My Hacker Theory in a nutshell (1): Turin Shroud Encyclopedia

Copyright © Stephen E. Jones[1]

My Hacker Theory in a nutshell (1) #36

This is "My Hacker Theory in a nutshell (1)," part #36 of my Turin Shroud Encyclopedia. It will help me write chapter 16, "Were the laboratories duped by a hacker?," of my book in progress, "Shroud of Turin: Burial Sheet of Jesus!" See 06Jul17, 03Jun18, 04Apr22, 13Jul22, 8 Nov 22 & 20Jun24.

Newcomers start with: "The Turin Shroud in a nutshell"

[Index #1] [Previous: Neutron flux #35] [Next: My Hacker Theory (2) #37].

As I mentioned in my Shroud of Turin News, September - December 2024: I have realised that before I write my open letter to Nature (see here), I need to write a "My Hacker Theory in a Nutshell" post, along the lines of my, "The Turin Shroud in a nutshell." By "nutshell" I mean "in as few words as possible." However I have given up my hope that this would be a one-page summary of my Hacker Theory, hence the "(1)". It will now be a series of 4 parts: This Part 1, "1260-1390 and the 1989 Nature article." Part 2, "Evidence that the Shroud is older than the earliest 1260 radiocarbon date." Part 3, "Evidence that the hacker was Arizona laboratory physicist Timothy W. Linick (1946-89), aided by German hacker, Karl Koch (1965-89)." And Part 4 "Other Shroudie explanations don't work and Conclusion." But I will still try to keep it as brief as possible by providing links to my previous posts on topics, rather than references, unless there are no online references. This series will be based mainly on my previous series': "Were the radiocarbon dating laboratories duped by a computer hacker?" (18Feb14); "My theory that the radiocarbon dating laboratories were duped by a computer hacker" (24May14); "The 1260-1390 radiocarbon date of the Turin Shroud was the result of a computer hacking" (23Jul15) and "Steps in the development of my radiocarbon dating of the Turin Shroud hacker theory" (23Jan17).

■ Part 1, 1260-1390 and the 1989 Nature article

• The evidence is overwhelming that the Turin Shroud is Jesus' burial sheet[18Feb14; 24May14; 23Jul15], and therefore its linen is first century or earlier[09Jan14].

• In 1988 three radiocarbon dating laboratories dated the Shroud "1260-1390!" Yet in 1988 three radiocarbon dating laboratories,

[Right: Prof. E. Hall (Oxford), M. Tite (British Museum) and R. Hedges (Oxford) announcing on 13 October 1988 that the Shroud of Turin had been radiocarbon dated "1260-1390!"[24May14].]

Arizona, Oxford and Zurich, dated the Shroud's linen as "1260-1390!"[18Feb14; 07Mar14; 11Apr17]. In 2020 Tite admitted that he put the exclamation mark after "1260 - 1390" on the blackboard at the press conference in the British Museum on 13 October 1988, after claiming in 1990 that, "I can't remember who did that"[25Aug24]. This shows that Tite is not a scrupulous truth-teller but can tell lies when it suits him (see next).

• The mid-point of 1260-1390 is 1325 ± 65 The mid-point of 1260-1390 is 1325 ± 65, the mean year of which, 1325, `just happens' to be exactly 30 years before the Shroud first appeared in undisputed history at Lirey, France, in 1355[29Mar14; 02Dec14; 11Apr17]! But the actual date range of all three laboratories combined and averaged was "1262-1384"[22Jan25]. Tite, the author of the Nature article[22May22], committed "scientific fraud" by "making results appear just a little crisper or more definitive than they really are," first by rounding to the nearest 10 years the actual "1262-1384" dates, when he didn't need to, and second by rounding "1384" to "1390," when 1384 was closer to 1380 than 1390[22Jan25].

• Nature reported that the Shroud is medieval 1260-1390 In 1989, the scientific journal Nature reported the laboratories' results and claimed, "The results provide conclusive evidence that the linen of the Shroud of Turin is mediaeval ... AD 1260-1390" (my emphasis)[18Feb14; 24May14 & 23Jul15]. But "conclusive evidence" is, "Evidence that cannot be contradicted by any other evidence"[CVB]. It is a legal term which has no place in science because to be scientific a theory must be "falsifiable," that is, always open to being tested and found to be false[FFW]. But according to Tite, who wrote the Nature article (see above) if it was proposed that the Shroud be radiocarbon dated again, to test the claim that "the linen of the Shroud of Turin is mediaeval ... AD 1260-1390," he would have to say: "you can't do that: the 1988 radiocarbon dating of the Shroud provided conclusive evidence that the linen of the Shroud of Turin is mediaeval AD 1260-1390," and so it cannot be contradicted by any other evidence! So this was a scientifically false claim by Tite (see above that Tite can tell lies when it suits him).

• Table 1 of the 1989 Nature article [Left 23Jun18] "Sample 1" is the Shroud. The second column is the dating runs of each laboratory[DP89, 612]. Years are before 1950[DP89, 611], after which atmospheric nuclear testing ejected large amounts of carbon-14 into the atmosphere[17Feb19]. So Arizona's first run was 591 ± 30, i.e. 1950-591 = 1359 ± 30. Oxford's first run was 795 ± 65, i.e. 1950-795 = 1155 ± 65. And Zurich's first run was 733 ± 61, i.e. 1950-733 = 1217 ± 61.

See the spreadsheet below which converts each laboratory's dating runs to calendar years (before 1950). As can be seen: firstly, the mean date of Arizona's first run, 1359, was the most recent (youngest) of all three laboratories' 12 dating runs. Secondly, the mean date of Oxford's first run, 1155, was the least recent (oldest) of all three laboratories' 12 dating runs. Thirdly, the mean date of Zurich's first run, 1217, was the least recent (oldest) of Zurich's 5 dating runs. The chance of this happening is 1/4 x 1/3 × 1/5 = 1/60. But since the laboratories were each dating their sub-

[Right: Spreadsheet table of each laboratory's dating runs in the order they appear in Table 1 of the 1989 Nature article, converted to calendar years (before 1950). Note the range of the dates, from 1155 to 1359, is 204 years!]

samples, cut from the one Shroud ~10 mm x 70 mm[DP89, 612] (~0.4 x 2.75 in.) sample; and using their near-identical AMS systems[13Jun14] (see below), if the dates were real (and not computer-generated by a hacker's program), they would have been spread evenly across all three laboratories, with only a year or so difference between each date[RTB].

• Reverse engineering the hacker's algorithm Based on the above, the hacker's algorithm was: 1. Hardwire into the program the first-run dates of each laboratory: Arizona "1350"[22Feb14]; 07Mar14; 11May14] (adjusted later to 1359) (the most recent date of all three laboratories); Oxford "1155," the least recent date of all three laboratories; and Zurich "1217," the least recent of Zurich's dates). 2. For each successive dating run, add or subtract from that first date, and each successive date thereafter, to converge on the target date for that laboratory; 3. Which when combined and averaged across all three laboratories would yield the date, 1260-1390 = 1325 ±65, or close to it because Oxford didn't complete its dating.

Having said the above, it is not essential that the hacker's overall target date was 1325. By his first run date of "1350" he would have been aware that the Shroud first appeared in undisputed history at Lirey, France, in 1355. So his overall target date could have been any year before 1355 that allowed time for the Shroud's flax to grow, be harvested, spun into linen threads, woven on a loom, and for the forger to have painted the image (which didn't happen because the Shroudman's image is not painted[11Jul16]). As for the calculation which produced each year, it could have been a random number generated within limits, so it may be impossible to determine what it was. Nevertheless, since the alternative is that, purely by chance the first run dates of Arizona and Oxford `just happened' to be the most recent, and least recent, respectively, of all the laboratories' dates, and the range of dates of the three laboratories `just happened' to be 204 years (see above), when they should have been only a few years apart, having been cut from the same ~10 mm x 70 mm (~0.4 x 2.75 in.) sample and dated by near-identical AMS systems (see above), the three laboratories' radiocarbon dates of Sample 1, the Shroud, must have been generated by a hacker's program!

• Chi-square test The Shroud radiocarbon dating failed its own chi-square test! A chi-square test is "a statistical method assessing the goodness of fit between a set of observed values and those expected theoretically"[17Feb19]. In the below extract from Table 2, it can be seen that the chi-square value ("Χ² value (2 d.f.)") of sample 1 (the

Shroud) was 6.4. This contrasts markedly with the table's chi-square values of the control samples 2 (0.1), 3 (1.3) and 4 (2.4). For a chi-square test with 2 degrees of freedom, "(2 d.f.)," the maximum upper limit of homogeneity, at 95% confidence, is 5.99[17Feb19] (see below).

[Above: Extract from a chi-squared test table showing that 5.991 is the upper limit of a 2 degrees of freedom, 0.95% confidence, test for homogeneity[NST].]

The chi-square value of 6.4 of the Shroud samples in Table 2 of the 1989 Nature article means the 3 laboratories' radiocarbon dating samples were not homogeneous[AD19; CT19; 17Feb19; 09Sep23]. That is, the laboratories' results are so different that they cannot be considered as the one dataset. This can be seen in the spreadsheet table above. Arizona and Oxford's years don't overlap: Arizona's oldest date is 1249 and Oxford's youngest date is 1220. And Zurich and Oxford only overlap by 3 years: Zurich's oldest date is 1217 and again Oxford's youngest date is 1220. Fig. 1 of the Nature article actually shows this.

[Left: Fig. 1 Mean radiocarbon dates of Sample 1 (the Shroud) and the three control samples[DP89, 611].]

As can be seen, there is no overlap between Arizona's and Oxford's dates of the Shroud sample (shown by my red box between them). But there is overlap between Arizona's, Oxford's and Zurich's dates of the three control samples]. So the control sample dates were real radiocarbon dates, but the Shroud sample dates were computer-generated by a hacker's program!

• "... with at least 95% confidence"[DP89, 611]. This is false! Because the chi-square test result of the Shroud sample, at 6.4 exceeded the limit of 5.99 (2 d.f, 95% confidence), the age of the Shroud sample was not "AD 1260-1390, with at least 95% confidence[VR90, 21].

• Arizona's dates in Nature are fraudulent [17Feb19] Remi van Haelst (1931-2003), a Belgian industrial chemist and expert in statistical analysis, discovered that Arizona had provided the British Museum with eight radiocarbon dates of the Shroud, some of which when calibrated and converted to calendar years, were more recent than 1355, when the Shroud first appeared in undisputed history at Lirey, France:

"Arizona did not provide FOUR but EIGHT data ... The error-values between brackets are estimated ... Mathematically, the calculations following Wilson-Ward, with EIGHT and FOUR data will give the same result. So why were this data reduced from EIGHT to FOUR???? Because with the quoted errors the Arizona data overspans an era of 540-95 = 445 to 753+93 = 846. About FOUR centuries. Converted into calendar date 1270-1430. And one may not forget that any date below 650 rc conflicts with the historical deadline of 1355, when started the veneration of the Shroud in Lirey. After receiving the Zurich results, with also TWO dates below 650 rc, Dr. Leese wrote a letter to Arizona (dated July 28 1988), asking to REDUCE the EIGHT data to FOUR, by considering the TWO runs made the same day, like ONE run. So the data presented in table 1 are not INDIVIDUAL measurements, but the mean of TWO measurements. Which are in fact the average of between 10-20 measurements. Arizona agreed. because they knew that their mean result 646±31 was in fact conflicting with the historical deadline of 1350" (his emphasis)[17Feb19].

Below is my more compact spreadsheet copy of van Haelst's table in his Shroud News article:

[Above (enlarge)[17Feb19]: Arizona laboratory's original eight dates ..., which were secretly statistically manipulated by the British Museum's statistician Dr. Morwen Leese (with Tite and Arizona's approval) to become four dates in the 1989 Nature article (see below). Note that the midpoint of 574±45 is 1950-574 = 1376, which 21 years after 1355. So that was combined and averaged with 606±41 to make it 591±30, the midpoint of which is 1950-591 = 1359, still 4 years past 1355. And 540±57, the midpoint of which is 1950-540 = 1410, 55 years after 1355, was combined and averaged with 676±59 to make it also 606±41, the midpoint of which is 1950-606 = 1344, now 11 years before 1355.]

This was scientific fraud, "making results appear just a little crisper or more definitive than they really are"[see above]. It was also scientific dishonesty to state in the heading of Table 1 that the dating runs were "individual measurements" when for Arizona they were not measurements at all, but averages of measurements. It was also dishonest to not state in a footnote that Arizona's four dating runs were in fact eight. Arizona's first dating run which originally was "1350" (see above) is presumably represented by the "606 ±41" = 1950 - 606 = 1344 ±41. This later statistical manipulation does not affect my Hacker Theory because it was the original "1350" which was `hardwired' into the hacker's program. Moreover, according to Van Haelst, the chi-square value of the Shroud samples is actually 7.13[17Feb19], not 6.4, which means that the Shroud samples' dates across the three laboratories were even less homogeneous[17Feb19]!

• "The spread of the measurements for sample 1 is somewhat greater than would be expected ..." Under Table 2 the Nature article admits that, "An initial inspection of Table 2 shows that the agreement among the three laboratories for samples 2, 3 and 4 [controls] is exceptionally good" but "The spread of the measurements for sample 1 is somewhat greater than would be expected from the errors quoted" (my emphasis)[DP89, 613; 13Jun14; 11Feb15; 18Nov15, etc]. But this is impossible for real Shroud samples, not computer-generated by a hacker's program. The laboratories' Shroud sub-samples were cut from the same ~10 mm x 70 mm (or 1.2 cm x 8 cm - Wilson) Shroud sample (see below), and were dated by the laboratories' near-identical AMS

[Above (enlarge): Drawing of the approximately 1.2 cm x 8 cm sample area, from A1 (Arizona 1), O (Oxford), Z (Zurich) to A (Arizona), with a photo of the 8 cm x 1.2 cm sample superimposed over the drawing on the bottom right hand side[13Jun14; 11Feb15; 18Nov15]. The mean of the Oxford sample's dates is 1193 and the mean of the adjacent Zurich sample's dates is 1268, a difference of 75 years! Clearly there can be no significant difference in radiocarbon dates between sub-samples cut from such a tiny area, if these were real dates, not computer-generated!]

systems[13Jun14; 05Jul14]. In each dating run, the Shroud and the control samples were reduced to pure carbon and irradiated together

[Right (enlarge): Oxford radiocarbon dating laboratory's carousel wheel (2017)[LS17. ]

with the same caesium beam on the same ~25 mm (~1 inch) diameter carousel wheeel)[13Jun14; 11Feb15]. The AMS system is designed so that if something went wrong in a dating run, the Shroud sample and the controls which had a known date, would be wrong together[18Nov15]. It cannot be that the dates of the control samples across three laboratories (which were also each respectively cut from their one piece of cloth) can agree, yet the dates of Shroud samples across the three laboratories can disagree. That is, if the Shroud sample's dates were real and not computer-generated by a hacker''s program!

To be continued the next part 2, "Evidence that the Shroud is older than the earliest 1260 radiocarbon date" of this series.

Notes:
1. This post is copyright. I grant permission to extract or quote from any part of it (but not the whole post), provided the extract or quote includes a reference citing my name, its title, its date, and a hyperlink back to this page. [return]

Bibliography
AD19. Agasso, D., 2019, "The Shroud is not from the medieval era. New studies are needed to know its age," Vatican Insider, 11 June.
CT19. Casabianca, T., et al., 2019, "Radiocarbon Dating of the Turin Shroud: New Evidence from Raw Data," Archaeometry, Vol. 61, No. 5, October, 1223-1231.
CVB. "Conclusive Evidence: Legal Definition," Bar Prep Hero, 2025.
FFW. "Falsifiability," Wikipedia, 24 January 2025.
DP89. Damon, E., et al., 1989, "Radiocarbon Dating of the Shroud of Turin," Nature, Vol. 337, 16 February, 611-615.
NST. "1.3.6.7.4. Critical Values of the Chi-Square Distribution," Engineering Statistics Handbook: National Institute of Standards and Technology, 2025.
RTB. Reference(s) to be provided.
DP89. Damon, E., et al., 1989, "Radiocarbon Dating of the Shroud of Turin," Nature, Vol. 337, 16 February, 611-615.
LS17, "Laboratory spotlight: Oxford Radiocarbon Accelerator Unit (ORAU)," Current Archaeology, 26 December 2017.
VR90. Van Haelst, R., 1990, “Statistical doubt about the C 14 dating of the Shroud,” Shroud News, No. 57, February, 20-23, 21.
VR91. Van Haelst, R., 1991, "Radiocarbon data indeed manipulated," Shroud News, No. 68, December, 5.

Posted 28 January 2025. Updated 15 February 2025.

Shroud of Turin News, September - December 2024

© Stephen E. Jones[1]

Newcomers start with: "The Turin Shroud in a nutshell"

[Previous: July - September 2024] [Next: January - June 2025].

This is my Shroud of Turin News for September - December 2024 (see below why). The first instalment has been moved to "Neutron flux," part #35 of my Turin Shroud Encyclopedia. Blogger would not allow me to re-date the original 12 January 2025 post, so I published this today, 21 January 2025, and deleted that original post. The articles will be in date order (earliest first). My words will be in [bold square brackets] to distinguish them from the articles' words. I have realised that before I write my open letter to Nature (see below), I need to write a "My Hacker Theory in a Nutshell" post, along the lines of my, "The Turin Shroud in a nutshell." That is, a (hopefully) one-page summary of my Hacker Theory, with links to my previous posts on it.

---

"Reverse-engineering Linick's Shroud hacking algorithm." This is an

[Right (enlarge): Photograph of Arizona laboratory physicist Timothy Weiler Linick (1946-89) and report that "He died at the age of forty-two on 4 June 1989, in very unclear circumstances ..." (my emphasis)]

item of my news. For those who don't know who Linick was, read 21Mar23.

I am no mathematician, unlike the "extremely mathematically gifted" Timothy Linick[JS89]. That said, in chapter "16. Were the laboratories duped by a hacker?" of my book in progress, "Shroud of Turin: Burial Sheet of Jesus!" (see 06Jul17, 03Jun18, 04Apr22, 13Jul22, 8 Nov 22 & 20Jun24), I will include a section headed, "Reverse engineering Linick's Shroud hacking algorithm." My starting point is that the very first of all dating runs of the Shroud, that of Arizona on 6 May 1988 (see 08Dec22) which produced the `psychological hammer blow' date,"1350," was, according to Table 1 of the 1989 Nature article[DP89, 612], the most recent of all dating runs at all three laboratories (see 03Aug19).

[Left (enlarge): Dating runs of "Sample 1" (the Shroud) across all three laboratories, in Table 1 of the 1989 Nature article. Years are before 1950[DP89, 611] after which atmospheric nuclear testing ejected large amounts carbon-14 into the atmosphere.]

Recently I finally got around to checking Table 1 for the first dating run years of the other two laboratories, Zurich and Oxford. I expected there to be no clear pattern to support my reverse engineering of Linick's algorithm. But much to my surprise, there is a pattern! The first dating run of Oxford and Zurich is the least recent of those two laboratories' dates. See the spreadsheet below which converts each laboratory's dating runs to calendar years (before 1950). As can be seen, Arizona's first run date, "1359" is the most recent of not only Arizona's but of all three laboratories' dates!

[Right: Spreadsheet table of each laboratory's dating runs in the order they appear in Table 1 of the 1989 Nature article, converted to calendar years (before 1950).]

And Oxford's first run date, "1155" is the least recent of not only Oxford, but of all three laboratories' dates! Finally, Zurich's first run date, "1217" is the least recent of Zurich's dates. If these were real dates, they would be evenly spread across all three laboratories. But because Linick, according to my Hacker Theory, chose "1350" (later adjusted to "1359") for its psychological value: "1350 ... corresponds very closely to the shroud's known historic date"[GH96, 279], he had to ensure his program balanced Arizona's recent dates with Oxford and Zurich's older dates. The "Change" column indicates that Linick's algorithm was a simple: 1. start with the first date of each laboratory, which was `hardwired' into the program; 2. then for each successive dating run, add or subtract from that first date, and each successive date thereafter, to converge on the target date for that laboratory; 3. which when combined and averaged across all three laboratories would yield the next important psychological date, 1260-1390, or 1325 ±65! Which was exactly 30 years before the Shroud first appeared in undisputed history at Lirey, France, in 1355!

It may be argued that had Oxford continued its dating runs, the final combined average of all three laboratories would not have been 1260-1390 and therefore not 1325 ±65. And that Linick may not have intended his program to yield a combined average date of 1260-1390 = 1355 ±65. However, Linick's program was trending towards 1260-1390 = 1355 ±65 when Oxford ceased its dating after only 3 dating runs.

So I have reverse-engineered Linick's hacking algorithm! Which was: 1. Hardwire into the program the first-run dates of each laboratory: Arizona 1350 (adjusted later to 1359), the most recent date of all three laboratories; Oxford 1155 the least recent date of all three laboratories; and Zurich 1217, the least recent of Zurich's dates. 2. For each successive dating run, add or subtract from that first date, and each successive date thereafter, to converge on the target date for that laboratory; 3. Which when combined and averaged across all three laboratories would yield the important psychological date, 1260-1390, or 1325 ±65, or close to it because Oxford didn't complete its dating. And therefore I claim that, together with my other evidence for it (see 24May14 and 23Jul15), my Hacker Theory is the only true explanation of why the first-century Shroud has a 1260-1390, or (because Oxford did not complete its dating runs) a 13th-14th century, radiocarbon date.

I am considering writing an open letter to Nature here on my blog, and then emailing and snail-mailing it as a letter for publication to Nature. I will point out:

"The curious fact that in Table 1, Sample 1 (the Shroud), of the article, "Radiocarbon Dating the Shroud of Turin," Nature, Vol. 337, 16 February, 1989, pp. 611-615, the very first dating run, that of Arizona laboratory (1359), was the most recent of that laboratory's 5 runs and in fact the most recent of all three laboratories' dating runs. And the first dating run of Oxford (1155), was the least recent of that laboratory's 3 runs, and in fact the least recent of of all three laboratories' dating runs. Finally, the first dating run of Zurich (1217), was the least recent of that laboratory's 5 dating runs. The chance of this occurring would be 1/4 x 1/3 x 1/5 = 1/60. But clearly the dates should be spread evenly across all three laboratories, considering their sub-samples were cut from the same ~10 mm x 70 mm (~0.4 x 2.75 in.) sample of the Shroud and dated by identical Accelerator Mass Spectrometry (AMS) systems at each of the three laboratories. An explanation of this curious fact, which has been hiding in plain sight for 37 years, is that the dates of Sample 1, the Shroud, are not real dates, but computer-generated by a hacker's program which was inserted into each of the three laboratories' AMS system computer. The hacker's algorithm has been plausibly reverse-engineered and it is surprisingly simple!"

Nature probably won't publish my letter, ostensibly on the grounds it is such an old article, but at least it will be on the Web!

And as we shall see below, the British Museum's Michael Tite (1938-) committed scientific fraud by inventing the "1260-1390" date! Oxford was the last of the three laboratories to commence its dating in July 1988 because of equipment problems[08Dec22; WI95, 16-17; PM96, 91; WI98, 310]. Having overcome those problems Oxford could presumably have continued for one or two more runs. But Tite, the coordinator of the laboratories' dating and receiver of their results[AM00, 183; RC99, 118; GV01, 112] would have realised that if Oxford stopped its dating after only 3 runs, the mean date of all three laboratories of the Shroud sample stood at 691 ±31[DP89, 613] or 1,259 ±31. By statistical manipulation Tite could then get the date to 1262-1384[DP89, 614], which he could then fraudulently round "down/up to [the] nearest 10 yr"[DP89, 614], so he could then claim that "The age of the shroud is obtained as AD 1260-1390"[DP89, 611]! But why round "down/up" at all, when the actual range was "1262-1384," unlesss it was to make the "results appear just a little crisper or more definitive than they really are," which is "scientific fraud" (see ). And since 1384 is closer to 1380 than it is to 1390, if Tite was going to round 1384, he should have rounded it down to 1380. But then 1320, the mid-point of 1320 +/- 60, is 35 years before 1355, which doesn't have the same round number psychological impact as 30 years before 1355.That Tite was aware of the significance of 1260-1390 being 1325 ±65, is evident that when he announced to those present at the press conference in the British Museum on 13 October 1988, that the Shroud's radiocarbon date was "1260-1390," he added that that was "on or about the year AD 1325, give or take sixty-five years either way"[WI98, 6-7]. As science writers William Broad (1951-) and Nicholas Wade (1942-), pointed out in their book: "Betrayers of the Truth: Fraud and Deceit in the Halls of Science" (1982), scientists "making results appear just a little crisper or more definitive than they really are" is "scientific fraud":

"The term `scientific fraud' is often assumed to mean the wholesale invention of data. But this is almost certainly the rarest kind of fabrication. Those who falsify scientific data probably start and succeed with the much lesser crime of improving upon existing results. Minor and seemingly trivial instances of data manipulation-such as making results appear just a little crisper or more definitive than they really are, or selecting just the `best' data for publication and ignoring those that don't fit the case-are probably far from unusual in science. But there is only a difference in degree between `cooking' the data and inventing a whole experiment out of thin air"[BW82, 20.]

So Tite was doubly guilty of "scientific fraud" in making the final radiocarbon date "appear just a little crisper or more definitive than" it really was: first by rounding the actual range "1262-1384," and second, rounding 1384 to 1390.

Tite and Hall had a motive to stop Oxford's dating after only 3 runs (not knowing that had the dating continued for another one or two runs, Linick's program would have dated the Shroud 1260-1390 = 1355 ±65 anyway), and fraudulently round up 1384 to 1390, so that Tite could falsely claim that, "The age of the shroud is obtained as AD 1260-1390." And that motive was, the Oxford Radiocarbon Dating Laboratory had been largely privately funded by Hall, who was independently wealthy due to an inheritance from his grandfather, who had `struck it rich' investing in a gold mine in Australia[WI01, 59]. But Hall was due to retire and so he had arranged for his "rich friends" to donate £1 million to fund a new Oxford Chair of Archaeological Science, so that the laboratory would continue[WI89, 7; GH96, 254; PM96, 125]. However, if the radiocarbon dating failed to prove the Shroud was medieval, those promised donations might be in doubt[RTB]. With so much at stake, it is not hard to imagine Hall privately promising Tite, words to the effect, "Get this right Michael, and the job is yours"[RTB]! And as it turned out, the radiocarbon date of the Shroud was medieval (thanks to Linick's program!), Hall's rich friends did donate £1 million to fund a new Oxford Chair of Archaeological Sciences[WI89, 7; WI98, 311; GV01, 134], and Tite was appointed to that new Chair and succeeded Hall as Director of the Oxford Radiocarbon Dating Laboratory[WI89, 7; PM96, 111; WI98, 311; GV01, 134]!

Twentieth anniversary of my discovery of the Shroud! As I wrote in my first post to this blog, on 30 June 2007, it was on a day in January 2005, now twenty years ago, that I discovered the Shroud and my life changed forever:

"My interest in the Shroud of Turin began in January 2005 when, as I posted to my then Yahoo group, after reading Stevenson & Habermas' "Verdict on the Shroud" (1981) [Right], I accepted (then provisionally but now fully) that the Shroud of Turin is the actual burial sheet of Jesus Christ and therefore extrabiblical evidence of His death and resurrection."

In a 2019 post I gave more details:

"... in January 2005 I found in a secondhand bookstall a book, "Verdict on the Shroud" (1981) ... which was co-authored by Gary Habermas. I knew from Habermas' other writings that he was a sound, evidence-based, evangelical Christian philosopher, so I bought the book. I was amazed at the evidence that Habermas and his co-author Ken Stevenson presented for the Shroud being the burial sheet of Jesus mentioned in the Gospels (Matthew 27:59; Mark 15:46 & Luke 23:53).

According to Blogger I have published 668 posts. Days between 30 June 2007 and today, 22 January 2025 = 6416. Divided by 668, is an average of 1 post every ~9.6 days. As of tonight my blog has had 1,935,191 pageviews. Which divided by 6416 days is an average of 301.6 views a day! I hope I am still blogging about the Shroud when Jesus returns, which I expect will happen before 2037, only 12 years away!

Notes:
1. This post is copyright. I grant permission to extract or quote from any part of it (but not the whole post), provided the extract or quote includes a reference citing my name, its title, its date, and a hyperlink back to this page. [return]

Bibliography
AM00. Antonacci, M., 2000, "Resurrection of the Shroud: New Scientific, Medical, and Archeological Evidence," M. Evans & Co: New York NY.
BW82. Broad, W. & Wade, N., 1982, "Betrayers of the Truth: Fraud and Deceit in the Halls of Science," Simon and Schuster: New York NY.
DP89. Damon, E., et al., 1989, "Radiocarbon Dating of the Shroud of Turin," Nature, Vol. 337, 16 February, 611-615.
GH96. Gove, H.E., 1996, "Relic, Icon or Hoax?: Carbon Dating the Turin Shroud," Institute of Physics Publishing: Bristol UK.
GV01. Guerrera, V., 2001, "The Shroud of Turin: A Case for Authenticity," TAN: Rockford IL.
JS89. Jull, A.J.T. & Suess, H.E. , 1989, "Timothy W. Linick," Radiocarbon, Vol 31, No 2.
MR90. Morgan, R., 1990, "Interview With Dr. Michael Tite by Orazio Petrosillo and Emanuela Marinelli, 8 September 1989, during the Paris Symposium," Shroud News, No 59, June, 3-9.
PM96. Petrosillo, O. & Marinelli, E., 1996, "The Enigma of the Shroud: A Challenge to Science," Scerri, L.J., transl., Publishers Enterprises Group: Malta.
RC99. Ruffin, C.B., 1999, "The Shroud of Turin: The Most Up-To-Date Analysis of All the Facts Regarding the Church's Controversial Relic," Our Sunday Visitor: Huntington IN.
RTB. Reference(s) to be provided.
WI89.Wilson, I., 1989, "Dr. Tite to succeed Professor Hall at Oxford," STS Newsletter, No. 22, May, 7-8. https://www.shroud.com/pdfs/n22part4.pdf.
WI95. Wilson, I., 1995, "From a Forgotten Memorandum: A Visit to the Oxford Research Laboratory 7 July 1988," BSTS Newsletter, 15-18, 16-17.
WI98. Wilson, I., 1998, "The Blood and the Shroud: New Evidence that the World's Most Sacred Relic is Real," Simon & Schuster: New York NY.
WI01. Wilson, I., 2001, "Obituary: Professor Edward Hall, CBE, FBA," BSTS Newsletter, No. 54, November, 57-60.

Posted 22 January 2025. Updated 7 February 2025.

Neutron flux: Turin Shroud Encyclopedia

Copyright © Stephen E. Jones[1]

Neutron flux #35

This is "Neutron flux," part #35 of my Turin Shroud Encyclopedia, which will help me write chapter 16, "Were the laboratories duped by a hacker?," of my book in progress, "Shroud of Turin: Burial Sheet of Jesus!" See 06Jul17, 03Jun18, 04Apr22, 13Jul22, 8 Nov 22 & 20Jun24.

Newcomers start with: "The Turin Shroud in a nutshell"

[Index #1] [Previous: Science and the Shroud #34] [Next: My Hacker Theory #36].

This post was originally a news item in my Shroud of Turin News for September - December 2024. But it grew too long, so I extracted that news item and have reposted it here. My words are in [bold square brackets] to distinguish them from the news articles' words. There are a lot of "RTB's" (references to be provided) in this post, which I haven't had time to find refererences for. I have updated almost all of it, since my Shroud of Turin News post, so it would be worth reading all of it.

---

"Nuclear engineer says latest research confirms first-century date of

[Right (enlarge): The radioactive isotopes chlorine-36 (Cl-36) and calcium-41 (Ca-41), and stable isotope chromium-53 (Cr-53), that according to Mark Antonacci's Neutron Flux Theory should still be detectable on the Shroud. See 01Nov13]

Shroud of Turin," 28 September 2024, Martin Barillas. For centuries Christians have attributed a first-century date to the Shroud of Turin. Nuclear engineer Robert Rucker says that his latest research on the shroud verifies that. "The Shroud of Turin is the second-most valuable possession of the human race next to the Bible itself," Rucker told CNA.[Agreed!] The shroud is currently preserved in the Chapel of the Holy Shroud adjacent to St. John the Baptist Cathedral in Turin (Torino), Italy. For more than 10 years, Rucker has studied the physics of the disappearance of the body of Jesus and its imprint on the shroud. His website, Shroud Research, challenges conclusions that the shroud dates to the period of 1260 to 1380 A.D., leading skeptics to conclude it is a medieval fake. ... In 1988, scientists used tiny samples snipped from the shroud to determine the amount of carbon 14 isotopes they contained, destroying the samples in the process. The radioactive carbon 14 isotope is a variant of carbon-containing excess neutrons, which are particles smaller than atoms. Over time, carbon 14 decays into nitrogen 14 in organic materials such as bone and plant matter. The ratio of carbon 14 atoms remaining in a sample provides the data needed to estimate the sample's age. Rucker said his calculations show that the 1988 carbon 14 dating is erroneous because it does not take into account the radiation emitted from Jesus' body at the resurrection, which included neutrons that were absorbed by the shroud and formed new carbon 14 atoms, thus leading to a misinterpretation of the data ... " [I have not studied Rucker's or Antonacci's Neutron Flux Theory, which attempts to explain why the 1260-1390 radiocarbon date of the Shroud was wrong. So the following are my generic criticisms of the theory (see also 23Jul15). This will help me write chapter 16, "Were the laboratories duped by a hacker?," of my book in progress, "Shroud of Turin: Burial Sheet of Jesus!" See 06Jul17, 03Jun18, 04Apr22, 13Jul22, 8 Nov 22 & 20Jun24.

• No Biblical support While there is Biblical support for the Light Radiation Theory (see 25Oct24), there is none for the Neutron Flux Theory. Paul, on the topic of the resurrection of Christians' bodies, taught "we shall all be changed" when "this perishable body must put on the imperishable" (1Cor 15:51-53) and Jesus, at his return "will transform our lowly body to be like his glorious body" (Php 3:20-21 ). In his resurrection body Jesus could pass through walls (Jn 20:19, 26), and instantly appear and disappear (Lk 24:31, 36)[AM00, 235; OM10, 244]. Clearly Jesus' resurrection involved a qualitative change of his earthly body, not a quantitative change (for the worse) to it that the mere removal of neutrons would be (see next).

• Source of the neutrons According to the Neutron Flux Theory, the source of the neutron flux is the resurrecting body of Jesus[AM00, 159; AM16, 100;CW20, 87]. About 99% of the mass of the human body is made up of six elements: oxygen, carbon, hydrogen, nitrogen, calcium, and phosphorus[CHB]. Oxygen has 8 neutrons, carbon has 6, hydrogen 0, nitrogen 7, calcium 20, and phosphorus 16[PNE]. If each element of Jesus' body, excepting hydrogen which doesn't have any neutrons, lost 1 neutron, it would become respectively: oxygen-15 (which has a half-life of ~2 minutes and decays to nitrogen-15), carbon-11 (with a half-life of ~20 minutes and decays to boron-11), nitrogen-13 (which has a half-life of ~10 minutes and decays to carbon-13), calcium-39 which decays instantly to potassium-39), and phosphorus-30 (which has a half-life of ~2.5 minutes and decays to silicon-30). The loss of normal oxygen, nitrogen, calcium and phosphorus atoms would likely be incompatible with human life, depending on how many neutrons are lost from them. And it would not be a valid explanation that it didn't matter if Jesus' resurrection body was not viable as a human body. The risen Jesus went out of his way to impress on his disciples that his resurrection body was still a human body. To the two disciples on the road to Emmaus he told them to see and touch his hands and feet, with their nail wounds, to confirm that his resurrected body was not "a spirit" but was still "flesh and bones"(Lk 24:39). To the disciples in a locked Jerusalem room, Jesus showed them the wounds in his hands and side and even asked Thomas to feel them (Jn 20:19-20; 26-27). The Council of Chalcedon (451), the fourth ecumenical council of the united Christian Church, ruled that Jesus was "perfect in manhood"[CCW]. But a risen Jesus with a great many of his neutrons missing, would definitely not be perfect in manhood (to put it mildly)!

• No nitrogen in cellulose The Neutron Flux Theory claims that a neutron flux in Jesus' tomb converted nitrogen-14 in the Shroud into carbon-14, shifting the radiocarbon date of the first-century Shroud ~thirteen centuries into the future to 1325 +/- 65 or 1260-1390[GH96, 264; WI98, 7; OM10, 60-61; DT12, 170]. But there is no nitrogen in cellulose which comprises the Shroud's linen[CFW]. The chemical

[Left (enlarge): Cellulose molecular structure [CDL].

formula of cellulose is (C₆H₁₀O₅), so cellulose consists only of carbon, hydrogen and oxygen in repeating molecular chains[CLW]. The Neutron Flux Theory therefore claims that that the nitrogen in the Shroud's air spaces was converted to carbon-14 by a neutron flux generated by Jesus' resurrection[AM00, 160, 162]. But even if that was true, the carbon-14 in the Shroud's air spaces would not become part the Shroud's cellulose fibres[RTB]. And when each Shroud sample was reduced to pure carbon by converting it to carbon dioxide and then converting that gas into pure carbon as graphite[SH88, 140; IJ98, 163], as a preliminary to radiocarbon dating it[PM96, 84; IJ98, 162-163], anything in the sample that was not carbon within the Shroud's cellulose would be excluded from the radiocarbon dating process[RTB]. So the Neutron Flux Theory would not change the Shroud's radiocarbon date!

• Would add neutrons to cellulose atoms The same neutron flux which the Neutron Flux Theory claims would add a neutron to an atom of nitrogen-14 in the Shroud's air spaces and convert it to an atom of carbon-14[RTB], would also add a neutron to atoms in the Shroud's cellulose fibre molecules[RTB]. Specifically one or more of the 6 carbon-12 atoms in each of the Shroud's millions of cellulose molecules would likely be converted to carbon-13[RTB]. One or more of the 10 hydrogen-1 atoms in each of the Shroud's cellulose molecules would likely be converted to deuterium-2[RTB]. And one or more of the 5 oxygen-16 atoms in each of the Shroud's cellulose molecules would likely be converted to oxygen-17[RTB]. The likely effect on the chemical bonds: -O- x 3, -OH x 2 and -CH₂OH x 1, would be the disintegration of that cellulose molecule[RTB]. Particularly since the sudden arrival of a neutron from a nearby neutron flux into the nucleus of a cellulose atom would likely be energetic[RTB]. This would have happened many millions of times across the Shroud, if the Neutron Flux Theory was true. In which case the Shroud fabric would likely have disintegrated in the first century! That it hasn't, and the opposite is true: the Shroud has been closely examined many times and found to be in "good condition"[WI79, 21; WM86, 2; WI98, 261; AM00, 98; GV01, 55; DT12, 13; WI10, 21], and "the fiber showed no signs of disintegration" (my emphasis)[WI79, 21], is a falsificaton of the Neutron Flux Theory! Neutron Flux theorists can't have it both ways: the neutron flux emitted by Jesus' resurrecting body converted millions of the Shroud's nitogen-14 atoms into carbon-14, yet it had little or no effect on the atoms in the Shroud's cellulose molecules!

Neutron flux would have killed the guards at the tomb A neutron flux strong enough to convert enough nitrogen-14 to carbon-14, to shift the Shroud's first-century radiocarbon date ~thirteen centuries into the future to 1325 +/-65 (1260-1390), would have killed the guards stationed outside the tomb (Mt 27:65-66). The guards would have been stationed around the circular rolling stone at the entrance of the tomb (Mt 27:60; Mk 15:46), which would have had a gap between it and the tomb entrance around its edges, so the full-force of any neutron flux in the tomb would have been experienced by the guards, unimpeded by the tomb's limestone (which wouldn't have been an impediment anyway since neutrons pass through buildings). A neutron bomb creates a neutron flux which passes through a military tank's metal armour and kills its occupants[NBW]. They are killed by Neutron Activation which makes a body's ordinary chemicals radioactive:

"Neutron activation is the process in which neutron radiation induces radioactivity in materials, and occurs when atomic nuclei capture free neutrons, becoming heavier and entering excited states. The excited nucleus decays immediately by emitting gamma rays, or particles such as beta particles, alpha particles, fission products, and neutrons (in nuclear fission). Thus, the process of neutron capture ... often results in the formation of an unstable activation product. Such radioactive nuclei can exhibit half-lives ranging from small fractions of a second to many years ... All naturally occurring materials, including air, water, and soil, can be induced (activated) by neutron capture into some amount of radioactivity in varying degrees, as a result of the production of neutron-rich radioisotopes. Some atoms require more than one neutron to become unstable, which makes them harder to activate ... Thus water is relatively difficult to activate, as compared to sodium chloride (NaCl), in which both the sodium and chlorine atoms become unstable with a single capture each" (my emphasis)[NAW].

The guards were alive when an angel descended to roll back the large stone across the entrance of the tomb and announce to Jesus' women disciples who had come to the tomb to anoint Jesus' body (Mt 28:1; Mk 16:1; Lk 23:55-24:1; Jn 20:1), that Jesus had been resurrected (Mt 28:1-6; Mk 16:1-6; Lk 24:1-6). For fear of the angel the guards became like dead men (Mt 28:1-4). This must have been a paralysis, not unconsciousness, because the guards heard the angel's announcement that Jesus had been resurrected, since after the women had left the tomb, the guards recovered and some of them went into Jerusalem and told the chief priests "all that had taken place" (Mt 28:11-13). The guards evidently were unaware until the angel's announcement that Jesus had been resurrected inside the tomb, and so they had not heard, nor felt, any neutron flux from inside the tomb, which they surely would have, if they were not killed instantly by it! Which means that there was no neutron flux inside Jesus' tomb!

Neutron flux would have killed the disciples who went inside the tomb soon after Jesus' resurrection The women disciples, and the Apostles Peter and John, who went into the tomb soon after Jesus' resurrection (Mt 28:1-6; Mk 16:1-6; Lk 23:56-24:3; Jn 20:1-8), would likely have been killed by the residual radioactivity inside the tomb. Jesus's tomb was limestone[AM00, 109, 160; DT12, 114; WI10, 66-67], which is mainly calcium cabonate (CaCO₃)[AM00, 109; WI98, 106]. If the Neutron Flux Theory was true, the inside of Jesus' tomb would have been filled with residual radioactive calcium, carbon and oxygen!! Yet one of the women, Mary Magdalene, ran from the tomb to tell Peter and John that Jesus' body was not in it (Jn 20:1-2). And Peter and John were still alive and well 2-3 years later when in Acts 8:14 they were together sent by the Jerusalem church to minister to the new Christian converts in Samaria! So again there was no neutron flux inside Jesus' tomb!

Tests of the Neutron Flux Theory Mark Antonacci (1949-) has claimed that if the first-century Shroud's 1260-1390 radiocarbon date was caused by a neutron flux at the resurrection of Jesus, which converted nitrogen-14 into carbon-14, the Shroud would contain the following isotopes that are rare, or non-existent, in nature:

• Calcium-41 (Ca-41):

"... STURP scientists discovered that calcium (along with strontium and iron) was distributed uniformly throughout the Shroud, probably as a result of the retting process when the cloth was originally manufactured. Almost 97 percent of all calcium consists of calcium-40 (Ca-40); the other 3.1 percent consists of Ca-42, 43, 44, 46, and 48. Conspicuously absent is Ca-41, which does not occur naturally. However, if a neutron flux had irradiated the Shroud, it would convert the Ca-40 in the cloth to Ca-41. If Ca-41 were found on the Shroud, it would confirm that the cloth had been irradiated with neutrons. Since calcium has been found distributed uniformly over the Shroud, any portion of the original doth could be examined for the presence of Ca-41"[AM00, 186; 01Nov13a].

This is substantially correct. Calcium-41 is found in nature, but only "in the upper metre of the soil column," because it is only created on Earth by nuclear fluxes from outer space:

"Calcium also has a cosmogenic isotope, 41Ca, with half-life 99,400 years. Unlike cosmogenic isotopes that are produced in the air, 41Ca is produced by neutron activation of 40Ca. Most of its production is in the upper metre of the soil column, where the cosmogenic neutron flux is still strong enough"[ICW].

• Chlorine-36 (Cl-36)

"In addition, when STURP scientists made X-ray fluorescence measurements on thirteen threads that had been removed from the Raes sample, they detected small traces of chlorine. [Schwalbe, L.A. & Rogers, R.N. "Physics and Chemistry of the Shroud of Turin," Analytica Chimica Acta 135 (1982): 3-49,47.] If a neutron flux irradiated the Shroud, it would convert chlorine-35 (Cl-35), found naturally, to chlorine-36 (Cl-36). Like Ca-41, Cl-36 does not occur naturally. As stated by Thomas Phillips in the scientific journal Nature, `The presence of either [Ca-41 or Cl-36] would confirm that the Shroud had been irradiated with neutrons'" [Phillips, 1989, p.594]."[AM00, 188 01Nov13b].

This looks like a failure of a test for chlorine-36 on the Shroud. Because if there are only "traces" of ordinary chlorine-35 on the Shroud, a neutron flux would not likely convert enough chlorine-36 to be measurable.

• Carbon-14 in blood:

"Moreover, if the Shroud was irradiated with neutrons, it could have affected the blood in another significant way. The solid part of dried blood contain mostly proteins, which typically contains about 12 percent nitrogen by weight. This is a much larger amount of nitrogen than is found in cloth. If a neutron flux irradiated the blood on the cloth, it could convert the nitrogen-14 (N-14) into C-14 on a much larger scale than it would convert in cloth. As such, the blood would carbon date to a much younger date than the cloth. In fact, it could easily date well into the future"[AM00, 188-189 01Nov13c].

This sounds like an admission that there was not enough nitrogen-14 in the Shroud's fibres for a neutron flux to convert to carbon-14 and account for its 1260-1390 radiocarbon date! Otherwise, why not simply propose that the Shroud's linen fibres be tested for carbon-14? And as we saw above the Shroud's blood is not included in radiocarbon dating of the Shroud's cellulose fibres. Also, as mentioned in my 2013 post, the Vatican is unlikely to ever approve the radiocarbon dating of the Shroud's blood.

As I also mentioned in my 2013 post re Antonacci's proposal that the Shroud be tested for the isotopes calcium-41, chlorine-36 and chromium-53, which would confirm the Neutron Flux Theory, it is very unlikely that the Vatican would approve a test requested by individuals. However, it may be that Antonacci and Rucker's request would be included in a future suite of scientific tests of the Shroud proposed by a broad consensus of Shroud scholars. Or it may that threads from the Shroud, which exist apart from it, could be tested for those isotopes without involving the Archdiocese of Turin or the Vatican. If either were to happen, I predict that the Neutron Flux Theory would fail that test, for the above reasons.

• Does not explain the Shroud's 1260-1390 radiocarbon date Finally, the Neutron Flux Theory does not explain why a neutron flux from Jesus' resurrection converted nitrogen-14 in the Shroud to carbon-14, which `just happened’ to shift the first century radiocarbon date of the Shroud thirteen centuries into the future, to the `bull's eye’ 1325 +/- 65 years radiocarbon date! Which `just happens' to be exactly 30 years before the Shroud first appeared in undisputed history at Lirey, France, in 1355! As the physicist Frank Tipler (1947-) pointed out, it "would be an extraordinary and very improbable coincidence if the amount of carbon added to the Shroud were exactly the amount needed to give the date that indicated a fraud"[TF07, 178]. But that is what the Neutron Flux Theory is either claiming, or ignoring. Only my Hacker Theory (and Tipler's Supernatural Deceptive Miracle by God Theory) explains that!

Notes:
1. This post is copyright. I grant permission to extract or quote from any part of it (but not the whole post), provided the extract or quote includes a reference citing my name, its title, its date, and a hyperlink back to this page. [return]

Bibliography
AM00. Antonacci, M., 2000, "Resurrection of the Shroud: New Scientific, Medical, and Archeological Evidence," M. Evans & Co: New York NY.
AM16. Antonacci, M., 2016, "Test The Shroud: At the Atomic and Molecular Levels," Forefront Publishing Company: Brentwood TN.
CCW. "Council of Chalcedon," Wikipedia, 4 January 2025.
CHB "Composition of the human body," Wikipedia, 28 December 2024.
CDL "Cellulose: A Plant’s Building Block," Duluth Labs, 2016
CLW "Cellulose," Wikipedia, 30 December 2024.
CFW "Cellulose fiber," Wikipedia, 3 January 2025
CW20. Chiang, R.G. & White, E.M., eds, 2020, "Science, Theology and the Holy Shroud: Edited papers from the 2019 International Shroud Conference," Doorway Publications, Ancaster, Ontario, Canada.
DT12. de Wesselow, T., 2012, "The Sign: The Shroud of Turin and the Secret of the Resurrection," Viking: London.
GH96. Gove, H.E., 1996, "Relic, Icon or Hoax?: Carbon Dating the Turin Shroud," Institute of Physics Publishing: Bristol UK.
IJ98. Iannone, J.C., 1998, "The Mystery of the Shroud of Turin: New Scientific Evidence," St Pauls: Staten Island NY.
ICW "Isotopes of calcium," Wikipedia, 6 November 2024.
NAW "Neutron activation," Wikipedia, 11 September 2024.
NBW "Neutron bomb," Wikipedia, 25 November 2024.
OM10. Oxley, M., 2010, "The Challenge of the Shroud: History, Science and the Shroud of Turin," AuthorHouse: Milton Keynes UK.
PM96. Petrosillo, O. & Marinelli, E., 1996, "The Enigma of the Shroud: A Challenge to Science," Scerri, L.J., transl., Publishers Enterprises Group: Malta.
PNE. "Protons Neutrons & Electrons for All Elements," The Chemical Elements, 2025.
RR20. Rucker, R., 2020, "The Radiocarbon Dating of the Shroud is Explained by Neutron Absorption," in CW20, 87-100.
RTB. Reference(s) to be provided.
SH88. Sox, H.D., 1988, "The Shroud Unmasked: Uncovering the Greatest Forgery of All Time," Lamp Press: Basingstoke UK.
SR82. Schwalbe, L.A. & Rogers, R.N., 1982, "Physics and Chemistry of the Shroud of Turin: A Summary of the 1978 Investigation," Analytica Chimica Acta, No. 135, 3-49.
TF07. Tipler, F.J., 2007, "The Physics of Christianity," Doubleday: New York NY.
WM86. Wilson, I. & Miller, V., 1986, "The Evidence of the Shroud," Guild Publishing: London,.
WI79. Wilson, I., 1979, "The Shroud of Turin: The Burial Cloth of Jesus?," [1978], Image Books: New York NY, Revised edition.
WI98. Wilson, I., 1998, "The Blood and the Shroud: New Evidence that the World's Most Sacred Relic is Real," Simon & Schuster: New York NY.
WI10. Wilson, I., 2010, "The Shroud: The 2000-Year-Old Mystery Solved," Bantam Press: London.

Posted 20 January 2025. Updated 8 February 2025.