valley-k-small
Validation

Chapter 6: Reproducibility & Validation

Show command-level reproducibility, audit constraints, and practical error boundaries for the full pipeline.

Read time 12 min Reports 7 Interactive panels 7

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Chapter Guide

Reproducibility is treated as part of the scientific claim: commands, generated data, and validation records are all first-class artifacts.

This chapter lists the operational checkpoints used by CI and agent handoff packages.

The emphasis is not only on rerunning scripts, but also on verifying claim-evidence integrity after each change.

Bridge from Chapter 5: after cross-model synthesis, we now test whether every key claim remains reproducible under command-level and schema-level checks.

Narrative Walkthrough

We then move to an auditable method chain: Reproducibility is enforced as an executable contract: web data, glossary, book chapters, backbone, agent sync, and validators run in one closed pipeline.

Under the same diagnostic criterion, the chapter-level result and finding are: Schema gates now cover both report payloads and book backbone, preventing hidden contract drift across releases. Agent handoff is traceable because manifest, chapter jsonl, claim graph, and translation QC are generated together with provena…

Only unresolved items that pass reproducibility constraints should enter the outlook as auditable hypotheses.

Concept Cards

First-passage distribution

Core PMF/CDF/survival quantities used across the major report families.

Reports 26

Survival and hazard

Links between f(t), S(t), and hazard-style diagnostics.

Reports 14

Beta / shortcut scan

How shortcut strength changes bimodality and phase behavior.

Reports 13

Hazard interpretation

Peak/valley interpretation using hazard dynamics.

Reports 12

AW inversion

Discrete Cauchy / FFT inversion from generating functions.

Reports 11

Spectral decomposition

Eigenvalue / resolvent based derivations.

Reports 3

Theory Chain

validation grid2d_bimodality

Schema-gated reproducibility contract

Each release requires schema pass for web/book/agent payloads before publication.

∀a∈Arelease, validate⁡(a)=PASS\forall a\in\mathcal{A}_{release},\ \operatorname{validate}(a)=\mathrm{PASS}

validation grid2d_bimodality

Artifact hash stability

Traceability is enforced by deterministic build outputs with file hash and size checks.

trace⁡(f)={sha256(f),∣f∣}\operatorname{trace}(f)=\{\mathrm{sha256}(f),|f|\}

validation grid2d_bimodality

Cross-check closure

Release is allowed only when multi-agent cross-check high-priority findings are closed.

∑i∈H1[openi]=0\sum_{i\in\mathcal{H}}\mathbf{1}[\mathrm{open}_i]=0

Derivation Link grid2d_bimodality

Grid2D Bimodality Baseline · Derivation Link

Adds a relation that links neighboring steps in the derivation chain.

(gx,gy,δ)=(−0.25,0.40,0.70)(g_x,g_y,\delta)=(-0.25,0.40,0.70)

Derivation Link grid2d_bimodality

Grid2D Bimodality Baseline · Derivation Link

Adds a relation that links neighboring steps in the derivation chain.

pleft=q4(1+gx),pright=q4(1−gx),pdown=q4(1+gy),pup=q4(1−gy),pstay=1−q.\begin{aligned} p_{\text{left}} &= \frac{q}{4}(1+g_x),\quad p_{\text{right}} = \frac{q}{4}(1-g_x),\\ p_{\text{down}} &= \frac{q}{4}(1+g_y),\quad p_{\text{up}} = \frac{q}{4}(1-g_y),\\ p_{\text{stay}} &= 1-q. \end{aligned}

Distribution Setup grid2d_rect_bimodality

Grid2D Rectangle Bimodality · Distribution Setup

Defines first-passage probability objects used by later diagnostics.

f(t)=Pr⁡[T=t],S(t)=Pr⁡[T>t],h(t)=f(t)S(t−1)f(t)=\Pr[T=t],\quad S(t)=\Pr[T>t],\quad h(t)=\frac{f(t)}{S(t-1)}

Derivation Link grid2d_reflecting_bimodality

Grid2D Reflecting-Boundary Bimodality · Derivation Link

Adds a relation that links neighboring steps in the derivation chain.

pleft=q4(1+gx),pright=q4(1−gx),pdown=q4(1+gy),pup=q4(1−gy),pstay=1−q.\begin{aligned} p_{\text{left}} &= \frac{q}{4}(1+g_x),\quad p_{\text{right}} = \frac{q}{4}(1-g_x),\\ p_{\text{down}} &= \frac{q}{4}(1+g_y),\quad p_{\text{up}} = \frac{q}{4}(1-g_y),\\ p_{\text{stay}} &= 1-q. \end{aligned}

Derivation Link grid2d_reflecting_bimodality

Grid2D Reflecting-Boundary Bimodality · Derivation Link

Adds a relation that links neighboring steps in the derivation chain.

Δ=δpstay\Delta=\delta p_{\text{stay}}

Distribution Setup grid2d_two_target_double_peak

Grid2D Two-Target Double-Peak · Distribution Setup

Defines first-passage probability objects used by later diagnostics.

f(t)=Pr⁡[T=t],S(t)=Pr⁡[T>t],h(t)=f(t)S(t−1)f(t)=\Pr[T=t],\quad S(t)=\Pr[T>t],\quad h(t)=\frac{f(t)}{S(t-1)}

Derivation Link ring_lazy_flux

Lazy Ring Flux Baseline · Derivation Link

Adds a relation that links neighboring steps in the derivation chain.

target=⌊N/2⌋\text{target}=\lfloor N/2\rfloor

Derivation Link ring_lazy_flux

Lazy Ring Flux Baseline · Derivation Link

Adds a relation that links neighboring steps in the derivation chain.

v=target+1v=\text{target}+1

Derivation Link ring_lazy_jump_ext_rev2

Lazy Ring Shortcut Figure-1 Revision · Derivation Link

Adds a relation that links neighboring steps in the derivation chain.

Δ=max⁡{1,⌊0.05(t2−t1)⌋}\Delta=\max\{1,\lfloor 0.05(t_2-t_1)\rfloor\}

Distribution Setup ring_valley_dst

Destination-Scan Valley Control · Distribution Setup

Defines first-passage probability objects used by later diagnostics.

f(t)=Pr⁡[T=t],S(t)=Pr⁡[T>t],h(t)=f(t)S(t−1)f(t)=\Pr[T=t],\quad S(t)=\Pr[T>t],\quad h(t)=\frac{f(t)}{S(t-1)}

Interactive Evidence Panel

Grid2D Bimodality Baseline · scan_candidate_B_corridor [probability]

Compare first/second peak prominence first, then adjust smoothing to test valley stability.

Interactive Dataset

Plot controls
window=1

l mass [probability]

Loading plot data…

Provenance: research/reports/grid2d_bimodality/artifacts/data/scan_candidate_B_corridor.json

Grid2D Rectangle Bimodality · ot_scan_bias2d

Toggle series and tune smoothing to see how parameter shifts reweight fast versus delayed pathways.

Interactive Dataset

Plot controls
window=1

bx_values by_values

Loading plot data…

Provenance: research/reports/grid2d_rect_bimodality/artifacts/data/ot_scan_bias2d.json

Grid2D Reflecting-Boundary Bimodality · cases_reflecting_summary [probability]

Compare first/second peak prominence first, then adjust smoothing to test valley stability.

Interactive Dataset

Plot controls
window=1

gx q [probability]

Loading plot data…

Provenance: research/reports/grid2d_reflecting_bimodality/code/config/cases_reflecting_summary.json

Grid2D Two-Target Double-Peak · method_comparison_c1 [probability]

Compare first/second peak prominence first, then adjust smoothing to test valley stability.

Interactive Dataset

Plot controls
window=1

mfpt_truncation_scan_t_max mfpt_truncation_scan_mass_any [probability]

Loading plot data…

Provenance: research/reports/grid2d_two_target_double_peak/artifacts/data/method_comparison_c1.json

Lazy Ring Flux Baseline · lazy_K2_equal4_paper_geometry_summary_cn [tabular metric]

Toggle series and tune smoothing to see how parameter shifts reweight fast versus delayed pathways.

Interactive Dataset

Plot controls
window=1

N v [metric]

Loading plot data…

Provenance: research/reports/ring_lazy_flux/artifacts/tables/lazy_K2_equal4_paper_geometry_summary_cn.tex

Lazy Ring Shortcut Figure-1 Revision · luca_k2_fixed_shortcut_metrics [probability]

Compare first/second peak prominence first, then adjust smoothing to test valley stability.

Interactive Dataset

Plot controls
window=1

beta q [probability]

Loading plot data…

Provenance: research/reports/ring_lazy_jump_ext_rev2/artifacts/data/luca_k2_fixed_shortcut_metrics.csv

Destination-Scan Valley Control · scan [probability]

Compare first/second peak prominence first, then adjust smoothing to test valley stability.

Interactive Dataset

Plot controls
window=1

steps mass, remaining [probability]

Loading plot data…

Provenance: research/reports/ring_valley_dst/artifacts/data/bimodality_flux_scan/N100K2_n0_1_target_50_src_1/latest/scan.csv

Evidence Trail

This chapter is presented as one coherent story. The underlying report artifacts are preserved as auditable evidence nodes.

Open evidence-node index
  • Grid2D Bimodality Baseline (Bimodality emerges when fast direct routes and delayed wrap-around/detour routes coexist at measurable weights under the same diagnostic criterion.)
  • Grid2D Rectangle Bimodality (Aspect ratio and endpoint arrangement shift the balance between direct and detour channels; robust double peaks persist only in specific rectangular geometry bands.)
  • Grid2D Reflecting-Boundary Bimodality (Several reflecting cases preserve clear early/late channel separation, while others collapse toward long-tail unimodality depending on geometric bottlenecks.)
  • Grid2D Two-Target Double-Peak (Double-peak regions appear when direct-to-near-target and delayed-to-far-target channels both carry substantial mass; phase boundaries shift predictably with coupling strength.)
  • Lazy Ring Flux Baseline (A small-p selfloop regime yields clear two-peak structure, whereas equal4 and stronger shortcut injection collapse the distribution toward unimodality.)
  • Lazy Ring Shortcut Figure-1 Revision (Across the three sensitivity tracks, the qualitative mechanism interpretation remains stable, and uncertainty bars do not contradict the phase-level conclusions used in the main narrative.)
  • Destination-Scan Valley Control (Destination scanning reveals structured dst windows where the second peak is amplified and trajectory-class usage shifts, with deterministic and Monte Carlo diagnostics remaining consistent.)

Claim Ledger

method chapter-6-repro-validation-cmd-closure grid2d_bimodality

Reproducibility is enforced as an executable contract: web data, glossary, book chapters, backbone, agent sync, and validators run in one closed pipeline.

Open evidence links
  • source_document scripts/reportctl.py

    reportctl wires web-data/book-data/agent-sync/validate into unified commands.

  • source_document platform/tools/web/build_three_deliverables.py

    deliverables pipeline includes publication and agent pack outputs.

result chapter-6-repro-validation-schema-gate grid2d_bimodality

Schema gates now cover both report payloads and book backbone, preventing hidden contract drift across releases.

Open evidence links
  • source_document platform/tools/web/validate_web_data.py

    validator checks book manifest/chapters/backbone and cross-file consistency.

  • source_document platform/schemas/book_backbone_v1.schema.json

    book backbone has explicit schema contract for chapter spine and acts.

result chapter-6-repro-validation-ci-publish grid2d_bimodality

Deployment and audit checks are automated in CI so publishing is gated by machine-verifiable quality checks instead of manual inspection.

Open evidence links
  • source_document .github/workflows/site-pages.yml

    Pages workflow builds and publishes static site artifacts.

  • source_document .github/workflows/repo-audit.yml

    repository audit workflow preserves baseline research integrity checks.

finding chapter-6-repro-validation-agent-handoff grid2d_bimodality

Agent handoff is traceable because manifest, chapter jsonl, claim graph, and translation QC are generated together with provenance pointers.

Open evidence links
  • source_document platform/tools/web/build_agent_sync.py

    agent sync exports manifest, reports/events jsonl, book files, claim graph, and guide.

  • dataset /data/v1/agent/manifest.json

    manifest enumerates machine-readable files for downstream agents.

finding grid2d_rect_bimodality-c5 grid2d_rect_bimodality

Two-target endpoint constructions offer a reproducible mechanism for separating fast and delayed channels.

Open evidence links
  • source_document research/reports/grid2d_rect_bimodality/artifacts/tables/ot_anchor_selection.tex

    Two-target endpoint constructions offer a reproducible mechanism for separating fast and delayed channels.

  • section_summary research/reports/grid2d_rect_bimodality/artifacts/tables/ot_anchor_selection.tex

    Research report grid2d_rect_bimodality.

  • math_block research/reports/grid2d_rect_bimodality/artifacts/tables/ot_anchor_selection.tex

    Finding formula context in Grid2D Rectangle Bimodality: Two-target endpoint constructions offer a reproducible mechanism for separating

  • dataset /data/v1/reports/grid2d_rect_bimodality/series/ot_scan_bias2d.json

    ot_scan_bias2d: bx_values -> by_values

finding grid2d_reflecting_bimodality-c5 grid2d_reflecting_bimodality

Pore/track structures modify delay channels through accessibility, not only through drift magnitude.

Open evidence links
  • source_document research/reports/grid2d_reflecting_bimodality/manuscript/grid2d_reflecting_bimodality_cn.tex

    Pore/track structures modify delay channels through accessibility, not only through drift magnitude.

  • section_summary research/reports/grid2d_reflecting_bimodality/manuscript/grid2d_reflecting_bimodality_cn.tex

    ： R1（ ）、R7（ + ）、C3（ ）、R6（door ）、NB4（ “ ” ）、NB5（ + ）、S1/S2（ barrier/door ）， 。 vs ：R1/R7/C3 " + " / ；R6 door ；NB4/NB5 + ；S1/S2 sticky + ， " " fast/slow

  • section_summary research/reports/grid2d_reflecting_bimodality/manuscript/grid2d_reflecting_bimodality_cn.tex

    ： propagator -> propagator -> FPT -> AW 。 。 A ， A v,u = ， 1， p t+1 =A p t 。 P n0 (n,t)= e n^->p A^t e n0, P (z)= t0 A^t z^, P n0 (n,z)= e n^->p (I-zA)e-1 e n0.

  • math_block research/reports/grid2d_reflecting_bimodality/manuscript/grid2d_reflecting_bimodality_cn.tex

    Finding formula context in Grid2D Reflecting-Boundary Bimodality: Pore/track structures modify delay channels through accessibility, not

  • dataset /data/v1/reports/grid2d_reflecting_bimodality/series/cases_reflecting_summary-probability.json

    cases_reflecting_summary [probability]: gx -> q [probability]

finding grid2d_two_target_double_peak-c4 grid2d_two_target_double_peak

Phase maps identify stable double-peak bands and transition zones to unimodal behavior.

Open evidence links
  • source_document research/reports/grid2d_two_target_double_peak/artifacts/tables/case_mechanism.tex

    Phase maps identify stable double-peak bands and transition zones to unimodal behavior.

  • section_summary research/reports/grid2d_two_target_double_peak/artifacts/tables/case_mechanism.tex

    Research report grid2d_two_target_double_peak.

  • math_block research/reports/grid2d_two_target_double_peak/artifacts/tables/case_mechanism.tex

    Finding formula context in Grid2D Two-Target Double-Peak: Phase maps identify stable double-peak bands and transition zones to unimodal

  • dataset /data/v1/reports/grid2d_two_target_double_peak/series/method_comparison_c1-probability.json

    method_comparison_c1 [probability]: mfpt_truncation_scan_t_max -> mfpt_truncation_scan_mass_any [probability]

finding ring_lazy_flux-c4 ring_lazy_flux

A minimal reproducible bimodal case appears at N=10 under small shortcut strength in the selfloop construction.

Open evidence links
  • source_document research/reports/ring_lazy_flux/artifacts/tables/lazy_K2_equal4_paper_geometry_summary_cn.tex

    A minimal reproducible bimodal case appears at N=10 under small shortcut strength in the selfloop construction.

  • section_summary research/reports/ring_lazy_flux/artifacts/tables/lazy_K2_equal4_paper_geometry_summary_cn.tex

    Research report ring_lazy_flux.

  • math_block research/reports/ring_lazy_flux/artifacts/tables/lazy_K2_equal4_paper_geometry_summary_cn.tex

    Finding formula context in Lazy Ring Flux Baseline: A minimal reproducible bimodal case appears at N=10 under small shortcut strength in

  • dataset /data/v1/reports/ring_lazy_flux/series/lazy_k2_equal4_paper_geometry_summary_cn-binary.json

    lazy_K2_equal4_paper_geometry_summary_cn [tabular binary]: N -> paper [binary]

Chapter Summary

Show command-level reproducibility, audit constraints, and practical error boundaries for the full pipeline.

Open chapter glossary links
  • AW Inversion: Discrete Cauchy/FFT-based inversion from generating functions to time-domain FPT quantities.
  • Beta Scan: Parameter sweep over shortcut strength β to identify phase shifts and regime boundaries.
  • Bimodality Criterion: Operational criterion to separate true two-peak structure from noisy shoulders.
  • Claim Ledger: Structured mapping from statement to evidence paths and cross-report links.
  • Equal4 Baseline: Four-way equalized baseline used to compare shortcut effects under symmetric local movement.
  • First-Passage Time (FPT): Random time needed for the trajectory to hit an absorbing target for the first time.
  • Hazard Rate: Conditional probability of first passage at step t given survival up to t.
  • Renormalize Shortcut Mode: Base transition weights are rescaled after shortcut injection to preserve normalization constraints.
  • Selfloop Shortcut Mode: Shortcut probability mass is taken from self-loop probability without renormalizing other moves.
  • Survival Function: Probability that first passage has not happened by step t.
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