References

XVA

Manuscript XV-A, supplied XV-A-va.tex. A Model-and-Domain Audit of the Ramp, Graviton, and Joint-Extension Tracks. Full text supplied. Used for Proposition prop:transfer (the transfer rule: same notation is not an identification).

XVB

Manuscript XV-B, supplied XV-B-va.tex. Relative Lifting and Reconstruction Descent for the Full Joint Characteristic Target. Full text supplied. Used for the linear interface, Proposition prop:descent, Theorem thm:lifting, Theorem thm:contact, and Proposition prop:allcontacts.

XVC

Manuscript XV-C, supplied XV-C-va.tex. The Full Joint Characteristic Target: Verified Reconstruction Tests and the Instantiation Boundary. Full text supplied. Used for the ambiguity space eq:ambiguity.

XVD

Manuscript XV-D, supplied as XV-D.tex. Instantiating the Frozen Joint Graph: Source Recovery, the Null Defect of Extension Lifts, and the Boundary of the First Full Calculation. Full text supplied. Used for Definition D0.1–D0.20, Lemmas lem:normalform, lem:extraction, Theorems thm:kernels, thm:defect, Propositions prop:example and prop:onenull.

XVE

Manuscript XV-E, supplied XV-E-va.tex. Source Recovery for the Frozen Joint Graph, Descending Extensions in the Punctured Normal-Jet Module, and the Boundary of the Full Lift. Full text supplied. Used for the E0 manifest, the transcription of the XII-A/XII-D candidate formulas, Lemma lem:surj, Theorem thm:ann, Definition def:kinds (corrected here), Lemma lem:flat, Theorems thm:jetdep, thm:point, thm:relative, Remark rem:open, Proposition prop:erratum.

XIIB

Manuscript XII-B, supplied XII-B.tex. Admission and one retarded response of the ramped cubic Einstein source, at fixed regulator width. Full text supplied. Used only for its own objects: the ramp ${\sigma }_{\epsilon }(t)=\chi (t/\epsilon )$ with explicit $\chi$, trace reversal $\mathcal{P}r=r-\frac{1}{2}\eta {\mathrm{tr}}_{\eta }r$, $\mathcal{R}=\frac{1}{2}K$, the conventions $\square ={{\partial }_t}^2-\Delta$, $P_m=\square +m^2$, ${G^{\mathrm{R}}}_{\mathrm{gr}}=-\mathcal{P}{E_0}^{\mathrm{R}}$, its Lemma lem:weighted, and its own B0 stop. It does not display ${E_0}^{\mathrm{R}}$ and defines no response.

Hkernel

Manuscript XIV-H, version 1. XIV-H.tex, identifier 05d90ea1. Proposition prop:K5exact, lines 1135–1202. Direct excerpt supplied.

HeqL

Manuscript XIV-H, version 1. “The existing tree maps with $z$ retained,” lines 1108–1134, equation eq:L at lines 1111–1119. Direct excerpt supplied in the second retrieval; confirmed in the fourth. Source of (eq:L).

Hfiber

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

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, with $|\alpha |+|\beta |\le 2$. Paraphrased in the fifth retrieval.

Hrefuse

Manuscript XIV-H, version 1. Lines 1661–1667: no equality $U_{\mathrm{can}}=W\setminus \overline{{\mathcal{N}}_{\mathrm{att}}}$ is asserted. Located in the fifth retrieval (refusal).

HK9

Manuscript XIV-H, version 1. Equation eq:K9, line 1055. Located in the fourth retrieval; display not reproduced.

Hverdict

Manuscript XIV-H, version 1. Theorem thm:H2, lines 1539–1582; Theorem thm:release, lines 1847–1895. Direct excerpts supplied.

Ipole

Manuscript XIV-I, version 1. XIV-I.tex, identifier 13365486. Proposition prop:pole, lines 726–826. Direct excerpt supplied.

IeqR

Manuscript XIV-I, version 1. Equation eq:R, lines 329–335. Display reproduced in the fourth retrieval. Source of (eq:R)–(eq:RR).

Ichart

Manuscript XIV-I, version 1. Lines 828–855: the two placements $d_{\pm }$, $r_{\pm }$, the maps ${\Phi }_{\pm }$, the coordinates $(q_{\pm },{\zeta }_{\pm })$ near the null cone, and the adapted chart $w_{\pm }=(u_{\pm },{\zeta }_{\pm },q_{\pm },r_{\pm },y)$ of dimension sixteen. Reproduced in the fifth retrieval. Source of (eq:chart).

Iamodule

Manuscript XIV-I, version 1. Definition def:amodule, lines 873–901. Reconstruction rule reproduced in the fourth retrieval; generators and coefficient class paraphrased. Source of (eq:Recrule).

Iamplitude

Manuscript XIV-I, version 1. Theorem thm:I2 and adjacent precomposition formulas, lines 1288–1378. Direct excerpt supplied.

Ijoint

Manuscript XIV-I, version 1. Proposition prop:canonical, Theorem thm:I3, lines 1459–1548. Direct excerpt supplied.

Irefuse

Manuscript XIV-I, version 1. Proposition prop:canonical, lines 1492–1496: no equality $U_{\mathrm{can}}=W\setminus \overline{{\mathcal{N}}_{\mathrm{att}}}$ is asserted. Located in the fifth retrieval (refusal).

Irelease

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

Ipackage

Manuscript XIV-I, version 1. Input statement input:Hpackage, lines 224–245. Direct excerpt supplied in the second retrieval.

Iresponse

Manuscript XIV-I, version 1. Input statement input:Hresponse, lines 257–321 (formulas at 285–310), equations eq:Q, eq:T, eq:K8, eq:K9. Direct excerpt supplied in the second retrieval; confirmed in the fourth. Source of (eq:Q)–(eq:Lresp).

Jdescent

Manuscript XIV-J, version 1. XIV-J.tex, identifier 3c48e041. Proposition prop:descent, lines 813–846. Direct excerpt supplied.

Jnull

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

Jrconv

Manuscript XIV-J, version 1. Equation eq:Rconvention, lines 631–636. Display reproduced in the fourth retrieval. Source of (eq:Rconv).

Jtarget

Manuscript XIV-J, version 1. Equation eq:target, lines 720–730. Paraphrased in the fourth retrieval; display not reproduced.

Jmapclass

Manuscript XIV-J, version 1. Definition def:mapclass, lines 732–762. Four clauses paraphrased in the fourth retrieval; display not reproduced.

Jcross

Manuscript XIV-J, version 1. Grouped cross-line operator, lines 1112–1123. Definition reproduced in content in the fourth retrieval; the symbol for the replaced blocks returned by that pass ($\hat{H}$) is not found by the fifth (F3). Source of (eq:cross).

Jhessian

Manuscript XIV-J, version 1. Mixed vertex Hessian, lines 1128–1145. Display reproduced in the fourth retrieval; $T^{\mu \nu }(\varphi ,\psi )$ named “the inherited polarized tensor,” not expanded. Source of (eq:hess).

Jstress

Manuscripts XIII-C and XIV-J, version 1. Display of ${T_0}^{\mu \nu }={\partial }^{\mu }\varphi {\partial }^{\nu }\varphi -\frac{1}{2}{\eta }^{\mu \nu }((\partial \varphi {)}^2-m^2{\varphi }^2)$ and the vertex $-\frac{1}{2}\int g{\gamma }_{\mu \nu }{T_0}^{\mu \nu }$, returned in the fifth retrieval; line numbers not returned. Source of (eq:T0).

Jrefuse

Manuscript XIV-J, version 1. Lines 1305–1309: no equality $U_{\mathrm{can}}=W\setminus \overline{{\mathcal{N}}_{\mathrm{att}}}$ is asserted. Located in the fifth retrieval (refusal).

Jreference

Manuscript XIV-J, version 1. Theorem thm:reference, lines 1215–1299. Direct excerpt supplied; $v_{\alpha }$, $c_{D,\beta }$, and the equation of $S_{\mathrm{resp}}$ not defined there.

Jconditional

Manuscript XIV-J, version 1. Theorem thm:conditionalextension, lines 1427–1470. Direct excerpt supplied.

Jverdict

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

Jrelease

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

Jadmission

Manuscript XIV-J, version 1. Corollary cor:noadmission, lines 1808–1822, and admission-interface passage, lines 1794–1807. Direct excerpts supplied.

Crelease

Manuscript XIV-C, version 1. XIV-C.tex, identifier 97aa7215. Theorem thm:release, lines 1307–1340. Used only for the named codimension-four stratum.

Grelease

Manuscript XIV-G, version 1. XIV-G.tex, identifier 4fcac266. Theorem thm:release, lines 1710–1751. Used only for the dimensions of $W$ and $N$.

XIIA

Manuscript XII-A, version 2. XII-A-v2.tex, identifier acb05c0f. “Named composites and their formal sector,” lines 969–1059; the tensor $\mathfrak{a}$ and the composite $\Lambda$ at lines 974–980. Transcribed in XV-E; confirmed in the fourth and fifth retrievals. Source of (eq:XIIA) and (with XIIDfiber) of (eq:a1).

XIIAhad

Manuscript XII-A, version 2. “The frozen Hadamard matrix,” lines 442–492, equations eq:H, eq:Hfrozen; Definition def:admissible, lines 518–528 (four clauses). Direct excerpt supplied in the second retrieval; clauses confirmed in the fifth. Source of (eq:Hblocks).

XIID

Manuscript XII-D, version 1. XII-D.tex, identifier e3e3f67d. “The first root and its transpose,” lines 571–611. Transcribed in XV-E.

XIIDfiber

Manuscript XII-D, version 1. Lines 519–525: $\mathfrak{a}$, ${a_1}^{\mu \nu }[r]={\mathfrak{a}}^{\mu \nu ,ab}{r}_{ab}$, $b_1[r]=\frac{1}{2}{\eta }^{ab}{r}_{ab}$. Reproduced in the fifth retrieval. Source of (eq:a1).

XIIDweight

Manuscript XII-D, version 1. Lines 545–552: arbitrary $f\in {C^{\infty }}_c({\mathring{M}}_T)$ and the observable ${\mathcal{A}}_1[f,g](r;\varphi )$. Reproduced in the fifth retrieval.

XIIDsource

Manuscript XII-D, version 1. “The actual local source kernel,” lines 841–860. Direct excerpt supplied in the second retrieval. Not used.

XIIDrelease

Manuscript XII-D, version 1. Front matter, “Release and proof boundary,” lines 171–195. Direct excerpt supplied in the third retrieval. Non-input (sec:thirdpass).

XIIEa2

Manuscript XII-E, version 1. Lines 401–403: $b_2[r]$ and ${a_2}^{\mu \nu }[r]$. Reproduced in the fifth retrieval. Source of (eq:a2). Used only for this display.

XIICsource

Manuscript XII-C. The density-weighted cubic source, named as the undifferentiated source behind Hq; locator not returned; display not reproduced.

XIIICcoll

Manuscript XIII-C, version 1. XIII-C.tex, identifier bb647493. Definition “Collision sets,” lines 338–349. Direct excerpt supplied in the second retrieval. Source of Definition def:collision.

XIIICpart

Manuscript XIII-C, version 1. Definition def:Cpart, lines 358–392, equation eq:partial-counterterm. Direct excerpt supplied in the second retrieval; confirmed in the fourth and fifth, which record that $D_{\Gamma }$, $w_{\Gamma }$, $S_{\Gamma /I}$ are roles, not formulas. Source of Definition def:Cpart.

XIIICvertex

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

XIVArel

Manuscript XIV-A, version 1. XIV-A.tex, identifier c10ee4de. Theorem thm:relative, lines 887–915. Relative classical branch; not imported.

Ione

Manuscript I, version 1. I.tex, identifier 87fdaa5e. “Context transport and the Frauchiger–Renner example,” lines 2189–2268. Not imported.

XBsum

Retrieval summary of Manuscript X-B, version 3 (X-B-v3.tex, identifier 103c6c32), lines 202–236, 846–859, 920–958, 982–990, with an accompanying plan. Scalar-only one-contraction normalization of a different track. Non-input.

record

Supplied coverage account, retrieval corpus identifier 3883b893, retrievals 3–5. Explicitly disclaims a complete corpus scan and independent verification. Used only as documentary context, for reported codimension bookkeeping, for its reading rule and cautions, and as the carrier of the file, label, and line locators of the reproduced displays and refusals.

Horm

L. Hörmander, The Analysis of Linear Partial Differential Operators I, 2nd ed., Springer, 1990. Used for: distributions supported at a point (Thm. 2.3.4); convolution under support conditions (4.2); Paley–Wiener–Schwartz (Thm. 7.3.1); pullback by submersions and its wavefront bound (Thm. 8.2.4); wavefront sets of tensor products (Thm. 8.2.9).