# Sundog Isotrophy - K_facet v0.3h Ledger Working hook: > Twenty structural-zero receipts and one quarantine that explains itself. > The audit chain catches itself working. Status: 2026-05-22, corrected after the O_617 orientation-aware deep dive. This ledger stages the v0.3h K_facet result for public communication and external review. The internal methodology + result writeup remains the authoritative source. This is **not** a roadmap. It is a staging document that translates the v0.3h technical result into a Sundog-discipline-shaped public surface, with explicit claim boundary and falsification surface. The deep research roadmap continues to live at [`sundog_v_isotrophy.md`](sundog_v_isotrophy.md). ## Anchor Documents - [`internal/anniversary/kfacet_v03h_writeup.md`](../internal/anniversary/kfacet_v03h_writeup.md) - v0.3h methodology + result + reproducibility surface. Authoritative. - [`internal/anniversary/kfacet_v03h_o617_deep_dive.md`](../internal/anniversary/kfacet_v03h_o617_deep_dive.md) - six-probe O_617 bridge anatomy. Corrected attribution: O_617 is a clean opposite-strict row; its quarantine comes from a bridge direction outside the valid D3 representation, not an admission weakness. - [`internal/anniversary/kfacet-runner-spec.md`](../internal/anniversary/kfacet-runner-spec.md) - runner spec for the audit chain. - [`sundog_v_isotrophy.md`](sundog_v_isotrophy.md) - deep research roadmap covering the full Z3-choreography to Z2-piano-trio descent program. - [`/isotrophy`](../isotrophy.html) - public-facing page rendering the v0.3h verdict and audit chain in plain English with explicit claim boundary. ## The Load-Bearing Statement The single sentence that all public copy must trace back to: > v0.3h resolves 20 strict catalog rows as structural zeros. The sole > quarantined row, O_617, is a clean opposite-strict row whose bridge direction > sits outside the valid D3 representation; it is not a Gamma_i audit-chain > failure and not an admission weakness. In compact form: **"20/21 structural zeros plus one quarantined O_617 defective-D3 bridge - not a closed 21/21 theorem-facing result."** The phrasing is load-bearing. The 20/21 and the quarantine appear in the same sentence. O_617 is named. Any communication that collapses this to "21/21" or to "Sundog proved the choreography isotrophy theorem" silently retires the discipline that makes the result interesting. ## What v0.3h Is And Is Not ### What v0.3h Is - A **pre-registered three-stage audit chain**: sentinel/Gamma runner, adaptive-floor reprocessor, and bridge audit on the 21 strict G.2 single-curve choreographies at `m3 = 1`. - A **named class of artifact**: the structural-zero receipt. For 20 rows, `c_i = d_i = 0` by construction because the standard D3 sector is absent in `ker(M_i - I)`. Not by tolerance. Not by post-hoc pruning. - A **named quarantine**: O_617. The bridge vector is physically valid and tangent to the `(E, |L|)` level set, but admitting it produces an invalid odd `E(1)` residual and `sigma3^3-I = 3.96e-2` at the bridge-admitted kernel. The defect lives in the representation at that boundary, not in the Gamma_i audit chain. - A **method that generalizes**. The receipt-first, closure-relative, adaptive-floor, bridge-audit template is the first Sundog audit-chain instance applied to theorem-adjacent mathematics rather than a MuJoCo controller or a chat widget. ### What v0.3h Is Not - **Not a closed 21/21 theorem-facing result.** The team explicitly disclaimed it. The audit chain is intact; the theorem is not closed. - **Not a proof of Sundog.** Structural zeros at `m3 = 1` for the strict G.2 catalog are a specific, defensible, narrow finding. - **Not a weak-admission story.** The corrected deep dive shows O_617 is opposite-strict with admission residual `1.01e-8`. The earlier `1.62e-1` figure was its canonical residual, diagnostic-only for an opposite-strict row. - **Not the wider isotrophy program.** The broader Z3-to-Z2 piano-trio descent program remains live in [`sundog_v_isotrophy.md`](sundog_v_isotrophy.md). - **Not an interactive workbench.** The K_facet test is a one-shot audit on a fixed catalog; the public surface is the static narrative at `/isotrophy`. ## Falsification Surface The v0.3h verdict can be falsified or weakened in three named ways. 1. **An eligible row is shown to contain a valid standard D3 block after all.** That would invalidate that row's structural-zero receipt. The contract is the pre-registered guard set: D3 leakage `<= 1e-3`, gap ratio `<= 1e-3`, and first-rejected singular value `>= 1e-3`. 2. **O_617's defect is shown to live in the Gamma_i audit chain rather than in the bridge representation.** That would reopen the bridge-audit verdict. The six-probe deep dive is the surface to attack. 3. **A row resolved at the adaptive floor is shown to depend on a floor choice outside the pre-registered guards.** That would make the receipt conditional on the floor rather than structural. ## Evaluation Criteria Reviewers should look for: - Pre-registered constants and outcome categories that pre-date row interpretation. See `kfacet-runner-spec.md`. - A receipt directory for every row referenced by the audit chain. See `results/isotrophy/k-facet-v03-*`. - A specific, falsifiable attribution for the quarantined row. See `kfacet_v03h_o617_deep_dive.md`. - A public-facing summary that preserves the same load-bearing phrasing as the internal writeup. See [`/isotrophy`](../isotrophy.html). If any of those are missing or weakened, this ledger is wrong and should be updated. ## Brand And Promo Notes Brand and promo copy may reference v0.3h as the theorem-adjacent instance of the same audit-chain discipline used in the photometric controller and the trace-conditioned chat experiment. Standing rules: 1. **The 20/21 and the quarantine appear in the same sentence.** 2. **O_617 is named.** 3. **"Audit chain is intact; theorem-facing result is not closed"** is the load-bearing distinction. 4. **"Structural-zero receipt"** is the named artifact class. 5. **No "21/21" framing.** 6. **No weak-admission framing for O_617.** It is clean opposite-strict; the quarantine is a defective-D3 bridge at the kernel boundary. ## Cross-References - [`PROMO_HIGHLIGHTS.md`](PROMO_HIGHLIGHTS.md) - [`BRAND_POSITIONING.md`](BRAND_POSITIONING.md) - [`SUNDOG_V_CAPSET.md`](SUNDOG_V_CAPSET.md) - [`SEO_AND_SOCIAL_READINESS_ROADMAP.md`](SEO_AND_SOCIAL_READINESS_ROADMAP.md) - [`SUNDOG_V_THREEBODY.md`](SUNDOG_V_THREEBODY.md) ## Inspection Trail - 2026-05-22 - v0.3h writeup and O_617 deep dive shipped to `internal/anniversary/`. - 2026-05-22 - corrected O_617 attribution after orientation-aware admission residual check: opposite-strict admission residual `1.01e-8`, canonical residual `1.62e-1` diagnostic-only. - 2026-05-22 - `/isotrophy` public-facing page filed at root. - 2026-05-22 - promo and brand notes filed. Open follow-ups: - SEO readiness matrix treatment for `/isotrophy`. - Homepage pillar or rail card for `/isotrophy`. - A public-facing v0.4 plan, if any.