings
  • `P_i(x, x) = 1 - Q_i`

Connected Reports

This report sits inside a shared chain. Use links below to move upstream/downstream and across model families.

Narrative Arc Position

This report appears in one or more global arcs. Use these checkpoints to keep reading continuity across pages.

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
  1. Lazy Ring Jump-Over Mechanism (K2 vs K4)
  2. Lazy Ring Shortcut Beta Scan
  3. Lazy Ring Shortcut Figure-1 Revision
  4. Lazy Ring Flux Baseline
  5. Ring Valley Regime Map
  6. Destination-Scan Valley Control
  7. Ring Derivation Backbone
  8. Two-Target Lazy Ring Mechanics
  9. 1D Ring Two-Walker Encounter With Shortcut
  10. Grid2D Bimodality Baseline
  11. Grid2D Reflecting-Boundary Bimodality
  12. Grid2D Blackboard Endpoint Case
  13. Grid2D Two-Target Double-Peak
  14. 2D Two-Walker Encounter With Shortcut
  15. Grid2D Rectangle Bimodality
  16. Grid2D Membrane Near Target
  17. Grid2D One Target — Base
  18. Grid2D One Target — Exit Timing
  19. Grid2D One Target — Valley/Peak Budget
  20. Grid2D One Target — Window Measures
  21. Grid2D One vs Two Target — Gating
  22. Grid2D Two-Target Bias-Radius Scaffold
  23. Cross-Model Luca Regime Map
  24. Final Multitimescale FPT and Encounter Report
  25. Exact Recursion — Method Guide
  26. Reflecting Encounter Diagonal Decomposition
  27. 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 encounter_reflecting_mean_validation.

Verification Steps
  1. Read the key claims and their evidence references first.
  2. Verify at least one equation card and one dataset panel against source paths.
  3. Cross-check this report with upstream/downstream linked reports.

FINDING

finding encounter_reflecting_mean_validation-c4

Interval: {0, L-1}.

Evidence trail
  • source_document research/reports/encounter_reflecting_mean_validation

    Source-backed finding claim in Reflecting Encounter Mean Validation: Interval: {0, L-1}.

  • section_summary research/reports/encounter_reflecting_mean_validation

    Overview: Interval: {0, L-1}.

  • math_block research/reports/encounter_reflecting_mean_validation

    Finding formula context in Reflecting Encounter Mean Validation: Interval: {0, L-1}.

  • dataset /data/v1/reports/encounter_reflecting_mean_validation/series/diagonal_asymmetric_f_total.json

    diagonal_asymmetric_f_total: t -> f_total, survival_before, survival_after

Linked reports Reflecting Encounter Diagonal DecompositionExact Recursion — Method GuideFinal Multitimescale FPT and Encounter Report

finding encounter_reflecting_mean_validation-c5

Joint state: Y_t = (X_t^(1), X_t^(2)).

Evidence trail
  • source_document research/reports/encounter_reflecting_mean_validation

    Joint state: Y_t = (X_t^(1), X_t^(2)).

  • section_summary research/reports/encounter_reflecting_mean_validation

    Overview: Joint state: Y_t = (X_t^(1), X_t^(2)).

  • math_block research/reports/encounter_reflecting_mean_validation

    Finding formula context in Reflecting Encounter Mean Validation: Joint state: Y_t = (X_t^(1), X_t^(2)).

  • dataset /data/v1/reports/encounter_reflecting_mean_validation/series/diagonal_asymmetric_f_total.json

    diagonal_asymmetric_f_total: t -> f_total, survival_before, survival_after

Linked reports Reflecting Encounter Diagonal DecompositionExact Recursion — Method GuideFinal Multitimescale FPT and Encounter Report

Interactive Dataset

Plot controls
window=1

t f_total, survival_before, survival_after

Loading plot data…

Provenance: research/reports/encounter_reflecting_mean_validation/artifacts/data/diagonal_asymmetric_f_total.csv

Mathematical Logic Chain

From model assumptions to interpretation in a short, ordered chain.

Distribution Setup

Defines first-passage probability objects used by later diagnostics.

f(t)=Pr⁡[T=t]f(t)=\Pr[T=t]

Fallback

Mathematical Principles

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Fallback EN

f(t)=Pr⁡[T=t]f(t)=\Pr[T=t]
Formula source

research/reports/encounter_reflecting_mean_validation

Narrative Sections

Cleaned chapter summaries are shown first; low-value placeholders are hidden.

Overview

Overview: this section connects Encounter Reflecting Mean Validation assumptions to measurable observables, verification commands, and downstream chapter claims.

Source

research/reports/encounter_reflecting_mean_validation

Reproducibility Commands

Open command list
  • python3 scripts/reportctl.py build --report encounter_reflecting_mean_validation --lang en
  • python3 scripts/reportctl.py translation-qc
  • python3 scripts/reportctl.py web-build --mode changed --skip-npm-ci

Download Assets

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Figure Gallery

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