References

XVFpatch

Manuscript XV-F-patch (Landmark XV-F, first patch), supplied. Full text supplied. Used for its manifest and ledgers, its F0 verdict (Proposition prop:F0, cited in the commissioning plan as prop:F0patch), and its verified Lemmas lem:R, lem:RR, lem:taylor, lem:recrule, lem:chart, lem:Q, lem:advanced, Theorem thm:exist, and Propositions prop:K5chart, prop:support, prop:checks. Its Remark rem:conormal is corrected here (G1).

Grelease

Manuscript XIV-G, version 1. XIV-G.tex, identifier 4fcac266. Theorem thm:release, lines 1710–1751. Used for $\dim W=16$, $\dim N=8$, $N={\tilde{\mathcal{N}}}_{\mathrm{att}}$.

Gresidual

Manuscript XIV-G, version 1. Residual test $G\in {C^{\infty }}_c(Z;{\mathrm{Sym}}^2{T}^{\ast }M)$ and the order-at-most-two statement for ${\mathrm{JD}}^{\prime }[G]$; passage named in the commissioning plan, line numbers not returned in the record. $E_{\mathrm{res}}$ not defined there.

GG34

Manuscript XIV-G, version 1. “G3 and G4: no joint section and no remainder theorem,” lines 1494–1553. Used for the non-claims of sec:patch1.

Hkernel

Manuscript XIV-H, version 1. XIV-H.tex, identifier 05d90ea1. Proposition prop:K5exact, lines 1135–1202. Source of (eq:K5a)–(eq:K5z); “fixed smooth weights”; the products $R(b-a)R(a-z)$, $R(b-z)R(z-a)$.

HeqL

Manuscript XIV-H, version 1. “The existing tree maps with $z$ retained,” lines 1108–1134, equation eq:L at lines 1111–1119. Source of (eq:L). The definitions of $f$, ${\sigma }_{\epsilon }$ preceding it are not in the record.

Hfiber

Manuscript XIV-H, version 1. Display ${a_1}^{\alpha \mu }[r]={\mathsf{A}}^{\alpha \mu ,I}{r}_I$; line numbers not returned. Source of (eq:a1H).

HinputEC

Manuscript XIV-H, version 1. Input statement input:EC, named in the commissioning plan as the place where XII-E's $a_1$, $b_1$, $a_2$ and completion kernels would be quoted. Content not in the retrieved record. Locator only.

Hq

Manuscript XIV-H, version 1. Lines 653–665: the ${q^{L,I,J}}_{\alpha \beta }$ as coefficients of the actual differentiated source, including ramp derivatives, $|\alpha |+|\beta |\le 2$; symmetrization factors absorbed. Paraphrased.

HK9

Manuscript XIV-H, version 1. Equation eq:K9, line 1055, and Proposition prop:sourceincidence. Located; displays not reproduced.

Hrefuse

Manuscript XIV-H, version 1. Lines 1661–1667: no equality $U_{\mathrm{can}}=W\setminus \overline{{\mathcal{N}}_{\mathrm{att}}}$ is asserted. Refusal.

HH2

Manuscript XIV-H, version 1. Theorem thm:H2, lines 1539–1582: exact H2 verdict; regular conormal amplitudes for $K_8$, $K_9$ on the retained separated-endpoint patch; unresolved at H2.

Hrelease

Manuscript XIV-H, version 1. Theorem thm:release, lines 1847–1895.

Ipole

Manuscript XIV-I, version 1. XIV-I.tex, identifier 13365486. Proposition prop:pole, lines 726–826: pole chart; ${{\mathcal{F}}^{-1}}_{\omega }{M}_{\mathrm{R}}=\Theta (t)\sin (\rho t)/\rho$; the kernel eq:R.

IeqR

Manuscript XIV-I, version 1. Equation eq:R, lines 329–335: $R=\frac{\Theta (t)}{2\pi }\delta (t^2-|\mathbf{x}{|}^2)$ and $R\ast R$.

Ichart

Manuscript XIV-I, version 1. Lines 828–855: placements $d_{\pm }$, $r_{\pm }$, maps ${\Phi }_{\pm }$, coordinates $(q_{\pm },{\zeta }_{\pm })$, adapted chart $w_{\pm }=(u_{\pm },{\zeta }_{\pm },q_{\pm },r_{\pm },y)$.

Iamodule

Manuscript XIV-I, version 1. Definition def:amodule, lines 873–901: reconstruction rule reproduced; generators and coefficient class paraphrased.

II2

Manuscript XIV-I, version 1. Theorem thm:I2 and Section sec:I3, lines 1288–1378: the amplitude module for both $K_5$ placements; eq:K47; the definition of $\mathsf{D}$ by ${\dot{a_2}}^{\alpha \mu }[G;h]={\mathsf{D}}^{\alpha \mu ,I,J}{h}_I{G}_J$; eq:K6; the precomposition sum eq:presum. Source of (eq:K47), (eq:Dfrom), (eq:K6), (eq:retained).

II3

Manuscript XIV-I, version 1. Equation eq:jointmap, Proposition prop:canonical, Theorem thm:I3, lines 1459–1548: the required map $\mathsf{M}:{\mathcal{K}}_{\mathrm{int}}\to {\mathcal{D}}^{\prime }(W;\text{residual species})$; canonical-domain representation; unresolved at I3.

Irefuse

Manuscript XIV-I, version 1. Proposition prop:canonical, lines 1492–1496: no equality $U_{\mathrm{can}}=W\setminus \overline{{\mathcal{N}}_{\mathrm{att}}}$ follows. Refusal.

Irelease

Manuscript XIV-I, version 1. Theorem thm:release, lines 1729–1814.

Iresponse

Manuscript XIV-I, version 1. Input statement input:Hresponse, lines 257–321 (formulas at 285–310): eq:Q, eq:T, eq:K8, eq:K9, copied from XIV-H. Source of (eq:Q)–(eq:K9).

Jdescent

Manuscript XIV-J, version 1. XIV-J.tex, identifier 3c48e041. Proposition prop:descent, lines 813–846. Source of (eq:descent) and of Proposition prop:restricted.

Jnull

Manuscript XIV-J, version 1. Lemma lem:null, lines 853–883.

Jtarget

Manuscript XIV-J, version 1. Equation eq:target, lines 720–730. Paraphrased; display not reproduced (carried open).

Jmapclass

Manuscript XIV-J, version 1. Definition def:mapclass, lines 732–762. Four clauses paraphrased; residual species with metric slot at $z$ and scalar slot at $y$ named.

Jcross

Manuscript XIV-J, version 1. Grouped cross-line operator, lines 1112–1123. Source of (eq:cross); symbol of the replaced blocks disputed between passes (patch, (F3)).

Jhessian

Manuscript XIV-J, version 1. Mixed vertex Hessian, lines 1128–1145; “$g$ the switch.”

Jreference

Manuscript XIV-J, version 1. Theorem thm:reference, lines 1215–1299: ${\mathcal{C}}_{\mathrm{cross}}{}_D{K}_{\mathrm{supp}}$ on $U\setminus N_U$; normal form ${t^{\circ }}_D$; wavefront bound; “a local reference theorem for $K_{\mathrm{supp}}$, not for the full $K_{\mathrm{ret}}$.”

Jconditional

Manuscript XIV-J, version 1. Theorem thm:conditionalextension, lines 1427–1470: normal order at most three; coefficients $b_{D,\gamma }\in {\mathcal{D}}^{\prime }(S_0)$, $|\gamma |\le 3$.

JJ2

Manuscript XIV-J, version 1. Theorem thm:J2, lines 1608–1649.

Jrefuse

Manuscript XIV-J, version 1. Lines 1305–1309: no equality $U_{\mathrm{can}}=W\setminus \overline{{\mathcal{N}}_{\mathrm{att}}}$ is asserted. Refusal.

Jrelease

Manuscript XIV-J, version 1. Theorem thm:release, lines 1894–1939.

Jadmission

Manuscript XIV-J, version 1. Corollary cor:noadmission, lines 1808–1822, and lines 1794–1807. No admitted ${R_1}^{(1)}$.

XIIICcoll

Manuscript XIII-C, version 1. XIII-C.tex, identifier bb647493. Definition “Collision sets,” lines 338–349.

XIIICpart

Manuscript XIII-C, version 1. Definition def:Cpart, lines 358–392, equation eq:partial-counterterm. $D_{\Gamma }$, $w_{\Gamma }$, $S_{\Gamma /I}$ are roles.

XIIICvertex

Manuscript XIII-C, version 1. Cycle-vertex table, lines 603–620; examples $\{y,u,v\}$, $\{y,v\}$ on $B_1$.

XIIICU

Manuscript XIII-C, version 1. The open set ${\mathcal{U}}_{\Gamma }$ on which the Hörmander sum condition holds; statement that ${\mathcal{U}}_{\Gamma }$ is not identified with the complement of the collision diagonals. Line numbers not returned.

XIIICT0

Manuscript XIII-C, version 1. Display of ${T_0}^{\mu \nu }={\partial }^{\mu }\varphi {\partial }^{\nu }\varphi -\frac{1}{2}{\eta }^{\mu \nu }((\partial \varphi {)}^2-m^2{\varphi }^2)$. Line numbers not returned. Carried; not reassessed here.

XIIIB

Manuscript XIII-B, version 1. XIII-B.tex, identifier 17fb280a. Release and proof boundary, lines 185–204. Time-ordered line convention copied into XIII-C; used only as such.

XIIEa2

Manuscript XII-E, version 1. XII-E.tex, identifier 26f86eb3. Lines 401–403: $b_2[r]$, ${a_2}^{\mu \nu }[r]$. Copied premise; usable only through a quotation in XIV-H.

XIIDfiber

Manuscript XII-D, version 1. XII-D.tex, identifier e3e3f67d. Lines 519–525: $\mathfrak{a}$, $a_1$, $b_1$. Copied premise.

XIIDweight

Manuscript XII-D, version 1. Lines 545–552: $f\in {C^{\infty }}_c({\mathring{M}}_T)$, ${\mathcal{A}}_1[f,g](r;\varphi )$; $v_f=E^{\mathrm{A}}f$ without a display of $E^{\mathrm{A}}$. Copied premise.

XIICrelease

Manuscript XII-C, version 1. XII-C.tex, identifier e0611fd7. Release and specification correction, lines 165–194. Names the density-weighted cubic; the polynomial is not displayed in the record.

record

Supplied coverage account, retrieval corpus identifier b0c93438 (retrieval-3), with the earlier corpus 3883b893. Explicitly disclaims a complete corpus scan and independent verification. Used for its reading rule and as the carrier of locators.

Horm

L. Hörmander, The Analysis of Linear Partial Differential Operators I, 2nd ed., Springer, 1990. Used for: Paley–Wiener–Schwartz (Thm. 7.3.1); pullback by submersions (Thm. 8.2.4); wavefront sets of operators and pushforwards (Thm. 8.2.12).