In this paper, we define the spectral Einstein functionals of spin manifolds with boundary, and we give a complete proof of the Dabrowski-Sitarz-Zalecki type theorem for six dimensional spin manifolds with boundary.

1.
M.
Wodzicki
, “
Local invariants of spectral asymmetry
,”
Invent. Math.
75
(
1
),
143
177
(
1984
).
2.
M.
Wodzicki
,
Non-Commutative Residue I
,
Lecture Notes in Mathematics Vol. 1289
(
Springer
,
Berlin
,
1987
), pp.
320
399
.
3.
A.
Connes
, “
Quantized calculus and applications
,” in
XIth International Congress of Mathematical Physics (Paris, 1994)
(
Internat Press
,
Cambridge, MA
,
1995
), pp.
15
36
.
4.
A.
Connes
, “
The action functional in non-commutative geometry
,”
Commun. Math. Phys.
117
,
673
683
(
1988
).
5.
A.
Connes
and
J.
Lott
, “
Particle models and non-commutative geometry
,”
Nucl. Phys. B, Proc. Suppl.
18
,
29
47
(
1990
).
6.
D.
Kastler
, “
The dirac operator and gravitation
,”
Commun. Math. Phys.
166
,
633
643
(
1995
).
7.
W.
Kalau
and
M.
Walze
, “
Gravity, non-commutative geometry and the Wodzicki residue
,”
J. Geom. Phys.
16
,
327
344
(
1995
).
8.
B. V.
Fedosov
,
F.
Golse
,
E.
Leichtnam
, and
E.
Schrohe
, “
The noncommutative residue for manifolds with boundary
,”
J. Funct. Anal.
142
,
1
31
(
1996
).
9.
E.
Schrohe
, “
Noncommutative residue, Dixmier’s trace, and heat trace expansions on manifolds with boundary
,”
Contemp. Math.
242
,
161
186
(
1999
).
10.
Y.
Wang
, “
Differential forms and the Wodzicki residue for manifolds with boundary
,”
J. Geom. Phys.
56
,
731
753
(
2006
).
11.
Y.
Wang
, “
Gravity and the noncommutative residue for manifolds with boundary
,”
Lett. Math. Phys.
80
,
37
56
(
2007
).
12.
W.
Yong
, “
Lower-dimensional volumes and Kastler–kalau–Walze type theorem for manifolds with boundary
,”
Commun. Theor. Phys.
54
,
38
42
(
2010
).
13.
A.
Connes
, “
C* algèbres et géométrie différentielle
,”
C. R. Acad. Sci. Paris
290
,
A599
A604
(
1980
).
14.
S.
Baaj
, “
Calcul pseudo-difféentiel et produits croisés de C*-algèbres I
,”
C. R. Acad. Sci. Paris Ser. 1
307
,
581
586
(
1988
).
15.
S.
Baaj
, “
Calcul pseudo-différentiel et produits croiss de C*-algèbres II
,”
C. R. Acad. Sci. Paris Ser. 1
307
,
663
666
(
1988
).
16.
L.
Dąbrowski
,
A.
Sitarz
, and
P.
Zalecki
, “
Spectral metric and Einstein functionals
,”
Adv. Math.
427
,
109128
(
2023
).
17.
J.
Wang
and
Y.
Wang
, “
The Kastler-Kalau-Walze type theorem for six-dimensional manifolds with boundary
,”
J. Math. Phys.
56
,
052501
(
2015
).
18.
J.
Wang
,
Y.
Wang
,
T.
Wu
, and
Y.
Yang
, “
One-forms, spectral Einstein functionals and the noncommutative residue
,” arXiv:2307.15921.
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