18
Journal of Pacific ArchaeologyVol.  · No.  · 
–  –
A Note on Hawaiian Stone Axes
Jennifer G. Kahn¹ & omas S. Dye²

As part of a project to describe and classify more than 800 Hawaiian stone adzes held in the
ethnographic and archaeo-
logical collections at Bishop Museum in Honolulu, 11 finely-finished,
double-beveled stone tools, which resemble modern
axe or hatchet blades, were identified and described. ese 11 axes were surprising finds in the collection because
double-beveled
stone tools have been reported as absent in Hawai‘i and in the Duff typology are restricted to heavy,
crudely-finished tools commonly recovered in Mangareva but not found elsewhere in
Polynesia. Building on the replica-
tion experiments carried out by Turner and her colleagues in
New Zealand, it is suggested that stone tools in Hawai‘i and
elsewhere in Polynesia be classified
functionally, rather than grouped according to the type/variety system devised by Duff.
Keywords: Hawaii, axe, adze, classification
1 Anthropology Department, College of William & Mary, Wash-
ington Hall, Room 103, 241 Jamestown Rd., Williamsburg, VA
23185
2 T. S. Dye & Colleagues, Archaeologists, 735 Bishop St., Suite 315,
Honolulu, HI 96813
Corresponding author: tsd@tsdye.com
Submitted 9/6/14, accepted 28/10/14

Traditional Polynesian stone wood-working tools, typi-
cally denoted in English as adzes’, axes, and chisels, have
been arranged by archaeologists for more than half a cen-
tury using a culture historical typology associated with
the New Zealand prehistorian Roger Duff (1956). A recent
replication experiment using stone tools in the manufac-
ture of an outrigger canoe identified six functional types
of stone adzes that correspond generally with the six cul-
ture historical types established by Duff (Turner 2000,
2004). e replication experiment concluded that variabil-
ity in New Zealand stone adzes captured by the Duff types
is due to the function performed by the tool, which dic-
tated what features and dimensions were required (Turner
2004: 97), and by raw material and manufacturing tech-
niques. e functional basis of the Duff types casts doubt
on their utility for culture history, which requires that arti-
fact types be founded in stylistic variability (Dunnell 1978).
In Hawaii, archaeologists arrange stone wood-working
tools by cross-section shape using a typology derived
from Duffs (Emory 1968), yet the adze types this yields
fail to satisfy the historical significance criterion (Krieger
1944; Dunnell 1978: 196; Lyman & O’Brien 2002: 78). Prob-
lematically, each cross-section shape is found throughout
the traditional Hawaiian period (Cleghorn 1992). Together,
the results of the replication experiment (Turner 2000,
2004) and the distribution study (Cleghorn 1992) indicate
that the Duff types are unsuitable for culture history and
thus fail to function as intended.
Despite this failure, archaeologists are understand-
ably reluctant to abandon the Duff typology. Several
generations of archaeologists in the Pacific have learned
to arrange Polynesian adzes according to the Duff types
and many stone tool collections have been described in
its terms. Turner was eager to dispel the notion that the
Duff types needed to be abandoned and wrote of the
good news . . . that for ease of description . . . Duffs basic
terminology can be retained with the bonus of now be-
ing able to explain the distinctions between the different
types (Turner 2004: 63). However, this assessment fails to
take into account that the Duff types, along with the func-
tional types derived from them (Turner 2004: 63–90), are
defined as groups rather than classes (Dunnell 1971, 1986).
e groups are defined by enumerating attributes shared
by the members of each group rather than the attributes
that distinguish one class from another. is characteristic
binds the types to particular sets of objects and locations,
when what is required are distinguishing criteria that can
be applied irrespective of time and place.
is brief note begins the project of building a func-
tional classification of Hawaiian stone wood-working
tools by considering the case of the axe. As part of a
project to describe and classify more than 800 Hawaiian
stone adzes held in the ethnographic and archaeological
collections at Bishop Museum in Honolulu, 11 double-bev-
eled stone tools, which resemble modern axe or hatchet
blades, were identified and described. ese 11 tools can
be distinguished from adzes by the presence of a double
bevel, which represents the necessary and sufficient condi-
tion for membership in the axe class. ey were surprising
finds in the collection because double-beveled stone tools
19
 Journal of Pacific ArchaeologyVol.  · No.  · 
have been reported by some as absent in Hawai‘i (Duff
1959: 141; Hiroa 1950: 194; Weisler & Green 2001), and in
the Duff typology are restricted to heavy, crudely-finished
tools commonly recovered in Mangareva but not found
elsewhere in Polynesia (Buck 1938: 277; Weisler & Green
2001; Weisler, Conte & Kirch 2004; Figueroa & Sanchez
1961: 199). However, stone axes from Hawai‘i were noted
more than a century ago in a descriptive work that figures
two double-bevel tools: an unusual, thick wedge-like tool,
catalog 4603 (Brigham 1902: 75), that does not look as if it
could be readily haed, and which was not re-identified
in the Bishop Museum collection during the project; and
catalog 3141 (Brigham 1902: 74), a finely-made tool whose
double-beveled longitudinal section was also illustrated
(Brigham 1902: 76). For many years, investigations of Ha-
waiian stone tools have focused exclusively on adzes (e.g.,
Emory 1968; McCoy 1977; Cleghorn 1982, 1984; Bayman
& Nakamura 2001; Weisler 2011), and this has had the ef-
fect of reinforcing the mistaken notion that stone axes are
absent.
  
e study of stone tools in Polynesia has, for the last 70
years, been carried out largely within the framework of a
descriptive arrangement developed initially for adzes from
southern South Island in New Zealand (Skinner 1943a, b)
and later rearranged and revised to accommodate tools
from the rest of Polynesia (Duff 1956, 1959). e culture-
historical and diffusionist rationale for grouping (Dunnell
1971) stone tools in this way was questioned by Marianne
Turner and her colleagues, whose replication experiments
demonstrated beyond a reasonable doubt the functional
basis for the stone tool groups established by the diffu-
sionists (Turner 2000, 2004). In many ways, Turner’s work
harkens back to an interest in function that underlay
earlier published descriptions of Polynesian stone tools
in Hawai‘i (Brigham 1902) and New Zealand (Best 1912;
Hiroa 1950).
In the introductory remarks to e Stone Implements
of the Maori, written more than a century ago, Best found
it necessary to clarify the English-language terminology
used to describe Maori stone implements. He was con-
cerned to counter the indiscriminate use by other writ-
e r s o f t h e t e r m s c e l t ’, ‘a x e’, ‘a d z e’, ‘ h a t c h e t ’, ‘c h i s e l ’, a n d g o u g e ’.
He distinguished chisels, which were ‘lashed on in a line
with the handle (Best 1912: 10), from adzes and axes, which
were lashed at an angle to the line of the handle (see Leroi-
Gourhan 1945). He also presented several Maori accounts
that describe stone axes and their use (Best 1912: 137–155)
and a photograph of a genuine axe-form, haed with the
cutting edge in line with the handle (Best 1912: 142) from
the Buller Collection in the Dominion Museum (Best
1912: 389). He gave the Maori name of the axe as toki titaha.
Hiroa (1950: 191–192) noted that the specimen in the Buller
Collection was haed in the post-Contact period, and that
its cutting edge was not in the direct axis of the handle but
parallel to it due to the method of haing. Nevertheless, he
agreed with Best that Maori made and used axes, and that
they called them toki titaha.
e terminological clarity achieved by Best (1912)
and Hiroa (1938) was later muddied by a grouping of
greywacke and nephrite adzes from Murihiku, New Zea-
land into ‘types and ‘varieties that failed to distinguish
between single- and double-beveled tools (Skinner 1943a,
b). Skinner was concerned to problematize ‘whether
in pre-European times the Maori used an axe (Skinner
1943b: 159). His argument that such a use must have been
uncommon (Skinner 1943b: 159) was based on the polyse-
my of the Maori term toki titaha, which was used for steel
axes, side-haed adzes, and stone axes, and by the curious
argument that the double-beveled stone tools of the Maori
werent true axes because the cutting edge wasn’t strongly
curved convexly [such that it] fades into the sides of the
implement (Skinner 1943b: 159).
Skinners approach was followed by Duff (1977: 190),
who accepted all of Skinner’s varieties, but grouped them
into five types instead of ten. Duff grouped axes as Vari-
ety B of the laterally haed adze, Type 5. Working in an
essentialist tradition that fails to distinguish empirical
entities from tools of measurement (Dunnell 1986: 154),
Duff referred to Type 5 Variety B as a local phenomenon
of Mangareva, where stone axes were once common (Buck
1938: 277; Weisler & Green 2001; Weisler, Conte & Kirch
2004; Figueroa & Sanchez 1961: 199). e Mangarevan axes
are different from the finely-finished axes illustrated by
Best (1912: 389) and by Brigham (1902: Plate LVII). ey are
mostly large tools made from coarse-grained rock (prob-
ably all local) and . . . ground mostly at the bevel leaving
the rest of the tool unfinished, thus exhibiting the original
weathered rock surface (Weisler, Conte & Kirch 2004: 142).
Duff does not mention the double-beveled tools discussed
at length by Best (1912), nor the descriptions of axes in
Hawai‘i (Brigham 1902: 73–76). Recent work on New Zea-
land stone tools (Turner 2004) fails to distinguish among
the varieties of Type 5, effectively lumping axes with adzes.
Outside of Hawai‘i, New Zealand, and Mangareva, the
Eastern Polynesian ethnographic and archaeological lit-
erature yields scant evidence of axes in other Eastern Poly-
nesian island groups. A tool with a rough axe-like form
is described from Tubuai in the Austral Islands (Aitken
1930: 145). Subsequently, another possible example from
Tubuai was noted in an unpublished manuscript (Miller
n.d.). Specimen 452–351–2Ec-1f is described as having an
axe-like nature . . . [where t]he front has been deliberately
flattened. e artifact illustration demonstrates that the
specimen is broken around the mid-section.
At the current stage of research, it is difficult or impos-
sible to distinguish possible explanations for the observed
distribution of axes. Are so few axes reported because they
are not distinguished in the Duff typology? Were there
historical forces at work in New Zealand (Hiroa 1950: 193),
20
Kahn & Dye – A Note on Hawaiian Stone Axes 
Hawai‘i and Mangareva that were not felt elsewhere? Or,
is the apparent absence of axes outside New Zealand,
Hawai‘i, and Mangareva due to the rarity of axes and their
likely absence from small collections? ese explanations
are not mutually exclusive and one or more of them might
be operating at the same time.
     
Ten of the 11 Hawaiian axes reported here were identified
in the ethnological collection at Bishop Museum. ese
range from short, irregular tools to long, finely polished,
and neatly symmetrical double-beveled tools. Here, we
generally describe tool form, shape, raw material, and size
for each axe. Forthcoming publications on the Bishop Mu-
seum axe and adze collections will include data on tool
location and site function, whether the find site has been
dated, and details of source geochemistry.
B.
is is an unusual tool with a nearly constant thickness
along most of its length
(fi g. 1, a). Most of the edge is miss-
ing, but one corner is intact. Too little remains of the
edge
to describe its shape, but the obtuse angle of the surviv-
ing corner suggests the edge
was convex in plan view. e
opposite end at the poll is also incomplete, so a complete
longitudinal section is absent. e tool is made from a dark
grey basaltic rock that has a
pitted texture and feels light for
its size. It is 18.4 cm long, 4.8 × 1.3 cm at mid-section, and
weighs 223 g. e cutting edge measures 5.1 cm.

e smallest axe among the ethnographic specimens is
from the Ka‘iulani Collection
(g. 1, b). It is made from a
dark grey basalt. One face and one side are well polished,
but the other side and face exhibit flake scars and are not
as well polished. e edge is
convex in plan, with rounded
corners. e poll is intact and is not polished. e tool is
4.6 cm long, 1.9 × 1.3 cm at mid-section, and weighs 23 g.
e cutting edge measures 1.7 cm.
B.
is short axe is well polished on both faces and sides
(g. 1, d).
e edge is straight and meets the side at a sharp
angle. e butt is the only portion of the artifact that is not
polished and that has an unfinished look. e butt may
have been
pecked as a way of shaping it to fit the lashing, or
alternatively it may have some use-wear
resulting from its
having been haed. ere are a few flakes removed from
the sides,
probably from use but possibly during rework-
ing. The tool is made from basaltic rock that has
turned reddish-brown in color, presumably due to
the original surrounding soil matrix. e tool is 8.7
cm long, 3.2 × 2.1 cm
at mid-section, and weighs 125 g. e
cutting edge measures 3.2 cm.

is axe has a pitted surface similar to
catalog B.01397
but is better polished than that tool (fig. 1, e). e edge is
straight and meets
the sides at a sharp angle. Both faces
and sides are well polished, with the exception of one face
near the poll that has flake scars, perhaps to facilitate ha-
ing. e poll itself is
polished and intact. ere are several
small flake scars on the edges of one face. e tool is fash
-
ioned from a dark black basaltic rock. e artifact
is 16.4
cm long, 5 × 1.9 cm at mid-section, and weighs 332 g. e
cutting edge measures 5.6 cm.

is specimen from the George H. Dole Collection is one
of the longer axes in the collection (fig. 1, f ). e color is
typically light grey but is discolored a light brown in places.
e tool is well polished on both faces and sides close to
the cutting edge, but surfaces farther away from the cut-
ting edge exhibit flake scars with some polish on the high
points. e edge is straight and meets the sides at a sharp
angle. e edge is quite a bit wider than the poll. Approxi-
mately two-thirds of the way toward the poll the cross-
section becomes triangular and remains so until the poll.
Near the poll, one face that has been minimally worked
looks to be the ventral surface of a larger flake. e tool is
made from a light grey basaltic rock that has discolored
to a light brown in places. e tool is 20 cm long, 3.7 × 2.7
cm at mid-section, and weighs 1,434 g. e cutting edge
measures 5.5 cm.
D.
is tool is partially polished, with areas near the edge be-
ing the most highly polished (fig. 1, g). e edge is very
slightly convex in plan and the corners where it meets
the sides are both rounded. It is wider than the poll. e
butt portion has been reduced and the flake scars have
not been polished. e axe is fashioned from a basaltic
rock that has discolored to a dark brown. e tool is 8.5
cm long, 3 × 1.8 cm at mid-section, and weighs 71 g. e
cutting edge measures 4.3 cm.

is relatively short tool from the George H. Dole Collec-
tion appears to have been fashioned from a flake (fig. 1, h).
It is well polished at the cutting edge, but the rest of the
surfaces exhibit flake scars. e edge is very slightly con-
vex in plan and meets the sides at rounded corners. e
axe is fashioned from a light grey basaltic rock with some
brown patination. e tool is 8.4 cm long, 4.7 × 1.4 cm at
mid-section, and weighs 90 g. e cutting edge measures
4.6 cm.
B.
is tool is well polished from butt to cutting edge on both
faces and sides (fig. 1, i). e edge is slightly convex in plan
with somewhat rounded corners. e butt was either le
21
 Journal of Pacific ArchaeologyVol.  · No.  · 
Figure 1. Axes in the ethnographic and archaeological collecons: a, catalog B.01397; b, catalog 10454; c, 50-Oa-B1–75–518;
d, catalog B.01700; e, catalog 11021; f, catalog 3127; g, catalog D.04030; h, catalog 4561; i, catalog B.02518; j, catalog 3141
(see Brigham 1902: Plate LVII); k, catalog B.01671. The scale bar is 1 cm.
unfinished and unpolished or it has been broken and
slightly reworked. e axe is made from a dark grey basal-
tic rock. e tool is 17.1 cm long, 5 × 1.8 cm at mid-section,
and weighs 349 g. e cutting edge measures 5.8 cm.

is tool is well polished on both faces and sides, although
the sides exhibit remnant flake scars that have been mod-
erately polished down (fig. 1, j). e edge is slightly convex
22
Kahn & Dye – A Note on Hawaiian Stone Axes 
in plan with somewhat rounded corners. e poll is intact
and is slightly polished. is tool was described previously
(Brigham 1902). is tool is made from fine-grained dark
grey/black basaltic rock. It is 18.5 cm long, 3.9 × 2 cm at
mid-section, and weighs 332 g. e cutting edge measures
5 cm.
B.
is is an unfinished tool with a small bit of polished sur-
face, or perhaps cortex, near the edge (fig. 1, k). It is made
of fine-grained, medium-grey rock with small phenocrysts.
One face of the tool appears to be a ventral flake surface.
e cutting edge is extensively flaked along one surface
and is not ground. It appears that the intent was to have
a cutting edge convex in plan with rounded corners, and
wider than the poll. One face and both sides have fine
flaking originating from each surface. e tool is made of
fine-grained, medium grey basaltic rock with small phe-
nocrysts. e tool is 25.1 cm long, 4.7 × 2.6 cm at mid-sec-
tion, and weighs 568 g. e cutting edge measures 7.8 cm.
Five smaller tools with double bevels were identified
in the Bishop Museum archaeological collections deriv-
ing from the Hawaiian archipelago. Most of them are ei-
ther broken, crudely fashioned, or incomplete and are not
described here. However, one complete double-beveled
tool from the archaeological collection can be confidently
identified as an axe.
-Oa-B––
is tool is fully polished near the cutting edge (fig. 1, c).
e edge is slightly convex in plan and meets the sides
in sharp angles. e poll end has been reworked and le
unpolished, and the sides have been diminished over more
than half the length of the tool. e axe is fashioned from
a basaltic rock. is tool is 10.6 cm long, 3.7 × 2 cm at
mid-section, and weighs 147 g. e cutting edge measures
3.6 cm.
 
Elsewhere in Polynesia, axes are considered a variety
of Type 5 (Duff 1977), which includes
side-haed adzes.
Turner considers Type 5 among a small group of specialized
forms’ (Turner
2000: 107) that were designed for specific
tasks unlike other forms that were used under
a wider
variety of conditions and attributes their rarity to this
functional specificity. One
function of Type 5 tools was
to remove material from the interior surface of a piece of
work,
such as a canoe hull, a bowl, or a trough. In this ap-
plication, the tool would typically be haed
with the edge
in line with the handle and the tool would enter the work
at a low angle to shave
off long, thin chips.
Side-haed adzes have not been reported from Hawai‘i.
Duff believed they were functionally
replaced in Hawai‘i by
a ‘normal adze in a rotating sleeve (Duff 1959: 141), which
Brigham
referred to as an adjustable adze of the Kupaai-
kee pattern (Brigham 1902: Plate LX), presumably for its
use in production of canoes, Kūpā‘aike‘e being a god of
canoe makers. e term ‘rotating sleeve describes a ha-
ing method in which the blade is not lashed directly to
the handle, but instead to a short rounded staff that was
lashed to a handle that was grooved to fit the sha (Hiroa
1950: 190). e staff could be rotated in the groove to ad-
just the alignment of the cutting edge. Duffs
reference to
a ‘normal adze suggests that there is no way to distinguish an
adze used side-haed
once it has been separated from its
ha. us, it is not possible to compare the axes with a
subset of the adze collection either known or inferred to
have been used with a side ha.
In the laboratory, the formal qualities of the axes that
stand out most strongly in a comparison
with adzes are
their length and low shoulder index (Buck 1944; Garang-
er 1972). Figure 2 compares the length and shoulder index
of the 11 axes with 871 complete adzes from the Bishop
Mu-
seum collection. Axes typically have a lower shoulder index
than an adze of similar length,
as can be seen by their posi-
tion mostly beneath the regression line for the adzes. e
inference
that some New Zealand axes are so thin that they
could not possibly have been used as anything
but cutting or
chipping tools (Best 1912: 236) applies equally to Hawai‘i.
Also, unlike the
adzes, where shoulder index increases
with length, longer axes tend to have a lower shoulder in-
dex than shorter axes. Whereas increasing the length of
an adze is one way to increase the
mass of the tool so
that it might deliver more force to the work (Cotterell &
Kamminga 1990),
this was not the case with Hawaiian axes,
which tend to thin out as they get longer.
Several of the axe specimens had evidence for flaking
or wear on the butt, suggestive of
lashing to the ha. In a
few cases flakes were removed from the sides of the butt. We
interpret
this as shaping the butt for haing and note that
such flaking around the butt is found in Eastern
Polynesian
adze assemblages widely. An alternative argument, that such
flakes around the butt
might have been removed when us-
ing the axes like chisels, by tapping the poll with a hammer,
is unlikely. Such use would not result in axes with flakes
removed at the sides of the butt; one
would expect flakes or
bashing to be found around the entire butt or concentrated
along its
center line rather than its extremities.

Identification of 11 stone axes in the Bishop Museum col-
lection was unexpected because axes are rarely identified
elsewhere in Polynesia and have oen been reported as
absent in Hawai‘i. One of the axes described here was first
reported more than a century ago, but the other ten are
identified and described here for the first time. Although
the number of axes seems large from this perspective, the
11 axes represent just over 0.1 percent of the more than 800
complete adzes and axes in the Bishop Museum collection.
23
 Journal of Pacific ArchaeologyVol.  · No.  · 
ey are rare in Hawai‘i, as they are elsewhere in Eastern
Polynesia.
e longer Hawaiian axes are notable for their low
shoulder index. In formal comparison with axes from
other Polynesian island groups, the Hawaiian axes appear
to be most closely related to the thin New Zealand axes
(Best 1912: 234). e thinness and fine finish of Hawaiian
axes differ sharply from the thick New Zealand axes and
from the large, roughly finished axes common in Man-
gareva (Buck 1938; Weisler, Conte & Kirch 2004).
ese long tools were not designed to transmit a large
force, as was typically the case for long adzes. is leaves
open the question of what purpose was served by axe
length. One possibility is that length was needed to achieve
a secure attachment to the ha. Although the antiquity of
a haed Polynesian axe described by Buck (1938: 274) is
suspect, he believed that the lashing reflected traditional
practice. e lashing of this particular axe was unusual in
extending well onto the blade, presumably to secure the at-
tachment. e length of the thin Hawaiian axes thus might
be linked functionally to details of the ha, rather than the
cutting performance of the tool.
e longer axes are unusual tools that are likely to be
functionally specific (Turner 2000: 107). ey were pre-
sumably designed for light chipping and cutting tasks. It
is difficult to know whether or not they were suited for
use on the inside of canoes or other pieces of work. e
straight edges might not curve enough toward the body
to protect the corners from taking excessive force (Turner
2004: 87). Replication experiments such as those carried
out in New Zealand (Turner 2000, 2004) might, if extend-
ed to include the various axe forms, indicate functions to
which the axes are most suited.
Hiroa (1950: 193–194) noted that axes are distinguished
from adzes in two ways – according to the relationship of
the cutting edge to the line of the handle when the tool
is haed, and by the presence of a single or double bevel.
Although he personally believed that haing was most
distinctive, he noted that most of the specimens le to us
today are not haed, which makes the bevel important. In
New Zealand, Best found that tools with an axe-like form
gradually merge into the adze-form (Best 1912: 234), ap-
parently because adzes with a curved front might have the
cutting edge near the axial center of the tool, much like an
axe. In practice, it was relatively easy to distinguish single-
beveled and double-beveled tools in the Bishop Museum
collection, perhaps due to the limited range of adze forms
produced in Hawai‘i. In the Hawaiian case, a nominal scale
attribute that distinguishes single-bevel and double-bevel
tools seems sufficient to distinguish adzes from axes.
e lack of axes from dated contexts in Hawai‘i makes
it impossible to address the question debated in New Zea-
land whether axes were used traditionally or were an his-
toric-era innovation. is is unfortunate because the issue
of material culture change brought on by Western contact
is an important one for archaeologists interested in histor-
ic process (Bayman 2003; Bayman & Dye 2013: 101–104). In
order to study historic process, it is necessary to move be-
yond grouping schemes, such as Skinner and Duffs adze
types and varieties, and to establish artifact classes that
Figure 2. Comparison of the shapes of axes and adzes. Shoulder index is dened by Buck (1944) as R7 × 100/R9, where R7
= thickness of the standard cross-secon and R9 = width of the standard cross-secon (see Garanger 1972). The robust
regression lines were calculated using the rlm method of Venables & Ripley (1994: 216).
24
Kahn & Dye – A Note on Hawaiian Stone Axes 
exist independently of space and time. Our work follows
other Polynesian scholarship, such as Allens (1996) analy-
sis of Cook Island fishhooks, that distinguishes style from
function and classes from groups in an effort to elucidate
cultural patterns. Differentiating the class of double-bev-
eled axes from the class of single-beveled adzes is the first
step toward unlocking the history of the rare and unusual
Polynesian stone axe.
Acknowledgments
We would like to thank Betty Kam and her assistants in the
Bishop Museum Cultural Resources Division for provid-
ing access to the ethnographic collections. Several Archae-
ology Collection Managers at Bishop Museum likewise
facilitated our research by providing access to the Hawai-
ian archaeological collections. Two anonymous reviewers
and Ethan Cochrane provided perceptive comments on a
dra of the paper. Any errors of fact or interpretation are
the authors.
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