docs: add v1.2.9 manuscript errata

README.md

@@ -201,6 +201,7 @@ Paper and claim boundary:
 - [Claim scope](docs/CLAIM_SCOPE.md)
 - [Published paper boundary](docs/PUBLISHED_PAPER_BOUNDARY.md)
 - [Paper wording](docs/PAPER_WORDING.md)
+- [Manuscript v1.2.9 clarifications and errata](docs/MANUSCRIPT_ERRATA_v1.2.9.md)
 - [Manuscript provenance](docs/MANUSCRIPT_PROVENANCE.md)
 - [Reviewer reproduction](docs/REVIEWER_REPRODUCTION.md)
 

SHA256SUMS.txt

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 13e34a4c8685ef538486b9708902c7138d5e34369605f7ec77df54c4d9cfc085  archive/milestones/01_local_foundation/response_fibre_normal_root_v0_9_7_oneclick.py
 014d265a818bbd82c8aa8805317e61222ccf13136df871947a71ffa9e0e38291  archive/milestones/01_local_foundation/response_fibre_recenter_preflight_v0_9_6_oneclick.py
@@ -56,7 +56,8 @@ f670f558efac0eb5c87077f9dcdaea465b89a8de911cfe999909030b0ee5b289  docs/ARTIFACT_
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docs/MANUSCRIPT_ERRATA_v1.2.9.md

@@ -0,0 +1,167 @@
+# Manuscript v1.2.9 - Clarifications and Errata
+
+This document records textual clarifications to the frozen manuscript
+`geometric_flow_v1_2_9_freeze_candidate.pdf`.
+
+The frozen PDF and source archive are preserved unchanged. These
+clarifications do not modify any theorem-bearing source, input, protocol,
+certificate, JSON record, atlas, numerical enclosure, or gate threshold.
+No Arb certificate rerun is required.
+
+## 1. Initial condition in Theorem 1
+
+The certified initial-value problem in Theorem 1 is Eq. (18) with
+
+\[
+a(0)=0,
+\qquad
+\theta(0)=\theta_0=\gamma_9(31/1024).
+\]
+
+Thus, "unique solution" means the unique solution of this initial-value
+problem inside the certified Picard tube.
+
+The associated Picard operator is
+
+\[
+(\mathcal T\phi)(t)
+=
+\int_0^t X(\phi(\sigma))\,d\sigma,
+\]
+
+acting on the closed tube
+
+\[
+\{\phi:\|\phi\|_\infty\le r\},
+\qquad
+r=10^{-11},
+\qquad
+0\le t\le10^{-14}.
+\]
+
+This clarification makes explicit the initial condition already fixed by
+the chart construction and used by the frozen verification code.
+
+## 2. Nominal target-state convention
+
+The nominal target ray is generated from the frozen reference phase
+vector by evaluating the declared analytic model at zero offset:
+
+\[
+|t\rangle
+=
+\frac{|\psi(0;\theta_{\rm ref})\rangle}
+{\|\,|\psi(0;\theta_{\rm ref})\rangle\|}.
+\]
+
+The projective response and loss use this normalized target ray and its
+declared projective orthogonal complement.
+
+## 3. Complex tangent domain
+
+The declared complex tangent domain used by the parametric Krawczyk
+graph verification is the coordinate polydisc
+
+\[
+\{a\in\mathbb C^6: |a_i|\le R\},
+\qquad
+R=2\times10^{-11}.
+\]
+
+It contains the real Picard tube of radius
+
+\[
+r=10^{-11}.
+\]
+
+The frozen verifier uses the same outer radius in the graph enclosure and
+the Cauchy estimate.
+
+## 4. Meaning of obligation (R3)
+
+In Theorem 1's namespace, obligation (R3) should be read as:
+
+> the composite normal derivative \(BJN\) is uniformly invertible, and
+> the pullback metric \(H=W^{T}W\) is positive definite throughout the
+> certified tube.
+
+Here \(H\) is real symmetric positive semidefinite by construction.
+The certified Neumann invertibility therefore implies positive
+definiteness.
+
+The phrase "whitened response Gram matrix" in the frozen manuscript is
+terminological shorthand and does not introduce an additional
+certificate quantity.
+
+## 5. Midpoint Stage-A rank certificate
+
+The midpoint rank condition used in Theorem 1 is supported in two
+compatible ways:
+
+1. Theorem 2(i) supplies the complete-parent-box certificate.
+2. The v0.9.3 verification run independently re-executes the Stage-A
+   audit on child 15 and fails closed unless that audit passes.
+
+Accordingly, the local theorem does not rely operationally on a failed
+aggregate gate from another certificate namespace.
+
+## 6. Location of the Theorem 2 certificate
+
+The stored certificate used for the broader-domain Theorem 2 constants
+is located in the repository at:
+
+`results/reference/certificate.json`
+
+Its identity and checksum are recorded in the repository checksum and
+provenance records. It is not contained in the v0.9.3 GitHub Release
+payload; the release remains the frozen delivery boundary for the
+v0.9.3 local-ODE assets.
+
+## 7. Table 2 aggregation convention
+
+The quantities
+
+- `tangent_projected_gradient_upper`,
+- `curve_speed_square_lower`,
+- `curve_speed_square_upper`
+
+occur within the per-child `child_box_records`.
+
+The manuscript values are conservative extrema over all sixteen
+children. In particular, the displayed curve-speed interval combines
+the minimum lower endpoint and maximum upper endpoint over the complete
+set of children; its two endpoints need not come from the same child.
+
+## 8. Withdrawal of a legacy parameter note
+
+The v0.7.4 release metadata fields
+
+- `certified_curve_parameter = "local Chebyshev coordinate s"`,
+- `legacy_field_name_note` asserting that the certified derivative is
+  with respect to \(s\),
+
+are obsolete and should not be used.
+
+The theorem-bearing derivative is with respect to affine atlas
+arclength \(\ell\). The conversion is
+
+\[
+\frac{d\ell}{ds}=\frac{\ell_+-\ell_-}{2}.
+\]
+
+This is confirmed by the frozen source convention and the frozen
+curve-speed values. The obsolete metadata does not alter any stored
+interval enclosure or theorem-bearing numerical result.
+
+## Scientific boundary
+
+These clarifications are textual and provenance-level only. They do not
+change:
+
+- the frozen PDF or source archive;
+- the v0.7.4 or v0.9.3 theorem-bearing numerical assets;
+- the response map \(R_3\);
+- the implementation objective \(L_6\);
+- any interval bound or gate threshold;
+- the local time interval \(0\le t\le10^{-14}\);
+- the statement that global continuation remains open.

docs/MANUSCRIPT_PROVENANCE.md

@@ -58,6 +58,8 @@ above has been exported and hashed for the immutable archival release candidate.
   `docs/manuscript/geometric_flow_v1_2_9_source.zip`
 - source SHA-256:
   `6c6d842c8ca6a31631cee3f83e42f52d8accabe34950d8c8683ce457b35b713a`
+- textual clarifications and errata:
+  `docs/MANUSCRIPT_ERRATA_v1.2.9.md`
 - pages: 19, A4
 - last displayed equation: (37)
 - references: [1]-[18]