Strange word diff

$ git diff --no-index --word-diff file1.txt file2.txt 
diff --git a/file1.txt b/file2.txt
index a9eaedc..a75008e 100644
--- a/file1.txt
+++ b/file2.txt
@@ -1,4 +1,4 @@
\subparagraph*{Context}
Our object of study is an extension of Turing degrees where the oracles can
feature certain forms of non-determinism, as in this riddle. We call these
generalized degrees the \emph{Arthur–Nimue–Merlin degrees}, owing to their
explicit description by Kihara using a three-player game whose players are
conventionally named Arthur, Nimue and
Merlin \cite{KiharaLT}.\footnote{In \cite{KiharaOracles}, Kihara uses the term
“extended Turing–Weihrauch degrees”. We prefer to eschew the association with
Weihrauch's name since we never deal with [-call-once oracles.}-]{+oracles that
can only be queried once.}+} Whereas Turing degrees are defined as a quotient of
oracles which are functions $\N \to \N$, Arthur–Nimue–Merlin degrees are a
quotient of a richer set of oracles, namely functions $\N \to \P(\P(\N))$.
Informally, when a program that uses $g : \N \to \P(\P(\N))$ as an oracle makes
a query $n \in \N$ to the oracle, a set $P \in g(n)$ is chosen in a benevolent
way (“angelic non-determinism”), then a value $v \in P$ is chosen in an
adversarial way (“demonic non-determinism”), and the program receives the answer
$v$. The mathematical meaning to “benevolent” and “adversarial” is made precise
by introducing a game where Arthur, a player restricted to computable
strategies, is allied to Nimue, the player choosing $P$, and both play against
Merlin, the player choosing $v$. (The details of the game are recalled in
\autoref{section-arthur-nimue-merlin-games}.)

While [-this game was-]{+Arthur–Nimue–Merlin games were+} introduced recently by
Kihara, [-the concept-]{+they are a concrete description+} of [-
Arthur–Nimue–Merlin degrees is-]{+objects that arose+} much [-older, having
arised,-]{+earlier,+} in a different guise, in the study of realizability. To
reassure the reader unfamiliar with realizability from the outset, this paper is
meant to be accessible with only a background in basic computability theory,
except for \autoref{section-topos-theory} where we explain how the proof of our
main result can be understood from the point of view of realizability.
Nevertheless, let us recall the historical link.

$ git diff --no-index file2.txt file3.txt 
diff --git a/file2.txt b/file3.txt
index a75008e..81c3eb9 100644
--- a/file2.txt
+++ b/file3.txt
@@ -1,4 +1,5 @@
 \subparagraph*{Context}
+
 Our object of study is an extension of Turing degrees where the oracles can
feature certain forms of non-determinism, as in this riddle. We call these
generalized degrees the \emph{Arthur–Nimue–Merlin degrees}, owing to their
explicit description by Kihara using a three-player game whose players are
conventionally named Arthur, Nimue and
Merlin \cite{KiharaLT}.\footnote{In \cite{KiharaOracles}, Kihara uses the term
“extended Turing–Weihrauch degrees”. We prefer to eschew the association with
Weihrauch's name since we never deal with oracles that can only be queried
once.} Whereas Turing degrees are defined as a quotient of oracles which are
functions $\N \to \N$, Arthur–Nimue–Merlin degrees are a quotient of a richer
set of oracles, namely functions $\N \to \P(\P(\N))$. Informally, when a program
that uses $g : \N \to \P(\P(\N))$ as an oracle makes a query $n \in \N$ to the
oracle, a set $P \in g(n)$ is chosen in a benevolent way (“angelic non-
determinism”), then a value $v \in P$ is chosen in an adversarial way (“demonic
non-determinism”), and the program receives the answer $v$. The mathematical
meaning to “benevolent” and “adversarial” is made precise by introducing a game
where Arthur, a player restricted to computable strategies, is allied to Nimue,
the player choosing $P$, and both play against Merlin, the player choosing $v$.
(The details of the game are recalled in \autoref{section-arthur-nimue-merlin-
games}.)
 
 While Arthur–Nimue–Merlin games were introduced recently by Kihara, they are a
concrete description of objects that arose much earlier, in a different guise,
in the study of realizability. To reassure the reader unfamiliar with
realizability from the outset, this paper is meant to be accessible with only a
background in basic computability theory, except for \autoref{section-topos-
theory} where we explain how the proof of our main result can be understood from
the point of view of realizability. Nevertheless, let us recall the historical
link.

$ git diff --no-index --word-diff file1.txt file3.txt 
diff --git a/file1.txt b/file3.txt
index a9eaedc..81c3eb9 100644
--- a/file1.txt
+++ b/file3.txt
@@ -1,4 +1,5 @@
\subparagraph*{Context}
[-Our object of study is an extension of Turing degrees where the oracles can
feature certain forms of non-determinism, as in this riddle. We call these
generalized degrees the \emph{Arthur–Nimue–Merlin degrees}, owing to their
explicit description by Kihara using a three-player game whose players are
conventionally named Arthur, Nimue and
Merlin \cite{KiharaLT}.\footnote{In \cite{KiharaOracles}, Kihara uses the term
“extended Turing–Weihrauch degrees”. We prefer to eschew the association with
Weihrauch's name since we never deal with call-once oracles.} Whereas Turing
degrees are defined as a quotient of oracles which are functions $\N \to \N$,
Arthur–Nimue–Merlin degrees are a quotient of a richer set of oracles, namely
functions $\N \to \P(\P(\N))$. Informally, when a program that uses $g : \N \to
\P(\P(\N))$ as an oracle makes a query $n \in \N$ to the oracle, a set $P \in
g(n)$ is chosen in a benevolent way (“angelic non-determinism”), then a value $v
\in P$ is chosen in an adversarial way (“demonic non-determinism”), and the
program receives the answer $v$. The mathematical meaning to “benevolent” and
“adversarial” is made precise by introducing a game where Arthur, a player
restricted to computable strategies, is allied to Nimue, the player choosing
$P$, and both play against Merlin, the player choosing $v$. (The details of the
game are recalled in \autoref{section-arthur-nimue-merlin-games}.)-]

[-While-]{+Our object of study is an extension of Turing degrees where the
oracles can feature certain forms of non-determinism, as in+} this [-game was
introduced recently-]{+riddle. We call these generalized degrees the
\emph{Arthur–Nimue–Merlin degrees}, owing to their explicit description+} by [-
Kihara,-]{+Kihara using a three-player game whose players are conventionally
named Arthur, Nimue and
Merlin \cite{KiharaLT}.\footnote{In \cite{KiharaOracles}, Kihara uses+} the [-
concept-]{+term “extended Turing–Weihrauch degrees”. We prefer to eschew the
association with Weihrauch's name since we never deal with oracles that can only
be queried once.} Whereas Turing degrees are defined as a quotient+} of
{+oracles which are functions $\N \to \N$,+} Arthur–Nimue–Merlin degrees {+are a
quotient of a richer set of oracles, namely functions $\N \to \P(\P(\N))$.
Informally, when a program that uses $g : \N \to \P(\P(\N))$ as an oracle makes
a query $n \in \N$ to the oracle, a set $P \in g(n)$ is chosen in a benevolent
way (“angelic non-determinism”), then a value $v \in P$ is chosen in an
adversarial way (“demonic non-determinism”), and the program receives the answer
$v$. The mathematical meaning to “benevolent” and “adversarial”+} is {+made
precise by introducing a game where Arthur, a player restricted to computable
strategies, is allied to Nimue, the player choosing $P$, and both play against
Merlin, the player choosing $v$. (The details of the game are recalled in
\autoref{section-arthur-nimue-merlin-games}.)+}

{+While Arthur–Nimue–Merlin games were introduced recently by Kihara, they are a
concrete description of objects that arose+} much [-older, having arised,-
]{+earlier,+} in a different guise, in the study of realizability. To reassure
the reader unfamiliar with realizability from the outset, this paper is meant to
be accessible with only a background in basic computability theory, except for
\autoref{section-topos-theory} where we explain how the proof of our main result
can be understood from the point of view of realizability. Nevertheless, let us
recall the historical link.