11. XI-002: attempt to trace the fixed native $q$-value

Bounded result (2026-10-06): UNRESOLVED_OBLIGATION. The currently hosted IUT III, Step (xi-f), asserts exact membership of the native $q$-pilot value in an output half-line. Three independent paper-native traces, a separate source-fidelity check, and a mathematical-inference check did not derive that membership from the preceding passages they inspected. This does not establish that the published claim is false, that a lemma is absent from the full literature, or that abc is true or false. This is a report on one arrow, the I-6 to I-7 obligation.

Fix initial $\Theta$-data satisfying the paper's hypotheses (IUT I Definition 3.1 includes $\ell\ge5$ and nonempty bad places), and write, in the paper's respective normalizations,

\[ r=-|\log(q)|<0,\qquad s=-|\log(\Theta)|,\qquad B_s=\{t\in\mathbb R:t\le s\}. \]

The claim at IUT III (xi-f), PDF/printed p. 184 is $r\in B_s$, equivalently $|\log(q)|\ge|\log(\Theta)|$. The reference in (xi-e) to an approximate construction of the input log-volume does not qualify away the exact membership printed in (xi-f).

Graduate-level walkthrough (intuition only)

The inequality in (xi-f) is $r\le s$ for one fixed native $r$, not a claim that some output in a hull has value at most $s$. Remark 3.9.5 (Ob8)/(Ob9) compares hull log-volumes vertically; the (xi-c)--(xi-d) hull and determinant operations build an output bound. The unresolved composition is a permitted, choice-compatible numerical route from that fixed $r$ to an output governed by the bound. The table below records where each candidate route starts and stops without asserting that they compose.

Normalization matters even for elementary inequalities: if both sides were multiplied by the same positive integer $M$, then $Mr\le Ms$ would imply $r\le s$. But the paper's tensor/determinant constructions require their own source-licensed identifications before one may write such an inequality for the native input. Likewise "approximate construction" in (xi-e) cannot simply replace the exact membership asserted in (xi-f). For a row in the trace, try naming its source, target, allowed choice, and numerical effect before using it as a map.

Background, not verification: the prerequisite route, the preceding XI-001 experiment, and Arakelov theory on Wikipedia for general degree/height motivation, not IUT's particular formulas.

Corpus, procedure, and status words

The XI-002 frozen packet records the eight PDF URLs, editions, and SHA-256 fingerprints (I1--I4, D1--D4). All eight packet copies matched that manifest; local IUT I, II, and the optional IV also matched freshly downloaded official PDFs. Three readers received the same neutral question and the same packet, without each other's drafts or the earlier XI-001 interpretation. A distinct reader checked the rendered glyphs, source attributions, and key page labels; a mathematical referee checked only the source-vetted premises. The PDF indices and printed folios coincide at the IUT passages cited below.

The two newly named IUT III and Scholze--Stix files supplied locally are byte-identical to the already pinned hosted copies; the supplied SS2018-08.pdf is a one-page Not Found response, not the August 2018 report cited in Mochizuki's comments. The historical 2018 SS revision and the contemporary IUT III text have not been compared with these editions. None of these PDFs is copied into this repository.

SOURCE_VERIFIED means a specified source passage says what its cell reports; STANDARD is a mathematical consequence we can check separately; ASSERTED_IN_IUT marks a printed conclusion, not a separately checked inference; SOURCE-MISMATCH rejects a proposed attribution to that passage; UNRESOLVED_OBLIGATION means a needed link was not established within the inspected corpus; COUNTEREXAMPLE would require an example satisfying all the relevant paper hypotheses. None was produced.

The two strands are not yet a composed map

In the table, $P_\beta$ is our shorthand, not a paper-defined point: a possible $\Theta$-output region for an admissible combined choice $\beta$ under (Ind1)--(Ind3). Let $H$ denote the one-column holomorphic hull of the output possibilities. Write $\mu$ for a normalized log-volume only where the cited passage licenses that evaluation. The rows record possible construction routes; their order does not assert that the fixed $q$-value passes through every row. Unless otherwise indicated, locators are one-based PDF and printed pages in the primary source register.

# / passage	Domain	Operation or map	Codomain	Allowed choices	Normalization	Quantitative consequence	Status
1 / `I-6`: I1 Def. 3.1, pp. 61--63, Ex. 3.2(iv), p. 71; I3 Def. 3.8(i), p. 112, Cor. 3.12, p. 174, (xi-c), p. 182	Native $q$-pilot in the $(1,0)$ global realified Frobenioid	One-column log-Kummer representation and log-volume	Represented $q$ class in $(1,\circ)$ packets; its fixed number $r$	Input is not subject to (Ind1)--(Ind3); local decorated $\mathbf q_v=q_{E,v}^{1/(2\ell)}$ up to roots of unity	Procession-normalized $r=-	\log(q)	<0$
2 / `I-1`: I2 Def. 4.9(viii), p. 158, Rem. 4.10.3(ii), p. 162; I3 Def. 3.8(ii), p. 113, Cor. 3.12(i), p. 175	$\Theta$-pilot prime-strip at $(0,0)$	Horizontal $\Theta^{\times\mu}_{\mathrm{LGP}}$ poly-isomorphism of weakened prime-strips	Corresponding $q$-pilot prime-strip at $(1,0)$	Paper-specified link; no ring identification	I2 says its value-group portion is not preserved; it gives no native-degree preservation law	Abstract pilot correspondence; not $\mu(\Theta)=r$	`SOURCE_VERIFIED`; attributing native-degree equality to this link is `SOURCE-MISMATCH`
3 / `I-2`: I3 Thm. 3.11(i)--(iii), pp. 153--159, (xi-b/c), pp. 181--182	$\Theta$ data in $(0,m)$ theaters	Kummer/mono-analytic construction and étale-picture permutation representation	Possible regions $P_\beta$ in $(1,\circ)$ packets	(Ind1) procession, (Ind2) independent local, (Ind3) upper-semi-compatible vertical log-link choices	Packet weights and procession average; bare $j^2$ powers are not final hull volumes	IPL links prime-strips, SHE permits one-column expressibility, APT is not set transport	`SOURCE_VERIFIED`; no native-volume equation here
4 / `I-4`: I3 Rem. 3.9.5(i)--(iv), pp. 127--129, rendered (xi-c), p. 182	One-column output possibilities $P_\beta$	Holomorphic hulling of their union	${}^{1,\circ}\overline{\mathcal U}=H\supseteq{}^{1,\circ}\mathcal U$	All permitted output possibilities; hull may enlarge volume strictly	One-column log-volume	$\mu(P_\beta)\le\mu(H)$ for compatible evaluated regions	Hull inclusion `SOURCE_VERIFIED`; monotonicity `STANDARD`; reading it as $q\subseteq H$ is `SOURCE-MISMATCH`
5 / `I-5`: I3 Rem. 3.9.5(vii), (Ob3)--(Ob5), pp. 131--135; (xi-d), p. 183	Rank-$>1$ hull $H$	Weighted, structure-sheaf-corrected $\det^{\otimes M}$	Comparable one-column rank-one line-bundle class	Compatible local packets and weights	$M>0$ is defined for the chosen weighted operation; compare with the $q$-pilot's corresponding $M$-th power, not an unscaled degree	Gives comparability of Frobenioid objects; no source-checked order of these two pointed classes yet	Machinery `SOURCE_VERIFIED`; native order `UNRESOLVED_OBLIGATION`
6 / `I-5v`: I3 Rem. 3.9.5(vii), (Ob8)/(Ob9), pp. 137--139	Hull log-volume classes at vertical log-link levels	Log-Kummer adjustment; realified semi-simplification	Bijection of hull log-volume classes across the vertical shift	Arbitrary allowed log-link iterates and their compatibility conditions	Matched hull-volume normalization	A positive numerical compatibility claim, not merely object comparability; it does not name the fixed native $q$ as an output	`SOURCE_VERIFIED`; using it as a selected $q$-output identity is `SOURCE-MISMATCH`
7 / pre-volume loop: I3 Rem. 3.9.5(ix), pp. 141--144	Output and input prime-strip structures	Claimed closed loop up to formal quotient indeterminacies	Prime-strip comparison before taking volume	Formal quotients and permissible choices matter	Volume follows the loop, not an assumed equality of raw values	The passage says this will yield an inequality, but supplies no separately displayed, choice-indexed fixed-$q$/output degree law in the passages inspected	Loop `SOURCE_VERIFIED`; typed numerical step `UNRESOLVED_OBLIGATION`
8 / `I-5`, `I-7`: I3 (xi-d)--(xi-f), pp. 183--184	Hull value $s$ and separately fixed input $r$	Form $B_s$, then assert input/output membership	Exact $r\in B_s$ in (xi-f)	Output includes (Ind1)--(Ind3); the native input does not	$r$ and $s$ must be on a common signed real scale; any approximation needs explicit limiting quantifiers	$r\le s$ is stated, not independently derived by rows 1--7	Statement `ASSERTED_IN_IUT`; preceding numerical implication `UNRESOLVED_OBLIGATION`

Where the trace stops. Output containment establishes bounds on output regions; Ob8/Ob9 establishes a meaningful vertical bijection of hull log-volumes. The horizontal link and the pre-volume prime-strip loop are also source-stated. None alone identifies or bounds the separately fixed input number $r$ against an admissible output under the same choices and signed normalization. The first unaccounted numerical inference, in this bounded reconstruction, is from the relationship described in (xi-e) to (xi-f)'s exact membership. This statement concerns our independent derivation, not the existence of a paper proof. The readers also followed candidate repairs in IUT III Theorem 1.5, Propositions 3.9--3.10, Remarks 2.4.2 and 3.12.2, and IUT II Definition 4.9/Corollary 4.10; none yielded a separately checked selection-and-degree law in their traces. Further cited foundations, including [FrdI], [FrdII], [AbsTopIII], and [EtTh], are outside this packet, not silently certified or ruled out.

Normalization mini-audit

Check	Source-located fact	What must not be silently inferred
Local pilot versus Tate parameter	I1 Ex. 3.2(iv), p. 71, decorates $q_{E,v}^{1/(2\ell)}$; I3 Def. 3.8(i), p. 112, uses the global realified pilot	Replace the decorated pilot by an unqualified $q_{E,v}$ in a numerical comparison
Packet baseline and signs	I3 Prop. 3.9(i), pp. 115--116, puts the local integral structure at volume zero; multiplying a local region by $p_v$ changes its log-volume by $-\log p_v$, and by $e$ at an archimedean place changes it by $+1$; Prop. 3.9(iii), p. 117, identifies global log-volume with arithmetic degree relative to a suitable normalization	These signs and the procession average specify local/global scales, not an inequality comparing the two pilots
Local weights, not a universal determinant exponent	I3 Rem. 3.1.1(iv), pp. 96--97, has a $1/N_E$ factor with $N_E=\prod_vN_v$ for direct-product regions; (Ob3-1), p. 132, calls for positive determinant tensor exponents matching the packet weights	The direct-product identity does not state $M=N_E$ for general hulls, or give a $1/M$ formula comparing $q$ with $\Theta$
Procession labels	I3 Rem. 3.11.1(i), p. 159, gives bare $q^{j^2}$ for $1\le j\le\ell^\star=(\ell-1)/2$; Prop. 3.9, pp. 115--117, sets positive packet weights and averaging	The arithmetic average $\ell^{\star-1}\sum_j j^2=\ell(\ell+1)/12$ is not the indeterminacy-subject, corrected hull volume
Hull direction	The overbar on the first $\mathcal U$ in I3 (xi-c), p. 182, is visible in the PDF image but lost in text extraction; I3 Rem. 3.9.5(iv), p. 129, allows strictly larger hull volume	Neither $H\subseteq U$ nor the native $q$ region's inclusion in $H$ follows
Corrected determinant and $M$	I3 (Ob3-1)--(Ob3-3), pp. 131--133, weights each local determinant and tensors it with the inverse weighted determinant of the structure sheaf; $M$ is the uniquely determined positive integer for that chosen operation, characterized by sending $\mathcal O(-)\otimes L$ to $L^{\otimes M}$, and may be chosen sufficiently divisible	No general closed formula $M=N_E$ or displayed $1/M$-normalized $q$-versus-hull inequality was found there; (Ob3-3) says the degree represents the original volume with suitable normalization factors, without displaying those factors
$M$-th pilot power and twists	I3 (Ob4), pp. 133--134, compares the corrected determinant with Frobenioid objects for the $M$-th $q$-pilot power and states that tensor-power-twist indeterminacies have no substantive effect on log-volumes	Such asserted comparability and twist invariance do not themselves state $\deg(Q_M)\le\deg(\widehat H_M)$; cancellation of $M$ would first require a proven, properly signed degree law
Vertical versus horizontal	I3 (Ob8)/(Ob9), pp. 137--139, compares hull log-volumes across vertical log-links; I2 Rem. 4.10.3(ii), p. 162, distinguishes the horizontal link's value-group portions	A vertical hull-volume bijection is not the missing horizontal identification of the native value

Here $\mathcal M(-)$ in Prop. 3.9 denotes admissible regions, not the integer $M$ in (Ob3). The basic tensor-power identity $\deg(L^{\otimes M})=M\deg(L)$ is mathematics; neither its use to divide by $M$ nor an order relation between the two different pilot-related objects is a printed formula in (Ob3)--(Ob4). The bare $j^2$ sum, the corrected determinant and its $M$, and the final hull volume are different operations. Optional IUT IV, pp. 27--29, gives downstream corrected hull bounds; they cannot be inserted as an unproved Step-(xi) pilot comparison.

Distinct readings and independent gates

Reading	Source path it probed	First numerical question it left open
A (native-pilot first)	IUT I's decorated $q$ generator; IUT II's value-group warning; the one-column hull and its corrected determinant	Which order-preserving, pointed comparison connects $q^M$ to the corrected hull determinant after permitted choices?
B (representation first)	IUT III's IPL/SHE/APT and étale-picture permutation, then Ob8/Ob9 and the pre-volume loop	What makes the separately fixed one-column $q$ number a bounded output value rather than merely expressible in the same column?
C (vertical-compatibility first)	Prop. 3.9 and arbitrary log-link iterates, then Ob8/Ob9 and Rem. 3.12.2's within-column equalities	What supplies the cross-object, choice-compatible signed degree law at (xi-e)--(xi-f)?

The source-fidelity gate confirmed the overbar, exact (xi-f) membership, both the vertical volume bijection and the pre-volume loop, and the IUT II warning that the horizontal link does not preserve value-group portions. It corrected a tempting attribution: the bare $j^2$ components occur in I3 Rem. 3.11.1(i), p. 159 (also p. 173), not as a final hull-volume formula in Rem. 3.9.5(i)--(iv). Agreement among readings is not a proof or a source-level refutation. Scholze--Stix's critique, Mochizuki's reply, and Project LANA's proposed compatibility (9-1) remain different interpretations and research directions, not substitutes for this paper-native arrow.

The mathematical referee checked only the preceding explicitly vetted facts. They give $\mu(P_\beta)\le s$, not $r\le\mu(P_\beta)$ or $r\le s$. For example, the reduced abstract data $r=-1$, $\mu(P)=-3$, $s=-2$ satisfy the first bound but fail $r\le s$. This is not an IUT counterexample: it does not model all the paper's hypotheses. Likewise a bare $j^2$ average or an abstract strip isomorphism supplies no missing order law.

An error term would help only with stated quantifiers: for the same fixed $r,s$, inequalities $r\le s+\varepsilon$ for every $\varepsilon>0$ imply $r\le s$; one unspecified approximation does not. If the output bound is $s_\varepsilon$, a separate limit control on those bounds is required. No such limiting law has been extracted from (xi-e) in this bounded trace.

The next expert-ready lemma, not a guessed proof

For initial data satisfying the paper's actual hypotheses, identify the numbered passage and admissible choices that compares the fixed native $q$ class with the corrected output hull in a common ordered, signed real-degree target. Specify the allowed log-link iterate, (Ind1)--(Ind3) permissions, local weights, any sheaf correction, and the same positive determinant power $M$ on both sides. For example, if source-grounded maps really give pointed classes $Q_M,\widehat H_M$ and an order-preserving evaluation $\nu$ with

\[ \nu(Q_M)=Mr,\qquad \nu(Q_M)\le\nu(\widehat H_M),\qquad \nu(\widehat H_M)=Ms,\qquad M>0, \]

then dividing by $M$ proves $r\le s$. These equalities and the order relation are a request for a justified bridge, not claims established by this audit. With the opposite signed degree convention the ordering must reverse. Alternatively, source-proved $r=\mu(P_\beta)$ for a compatible output, or the weaker $r\le\sup_\beta\mu(P_\beta)\le s$, would suffice. Such output realization is sufficient, not necessary; raw geometric $q\subseteq H$ is stronger still. Simply restating $r\le s$ as an unnamed degree inequality is circular.

If a cited lemma supplies this typed comparison, verify each hypothesis and inference in a new source gate. If an alleged bridge attributes a native numerical equality to the weakened horizontal poly-isomorphism or sends $q$ through Ob9 without a pointed selection, classify that particular proposal SOURCE-MISMATCH; do not turn it into a claim that IUT is refuted. A COUNTEREXAMPLE requires all the genuine paper hypotheses, which this run has not met. Until the lemma is identified and checked, defer Lean and wider adversarial agent runs as specified in the protocol.

Check	Source-located fact	What must not be silently inferred
Local pilot versus Tate parameter	I1 Ex. 3.2(iv), p. 71, decorates \(q_{E,v}^{1/(2\ell)}\); I3 Def. 3.8(i), p. 112, uses the global realified pilot	Replace the decorated pilot by an unqualified \(q_{E,v}\) in a numerical comparison
Packet baseline and signs	I3 Prop. 3.9(i), pp. 115--116, puts the local integral structure at volume zero; multiplying a local region by \(p_v\) changes its log-volume by \(-\log p_v\), and by \(e\) at an archimedean place changes it by \(+1\); Prop. 3.9(iii), p. 117, identifies global log-volume with arithmetic degree relative to a suitable normalization	These signs and the procession average specify local/global scales, not an inequality comparing the two pilots
Local weights, not a universal determinant exponent	I3 Rem. 3.1.1(iv), pp. 96--97, has a \(1/N_E\) factor with \(N_E=\prod_vN_v\) for direct-product regions; (Ob3-1), p. 132, calls for positive determinant tensor exponents matching the packet weights	The direct-product identity does not state \(M=N_E\) for general hulls, or give a \(1/M\) formula comparing \(q\) with \(\Theta\)
Procession labels	I3 Rem. 3.11.1(i), p. 159, gives bare \(q^{j^2}\) for \(1\le j\le\ell^\star=(\ell-1)/2\); Prop. 3.9, pp. 115--117, sets positive packet weights and averaging	The arithmetic average \(\ell^{\star-1}\sum_j j^2=\ell(\ell+1)/12\) is not the indeterminacy-subject, corrected hull volume
Hull direction	The overbar on the first \(\mathcal U\) in I3 (xi-c), p. 182, is visible in the PDF image but lost in text extraction; I3 Rem. 3.9.5(iv), p. 129, allows strictly larger hull volume	Neither \(H\subseteq U\) nor the native \(q\) region's inclusion in \(H\) follows
Corrected determinant and \(M\)	I3 (Ob3-1)--(Ob3-3), pp. 131--133, weights each local determinant and tensors it with the inverse weighted determinant of the structure sheaf; \(M\) is the uniquely determined positive integer for that chosen operation, characterized by sending \(\mathcal O(-)\otimes L\) to \(L^{\otimes M}\), and may be chosen sufficiently divisible	No general closed formula \(M=N_E\) or displayed \(1/M\)-normalized \(q\)-versus-hull inequality was found there; (Ob3-3) says the degree represents the original volume with suitable normalization factors, without displaying those factors
\(M\)-th pilot power and twists	I3 (Ob4), pp. 133--134, compares the corrected determinant with Frobenioid objects for the \(M\)-th \(q\)-pilot power and states that tensor-power-twist indeterminacies have no substantive effect on log-volumes	Such asserted comparability and twist invariance do not themselves state \(\deg(Q_M)\le\deg(\widehat H_M)\); cancellation of \(M\) would first require a proven, properly signed degree law
Vertical versus horizontal	I3 (Ob8)/(Ob9), pp. 137--139, compares hull log-volumes across vertical log-links; I2 Rem. 4.10.3(ii), p. 162, distinguishes the horizontal link's value-group portions	A vertical hull-volume bijection is not the missing horizontal identification of the native value

# / passage	Domain	Operation or map	Codomain	Allowed choices	Normalization	Quantitative consequence	Status
1 / `I-6`: I1 Def. 3.1, pp. 61--63, Ex. 3.2(iv), p. 71; I3 Def. 3.8(i), p. 112, Cor. 3.12, p. 174, (xi-c), p. 182	Native \(q\)-pilot in the \((1,0)\) global realified Frobenioid	One-column log-Kummer representation and log-volume	Represented \(q\) class in \((1,\circ)\) packets; its fixed number \(r\)	Input is not subject to (Ind1)--(Ind3); local decorated \(\mathbf q_v=q_{E,v}^{1/(2\ell)}\) up to roots of unity	Procession-normalized $r=-	\log(q)	<0$
2 / `I-1`: I2 Def. 4.9(viii), p. 158, Rem. 4.10.3(ii), p. 162; I3 Def. 3.8(ii), p. 113, Cor. 3.12(i), p. 175	\(\Theta\)-pilot prime-strip at \((0,0)\)	Horizontal \(\Theta^{\times\mu}_{\mathrm{LGP}}\) poly-isomorphism of weakened prime-strips	Corresponding \(q\)-pilot prime-strip at \((1,0)\)	Paper-specified link; no ring identification	I2 says its value-group portion is not preserved; it gives no native-degree preservation law	Abstract pilot correspondence; not \(\mu(\Theta)=r\)	`SOURCE_VERIFIED`; attributing native-degree equality to this link is `SOURCE-MISMATCH`
3 / `I-2`: I3 Thm. 3.11(i)--(iii), pp. 153--159, (xi-b/c), pp. 181--182	\(\Theta\) data in \((0,m)\) theaters	Kummer/mono-analytic construction and étale-picture permutation representation	Possible regions \(P_\beta\) in \((1,\circ)\) packets	(Ind1) procession, (Ind2) independent local, (Ind3) upper-semi-compatible vertical log-link choices	Packet weights and procession average; bare \(j^2\) powers are not final hull volumes	IPL links prime-strips, SHE permits one-column expressibility, APT is not set transport	`SOURCE_VERIFIED`; no native-volume equation here
4 / `I-4`: I3 Rem. 3.9.5(i)--(iv), pp. 127--129, rendered (xi-c), p. 182	One-column output possibilities \(P_\beta\)	Holomorphic hulling of their union	\({}^{1,\circ}\overline{\mathcal U}=H\supseteq{}^{1,\circ}\mathcal U\)	All permitted output possibilities; hull may enlarge volume strictly	One-column log-volume	\(\mu(P_\beta)\le\mu(H)\) for compatible evaluated regions	Hull inclusion `SOURCE_VERIFIED`; monotonicity `STANDARD`; reading it as \(q\subseteq H\) is `SOURCE-MISMATCH`
5 / `I-5`: I3 Rem. 3.9.5(vii), (Ob3)--(Ob5), pp. 131--135; (xi-d), p. 183	Rank-\(>1\) hull \(H\)	Weighted, structure-sheaf-corrected \(\det^{\otimes M}\)	Comparable one-column rank-one line-bundle class	Compatible local packets and weights	\(M>0\) is defined for the chosen weighted operation; compare with the \(q\)-pilot's corresponding \(M\)-th power, not an unscaled degree	Gives comparability of Frobenioid objects; no source-checked order of these two pointed classes yet	Machinery `SOURCE_VERIFIED`; native order `UNRESOLVED_OBLIGATION`
6 / `I-5v`: I3 Rem. 3.9.5(vii), (Ob8)/(Ob9), pp. 137--139	Hull log-volume classes at vertical log-link levels	Log-Kummer adjustment; realified semi-simplification	Bijection of hull log-volume classes across the vertical shift	Arbitrary allowed log-link iterates and their compatibility conditions	Matched hull-volume normalization	A positive numerical compatibility claim, not merely object comparability; it does not name the fixed native \(q\) as an output	`SOURCE_VERIFIED`; using it as a selected \(q\)-output identity is `SOURCE-MISMATCH`
7 / pre-volume loop: I3 Rem. 3.9.5(ix), pp. 141--144	Output and input prime-strip structures	Claimed closed loop up to formal quotient indeterminacies	Prime-strip comparison before taking volume	Formal quotients and permissible choices matter	Volume follows the loop, not an assumed equality of raw values	The passage says this will yield an inequality, but supplies no separately displayed, choice-indexed fixed-\(q\)/output degree law in the passages inspected	Loop `SOURCE_VERIFIED`; typed numerical step `UNRESOLVED_OBLIGATION`
8 / `I-5`, `I-7`: I3 (xi-d)--(xi-f), pp. 183--184	Hull value \(s\) and separately fixed input \(r\)	Form \(B_s\), then assert input/output membership	Exact \(r\in B_s\) in (xi-f)	Output includes (Ind1)--(Ind3); the native input does not	\(r\) and \(s\) must be on a common signed real scale; any approximation needs explicit limiting quantifiers	\(r\le s\) is stated, not independently derived by rows 1--7	Statement `ASSERTED_IN_IUT`; preceding numerical implication `UNRESOLVED_OBLIGATION`

Reading	Source path it probed	First numerical question it left open
A (native-pilot first)	IUT I's decorated \(q\) generator; IUT II's value-group warning; the one-column hull and its corrected determinant	Which order-preserving, pointed comparison connects \(q^M\) to the corrected hull determinant after permitted choices?
B (representation first)	IUT III's IPL/SHE/APT and étale-picture permutation, then Ob8/Ob9 and the pre-volume loop	What makes the separately fixed one-column \(q\) number a bounded output value rather than merely expressible in the same column?
C (vertical-compatibility first)	Prop. 3.9 and arbitrary log-link iterates, then Ob8/Ob9 and Rem. 3.12.2's within-column equalities	What supplies the cross-object, choice-compatible signed degree law at (xi-e)--(xi-f)?

11. XI-002: attempt to trace the fixed native \(q\)-value