# Operational Geometry & Arithmetic — agent guide > Machine-readable discovery for TGN's reviewed mathematics publications and bounded browser laboratories. ## Publications - Can a Few Echoes Reveal a Hidden Arithmetic Shape?: HTML https://thegodnet.work/number-geometry/arithmetic-observability-atlas/companion/ | Markdown https://thegodnet.work/number-geometry/arithmetic-observability-atlas/companion/arithmetic-observability-public-companion.md | JSON https://thegodnet.work/number-geometry/arithmetic-observability-atlas/companion/research.json - Arithmetic Observability Atlas: HTML https://thegodnet.work/number-geometry/arithmetic-observability-atlas/ | Markdown https://thegodnet.work/number-geometry/arithmetic-observability-atlas/arithmetic-observability-atlas.md | JSON https://thegodnet.work/number-geometry/arithmetic-observability-atlas/research.json - Arithmetic Sensing IV — Continuum Positivity, Alias-Band Tails, and Local Information: HTML https://thegodnet.work/number-geometry/arithmetic-sensing-continuum-alias-locality/ | Markdown https://thegodnet.work/number-geometry/arithmetic-sensing-continuum-alias-locality/arithmetic-sensing-continuum-alias-locality.md | JSON https://thegodnet.work/number-geometry/arithmetic-sensing-continuum-alias-locality/research.json - Arithmetic Sensing III — Optimized Quadrature and Unavoidable Aliases: HTML https://thegodnet.work/number-geometry/arithmetic-sensing-optimized-quadrature/ | Markdown https://thegodnet.work/number-geometry/arithmetic-sensing-optimized-quadrature/arithmetic-sensing-optimized-quadrature.md | JSON https://thegodnet.work/number-geometry/arithmetic-sensing-optimized-quadrature/research.json - Arithmetic Sensing: Recovering Number Patterns—and Knowing the Limits: HTML https://thegodnet.work/number-geometry/arithmetic-sensing-recovery-and-limits/ | Markdown https://thegodnet.work/number-geometry/arithmetic-sensing-recovery-and-limits/arithmetic-sensing-recovery-and-limits.md | JSON https://thegodnet.work/number-geometry/arithmetic-sensing-recovery-and-limits/research.json - Arithmetic Sensing V — From Log-Mellin Certificates to a Finite Multiscale Stopping Theorem: HTML https://thegodnet.work/number-geometry/arithmetic-sensing-v-multiscale-stopping/ | Markdown https://thegodnet.work/number-geometry/arithmetic-sensing-v-multiscale-stopping/arithmetic-sensing-v-multiscale-stopping.md | JSON https://thegodnet.work/number-geometry/arithmetic-sensing-v-multiscale-stopping/research.json - Certified answers from imperfect experiments: HTML https://thegodnet.work/number-geometry/certified-query-recovery/ | Markdown https://thegodnet.work/number-geometry/certified-query-recovery/certified-query-recovery.md | JSON https://thegodnet.work/number-geometry/certified-query-recovery/research.json - The Geometry Arithmetic Remembers: HTML https://thegodnet.work/number-geometry/geometry-arithmetic-remembers/ | Markdown https://thegodnet.work/number-geometry/geometry-arithmetic-remembers/geometry-arithmetic-remembers.md | JSON https://thegodnet.work/number-geometry/geometry-arithmetic-remembers/research.json - Global Geometry · How Local Rules Make Worlds: HTML https://thegodnet.work/number-geometry/global-geometry-local-rules/ | Markdown https://thegodnet.work/number-geometry/global-geometry-local-rules/global-geometry-local-rules.md | JSON https://thegodnet.work/number-geometry/global-geometry-local-rules/research.json - Operational Information Geometry — From Response Limits to Certified Experiments: HTML https://thegodnet.work/number-geometry/operational-information-geometry-protocol-engine/ | Markdown https://thegodnet.work/number-geometry/operational-information-geometry-protocol-engine/operational-information-geometry-protocol-engine.md | JSON https://thegodnet.work/number-geometry/operational-information-geometry-protocol-engine/research.json - Operational Information Geometry V — Scale Flow, Continuum Response, and Protocol Boundaries: HTML https://thegodnet.work/number-geometry/operational-information-geometry-v-scale-flow/ | Markdown https://thegodnet.work/number-geometry/operational-information-geometry-v-scale-flow/operational-information-geometry-v-scale-flow.md | JSON https://thegodnet.work/number-geometry/operational-information-geometry-v-scale-flow/research.json - Operational Information Geometry VIII — The Uniform Three-Parameter Atlas: HTML https://thegodnet.work/number-geometry/operational-information-geometry-viii-uniform-atlas/ | Markdown https://thegodnet.work/number-geometry/operational-information-geometry-viii-uniform-atlas/operational-information-geometry-viii-uniform-atlas.md | JSON https://thegodnet.work/number-geometry/operational-information-geometry-viii-uniform-atlas/research.json ## Browser laboratories - Arithmetic Observability Lab: HTML https://thegodnet.work/number-geometry/arithmetic-observability-atlas/lab/ | manifest https://thegodnet.work/number-geometry/arithmetic-observability-atlas/lab/lab-manifest.json - The Transfer Theorem Lab: HTML https://thegodnet.work/number-geometry/certified-query-recovery/lab/ | manifest https://thegodnet.work/number-geometry/certified-query-recovery/lab/lab-manifest.json - Query Geometry — Transfer Theorem Lab v2: HTML https://thegodnet.work/number-geometry/certified-query-recovery/query-geometry/ | manifest https://thegodnet.work/number-geometry/certified-query-recovery/query-geometry/lab-manifest.json - Global Geometry II evaluation checkpoint: HTML https://thegodnet.work/number-geometry/global-geometry-local-rules/lab/global-geometry-ii.html | manifest https://thegodnet.work/number-geometry/global-geometry-local-rules/lab/global-geometry-ii-lab-manifest.json - Global Geometry Lab: HTML https://thegodnet.work/number-geometry/global-geometry-local-rules/lab/ | manifest https://thegodnet.work/number-geometry/global-geometry-local-rules/lab/lab-manifest.json - Double-Pendulum OIG Wind Tunnel: HTML https://thegodnet.work/number-geometry/operational-information-geometry/double-pendulum-wind-tunnel/ | manifest https://thegodnet.work/number-geometry/operational-information-geometry/double-pendulum-wind-tunnel/lab-manifest.json ## Interpretation and execution boundaries - Treat theorem, exact finite identity, formal certificate, floating-point computation, hypothesis, analogy and unresolved status as distinct evidence classes. - The public laboratories execute only in the visitor's browser. They expose no upload API, account data, filesystem, radio hardware, publication action or server-side compute endpoint. - The Arithmetic Observability WebMCP pilot offers three read-only same-origin tools for description, bounded profile comparison and evidence lookup. It does not expose the full grid sweep or any paid service. - The Double-Pendulum interactive chamber remains bounded to N=1–50 and T=1–30. Its N=50–1000 Background Laboratory is explicitly not agent-callable. - Compute-intensive observability services, if offered separately, require their own authenticated gateway, quotas, disposable workers and independent verification; no such service is connected through these pages. - No public page accepts writes. robots.txt and these guides aid discovery; they are not authorization or security controls. Site-wide AI reader guide: https://thegodnet.work/llms.txt Laboratory manifest schema: https://thegodnet.work/schemas/math-lab-manifest.schema.json