# Build handoff: T602 Built **Torsional rigidity of classical planar domains** as the unpublished zeta3 draft https://numberdb.org/T602 (canonical address https://numberdb.org/Torsional_rigidity_of_classical_planar_domains). The draft contains 38 entries: 19 domains in two invertible scale conventions. No offer, publication, human-review action, queue completion, source edit or Git action was performed. The controller must run the separate critique and argument-selection review before any offer. ## Coordinated instructions and screening The canonical local and live skills were read from the runner's archives in `agents/runs/20261029T055510Z-build-skills`. The authoritative manifest is `agents/runs/20261029T055510Z-build-skills/manifest.json`, copied beside the artifacts and attached as `skill-manifest.json`. Both copies and the snapshot canonical skill have SHA-256 `28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`. The manifest status is ready, with no unavailable version or mismatch. Read family #239 first using queue.py; its full text is in family-239.md. `already_here` found related domain spectra but no torsion-integral family. `already_asked` encountered an anonymous GitHub HTTP error; the authenticated read-only GitHub search succeeded and found only #239. Both results are kept in screen.json and github-screen.json. Sample numeric API lookups found the unit disk's pi/8 in unrelated contexts and no torsion family. Existing tag `analysis` was confirmed and used. T390, T489 and T14 were read before their verified canonical addresses were used in the draft. The specific subject tag `partial differential equation` is worth considering: T390 (Dirichlet eigenvalues), T485 (Neumann eigenvalues), T488 (clamped plate), T489 (Steklov eigenvalues) and T602 would share it. The current tag search returned no differential-equation or spectral tag. No tag was created. ## Mathematical choices and coverage The definition is -Delta u=1 with zero Dirichlet values on the full boundary. The engineering constant J is 4T, as follows from Love §224. The second convention is T/area^2, preserving the exact inverse conversion and the two square identities. Radius, side, leg and semiaxis conventions follow #239. The slit disk's two banks are both Dirichlet; no annulus formula was imported. The proposal's entire 19-domain selection was retained after groupwise review: three symmetric controls; three classical boundary examples; nine additional rectangular reference ratios; and four elliptical reference ratios. argument-selection.md gives exhaustive identities, reference purposes, bounds, noncanonical choices, source locators and the breadth-versus-depth rationale. The completeness note and generator enumeration agree. The numerical aspect ratios inside symbolic identities are explicitly justified, not hidden. The downloaded Love edition is the **second edition (1906)**, not the often cited fourth edition; the bibliography names the actual inspected edition. The equilateral formula and sector formulas have independent PDE derivations. Comer–McDonald's triangle projection coefficients disagree with direct integration of their stated eigenfunctions; derivations.md resolves the specific {1,2} coefficient discrepancy. Only their rectangle result is used for production. The triangle uses the independently documented OEIS formula, checked against correctly integrated spectral modes and 91 decimal places. This discrepancy is not left as an unresolved convention choice. ## Computation and evidence - `generate.py` imports numberdb.sage first and names its Sage rings. It reproduces every value, has no external selection dependency, and lists all attached check resources. The first docstring line names T602. - `dry_run.py` computed all 38 entries; exactness and finite-enclosure checks passed. Written values are at most 104 characters, about 6.2 KB in the shared measurement's flat entry representation. - Production uses 501 working bits (about 150 decimal digits), 80 odd correction terms, and explicit geometric tail enclosures. The maximum correction tail bound is less than 2.005e-231 before prefactors. - All values retain at least 495 relative-accuracy bits (over 149 decimal digits). The maximum production ball radius is 1.306e-150. - A 665-bit computation with 120 correction terms agrees for all entries; every written 100-significant-digit interval contains the higher-precision enclosure. This is a diagnostic alongside, not a substitute for, the explicit tail proof. - Exact polynomial Poisson solutions and boundary conditions were checked for the disk, all ellipses and the equilateral triangle. Sector separation and telescoping check the half-disk and slit disk. All ten rectangular axis-exchange identities and all 19 normalization pairs passed. - Independent eigenfunction sums through indices 256, with Parseval remainder bounds, enclose all ten rectangles and the right triangle. These are coarse independent checks, explicitly not 100-digit certification. A nonzero square sine-mode control runs first. - OEIS checks compare 4T against A180314 at 91 decimal places and A180310, A180311 at 105 decimal places. The downloaded b-files are attached. - `verify(sample=None)` reports **38/38 matched, 0 differing, 0 missing, 0 extra**. `stored-evidence.json` records successful independent identities, normalization and spectral tests on all 38 intervals read from the database. - The final site audit returns `findings: []`, `clean: true`. Definition-length and convention-clarity findings were resolved. The remote API audit does not perform outward-link fetches; the mathematical sources and corpus links were read separately in this run. `numerical-evidence.json`, `stored-evidence.json`, `fill.log`, `audit.json`, `attachment-results.json` and `build-fingerprint.json` preserve the results. The generator, check scripts, shared check/flatten helpers, selection rationale, derivations, skill manifest, OEIS data and numerical evidence are attached to the website draft. The source PDFs, excerpts, hashes and version records are kept in the run work directory. The site refused a prose-only update of an empty draft, so the existing draft was filled once and its prepared prose was applied with the stored Numbers preserved. environment-notes.md records that API issue. The checks also needed normal API adaptation for nested entries and Sage ball methods; failed local attempts are retained, and no failed numerical comparison was accepted. ## Independent critique required This build does not create an acceptance sidecar. The separate critic must independently review all four domain groups and the normalization parameter, including both reference_policy objects. Run argument_review.py fingerprint again on the live table and all source dependencies, using the critic's own NUMBERDB_RUN_ID as reviewer_run. The build fingerprint is evidence of bytes, not a review decision. Critique should pay particular attention to the triangle source discrepancy, the distinction between coarse spectral checks and 100-digit ball certification, and the two invertible scale conventions. The controller handoff is `agents/runs/20261029T055510Z-build.table.json`, containing only the T-number filled in this build. The proposal remains for the controller to complete.