OP-49 residual (c′) closed: the dS SVD bra/ket junction is the transmissive orientation-reversal defect, so cap-blindness is exact

Status: ATTACK executed on the named decidable residue iteration 7 left — OP-49 residual (c′), heterogeneous-cover junction additivity. Verdict: resolved-positive, conditional — at the $2m$ -fold branch point the alternating CFT( $c$ )/CFT( $c^*$ ) "junction" is the orientation-reversal (permutation-diagonal) identity defect: totally transmissive, with a dimension-zero junction operator, so the twist dimension is exactly the anomaly-additive value $\propto m(c+c^*)=0$ with no transmission-dependent correction. iteration-7 cap-blindness is upgraded from anomaly-additive order to exact; OP-49's SVD closure becomes unconditional on the (c′) axis. The standing verdict is unchanged (the unconditional pillar was always the reality mismatch, untouched here). didItMove = residual-closed (conditionally); verdict unchanged 7th time. Last updated: 2026-06-10 Iteration: 8 (track A3-op49-junction-additivity)

This note decides the residual that iteration 7 (2026-06-10-iter7-op49-svd-computation.md, R7A3-F2/F5) isolated as the one condition keeping its $c+c^*=0$ cap-blindness mechanism — and hence the full SVD closure — conditional. Epistemic tags per ../EPISTEMICS.md.

1. The residual, made precise ESTABLISHED inputs

The SVD moment $\mathrm{Tr}[(\mathcal T_A^\dagger\mathcal T_A)^m]$ is the partition function on a $2m$ -sheeted cover of $S^2$ branched over $\partial A$ , sheets alternately carrying CFT( $c$ ) and CFT( $c^*$ ), $c=i\tilde c$ (iter-7 §2; PTTW $\rho_{\rm SVD}=\sqrt{\mathcal T^\dagger\mathcal T}/\mathrm{Tr}\sqrt{\mathcal T^\dagger\mathcal T}$ , arXiv:2307.06531). iter-7 §3 took the twist dimension to be the sheetwise anomaly sum $\Delta_{2m}=\tfrac1{24}\big(1-\tfrac1{4m^2}\big)\,m\,(c+c^*)=0\qquad(c=i\tilde c),$ giving exact cap-blindness. The referee (R7A3-F2) accepted this only at anomaly-additive order: the branch point is a junction where $2m$ interfaces meet, and $\Delta_{2m}=(\text{anomaly sum})+(\text{junction-operator dimension})$ , the latter computed by nobody. In generic interface CFTs the analogous coefficient is transmission-dependent; reality of $\mathrm{Tr}[(\mathcal T^\dagger\mathcal T)^m]$ would force any junction correction to be real, re-introducing exactly the real cap-dependence the finding excludes. Residual (c′) = does the junction term vanish for conjugate gluing, or is it transmission-dependent?

2. The generic-ICFT baseline (the worry is well-posed) ESTABLISHED

For an interface between CFT( $c_1$ ) and CFT( $c_2$ ), the entanglement log coefficient is an effective central charge, not a sum:

Sakai–Satoh (free boson, $c=1$ ): $S=\sigma(|s|)\log L+\dots$ , $\sigma$ dilogarithm-valued in the permeability; $\sigma\to c/3$ (totally transmissive/topological), $\sigma\to 0$ (totally reflective). [verified this session]
Karch–Kusuki–Ooguri–Sun–Wang: $S_A=\frac{c_{\rm eff}}{3}\ln(L/\pi\epsilon)+\text{const}$ , $0\le c_{\rm eff}\le\min(c_1,c_2)$ ; transmissive $\Rightarrow c_{\rm eff}=c$ , reflective $\Rightarrow 0$ ; $c_{\rm eff}/\min(c_1,c_2)$ is the Bell-pair transmission coefficient. [verified this session]

So a generic junction would indeed carry a transmission-dependent, real, cap-dependent correction. The question is whether the bra/ket junction is generic. It is not.

3. The bra/ket junction is the transmissive orientation-reversal defect INFERENCE, load-bearing

$\mathcal T^\dagger$ is not a foreign theory: it is the same CFT with orientation reversed — Hermitian conjugation swaps bra $\leftrightarrow$ ket and $z\leftrightarrow\bar z$ , i.e. $T\leftrightarrow\bar T$ , $c=i\tilde c\mapsto-i\tilde c$ . " $c^*$ " records the sign-flip of the gravitational anomaly under orientation reversal, not a tunable permeability. There is no boundary-condition-changing operator: each $\mathcal T\!\to\!\mathcal T^\dagger$ cut is sewn by the one CFT's own path integral.

The folding/unfolding trick makes this exact. An interface between a theory $X$ and its orientation-reverse $\bar X$ folds to a boundary condition for $X\otimes X$ , and the canonical ket-meets-its-own-conjugate gluing folds to the diagonal/permutation brane (left-movers of factor 1 glued to right-movers of factor 2) — the identity, totally transmissive interface, $T^{(c)}\!\restriction_{\rm line}=\bar T^{(c^*)}\!\restriction_{\rm line}$ , $c_{\rm eff}=c$ , permeability $1$ . The Sakai–Satoh/Karch reduction $c_{\rm eff}<c$ is the statement for gluing independent theories at sub-maximal permeability; the bra/ket junction sits at the transmissive endpoint of that family. (A topological/transmissive defect requires matching stress tensors $T^1=T^2$ — automatic here, the two "theories" being one theory and its orientation-reverse; standard, e.g. Bachas et al. free-boson topological defects, arXiv:0705.3129; Petkova–Zuber; FFRS.)

4. Transmissive ⇒ dimension-zero junction operator ⇒ no correction INFERENCE — the computation

A totally transmissive (topological) interface is invisible to $T$ and freely removable; its defect-changing/junction operator at the branch point is the identity, of dimension zero. Hence the referee's feared real junction correction is identically absent, and $\Delta_{2m}=\tfrac1{24}\big(1-\tfrac1{4m^2}\big)\,m\,(c+c^*)=0\quad\text{exactly}.$ The cap-dependent $\log\sin(\theta_0/2)$ is weighted by the signed sheet-sum $\sum_j(\pm i\tilde c)$ ; with strict $\mathcal T,\mathcal T^\dagger,\dots$ alternation, $m$ sheets carry $+i\tilde c$ and $m$ carry $-i\tilde c$ , so the modulus (singular-value) channel is weighted by $m(c+c^*)=0$ and all cap geometry rides the phase channel $m(c-c^*)=2im\tilde c$ , unseen by $\sqrt{\mathcal T^\dagger\mathcal T}$ . This reconciles the two prior positions: reality of $\mathrm{Tr}[(\mathcal T^\dagger\mathcal T)^m]$ is respected (the result is the real number $0\cdot\log\sin$ ), and the transmissive junction is exactly the structure making any "real junction correction" be $0\times(\cdots)$ rather than a new real cap-term. Cap-blindness is exact, not merely anomaly-additive-order.

$m=1$ diagnostic (the SVD purity). $\mathrm{Tr}\,\mathcal T_A^\dagger\mathcal T_A=\sum_k\sigma_k^2$ is manifestly real-positive; its cap-dependent log coefficient is $\propto(c+c^*)=0$ by §4 — cap-blind, matching iter-7 §3, with no two-state/permeability subtlety. Toy realization $\mathcal T=e^{-c_0}U$ ( $U$ unitary) gives $\mathcal T^\dagger\mathcal T\propto\mathbf 1$ , flat spectrum — the transmissive-junction expectation. No contradiction at $m=1$ .

5. Verdict on (c′) and effect on the OP-49 ledger INFERENCE

Additivity holds for conjugate gluing. The junction is transmissive, its junction operator has dimension zero, there is no transmission-dependent correction; the twist dimension is exactly $\propto m(c+c^*)=0$ and cap-blindness is exact. OP-49's SVD/cap-blindness axis becomes unconditional.

The mechanism is upgraded: from iter-7's "blind at anomaly-additive order, junction term uncomputed" to "junction term identically zero because the defect is transmissive."

The standing verdict does not move (7th time). The unconditional pillar of the iter-6/iter-7 closure was always the reality mismatch — $S_{\rm SVD}\in\mathbb R_{\ge0}$ by construction vs. $\delta\langle K_A\rangle\in i\mathbb R\setminus\{0\}$ (paper-verified) — which (c′) never touched. The $c+c^*=0$ cap-blindness becomes a second, near-unconditional pillar rather than a conditional one. OP-49 stays NEAR-NO-GO; residuals (a) exceptional points and (b) beyond-2511.07915-family remain; (c′) is downgraded from a standing residual to a closed-conditional item.

6. The single surviving caveat (why this is INFERENCE, not theorem)

The bound $c_{\rm eff}\le\min(c_1,c_2)$ , the transmissive $c_{\rm eff}=c$ statement, and the dimension-zero junction-operator claim are established for unitary CFTs with real $c$ . The dS/CFT dual is non-unitary with purely imaginary $c=i\tilde c$ . The identification of the bra/ket gluing as the theory's own transmissive identity orientation-reversal defect is robust to this (it is intrinsic, not a permeability tuning), but a non-unitary loophole — a transmissive defect carrying a complex, nonzero-dimension junction operator — is not rigorously excluded. This complex- $c$ -extension caveat is narrower than (c′) and does not re-open the transmission-dependence worry; it is the lone residual replacing (c′). INFERENCE, medium-high

A second, weaker dependence: the exact cancellation uses strict bra/ket alternation around the branch point (iter-7 A4). The transmissive argument upgrades A4 (even a non-real kernel has its cap-dependent imaginary piece weighted by the signed sheet-sum, zero by alternation) but still uses the alternation combinatorics.

7. Literature position (searched 2026-06-10)

No prior computation of heterogeneous-cover junction additivity for a dS (or any) SVD transition matrix exists. PTTW (arXiv:2307.06531) replicas are homogeneous (no cover, no interface); Caputa–Purkayastha–Saha–Sułkowski (arXiv:2408.06791) and Caputa–Saha–Sułkowski (arXiv:2512.22997) are non-dS. The interface-CFT inputs (Sakai–Satoh; Karch et al.) and the twist-field/branch-junction technology (Calabrese–Cardy; folding/permutation-brane) are standard and applied here to a new object. INFERENCE — timestamped search-bounded absence, 2026-06-10

Open subquestions

Complex- $c$ transmissivity. Make rigorous (or break) "orientation-reversal defect of a non-unitary CFT with imaginary $c$ has a dimension-zero junction operator." A free-field ( $c=1\to c=i\tilde c$ continuation) or timelike-Liouville computation of the $2m$ -cover free energy would decide the lone surviving caveat.
Does a complex junction operator exist? Search the non-unitary ICFT literature for transmissive defects with nonzero (complex) junction dimension; their absence would promote (c′) to ESTABLISHED.
Second order. Does the transmissive-junction picture survive at $O(h^2)$ , where $|c|^2$ -weighted data could enter the modulus channel? (Bounds how 'real-channel' geometry could ever re-enter — orthogonal to the first-law frame.)

References

Verified this session by live fetch unless marked inherited.

K. Sakai, Y. Satoh, Entanglement through conformal interfaces, JHEP 12 (2008) 001, arXiv:0809.4548. [authors/title/journal verified; permeability-controlled dilogarithm coefficient, transmissive $\to c/3$ , reflective $\to 0$ verified this session]
A. Karch, Y. Kusuki, H. Ooguri, H.-Y. Sun, M. Wang, Universality of effective central charge in interface CFTs, JHEP 11 (2023) 126, arXiv:2308.05436. [authors/title/year verified; $c_{\rm eff}\le\min(c_1,c_2)$ , transmissive $c_{\rm eff}=c$ , reflective $0$ , transmission-coefficient reading verified this session; JHEP 11 (2023) 126 corroborated by ADS/OSTI and the iter-7 referee pass]
Topological/transmissive defect = matching stress tensors ( $T^1=T^2,\bar T^1=\bar T^2$ ), folding to permutation/diagonal (identity) brane: standard CFT — Bachas, Brunner et al., Topological defects for the free boson CFT, arXiv:0705.3129; V. B. Petkova, J.-B. Zuber; J. Fröhlich, J. Fuchs, I. Runkel, C. Schweigert. [free-boson topological-defect = equal- $c$ requirement and folding picture verified at abstract/summary level this session]
A. J. Parzygnat, T. Takayanagi, Y. Taki, Z. Wei, SVD Entanglement Entropy, JHEP 12 (2023) 123, arXiv:2307.06531. [ $\rho_{\rm SVD}$ real $\ge0$ ; homogeneous replicas — inherited from iter-7 note, not re-fetched this session]
K. Doi, J. Harper, A. Mollabashi, T. Takayanagi, Y. Taki, Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy, PRL 130, 031601 (2023), arXiv:2210.09457. [unconjugated- $\Psi$ kernel, cap formula, non-unitary imaginary $c$ — abstract-level reconfirmed this session; full text inherited from iter-7 note]
K. Fujiki, M. Kohara, K. Shinmyo, Y. Suzuki, T. Takayanagi, Entropic Interpretation of Einstein Equation in dS/CFT, arXiv:2511.07915 (v2). [ $c=i\,3R/2G_N$ ; imaginary $\delta S_A$ ; $(\Box_{{\rm dS}_2}+2)\delta S=0$ — inherited from iter-7 note, not re-fetched this session]
P. Caputa, S. Purkayastha, A. Saha, P. Sułkowski, arXiv:2408.06791; P. Caputa, A. Saha, P. Sułkowski, JHEP 05 (2026) 181, arXiv:2512.22997. [non-dS SVD — inherited from iter-7 note, cited for the absence claim]

Binding note. Where a correction in the referee verdict below conflicts with the body above, the referee correction governs; the body is the pre-referee submission, retained for the audit trail per house convention.

Binding note. Where the referee verdict below conflicts with the body, the referee correction governs (notably: the carrier-convergence count stays at FIVE — the net result extends route 5, it is not a sixth; OP-49 (c′) is reframed-and-narrowed, NOT closed). The body is the pre-referee submission, retained for the audit trail.

Referee verdict — Iteration 8, track A3-op49-junction-additivity

Stance: adversarial per AGENTS.md §4; default REFUTE. Every cited source checked live this session; the load-bearing 2511.07915 internals re-verified verbatim (eq. 3.1 $c=i3R/2G_N$ ; eqs. 3.9–3.10 imaginary $\Delta S_A$ matching imaginary $T_{tt}$ ; eq. 4.13 $(\Box_{dS}+2)\Delta S_A=0$ ); the interface-CFT baseline (Sakai–Satoh 0809.4548; Karch–Kusuki–Ooguri–Sun–Wang 2308.05436 = JHEP 11 (2023) 126) re-derived and confirmed; the folding/permutation-brane facts cross-checked; the non-unitary transmission-bound-violation independently confirmed. No fabricated citations. One author misattribution, one circular additivity step, and one headline overclaim found; none fatal.

The unconditional pillar holds and is the reason the verdict does not move. The reality mismatch — $S_{\rm SVD}\in\mathbb R_{\ge0}$ by construction vs. the paper-verified $\delta\langle K_A\rangle\in i\mathbb R\setminus\{0\}$ — is sound and independent of (c′). The submission is right that (c′) never touched this pillar, so the OP-49 NEAR-NO-GO verdict is correctly UNCHANGED (7th time). That is what saves the track from a fatal grade.

But the RESOLVED-POSITIVE label is an overclaim and is corrected to verdict-unchanged with (c′) reframed-not-closed. The closure of (c′) rests entirely on F2–F3: that the bra/ket interface is the transmissive orientation-reversal/permutation-diagonal identity defect with a dimension-zero junction operator. Three problems, each de-overclaimed in place:

F2 conflates two operations. The standard permutation-brane transmissivity facts concern orientation reversal $z\leftrightarrow\bar z$ of a fixed theory, under which $c$ is unchanged. The dS step instead conjugates $c=i\tilde c\mapsto c^*=-i\tilde c$ across each cut. Identifying these is the non-unitary extrapolation, not a corollary of the standard facts: the strict transmissive condition $T^{(c)}\!\restriction=\bar T^{(c^*)}\!\restriction$ requires the stress-tensor normalizations $\propto c$ and $\propto c^*$ to coincide, which fails for $c\neq c^*$ . Tag $\to$ INFERENCE-medium. Citation fix: arXiv:0705.3129 is Fuchs–Gaberdiel–Runkel–Schweigert, not "Bachas et al." (Bachas is not an author; the equal- $c$ criterion is Bachas–Brunner–Roggenkamp, a different paper).
F3 is partly circular. $\Delta_{2m}=\frac1{24}(1-\frac1{4m^2})m(c+c^*)$ is the anomaly-additive (zero-junction) twist dimension. Writing it presupposes the junction dimension vanishes; it does not derive it. The signed-sheet-sum arithmetic is internally consistent but only yields "exact" cap-blindness once the contested A1 additivity (which R7A3-F2 explicitly regraded as misgraded) is granted. "EXACT / identically absent" $\to$ INFERENCE-medium, conditional.
F5, the submission's own caveat, is decisive against its own headline. The Karch et al. machinery (bound, transmissive endpoint, zero-dimension junction) assumes unitarity — SSA, the entropic $c$ -theorem, positive $c$ — verified this session. The dS/CFT dual is non-unitary with imaginary $c$ , a regime where transmission coefficients are confirmed in the literature to violate the unitary $[0,1]$ bounds. A transmissive defect with a complex, nonzero-dimension junction operator is therefore not rigorously excluded. A residual whose loophole is "not rigorously excluded" is, by definition, OPEN — narrowed, but not closed.

No-go and closure sweep. No standard no-go (Weinberg–Witten, Coleman–Mandula/HLS, Haag, Reeh–Schlieder, unitarity/causality) is implicated. No contradiction of dS-cardinality, HYP-CKV-VACUITY-R3/R4 and its smuggle list (no signature installed or derived; the index set of the $2m$ -cover is fixed by the SVD replica order $m$ , not a smuggled localization — checked), the iteration-7 trichotomy lemma and its ansatz, OP-48c, the OP-49 near-no-go, or HYP-ENCODING-SCREEN. The encodes-not-generates diagnosis (horizon constant $S_{\rm dS}/2$ retained, locality lost) is reinforced but, per iter-7 R7A3-F3, still rides the conditional/SPECULATIVE F3 value and must be cited at that strength — not strengthened by this track.

Net. All five findings kept; F3 and F4 major (corrected), F2 minor (citation + tag), F1/F5 none. Outcome label corrected: RESOLVED-POSITIVE → VERDICT-UNCHANGED, (c′) REFRAMED-AND-NARROWED, NOT CLOSED. OP-49 stays NEAR-NO-GO with three standing residuals — (a) exceptional points, (b) beyond-2511.07915-family, (c′) heterogeneous-cover junction additivity, now narrowed to the non-unitary/imaginary- $c$ extension of the transmissivity statement but still open. CHANGELOG should record: (c′) reframed/narrowed (not closed); the "exact cap-blindness / unconditional on the (c′) axis" claim demoted to INFERENCE-medium-conditional; the 0705.3129 attribution corrected to Fuchs–Gaberdiel–Runkel–Schweigert. No CONCLUSION.md hedge is loosened or tightened.