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Measurements of Ω and Λ from 42 High-Redshift Supernovae

1999 · paper · Astronomy

Analyzes 42 distant Type Ia supernovae together with nearby ones to measure the universe's mass density and cosmological-constant energy density. Finds a flat-universe matter density of about 0.28 and reports data favoring a non-zero, positive cosmological constant (99% confidence).

Checked: PDF from arxiv.org, fetched 4 Oct 2026. Page numbers are those of that PDF.

6 findings

Reference or label Fit E sample is described inconsistently: text says "the 53 SNe Ia with color measurements in our Fit C dataset", Fig. 5 caption says "the 53 supernovae with color measurements from the Fit B dataset", and Table 3 gives N = 51 for "Fit B SNe with colors measured" (Fit F) and N = 49 for "Fit C SNe with colors measured" (Fit G), while Fit E has N = 53.
  • p. 6 Section 4.1.3, first paragraph
    we applied it to the 53 SNe Ia with color measurements in our Fit C dataset
  • p. 28 Figure 5 caption, panel (d)
    Fit E of the 53 supernovae with color measurements from the Fit B dataset
  • p. 18 Table 1, Notes column, SN 1996cg and 1996cn
    C,D,G–L
  • p. 20 Table 3, Fits E, F, G
    Fit C SNe with colors measured

Only the authors can say what is right here.

Judge's note: Page 6 image, the Fig. 5 caption crop and the Table 3 image all confirm the printed wording and counts. The text and caption name different parent datasets (Fit B and Fit C differ by 1996cg and 1996cn), and 53 matches neither colour-measured subset in Table 3. Table 1 notes exclude 1996cg/1996cn from "C,D,G–L" (not E), which favours the caption's Fit B basis. But the notes also exclude five colourless SNe from "E–H" and four from "B–L", which gives 51 for Fit E, not 53. Table 3's DOF of 49 is consistent with N = 53. I found no statement explaining a looser colour criterion for Fit E. Only the authors can say which description and count are right.

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Reference or label Fit E is given N = 53 (Table 3 "E 53 62 49") and described as "the 53 SNe Ia with color measurements in our Fit C dataset" (Section 4.1.3) and "the 53 supernovae with color measurements from the Fit B dataset" (Fig. 5 caption), but Table 3 gives 51 for "Fit B SNe with colors measured" and 49 for "Fit C SNe with colors measured".
  • p. 20 Table 3, row E
    E 53 62 49
  • p. 20 Table 3, row F
    F 51 59 47 ... Fit B SNe with colors measured
  • p. 18 Table 1, Notes column
    E–H
  • p. 19 Table 2, Notes column
    B–L

Only the authors can say what is right here.

Judge's note: Page images 18, 19, 20, 28. Table 3 rows F and G give 51 and 49 for the colour-measured subsets of Fits B and C, so 53 fits neither description, and the text and caption also disagree with each other (Fit C vs Fit B). The Notes columns mark five supernovae E–H (1992bi, 1994F, 1994al, 1994am, 1994an) and four B–L (1994H, 1997O, 1992bo, 1992br), which leaves 51 for Fit E. 53 equals all supernovae with colours before any outlier exclusion: 17 low-redshift + 36 high-redshift (Fig. 6 caption), i.e. 60 minus "the six supernovae without color" minus SN 1992bc (Section 4.1.1). DOF 49 = 53 - 4 shows 53 was the number fitted, so the dataset description and the Notes columns are what is wrong. Searched Section 4.1 for a rule explaining it; none found. Related loose end: the text says six high-redshift supernovae lack colours but only five are marked E–H.

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Reference or label Two reference-list defects: (1) "Aldering et al. 1998" is cited in Section 6.3 but has no entry in the reference list, which begins with "Baade 1938, ApJ, 88, 285"; (2) "Kantowski, R. 1998, ApJ, 88, 285." carries the same volume and page as the Baade 1938 entry.
  • p. 13 Section 6.3, left column
    Aldering et al. 1998 for time-varying equations of state fit to our dataset
  • p. 15 Reference list, start (alphabetical)
    Baade 1938, ApJ, 88, 285
  • p. 16 References
    Kantowski, R. 1998, ApJ, 88, 285.

Judge's note: Page 13 image shows the citation 'Aldering et al. 1998 for time-varying equations of state fit to our dataset'. Crop C025-b shows the alphabetical list starting at Baade, and a text search of the reference pages finds no Aldering entry. Crop C025-c shows 'Kantowski, R. 1998, ApJ, 88, 285.', identical in volume and page to 'Baade 1938, ApJ, 88, 285'; other 1998 ApJ entries in the same list have volumes near 495, so volume 88 cannot belong to a 1998 paper and appears copied from the Baade entry. Both defects are established from the PDF alone. The correct Kantowski volume and page, and the details of the missing Aldering entry, must be supplied by the authors (one reviewer's suggested 'ApJ 507, 483' is from memory and is not verified here).

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Reference or label "Kantowski, R. 1998, ApJ, 88, 285." carries the same volume and page as "Baade 1938, ApJ, 88, 285"; separately, "Aldering et al. 1998" is cited in Section 6.3 but has no entry in the reference list.
  • p. 16 Reference list
    Kantowski, R. 1998, ApJ, 88, 285.
  • p. 15 Reference list, first entry
    Baade 1938, ApJ, 88, 285
  • p. 13 Section 6.3, left column
    Aldering et al. 1998 for time-varying equations of state

Judge's note: Page images 15 and 16: both entries read ApJ, 88, 285. The list's own 1998 ApJ entries are in volumes 493-509 (Chaboyer 494, Gordon 500, Garnavich 509), so volume 88 cannot be a 1998 volume; the data were copied from the Baade entry. The correct volume and page (reviewers say 507, 483) rest on outside knowledge and are not verified here. Aldering: the reference list on p15 starts Baade, Bahcall & Fan, Bernstein with no Aldering entry, and a text search finds the name in the reference section nowhere; the citation is on p13 (text layer, line "Aldering et al. 1998 for time-varying equations of state"). Two separate defects in one cluster, both real.

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Reference or label "Leibundgut B. et al. 1996b, Ap.J.Lett., 371, L23" gives a volume that does not fit 1996; the same list has "Leibundgut, B., et al. 1996a, Ap.J.Lett., 466, L21".
  • p. 16 Reference list
    Leibundgut B. et al. 1996b, Ap.J.Lett., 371, L23
  • p. 16 Reference list
    Leibundgut, B., et al. 1996a, Ap.J.Lett., 466, L21

Only the authors can say what is right here.

Judge's note: Page image 16. The inconsistency can be shown from the list itself: 1996 ApJ entries are in volumes 457-473 (Höflich 457, Carlberg 462, Kochanek 466, Pain 473), while 1989 is volume 345 (Cardelli) and 1992 is 395-397 (Pei, Jeffery). Volume 371 therefore falls between 1989 and 1992, most likely 1991. Either the year (and the 1996b label cited in Section 4.4) or the volume is wrong; only the authors can say which.

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Reference or label "Perlmutter, S., et al. 1996, IAU Circ. No. 6621" is dated 1996 although lower-numbered circulars are dated 1997: "1997a, IAU Circ. No. 6596" and "1997b, IAU Circ. No. 6540".
  • p. 16 Reference list
    Perlmutter, S., et al. 1996, IAU Circ. No. 6621
  • p. 16 Reference list
    Perlmutter, S., et al. 1997b, IAU Circ. No. 6540
  • p. 16 References
    Perlmutter, S., et al. 1997a, IAU Circ. No. 6596

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: IAU Circulars are numbered in order of issue. The page image of p16 prints the entries as quoted, and the list's other circulars follow that order (6270 in 1995, 6646 and 6804 in 1997, 6881 in 1998), so No. 6621 sits between two 1997 circulars. The year 1996 or the number is wrong; the 1997a/1997b lettering being out of number order is harmless.

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23 minor (typos and the like; most checked by the judge only)
Wording Abstract and the Fig. 3 and Fig. 4 captions give the 42 SCP supernovae "at redshifts between 0.18 and 0.83", but Table 1 lists SN 1997I at z = 0.172 (next lowest: SN 1997N at 0.180).
  • p. 1 Abstract
    at redshifts between 0.18 and 0.83
  • p. 18 Table 1, SN 1997I, column z
    0.172
  • p. 18 Table 1, SN 1997I
    1997I
  • p. 18 Table 1, SN 1997I
    1997I 0.172

Judge's note: Checked the abstract crop, the Fig. 3 caption crop and the Table 1 page image. SN 1997I is printed as 0.172 with no exclusion note, so it is one of the 42; 0.172 rounds to 0.17, not 0.18. The upper bound 0.830 (1997ap) matches. Section 4.1.1 calls the pair "the two SNe Ia at z ~ 0.18", so the authors are quoting the lower bound loosely. A small imprecision, not a substantive error.

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Wording Figure 5 caption says "(d) The 68% confidence region for Fit E of the 53 supernovae" and Section 4.1.3 refers to "the dashed contour in Figure 5(d)", but panel (d) shows two nested dotted contours labelled E.
  • p. 28 Figure 5 caption, panel (d)
    (d) The 68% confidence region for Fit E of the 53 supernovae
  • p. 27 Figure 5, panel (d)
    Bias with One-Sided De-reddening Method
  • p. 6 Section 4.1.3
    as the dashed contour in Figure 5(d)

Judge's note: Opened the crop and the full page 27. Panel (d) has an inner and a larger outer dotted contour around the Fit C shading, both belonging to the E label. The caption's default is 68% and 90% "unless otherwise indicated", and (d) is the one panel where it indicates 68% only, yet two contours are drawn (presumably 68% and 90%). The text also calls the line dashed where it is dotted. The figure is fine; the caption and text describe it loosely.

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Typo "(SN 1997ap and other 1998 supernovae have also been followed with HST photometry.)": SN 1997ap is a 1997 supernova, so "other 1998 supernovae" is inconsistent as worded.
  • p. 2 Section 2, right column
    (SN 1997ap and other 1998 supernovae have also been followed with HST photometry.)

Only the authors can say what is right here.

Judge's note: Crop of page 2 confirms the printed wording. By its designation 1997ap is not a 1998 supernova, so either "other" or the year is off (possible intended reading: "SN 1997ap and other, 1998, supernovae"). Only the authors can say which was meant. Wording only; no data affected.

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Typo Doubled full stop: "interpretation of these results.)." (the parenthetical sentence already ends with a period inside the bracket).
  • p. 3 Section 2, end of first full paragraph
    interpretation of these results.).
  • p. 3
    does affect the interpretation of these results.).

Judge's note: Page 3 image, left column, end of the K-correction paragraph, shows "results.)." as printed. Not an extraction artefact.

Second check: another model agreed

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Typo Inconsistent compounding: "light-curve width-luminosity relation" and "rest-frame B and V photometry" against the paper's usual "lightcurve" and "restframe" (e.g. "restframe days past maximum light").
  • p. 3 Section 2
    light-curve width-luminosity relation
  • p. 3 Section 2
    restframe days past maximum light
  • p. 5 Section 4.1.1
    rest-frame B and V photometry

Judge's note: Page 3 image shows "light-curve width-luminosity relation" and "light-curve widths" mid-line next to many instances of "lightcurve". Page 5 image shows "we fit the rest-frame B and V photometry" mid-line in the same sentence as "restframe color excess". The Fig. 6 caption also mixes "restframe" and "rest-frame". The text has 74 lines with "lightcurve" and 24 with "restframe". Style consistency only.

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Typo The name is spelled two ways: "Friedmann-Robertson-Walker (FRW) formula" (Section 4.3) but "Friedman-Robertson-Walker" in Section 3, later in the same Section 4.3 paragraph ("the Friedman-Robertson-Walker fit") and twice in the Figure 8 caption.
  • p. 8 Section 4.3, second paragraph
    Friedmann-Robertson-Walker (FRW) formula
  • p. 8 Section 4.3, second paragraph
    the Friedman-Robertson-Walker fit is already very close
  • p. 3 Section 3, first line
    Friedman-Robertson-Walker magnitude-
  • p. 31 Figure 8 caption
    Friedman-Robertson-Walker model of Fit C

Judge's note: Checked on the page 8 image (both spellings within one paragraph), crop C018-c (page 3, one n) and crop C018-d (Fig. 8 caption, one n twice). The inconsistency is internal to the PDF; standardise on 'Friedmann'.

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Typo Survey name spelled inconsistently: "Calán/Tololo" in most of the text, "Calan-Tololo supernovae" in Section 3, "CALÁN TOLOLO SNE IA DATA" in the Table 2 title (and "Calán Tololo" in its Col 1 note), "Calan/Tololo" in figure legends.
  • p. 4 Section 3, left column, last paragraph
    for the low-redshift Calan-
  • p. 19 Table 2 title
    CALÁN TOLOLO SNE IA DATA
  • p. 4 Section 3
    Calan-Tololo supernovae
  • p. 22 Fig. 1 legend
    Calan/Tololo

Judge's note: Page 4 crop shows "Calan-" / "Tololo" split across a line break with no accent; a slash-joined name would not pick up a hyphen. Table 2 crop shows "Calán Tololo" with no separator. The Fig. 1 legend shows "Calan/Tololo" without the accent, which may be a font limit in the figure. The abstract crop shows the standard form "Calán/Tololo". Cosmetic.

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Typo Page 5, Section 4.1.2: "that is intentional biased to be bluer than the low-redshift sample" should read "intentionally biased".
  • p. 5 Section 4.1.2, second paragraph
    that is intentional biased to be bluer
  • p. 5
    that is intentional biased to be bluer than the low-redshift sample.
  • p. 5 Section 4.1.2, Fit H paragraph
    that is intentional biased to be bluer than the low-redshift sample
  • p. 5
    that is intentional biased to be bluer than

Judge's note: Checked the crop of p.5, right column. The adjective 'intentional' is printed where the adverb 'intentionally' is needed.

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Typo Capital after semicolon: "is less than 5%; This subset is thus very unlikely to be biased".
  • p. 5 Section 4.1.2, second paragraph
    is less than 5%; This subset is thus

Judge's note: Page 5 image, right column, shows "5%; This subset" as printed. Either the semicolon should be a full stop or "This" should be lower case.

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Typo "The fact that Ω_M^flat changes so little from Case C" should read "Fit C"; the fits are called "Fit A" to "Fit M" everywhere else.
  • p. 6 Section 4.1.3, right column
    changes so little from Case C

Judge's note: Page 6 image, right column, shows "from Case C" as printed, two lines after "compared to Fit C". "Case C" is not defined anywhere. Terminology slip with an evident fix.

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Typo Section 4.1.3 writes "changes so little from Case C, even with the possible bias" where the fit is called "Fit C" everywhere else, including the preceding sentence ("compared to Fit C").
  • p. 6 Section 4.1.3, right column
    from Case C, even with the possible bias

Judge's note: Crop C016-a shows 'compared to Fit C' two lines above 'from Case C'. A text search finds no other 'Case X' label for a fit. Meaning is clear; label inconsistency only.

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Typo Page 7, Section 4.2, right column: "direct application of the the classical Malmquist bias formula" repeats the word "the".
  • p. 7 Section 4.2, right column
    of the the classical Malmquist bias formula, 0.04 mag
  • p. 7
    direct application of the the classical Malmquist bias formula,
  • p. 7 Section 4.2, right column
    direct application of the the classical Malmquist bias formula
  • p. 7 Sec 4.2, left column
    the classical Malmquist bias should be 0.03 mag

Judge's note: Checked the full page 7 image. 'the the' appears on a single line in the right column, so it is a real duplicated word. Reviewer note 4 calls 0.03 vs 0.04 mag a contradiction; that is not confirmed (see C018). The left-column 0.03 mag is for the high-redshift flux-limited survey with a counts slope of 0.4. The right column says low-redshift number counts are steeper (Maddox et al. 1990), so the low-z classical bias is expected to be nearer 0.04 mag. These are different quantities.

Second check: another model agreed, code check

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Typo Section 4.4: "as shown by the error bars of Figures 2." uses a plural noun with a single figure number.
  • p. 8 Section 4.4, right column
    as shown by the error bars of Figures 2.

Judge's note: Page 8 image, right column, shows 'of Figures 2.' Either 'Figure 2' or 'Figures 1 and 2' was intended (both show the error bars); elsewhere the paper writes 'Figure 2(a)', 'Figure 2(b)'.

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Typo Subject-verb disagreement in Section 6: "the results of such studies with small statistics has not shown any difference" (should be "have not shown").
  • p. 11 Section 6, right column, top
    sults of such studies with small statistics has not shown any dif-
  • p. 11
    results of such studies with small statistics has not shown any difference
  • p. 11 Section 6 closing paragraphs
    the results of such studies with small statistics has not shown any difference

Judge's note: Page 11 image, right column top, shows 'the results of such studies with small statistics has not shown any difference'. Plural subject 'results' with singular verb.

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Typo Subject-verb disagreement in Section 6.1: "The more recent analysis of 16 high-redshift supernovae by Riess et al. (1998) also show a very similar ΩM-ΩΛ confidence region" (should be "shows").
  • p. 11
    analysis of 16 high-redshift supernovae by Riess et al. (1998) also show
  • p. 11 Section 6.1
    The more recent analysis of 16 high-redshift supernovae by Riess et al. (1998) also show a very similar

Judge's note: Page 11 image, right column bottom, shows the sentence as quoted. The subject is the singular 'analysis'.

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Typo Acknowledgements: "National Energy Research Science Computing Center (NERSC)"; the facility's name is believed to be National Energy Research Scientific Computing Center.
  • p. 13 Acknowledgements
    National Energy Research Science Computing Center (NERSC)

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: the official name of NERSC is 'National Energy Research Scientific Computing Center'. The page 13 image shows 'National Energy Research Science Computing Center (NERSC)' as quoted. Nothing in the PDF gives the name in another form, so the authors should confirm.

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Typo Acknowledgements: "Contract No. DE-AC03-76SF000098"; the LBNL contract number is believed to be DE-AC03-76SF00098 (one zero fewer).
  • p. 13 Acknowledgements
    Contract No. DE-AC03-76SF000098

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: the standard DOE contract number for Lawrence Berkeley National Laboratory is DE-AC03-76SF00098. The page 13 image shows 'DE-AC03-76SF000098' with six digits after 'SF'. This cannot be checked from the PDF; the authors should confirm.

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Typo Acknowledgements: "grant No. ADT-88909616" for the NSF Center for Particle Astrophysics; the prefix is probably a typo for "AST" and the digit string may be garbled.
  • p. 13 Acknowledgements
    grant No. ADT-88909616

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: NSF astronomy grants use the prefix 'AST' and the Center for Particle Astrophysics grant is believed to be AST-8809616. The page 13 image shows 'No. ADT-88909616', and two lines below the other NSF grant is printed as 'AST-9417213' (prefix plus seven digits), which supports a typo in both prefix and digit count. The correct number can only be confirmed by the authors.

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Typo Appendix: "(e.g., color uncertainty, relative weighting). the true distribution P(A), and the choice of prior" has a full stop in mid-list followed by lower-case "the"; a comma is needed.
  • p. 14 Appendix, paragraph after Eq. A4
    relative weighting). the true distribution P(A), and the choice
  • p. 14
    relative weighting). the true distribution P(A)
  • p. 14 Appendix, paragraph after Eq. A4
    (e.g., color uncertainty, relative weighting). the true distribution P(A), and the choice of prior

Judge's note: Page 14 image shows 'relative weighting). the true distribution P(A), and the choice of prior' as printed. The sentence is a three-item list ('details of the dataset (...), the true distribution, and the choice of prior'), so the period should be a comma. Not an extraction artefact.

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Typo Appendix cross-references are styled inconsistently within one paragraph: "of Equation A2 is used" and "instead of the mode in equation A-3", while the equations are labelled (A2) and (A3).
  • p. 14 Appendix, paragraph after Eq. A4
    instead of the mode in equation A-3
  • p. 14 Appendix, paragraph after Eq. A4
    of Equation A2 is used

Judge's note: Page 14 image shows both forms in the paragraph after Eq. A4 and the label '(A3)' on the mode equation; page 13 shows '(A2)'. The targets are correct (A3 is the mode equation, A2 the one-sided prior); only the hyphenation and capitalisation differ.

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Typo Freedman et al. entry has an unfilled page placeholder: "In IAU Symposium 183, pages (astro–ph/9801080)"; two entries also lack punctuation after the surname or initial: "& Schramm T. 1996" and "Leibundgut B. et al. 1996b".
  • p. 15 Reference list
    In IAU Symposium 183, pages (astro–ph/9801080)
  • p. 16 References, Kayser et al.
    Kayser, R., Helbig, P., & Schramm T. 1996
  • p. 16 References, Leibundgut 1996b
    Leibundgut B. et al. 1996b

Judge's note: Read pages 15 and 16 as images. The word "pages" is followed directly by the parenthesis with no page numbers. "Schramm T." and "Leibundgut B. et al." lack the comma used in every other entry (compare "Leibundgut, B., et al. 1996a" one line above). Cosmetic only. The Kennicut spelling is handled in C032.

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Typo Reference list prints author names as "Kennicut, R. C." (Freedman et al. 1998) and "Clementina, G." (Gratton et al. 1997); the usual spellings are Kennicutt and Clementini.
  • p. 15
    Mould, J. R., Kennicut, R. C., & Madore
  • p. 15 References, Freedman et al.
    Kennicut, R. C.
  • p. 15 References, Gratton et al.
    Clementina, G.

Only the authors can say what is right here.

Judge's note: Rests on outside knowledge: that the authors' names are spelled Kennicutt and Clementini. The page image of p15 does print "Kennicut" and "Clementina" as quoted. Nothing in the paper itself gives the other spelling, so the files cannot settle it.

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Typo Figure 6 caption prints "Schlegel et. al. 1998" with a stray period after "et"; should be "et al.".
  • p. 29 Figure 6 caption
    Schlegel et. al. 1998
  • p. 29
    values from Schlegel et. al. 1998.

Judge's note: Page image 29: the caption reads "values from Schlegel et. al. 1998" in italics with a period after "et". Elsewhere the paper writes "et al." or names all three authors. Cosmetic.

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