# Isotrophy Promo Handoff (2026-05-24) Status: **SUPERSEDED FOR CLAIM COPY as of 2026-05-30.** This handoff remains as historical provenance for the v0.3-v0.9 pause. Use `docs/isotrophy/kfacet/kfacet_isotrophy_program_pause.md` and `docs/isotrophy/kfacet/kfacet_v11_m3_conditional_vf_rank_form.md` for current copy: the v0.10/v0.11 frontier now says velocity-fraction stratifies stability within fixed `m3` strata (`AUC_cond = 0.6783`, exact `p = 2.046e-7`) while failing as a mass-marginal held-out predictor (`AUC = 0.4125`). Original 2026-05-24 status: ready for promo-team execution. The isotrophy program paused at end-of-v0.9 on 2026-05-24; three public-facing pages need updating to reflect the seven-chapter arc, the load-bearing substantive positive at v0.7, and the program-pause framing. Audience: promo team writers, public-copy reviewers. Anyone who will edit `index.html`, `threebody.html`, or `isotrophy.html` to reflect the current state. Primary internal source documents (read before editing public copy): - `docs/isotrophy/kfacet/kfacet_isotrophy_program_pause.md` -- the authoritative program-pause document with seven-chapter summary, load-bearing findings, methodology surface, and eight reopening avenues for lab initiates. - `docs/isotrophy/kfacet/kfacet_v07_writeup.md` -- the v0.7 qualified-positive chapter close (the load-bearing positive lives here). - `docs/isotrophy/kfacet/kfacet_v09_writeup.md` -- the v0.9 structural-negative chapter close (the most-recent chapter; the monotone-increasing meta-finding lives here). - `docs/isotrophy/sundog_v_isotrophy.md` -- chapter-by-chapter dated log (cross-reference for every claim below). If any line below conflicts with the internal docs, the internal docs win. ## The Headline > The isotrophy program (Sundog vs Li-Liao supplementary-B > piano-trios) paused 2026-05-24 at end-of-v0.9 after seven > sequential pre-registered chapters with seven distinct > chapter-close types. The chain produced one load-bearing > substantive positive (v0.7a' chi^2 = 16.43, branch-independent, > on 250 of 273 catalog rows), one monotone-increasing > meta-finding (v0.9a), and a comprehensive methodology surface > (ten locked disciplines). Bandwidth has redirected to > three-body Phase 15+ (survival pocket). That headline is publishable as written. It's accurate at the load-bearing level and respects the chain's discipline. ## The Seven-Chapter Arc (Public-Friendly Version) ```text v0.3 domain-of-applicability: Gamma_i is D_3-equivariant; the strict G.2 piano-trio catalog yields 20 structural zeros + 1 named quarantine (O_617). Daughter catalog (supp-B) is Z_2-or-smaller -- outside the original mechanism's domain. v0.4 structural-negative on Z_2 shadow: The natural Z_2-equivariant mechanism candidates fail. v0.5 projection-limit: The catalog branch hash on (m_3, z_0) stratifies in-sample at p ~ 1e-7 but does NOT generalize across held-out mass bins. v0.6 conditional-independence: The continuous catalog-coordinate (E, |L|) shadow passes the in-sample audit but is essentially a re-projection of the v0.5 branch hash; no independent stability content. v0.7 integration-attrition + qualified-positive on restricted domain (THE LOAD-BEARING POSITIVE): The Floquet velocity-fraction direction shadow stratifies stability on 250 of 273 catalog rows at chi^2 = 16.43, p ~ 9.3e-4, branch-independent. 23 rows could not be evaluated at the locked variational precision; the restricted-domain positive is the chain's first non-branch-aligned substantive finding. v0.8 structural-negative on unsigned direction-purity: The hypothesized symmetric U-shape mechanism fails; the v0.7 signal lives in signed direction, not unsigned distance from mixed. v0.9 structural-negative on U-shape + monotone-increasing meta-finding: Under physical zones (not data-driven quartiles), the actual physical pattern is monotone-increasing in velocity-fraction (positional 11% S < mixed 34% S < velocity-heavy 44% S). chi^2 = 7.42 does not clear the registered p = 0.01 floor, but the trend is real and physically interpretable. ``` The program paused -- it did not retire. Eight concrete reopening avenues are documented internally; the first (a Jonckheere-Terpstra trend test on v0.9a data) is low-effort and likely to land a clean follow-on positive. ## The Load-Bearing Positive (With All Its Caveats) The v0.7a' result is the publishable substantive finding. **Every public claim about it must include the caveats**: ```text WHAT IT IS: The Floquet velocity-fraction (vf) of the largest-real-part eigenvector of the monodromy operator, projected as a geometric direction in phase space after center-of-mass reduction and mass-weighted normalization, stratifies stability on the Li-Liao supplementary-B piano-trio catalog. Numerically: chi^2 = 16.43 against chi-squared(3) at p = 0.01 (critical 11.34); p ~ 9.3e-4; quartile contingency 49% / 18% / 29% / 43% S-fraction across Q1 (positional-leaning) through Q4 (velocity-leaning). WHAT IT IS NOT: - NOT a catalog-wide result. The variational integrator at rtol = atol = 1e-12 attrited 23 of 273 rows (8.4%) at the long-period high-m_3 regime; the result holds on the 250 analyzable rows only. - NOT a held-out predictor. v0.7b (held-out) was not licensed under the catalog-wide attrition verdict; the in-sample chi-squared has not been promoted to a generalization claim. - NOT a U-shape mechanism. v0.9a confirmed the apparent U-shape was a quartile-boundary artifact; the actual physical pattern is monotone-increasing in vf. - NOT a circularity-free mechanism interpretation. The eigenvalue ordering (largest real part) is used to disambiguate which eigenvector to extract; the v0.7 form lock explicitly addresses this with a non-circularity sentence (Floquet eigenvectors as geometric directions only, never as growth rates). LANGUAGE GUARDRAILS: - SAY: "stratifies stability on the analyzable subset" - SAY: "branch-independent (alignment 0.70)" - SAY: "first non-branch-aligned positive in the chain" - SAY: "the monotone-increasing pattern (velocity-heavy = more stable) matches the broader physical thesis" - DO NOT SAY: "predicts stability" - DO NOT SAY: "the catalog confirms" - DO NOT SAY: "the sundog theorem proves" - DO NOT SAY: "U-shape mechanism" (v0.9 retired this) ``` The chain has been disciplined; the public copy should be too. ## Per-Page Update Priorities ### `index.html` -- LOW PRIORITY (mostly fine) **Current state**: The isotrophy pillar (lines ~1964-2032) reads "Isotrophy K_facet v0.3h" and quotes the v0.3h verdict directly ("20 of 21 strict G.2 single-curve choreographies returned structural-zero receipts; O_617 was quarantined"). This is accurate at the v0.3h level and honestly framed. **Update suggestion (optional, not urgent)**: Add one breadcrumb sentence after the v0.3h headline: > "The v0.3h verdict is the first chapter of the seven-chapter > isotrophy program; the program paused at v0.9 on 2026-05-24 > with a substantive positive at v0.7 (see the `/isotrophy` > page for the chain summary)." If you'd rather leave it alone, that's defensible -- the v0.3h pillar is a coherent standalone claim and the chain summary lives on the dedicated isotrophy page anyway. ### `threebody.html` -- MEDIUM PRIORITY **Current state**: The "Catalog sidecar — 21 + 4 choreographies" section (lines ~1441-1647) cites the v0.3h verdict and the sigma_3 detector reconciliation. The section is accurate but treats the isotrophy work as ENDING at v0.3h. **Specific edit targets**: 1. **Sources section (lines ~1629-1645)**: add a Cross-reference line for the seven-chapter pause: > "The K_facet audit chain extended through v0.9 after v0.3h; > the program paused 2026-05-24 with a substantive positive > at v0.7 (Floquet velocity-fraction direction shadow, > chi^2 = 16.43 on 250 of 273 catalog rows, branch-independent). > See `/isotrophy` for the full chapter summary." 2. **Catalog sidecar lede (lines ~1443-1447)**: expand the framing from "K_facet v0.3h verdict" to "K_facet v0.3-v0.9 audit chain" with the v0.3h verdict as the leading line and a single sentence noting the program paused with a substantive positive at v0.7. 3. **Optional: brief callout box** (similar pattern to the existing iso-crossref) pointing readers to the v0.7 positive and the methodology surface. **Tone**: this page is for technical readers; you can use the chi-squared values directly. Don't include the caveats in detail here -- link to `/isotrophy` for the full version. ### `isotrophy.html` -- HIGH PRIORITY **Current state**: The page is narrowly scoped to v0.3h. The hero, lede, status ribbon, and load-bearing statement all reflect the v0.3h verdict. None of v0.4-v0.9 is mentioned. **Specific edit targets**: 1. **Hero / lede (lines ~425-435)**: keep the v0.3h verdict as the leading claim, but add a paragraph immediately after situating it: > "v0.3h is the first chapter of a seven-chapter pre-registered > program (v0.3 through v0.9), now paused as of 2026-05-24. > The chain produced one load-bearing substantive positive at > v0.7 (Floquet velocity-fraction direction shadow, > chi^2 = 16.43 on 250 of 273 catalog rows, branch-independent) > and a comprehensive methodology surface (ten locked > disciplines)." 2. **Status ribbon (line ~435ish)**: expand from `v0.3h | 2026-05-22 | 20 structural-zero receipts | ...` to add a second ribbon below: `v0.7 (load-bearing positive) | v0.9 close | program paused 2026-05-24` 3. **Post-verdict section (after line ~475)**: insert a NEW "Program chapter arc" section between the v0.3h load-bearing statement and the "what's next" footer. Use the seven-chapter summary above (in this handoff) verbatim or paraphrased. Include all SEVEN chapter-close types as distinct entries. 4. **Add a "Load-bearing positive" callout**: a dedicated section for the v0.7a' result, with the caveats locked in copy. Use the exact language guardrails above. 5. **Add a "Reopening avenues" footer**: a brief note that the program paused with eight concrete reopening avenues for lab initiates, with a link to the internal pause document (`docs/isotrophy/kfacet/kfacet_isotrophy_program_pause.md`). Don't list all eight -- one or two examples (e.g., "a Jonckheere-Terpstra trend test on v0.9a is the low-effort first follow-on") is enough. **Tone**: this is the destination page for anyone curious about isotrophy. Be technical but explain the projection-language vocabulary briefly. The page should make the load-bearing positive visible without overstating it. ## Cross-References for Verification Every public claim in the proposed updates above traces back to one of: ```text docs/isotrophy/kfacet/kfacet_v03h_writeup.md v0.3h verdict docs/isotrophy/kfacet/kfacet_v04_writeup.md v0.4 close docs/isotrophy/kfacet/kfacet_v05_writeup.md v0.5 close docs/isotrophy/kfacet/kfacet_v06_writeup.md v0.6 close docs/isotrophy/kfacet/kfacet_v07_writeup.md v0.7 LOAD-BEARING POSITIVE docs/isotrophy/kfacet/kfacet_v08_writeup.md v0.8 close docs/isotrophy/kfacet/kfacet_v09_writeup.md v0.9 close docs/isotrophy/kfacet/kfacet_isotrophy_program_pause.md program pause + reopening avenues docs/isotrophy/sundog_v_isotrophy.md dated chapter-by-chapter log results/isotrophy/k-facet-v07a-velocity-fraction-audit/manifest.json load-bearing chi^2 = 16.43 receipt results/isotrophy/k-facet-v07a-prime-restricted-scope/manifest.json restricted-scope PASS receipt results/isotrophy/k-facet-v09a-signed-vf-three-zone/manifest.json v0.9a fails + monotone meta-finding ``` If you want a number, formula, or claim that isn't in one of these files, run it past me (or a research-side reviewer) before publishing. The chain has been disciplined; the public surface should mirror that discipline. ## What Promo Should NOT Do - Do NOT remove the v0.3h pillar from `index.html`. It is still load-bearing for the "audit chain catches itself working" pitch. - Do NOT promote the v0.7a' result to a catalog-wide claim. The attrition is permanent on the receipt; bypassing it in the copy would invalidate the chain's discipline. - Do NOT use the word "predict" for any v0.7 result. The held-out predictor (v0.7b) was not licensed. The result is an in-sample stratification finding, not a generalization claim. - Do NOT describe the program as "retired." It is **paused** with explicit reopening avenues; the language matters. - Do NOT remove the O_617 quarantine mention from any page. It is the methodological touchstone that proves the audit chain catches itself working. ## Suggested Sequence of Public-Copy Work 1. **First**: update `isotrophy.html` (high priority; the destination page for the chain narrative). Land the seven- chapter summary + load-bearing positive callout + reopening avenues footer. 2. **Second**: update `threebody.html` cross-references (medium priority). Link to the new isotrophy.html sections. 3. **Third**: optionally add a one-sentence breadcrumb to `index.html` (low priority). 4. **Fourth**: run a public-copy review pass for the language guardrails (no "predicts", no "catalog-wide", no "U-shape mechanism", no "retired", etc.). Estimated time: 2-4 hours for an experienced public-copy editor; 6-8 hours if also writing a new chapter-arc explainer. ## Open Questions for Promo Team - Does isotrophy.html want a visual element for the seven-chapter arc (timeline diagram, contingency-table reproduction, vf distribution histogram)? The v0.7a' contingency makes a clean bar chart; the v0.9a monotone-increasing pattern makes a clean 3-bar chart. Both could land within the existing page aesthetic. - Should the load-bearing positive get its own dedicated subpage (e.g., `/isotrophy/v0.7-positive`) for SEO purposes? Probably not necessary; the section on `/isotrophy` is sufficient. - Threebody.html's catalog-sidecar gallery is interactive; should v0.7-positive context be integrated into the gallery's modal copy, or kept in the sources/footer only? Recommend sources/footer for now to avoid scope creep on the gallery feature. ## Sign-Off Checklist for Each Page Update ```text [ ] All chi-squared values cited match an internal source doc. [ ] All caveats from "Load-Bearing Positive" section are present where the v0.7a' result is mentioned. [ ] No "predicts", "catalog-wide", "U-shape mechanism", or "retired" language. [ ] Links to internal pause document are functional. [ ] O_617 quarantine narrative preserved. [ ] Tone matches the chain's discipline (precise, hedged where appropriate, no overclaim). [ ] A research-side reviewer (the principal, or me) has signed off on the final copy before deploy. ``` --- Handoff complete. Public surfaces will reflect the load-bearing positive without overstating it. The chain's discipline carries through to the public copy by design.