text:
Talk:Maximum break

error in section: "Maximum breaks by territory"
2014 Murphy in Gdynia Open -> Poland — Preceding unsigned comment added by 86.88.175.79 (talk) 14:57, 6 August 2020 (UTC)

I think the text in brackets in the opening sentence is ambiguous
I think the text in brackets in the opening sentence is ambiguous. "The highest number of points that can be achieved from a break" is whatever is available when a player approaches the table. If there's just the black left on the table, then the highest number of points that can be achieved in that break is 7. I appreciate the need to be succinct in opening statement, but the text presented in the brackets is offered as an alternative to the main description "maximum break" - and I don't think it's a valid alternative.

Can I recommend the following changes:

In snooker, a maximum break is a term used to describe a break (that does not begin with a free ball) in which a player pots all 15 reds, 16 blacks, and each other coloured object ball once, in the order prescribed by the rules. This is often known as a maximum, a 147, or verbally a one-four-seven. The term maximum break is a misnomer, as 147 is not the maximum break possible in snooker.

Breaks greater than 147 are possible in a free ball situation, which, effectively, can give rise to 16 single point balls being available to the player (akin to 16 reds). In such situations, breaks of 147 to 154 are possible but in these cases the traditional requirement when compiling a maximum break—to always follow each single point value ball with a black—cannot be met. It is only following a free ball, and with all 15 reds on the table, that the highest break possible, 155, can be made. Such a break would involve the black being potted 17 times. Breaks in excess of 147, or breaks of 147 made using 16 single point balls, are so uncommon that terminology amongst players and commentators has not been established to describe them. It is also unclear how they would be treated for the purposes of distributing ‘maximum break’ prize money offered at some tournaments. Prizes for the highest break (usually of a monetary value much lower than those awarded for maximum breaks) are awarded simply to the highest value break achieved, therefore breaks over 147 would receive such prizes in precedence to a maximum break of 147 achieved under normal circumstances at the same tournament.

It is also possible, if a number of free ball situations occur, for both players to pot balls and accrue points before a red ball is potted. It is known from officially recognised maximum breaks that they can be achieved by players whose opponents have accrued points earlier in the frame due to foul strokes made by the player. Therefore, accrual of previous points is not a barrier to a maximum break, although it is not known whether a maximum would be accepted if previous pots have been made.

In snooker, refereeing mistakes are not retrospectively corrected (i.e. scores are not recalculated if errors are discovered). Therefore, a red (or reds) could be incorrectly re-spotted by the referee leading to legal breaks with no theoretical limit. — Preceding unsigned comment added by 185.60.80.114 (talk) 14:02, 20 January 2017 (UTC)

 * I have removed the sentence in brackets. I don't think it is necessary to get into details, breaks higher than 147 are covered later in the article. Under normal circumstances (i.e. without a free ball coming into play) the highest break possible is 147 and that is what the article covers. The various anomalies do not need to be covered in the lead, other than to point out that anomalous situations can arise. Betty Logan (talk) 15:04, 21 January 2017 (UTC)

What is an official 147?
Maybe I overlooked it, but the article does not mention the definition of an official 147. Bjorn Haneveer has now three 147s' none of which are mentioned in the list. The list of http://www.globalsnookercentre.co.uk/files/History/history_147.htm mentions Haneveer only in the footnotes, but not in the actual list. What am I missing? Voorlandt (talk) 21:39, 3 May 2008 (UTC)
 * Good question; the article should cover this. My guess is it means "in tournament competition, not practice, informal play or exhibition games. But whatever is added needs as reliable source. —  SMcCandlish  [talk] [cont]  ‹(-¿-)› 13:49, 2 September 2008 (UTC)
 * I found one reliable source containing this information, but it looks outdated after David Grays second maximum break. (It says official is in attendance of a referee, but in the amateur round of PTC there are no referees.) Armbrust Talk to me about my editsreview  16:36, 2 December 2011 (UTC)

David Gray's counts as its during a professional tournament its all professional tournaments using normal snooker rules (no shoot out) using full sized tables (exc general cup) PIOS is also included as used to be the challenge tour thats the definition (QueenAlexandria) 11:41, 24 August 2012 (UTC)
 * David Gray's only counts because World Snooker said it does. However no reliable source contains, what criteria needs to be fulfilled for an official maximum break. Also PIOS maximums doesn't count. Armbrust, B.Ed. WrestleMania XXVIII The Undertaker 20–0  22:06, 28 August 2012 (UTC)

Mike Dunn
Same question for : 2012_German_Masters : Mike Dunn got a 147 in the qualifying stage : he should be listed, shouldn't he? 89.217.132.78 (talk) 06:14, 21 February 2012 (UTC)
 * Mike Dunn is maximum number 79 on the list. It's a bit further back because the qualifiers were before xmas. Betty Logan (talk) 08:22, 21 February 2012 (UTC)

Maximums/maxima
I note there is a dispute over the plural or maximum. I would like to remind the editors that British English is used in this article.

According to the the Oxford English Dictionary both maxima and maximums are acceptable plural forms of maximum, with "maxima" being more widely used:

"Inflections: Plural maxima, (rare) maximums."

However, in the context of sport, maximums tends to be the preferred form:

"6. Sport. In darts, snooker, etc.: the highest score attainable; an instance of achieving this.

1986 Darts World Sept. 58/1   There are dartboard designs painted on the walls..and on the wooden beams the number of maximums scored by the visiting stars are recorded.

1987  Speedway '87 Mar. 3/1   He became the first rider to complete maximums in every away British League match last year and finished with a record 35 maximums in all competitions.

1999  Daily Tel. (Electronic ed.) 22 Apr.,   ‘I went for it when I had made nine, the reds opened perfectly,’ said O'Sullivan, whose maximum was the ninth in front of television cameras.''"

In addition to the OED, World Snooker (the professional governing body) also uses maximums as the plural form:.

In view of this, we should abide by WP:RETAIN, which stipulates that when different spelling variations are available we should retain the version that is first used by the article, which in this case is maximums. Betty Logan (talk) 23:36, 9 December 2012 (UTC)
 * Support retaining maximums, as every English language source uses it in the context of snooker. Armbrust The Homunculus 23:54, 9 December 2012 (UTC)

I can't believe this is not addressed in the article.
Or in the talk pages, for that matter: Who should take the prize for maximum break in an event where player A scores a conventional 147, and player B scores a 149 (say) break by potting yellow after his initial free ball, and then 14 blacks plus 1 pink (and clearing)? And who should win the prize for highest break?

What if both do a conventional 147 clearance, except one of them also scored additional points due to an initial free ball? Should they split the maximum break prize? And/or the highest break prize?

And finally: What if both achieve the exact same break (say, 150) taking advantage of an initial free ball, except that player A potted yellow after his free ball followed by the standard 15 blacks, but player B potted black after the free ball and yellow later on after a red (instead of black)? How should both prizes be assigned in this case?

Naturally, it should be assumed in every case that no other player in the event is a contender for either prize. — Preceding unsigned comment added by 85.242.102.172 (talk) 05:08, 14 February 2013 (UTC)
 * Comment If you have any reliable sources, which discuss this, than please add them to this section. Without (at least one), it would be original research, which isn't allowed on Wikipedia. Armbrust The Homunculus 12:24, 14 February 2013 (UTC)

 * It's not covered on the WSA site, but programmes used to clairfy that the maximum break was explicitly for "a 15-red 147 or a 16-red 155" (as covered by the article). I imagine it is still the same but there is nohing for us to cite. I don't think a player would get the prize for a 148 (Jamie Burnett didn't). There are other examples that could cause controversy: if a player gets a free ball at the start of the match, maybe pots it and then his opponent goes on to make a 15-red maximum, would that count as a maximum despite 155 points being available at one stage? Or if a player pots a red, and then his opponent gets a free ball and scores a 15-red maximum, would that count since only 147 points has been on at any point in the game? In short we don't cover it because the WSA don't address it. Betty Logan (talk) 13:48, 14 February 2013 (UTC)

This is covered in WSPBA regulations given to players. Only 'Maximum' breaks can win the maximum break prize. For breaks of 148,149,150,151,152,153 or 154 the player will not have scored the maximum number of points available to them at the start of the break. This could also be the case for a player who scores a 147 using 16 'reds' via a free-ball situation, again, not a maximum. In a tournament all breaks of 147 (15 reds) or 155 (16 reds) will share a 'maximum break' prize. The 'highest break' prize is awarded to the player(s) who achieve the highest score in a break. For this prize a 148 will beat a 147 off 15 reds.185.60.80.114 (talk) 13:59, 15 December 2016 (UTC)

Link to Jamie Cope reverted twice, seemingly inconveniencing readers for no good reason
I linked Jamie Cope to his biographical article. This got quickly reverted by one user saying it was already linked earlier in the section. I restored it asking 'why inconvenience readers by forcing them to look for a possible link elsewhere than where they are entitld to expect it to be?'. This got almost instantly reverted by a second user saying 'because it's already linked in the previous sentence'. This still inconveniences readers by forcing them to look for a possible link elsewhere than where they are entitled to expect it to be, and no justification has been offered for such inconveniencing, which thus seemingly disimproves Wikipedia for no good reason that I am aware of. As I cannot restore it again without edit warring, I am raising the matter here first, to see if it can be resolved by discussion without having to decide whether to seek arbitration. Please explain why you think the article is improved by removing the link, thus, at least in my opinion, seemingly inconveniencing readers without offering any good reason, at least up to now. I will shortly be contacting the afore-mentioned two users to ensure they are aware of this item. Tlhslobus (talk) 22:23, 6 May 2013 (UTC)

I might add that the tables in this article contain such multiple links, with Srephen Hendry being linked 6 times in a row, and quite rightly so, because the link costs nothing, while tables without such links are a pointless source of inconvenience where they are found in other articles. Jamie Cope is arguably already seriously under-reported here, as, at least in my view, he should be more prominently singled out as the only reported maximum 155. But even if that were not the case there would still be no good reason that I can see why a reader should be forced to go looking elsewhere for a possible link. Tlhslobus (talk) 22:37, 6 May 2013 (UTC) Tlhslobus (talk) 22:37, 6 May 2013 (UTC)
 * Because it's overlinking. Tables are excepted from that. Also I don't think our readers are that stupid, that they don't see the link just above 2 lines. Armbrust The Homunculus 23:01, 6 May 2013 (UTC)
 * I don't think there's any such thing as overlinking, in the sense that I don't see how extra links do any harm, and even if there were cases when they might, I don't see that this particular link does any harm. But there is such a thing as underlinking, which does harm through inconvenience and irritation for readers. And I think this is liable to be such a case, and I see no valid reason to take such a risk. I don't think failure to spot a link quite a distance away makes a reader stupid, but even if it did, there's no reason why Wikipedia should be making life any more inconvenient for people who have the misfortune of being stupid than it already is. Incidentally, it's actually 3 lines away, not 2, but even 1 line away is potentially missable by some readers, or at least potentially wastes their time looking for it, always assuming they think of looking before wasting time typing (or mistyping, as will often happen) 'Jamie Cope' into the search box; or sometimes they may simply give up. I see no particular reason why tables should be an exception (and in fact some tables are underlinked, as I've pointed out already). Perhaps you can show me somewhere where Wikipedia mentions overlinking and guidelines on avoiding it, preferably including instances where a person's name should not be linked to its biographical article when it's the only occurence of that name in a sentence (and indeed a bullet-point). I'm not asking for cases where it is said to be permissable to omit the link, but cases where such an omission is said to be recommended and/or compulsory. Tlhslobus (talk) 00:07, 7 May 2013 (UTC)
 * Now the two breaks are in the same bullet-point. Armbrust The Homunculus 00:23, 7 May 2013 (UTC)
 * (Incidentally my last paragraph should have mentioned that we also need to consider the needs of those with various kinds of poor eyesight, but I digress). As for your combining of the bullet-points, while it may make a second link less important, in my opinion it has now further disimproved the article (again for no good reason that I can see), by making the maximum 155 break even easier to miss, as it's now tucked away at the back of a bullet point that appears to be about a 151 break. As mentioned earlier I think this 155 break, the only reported case of a maximum 155, was arguably already getting less prominence than it deserved, and now this has been made significantly worse. Tlhslobus (talk) 00:43, 7 May 2013 (UTC)
 * I have now fixed reference, grammar, punctuation, and wording problems in your single-bullet-point amendment, but, as already mentioned, I think the single-bullet-point amendment disimproves the article. So I still want to bring back the version I had (2 bullet points each linking to his bio, along with the wording changes that I've added to properly reflect the citation). This would possibly require either your agreement or arbitration if I wish to avoid the impression of edit-warring. Meanwhile I would appreciate an answer to my above argument about the single-bullet-point being a disimprovement in the hope of avoiding having to think about going to arbitration. Tlhslobus (talk) 02:56, 7 May 2013 (UTC)
 * No, it isn't a "disimprovement" to the article. Also if it were to be split back to two bullets, than Cope's name should still not be linked, as it's already linked 2-3 rows above (depending the resolution of your monitor). Armbrust The Homunculus 10:48, 7 May 2013 (UTC)

My apologies, as I've now discovered and read WP:OVERLINK, and it seems you are right, as it states: Generally, a link should appear only once in an article, but if helpful for readers, links may be repeated in infoboxes, tables, image captions, footnotes, and at the first occurrence after the lead. I should add that I still think this is quite likely to be inconsiderate, inconvenient, and irritating to many readers, especially those with poor eyesight, etc, (and, for all I know, may well some day get Wikipedia sued for institutional discrimination against such people, perhaps rightly so), but this is not the place for such a discussion, and in any case I may well be completely wrong. Meanwhile I'm making the change below, which satisfies WP:OVERLINK, but which I thought up as a possible compromise even before finding WP:OVERLINK. If you don't like it, please feel free to revert it, or modify it as you see fit. I saw the format below as a possible compromise, because it has only one link to his bio, but in a harder-to-miss position, and relates the two breaks as if in a single bullet point, while giving greatly increased visibility to his 'maximum 155' :

 * Jamie Cope's 151 and 'maximum 155' breaks:
 * In April 2003 Jamie Cope made a 151 break at The Reardon Snooker Club during a practice game with David Fomm-Ward. After a foul by his opponent, Cope was snookered behind the brown ball. He took the brown as the free ball and then potted the blue, 13 reds with blacks and two with pinks, then the six colours.
 * It was also reported that Cope made snooker's first 'maximum 155' break in a witnessed practice frame in the summer of 2005.

Once again, my apologies.Tlhslobus (talk) 07:33, 8 May 2013 (UTC)

televised?
Can there be a video of an untelevised break? Nergaal (talk) 20:28, 2 March 2014 (UTC)
 * Of course it can. A streamed match isn't necessarily televised. Also a member of the audience at the venue could also make a video. Armbrust The Homunculus 20:33, 2 March 2014 (UTC)

Confusion over the definitions
Some editors seem to be confused over what counts as an official maximum or not, so I will attempt to clear up that confusion here.

An official/ratified/recognized maximum is basically the same thing: a maximum that was made on a templated table under the standard rules of snooker, officiated by a WSA credited referee. A ratified maximum can also be made in an exhibition match (as was Joe Davis' 1955 maximum) and amateur tournaments.

A maximum made in "professional competition" is any maximum that occurs in a WSA sanctioned tournament for its professional members, or any invitational event that is regarded as a professional event. There is no requirement for the maximum to be ratified. The most famous example of this is John Spencer's 1979 maximum which was officiated in a pro tournament, but not played on templated tables. A recent example was Ronnie O'Sullivan's maximum break at the 2007 Irish Masters which was played on non-templated tables.

The "official" list that is often referred to (and which is included in this article) pertains to ratified maximums in WSA sanctioned professional competition. To this end, O'Sullivan has made 13 maximums in professional competition but only 12 have been ratified, so only twelve are listed here. Betty Logan (talk) 00:53, 4 March 2014 (UTC)

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Is anybody maintaining this list?
It should probably be submitted to WP:FLC. Nergaal (talk) 15:28, 19 December 2016 (UTC)

The current list is consistent with that of the snooker governing body's official record of maximum breaks. http://www.worldsnooker.com/wpbsa/official-147s/ Woodlandscaley (talk) 16:31, 19 December 2016 (UTC)

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Sorting by Player
Becuase of the flagicon placed before the name on the player column, it means that when you try to sort by player you actually end up sorting by nationality as the flagicon precedes the players name (e.g.when you sort by name Neil Robertson is at the top because he is Australian), my solution to this is to put in a nationality colunm and then get rid of the flagicon next to it so then you can sort both by name and nationality, but before I proceed I would like to see if anyone else has any other ideas.

(For the first five rows it would look like this)

SSSB (talk) 19:05, 26 April 2018 (UTC)

 * I have never noticed that before! The alternative is to use a hidden sort key like at Snooker world ranking points 2017/2018. That might be simpler than overhauling the table. Obviously, having nationalities in their own column would give us the option of sorting the table by player or nationality. I am completely fine with either solution, but it definitely needs to be fixed. Betty Logan (talk) 19:20, 26 April 2018 (UTC)
 * My only worry would be the width of the table. It might be too wide for many devices without a considerable amount of wrapping. Nigej (talk) 20:05, 28 April 2018 (UTC)

 * Just use slag
 * Or even hs in front of the current flag icon, with the first three or so characters of the players' surnames. That'll fix it, and you could then remove the (now deprecated sortname template at the same time.  The Rambling Man (talk) 20:14, 28 April 2018 (UTC)

decider
means 17th frame out of a max 17. Nergaal (talk) 20:28, 2 May 2018 (UTC)
 * We all know what a "decider" is Nergaal, but this is unnecessary because the deciding frames are already marked out in the Round column. Betty Logan (talk) 21:55, 2 May 2018 (UTC)
 * Ah, completely missed the D. That's a weird way to mark it up, but I guess it does it job. Nergaal (talk) 00:12, 3 May 2018 (UTC)

What is going on
I'm not sure what's going on this page. Lot's of well-meaning edits but are they for the better? The "official list" section is now a complete disaster. Sorting on the "player" or "opponent" produces a dogs-dinner of a sort. Better to return to it's old state. Nigej (talk) 13:30, 16 May 2018 (UTC)
 * I have reverted the main table to the old style, pending agreement on the style to be used. See "Sorting by Player" section above, for discussion. Nigej (talk) 06:04, 18 May 2018 (UTC)

Youngest player to compile a maximum
This article——backed up by the source at Snooker Archive—states that Judd Trump is the record-holder, at the age of 14 years 206 days at the Potters Under-16 Tournament in 2004. However, Guinness World Records backed up by the WPBSA states it is Sean Maddocks, at the age of 15 years and 90 days at the LITEtask Pro-Am Series in 2017. It also states that O'Sullivan is the previous record-holder. So how should we play this? I am assuming that Snooker Archive is not mistaken, and the oversight is probably down to the fact that Guinness World Records can only award records when there is enough evidence to corroborate them. I am reluctant to scrub Trump from the list purely on the basis his 147 has not been corroborated by Guinness so are there any thoughts on how to approach this? (pinging ) Betty Logan (talk) 02:17, 19 June 2018 (UTC)
 * Can of worms all this. I note that http://www.snooker.org/plr/records.shtml says "The youngest to score a competitive maximum was Judd Trump (b. Aug 1989) at 14 yr 206 days in an under-16 series match against Chris Piech at the Potters Club in Coalville on 13 Mar 2004. (Not recognised by Guinness World Records as it wasn't an open-age competition)" Honestly can't see why it should not be acceptable to us. It continues "The official Guinness Book of World Records holder is Stean Maddocks from Liverpool, England. He was 15 yr 90 days old when he made the max on 8 July 2017, during a last 32 match against Jake Nicholson at the LITEtask Pro-Am Series in Leeds, England. Source: WPBSA. Ronnie O'Sullivan (b. 5 Dec 1975) made a maximum at 15 yr 98 days during the English Amateur Championship (Southern Area) at Aldershot, Hants on 13 Mar 1991." Judd Trump says "Trump was English Under-13 and Under-15 champion, and reached the World Under-21 Championship semi-finals at the age of 14. At the same age, he became the youngest player to make a competitive 147, beating Jamie Jones's record." although the ref given says "In 2004, aged 14 years and 208 days, he became the youngest player to make a competitive maximum 147 break, beating the record set by Ronnie O'Sullivan in 1991." So that's confusing too. The Jamie Jones maximum is doubtful I think. The ref in Jamie Jones (snooker player) is broken and unclear anyway. See http://news.bbc.co.uk/2/hi/uk_news/wales/2619551.stm which refers to "Jamie Jones was having a casual game with a friend in his local club" which is clearly not competitive in any real sense (assuming this is the one referred to). https://www.bbc.com/sport/snooker/32390374 says "Jamie Jones was the youngest player to make a maximum break when he scored 147 at the age of 14, a record since broken by Judd Trump." but doesn't mention the word "competitive". In summary: I would keep the Trump maximum, refer to the Maddocks and O'Sullivan ones and ignore the Jones one (as being non-competitive, pending further information). The Trump and Jones articles and perhaps others need to be updated too, to have a consistent story. Nigej (talk) 05:23, 19 June 2018 (UTC)
 * would be correct if the 13 March 2004 date is correct, not 14 years and 208 days as mentioned in one ref above. Nigej (talk) 05:27, 19 June 2018 (UTC)

Why?
On diagram max=11 in 2012, but not 11 on Y ordinate? GennadyL (talk) 19:30, 14 August 2018 (UTC)
 * The person who created this graph wasn't too precise, I'm afraid. 7 in 2014 when there should be 8. 2 in 1987, 1 in 1988 when it should be the other way round. Nigej (talk) 19:52, 14 August 2018 (UTC)

Why????!
Why can't I stop gifs at Wikipedia? I can't read the article because of the PowerPoint presentation on the top right side. 93.140.114.168 (talk) 19:58, 30 August 2018 (UTC)
 * In my browser (Vivaldi) the GIF plays once and then stops. I have just checked and this is controllable in the settings (i.e. my options are Loop/Once/Off). I would be surprised if this wasn't true of all browsers. Google will probably tell you how to do it. I can fully appreciate why you find it distracting but since we don't have an actual video of a maximum then it does illustrate the basic idea for anyone unfamiliar with snooker. Betty Logan (talk) 06:02, 1 September 2018 (UTC)
 * In Chrome you have to add an accessibility feature called "Animation Policy", this adds a lightning-bolt icon to the address bar which lets you control the Animation Policy. All a bit complicated. No idea why you browser would stop you reading the article because it had an animation in it. Nigej (talk) 08:56, 1 September 2018 (UTC)

Ratified?
Our main list is headed "Ratified maximum breaks achieved in professional competition" but none of the references seems to mention the word "ratified". The WPBSA list calls them "official". "Ratified" used to be used in situations where records were claimed in a variety of conditions and an official went along afterwards and checked that everything was bona fide and that the table was legal, pocket size, table size, etc. Presumably this doesn't happen nowadays in most cases, since most events are organised by World Snooker. Nigej (talk) 21:18, 30 December 2018 (UTC)
 * I suspect this was simply used as a way to not have to say "official". I'd just change this  Lee Vilenski (talk • contribs) 09:03, 31 December 2018 (UTC)
 * Probably right. "Official" really relates to them being made in official events. In reality the 147s become "official" when the last black is potted. There is no ratification process. Nigej (talk) 10:14, 31 December 2018 (UTC)
 * Well, I suppose that's a little bit presumptuous. Official is the right word here, but saying that they couldn't be retroactively ruled non-official is unlikely. O'Sullivan was DQed from an event he had won; so I don't see why -in the super unlikely event of another disqualification they could go back and deny it being a maximum. I'm sure the same thing could happen with a match fixing scandal etc.
 * It's all pretty mute, as it's not something that's ever happened, and the word "official" would cover this as well, and if it were to happen, we would document it.  Lee Vilenski (talk • contribs) 10:48, 31 December 2018 (UTC)
 * Your right. The difference is that in the old days everything was unratified until it was ratified but now its the other way round, everything's official unless its overturned and made unofficial. Nigej (talk) 12:22, 31 December 2018 (UTC)

New image
Am I the only one who finds the new image (with the coloured balls and numbers) completely pointless? Nigej (talk) 11:11, 1 January 2019 (UTC)
 * No. And even if other editors want to keep it it will have to be re-positioned because it currently looks atrocious. Betty Logan (talk) 22:55, 1 January 2019 (UTC)
 * I'd make the argument that it currently shows nothing, so it may be worth contacting someone about how much leinency there would be with copyright issues here.  Lee Vilenski (talk • contribs) 23:06, 1 January 2019 (UTC)

Looking a little closer, I was surprised to find that the image dates back to 2013 and was not created by the editor who added it here. Currently I've just shrunk it so it's not so intrusive, but I still find it useless. Nigej (talk) 07:44, 2 January 2019 (UTC)

Fastest maximum
There has been some recent edits by an editor removing important contextual information regarding the timing of the fastest maximum.

For 20 years the record was officially acknowledged as 5 minutes and 20 seconds and this time is widely documented everywhere, including Guinness World Records. However, it has recently come to light that this time was incorrect. The reason this mistake was made because the broadcaster times snooker breaks and World Snooker makse no provision for timing a break, except the one they introduced under the timed Premier League format. This was discussed in detail at Talk:Ronnie_O'Sullivan where the wording was discussed and chosen.

When this matter came to light World Snooker offered two plausible timing methodologies: the first being that timing starts when the player plays his first shot (resulting in a time of 5 minutes and 8 seconds), and the one used in the Premier League that the break time starts with the shot time (resulting in a time of 5 minutes and 15 seconds (see https://deadspin.com/the-greatest-break-in-snooker-history-was-even-better-t-1794695566). World Snooker retrospectively revised the record to 5 minutes and 8 seconds. They are perfectly entitled to select the criteria for the break time but there are some important caveats:
 * 1) This is revisionist. The record has been retrospectively created, and another time was accepted as the "standard" up until last year.
 * 2) The rules of snooker still make no provisions for timing a break so other broadcasters may deploy different timing techniques.
 * 3) The only timing method actually sanctioned in match-play by World Snooker is the one used in timed tournaments such as the Shoot-Out/defunct Premier League where the break starts when the shot starts. This means that if someone makes a 5 min 10 sec break in the Shoot-Out it may actually be faster than O'Sullivan's 5 min 8 sec break, using the different timing methodology.

For all of these reasons it is important to provide the context. Not just because the timing technique is is not universal and there are at least two different timing methodologies accepted by World Snooker, but also to be consistent with WP:NPOV. Betty Logan (talk) 00:01, 28 March 2019 (UTC)

Televised
Can anyone tell me what the definition of a "televised" maximum is. There is a video available for David Gilbert's 147th 147 which has a commentary but was apparently not "televised". I'm worried that it is not really a well-defined concept nowadays. Nigej (talk) 07:22, 4 April 2019 (UTC)
 * Well, televised basically means that round of the tournament was carried by a broadcaster. Obviously this excludes internet broadcasts which have sprouted up in the last decade. The distinction used to matter: there was obviously a huge difference between making a max on the BBC and making one in a cubicle at Pontins, but I think what you are asking is whether this is a purely arbitrary distinction to make these days? My own view is that the distinction is now a historical artefact and no longer matters because the nature of the sport has now changed so much. We are just lagging in our coverage of it. If you are explicitly asking me if I think we should remove the distinction I would support that. Betty Logan (talk) 12:05, 4 April 2019 (UTC)
 * The word "televised" could mean shown live on TV, but it could also cover maximums that were recorded and shown later. And does it also cover the internet, eg Eurosport Player? I'm thinking that the two tables in the "Televised maximum breaks" section can go, as being overly detailed for something that's not well defined. Nigej (talk) 13:06, 4 April 2019 (UTC)
 * "Televised" as I understand it actually means the televised stages carried by a broadcaster. Basically before Barry Hearn came along the WSA used to award the 147 prize only at the televised stages of an event, and this is what was used to define a televised maximum. So, if you made a maximum at at a BBC tournament in the televised stage (but you were on the back-stage table that was not televised) then that was a televised maximum. In fact, you could make a 147 in a qualifier hold-over match on BBC prime time and it wouldn't qualify for the maximum prize because it was not made at the "televised stage". If a tournament was carried by Eurosport but was only shown on the eurosport player then the 147 prize was still awarded. So the definition was very clear back then. Isn't this still the case now, though? For example, does the 147 prize not roll-over for televised tournaments, but excluded for qualifiers, or can you win the 147 prize at any stage these days? Betty Logan (talk) 13:18, 4 April 2019 (UTC)
 * I see what you say and it seems to apply to the high break prize. However our table seems to use a different definition. Bingham's maximum in last year's China Open (no. 138) is not down as a televised maximum, although Ronnie's (no. 137, the day before) is. Nigej (talk) 13:24, 4 April 2019 (UTC)
 * If that is the case it seems editors have misunderstood the criteria (which to be fair isn't their fault because it has never been clearly explained). I agree that the distinction has more or less been dissolved now, since virtually every match is broadcast in some form these days. If you are suggesting we scrap the distinction I am happy to support that proposal. Ultimately a maximum on a templated table in pro competition is no different to any other, regardless of whether a TV camera is present. Betty Logan (talk) 16:38, 4 April 2019 (UTC)

I have removed the two stats tables relating to "televised" maximums. I'll leave the other references to "televised" for now. There was a comment "Note that internet streaming is not the same as television coverage." at the top of the two tables. Nigej (talk) 06:44, 5 April 2019 (UTC)
 * I always assumed that "Televised" would be similar to the word "broadcast" in this regard. Best Wishes,  Lee Vilenski (talk • contribs) 08:11, 5 April 2019 (UTC)
 * True, but it doesn't help me decide whether something streamed live or perhaps recorded and then shown later is televised/broadcast. And even if we had a precise definition - where do we find a reference for each maximum: https://www.wpbsa.com/about/records/147-breaks/ makes no mention of the concept. Nigej (talk) 08:17, 5 April 2019 (UTC)

I have removed the distinction from the "official list". Renerpho (talk) 11:07, 6 August 2020 (UTC)

Sourcing issues
You recently overhauled the article which resulted in two problems. The first issue is the removal of the "multiple maximums" table on the grounds it was "completely unsourced". I don't agree with this assessment. It is true the table does not provide inline citations but the information contained within it is fully sourced through the primary table at the top, which provides the sources for each and every pro maximum. I have restored the table for now because at worst this is a citation issues not a sourcing issue; the citation issue can be easily addressed by replicating sources in the primary table if you insist on the citation being included here. Personally I don't think we need to reproduce them, but if you believe it is necessary I have no problem with undertaking this work myself. If you have another reason besides his for removing the table then ideally it should be discussed.

The second issue is the removal of the flag icons from the primary table. I have absolutely no problem with you enforcing WP:FLAGCRUFT but as with the multiple maximums table, the "maximum breaks by territory" table was sourced through it. Removing the flags now makes this table unverifiable. There are several possible solutions to this: i) add the countries back to the primary table (but without the flags); ii) add sources to the territory table; iii) remove the territories table. The problem needs to be addressed in some way so that the information in the table can be corroborated. Betty Logan (talk) 20:20, 6 August 2020 (UTC)
 * Hi - I hope you are well. Yeah, I am a bit of a stickler for cutting out cruft, and I can see how it might seem like a bit of a purge! I think my main issue is that we are creating tables, with no citations actually talking about something, and we are the ones creating the statistics for it, rather than following what RSs are commenting on. The multiple maximums per tournament isn't so bad, but is there any proof this is a something that is encyclopedic, rather than just good info for us?

 * The per territory table is the epitome of this, I can't imagine anyone really talking about how many maximums each country has made? I think that's doubly true in that we can only verify it by adding our own nationalities to a table. I'm a bit ambivalent about the multiple maximum tables, but the territory one seems like severe table cruft to me. Best Wishes,  Lee Vilenski (talk • contribs) 20:29, 6 August 2020 (UTC)
 * I hope you are keeping well and enjoying the WC! The only two tables in the article that are statistically logged by reliable sources are the primary list of maximums, and the number of maximums each player makers. The remaining three tables are not unencyclopedic per se but they are compiled by us. By this I mean it is often noted by the snooker press if there is more than one maximum at an event, and if a maximum is made to win a match that is often noted too. Likewise, if a player from a new country makes it a maximum it is often reported that "...is the first player from Poland to compile a 147 in professional competition etc". But as far as I am aware these are not statistical records that tracked and compiled, just simply noted as exceptional occurrences. Betty Logan (talk) 23:17, 6 August 2020 (UTC)

Split lists into separate article
It would seem reasonable to split out the many lists into List of maximum breaks (which currently redirects here). Thoughts? wjematherplease leave a message... 10:55, 14 September 2020 (UTC)
 * If we split it out there would only be a few paragraphs left in the article. I think there is porbbaly a good argument for renaming the article to List of maximum breaks because that is essentially what it is, but I don't see much value in splitting out content. The content left over wouldn't be a viable article. Betty Logan (talk) 11:06, 14 September 2020 (UTC)
 * No sure I agree with Betty Logan's comments. If we move the list and the statistics sections out, there's still plenty of stuff left behind. Nigej (talk) 11:34, 14 September 2020 (UTC)
 * I don't really get what you would get from a split. The article isn't even close to long enough to require being in two parts. Best Wishes,  Lee Vilenski (talk • contribs) 11:39, 14 September 2020 (UTC)
 * The problem as I see it, is that the article is becoming dominated by lists of statistics, which are ever growing and creating a WP:UNDUE/WP:NOTSTATS issue. This would be resolved by splitting. wjematherplease leave a message... 15:01, 14 September 2020 (UTC)
 * Or we could just remove some of the Cruft entirely? I'm not sure what benefit we have from having a separate article for the list. Best Wishes,  Lee Vilenski (talk • contribs) 16:36, 14 September 2020 (UTC)
 * Yes, that would also alleviate the issue – not sure where you draw the line with a list of all officially recognised maximums though; seems like an all or (almost) nothing deal. To be clear, my view is that both the list and statistics sections are problematic, being a distinct sub-topic that is starting to overwhelm the main subject. wjematherplease leave a message... 17:33, 14 September 2020 (UTC)

Proposed removal of gif
I'm a huge fan of Ronnie O'Sullivan, but I really think the gif at the top of the page should be removed. It is only annoying, and I have to scroll fast by it to avoid having a seizure. Mrloop (talk) 15:48, 28 October 2020 (UTC)
 * If you are not speaking proverbially and have a genuine medical condition most browsers have a setting that permit you to disable it. I agree it is distracting (and full disclosure here, I added it to the article) but it is not possible to convey a 147 through a still image. If you are not familiar with the game of snooker then the animation allows to get a quick grasp of the basic principle. I think for that reason alone we should retain it in the article, although I am receptive to suggestions for making it less distracting. For example, does anybody know if there is a way to put it on manual override? Maybe relocate it to a less distracting place in the article? Betty Logan (talk) 23:57, 28 October 2020 (UTC)
 * I suspect we should find ways to make it quicker. I'm sure it's been cut for copyvio reasons, but it seems a little overkill. Perhaps this could be cut in terms of quality, rather than panels, or we could have a computer simulation of this like we do at snooker. I'll have a word with someone who understands FUR better than I. Best Wishes,  Lee Vilenski (talk • contribs) 04:45, 29 October 2020 (UTC)
 * By trying to avoid copyright issues, the result is a fairly poor illustration of both the concept and the break itself – no aspect is clearly being demonstrated and some of the frames even manage to detract and lessen the value of the whole. As you say, I'm sure there are better ways it can be done and I would support removal (from the lead at least – relocating to the relevant section). wjematherplease leave a message... 10:17, 29 October 2020 (UTC)
 * Can it not be converted to compressed video format (WEBM file) so the reader has to actively play the video if they wish to? See this example. I would also vote to put it lower down the article as I don't think it's appropriate for the lead section. Rodney Baggins (talk) 06:49, 30 October 2020 (UTC)

It's awful. Just plain awful. You don't even see the final shot. It fails in its intended purpose of illustrating the feat, and is therefore useless. Seems to me that there's more people in this discussion objecting to its inclusion than supporting it. Therefore I feel safe in removing it. oknazevad (talk) 20:19, 14 February 2022 (UTC)
 * I can add my support for removal too. Nigej (talk) 20:31, 14 February 2022 (UTC)

 * no idea why such a nice animation couldn't be kept at the bottom of the article for those curious about it. keep removing encyclopedic content /s. 2A02:2F0B:B407:BD00:C027:E3F4:FD7C:4983 (talk) 20:07, 4 May 2022 (UTC)

Error in 'A break higher than 147 can be achieved when ...'
Where it reads:

'A break higher than 147 can be achieved when an opponent fouls before any reds are potted, and leaves the incoming player snookered on all 15 reds.'

This is incorrect if it is attempting to refer to the ONLY way a break > 147 can be achieved.

EXAMPLE: If on the break, player 1 rolls the white into the blue, but after hitting the blue the white continues, to rest in a position that means player 2 is not snookered, a free ball is NOT awarded as player 2 is not snookered. With player 2 still receiving the 5-point penalty - player 2 can still achieve a break > 147. 2A00:23C7:FE91:C01:B547:5C0D:2458:AB8D (talk) 12:25, 1 May 2023 (UTC)

Example 2: If on the break player one puts the ball straight into the pocket - player 2 can position the white anywhere within the D .. can certainly see the reds, does NOT therefore have a 'free ball' .. and can theoretically break for > 147 as they start on '4'.

 * Foul points do not count towards the break that follows. A free ball is required to achieve a break over 147. wjematherplease leave a message... 12:52, 1 May 2023 (UTC)

Deleted - I was wrong, no change required here — Preceding unsigned comment added by 2a00:23c7:fe91:c01:e835:c089:50c8:f24c (talk) 12:56, 6 May 2023 (UTC)

Shoot Out
Should Murphy's Shoot Out 147 be included in the "Match-winning maximum breaks" list? Alan  (talk) 19:24, 7 December 2023 (UTC)

 * I see that somebody has already done this.  Alan   (talk) 07:40, 8 December 2023 (UTC)
 * We ought to do what reliable sources do. However, probably this our own work. Seems to be an official 147, even with the variant rules As such it seems logical to include it. Nigej (talk) 08:04, 8 December 2023 (UTC)

Breaks exceeding 155
The Official WPBSA Rules of Snooker very clearly allow for the, however unlikely, event of a legal break exceeding 155 points. All you need to understand this is to combine the, already presented in this article, circumstances which would lead to a break of over 147 points (but only up to 155 points on their own) with Rule (d) on page 22 of the Rulebook: https://wpbsa.com/wp-content/uploads/Rulebook-Website-Updated-May-2022-2.pdf Kenway 135 (talk) 12:44, 11 December 2023 (UTC)

 * What you say may well be true, however one obstacle again it's inclusion is that Wikipedia works on the principle of Verifiability, not truth. See also No original research which says that "On Wikipedia, original research means material—such as facts, allegations, and ideas—for which no reliable, published source exists." So we'd need to see "reliable sources" that have discussed this issue is some detail. Even then I'm very doubtful about it being suitable. OK its possible if a player potted 100 blacks in a row which got re-spotted but there was some sort of mass delusion so that no-one noticed that they hadn't potted a red in between. However I don't really think this sort of idea is suitable for inclusion here. Nigej (talk) 13:14, 11 December 2023 (UTC)
 * I very much appreciate you taking your time to properly respond to me, although you did compare my "theory" to a far, far more absurd example. I don't know what else to do at this point - I still maintain that, while obviously my scenario is not described word-for-word in the Rulebook, it's still all there. Anyway, I might be able to get in contact with a top snooker referee, one who is actually credited in the Rulebook, and sort this out (at least for myself, since I don't know how I'd be able to "cite" what the referee tells me since I imagine it would be in person). Kenway 135 (talk) 13:25, 11 December 2023 (UTC)
 * I'd be curious to hear what a referee has to say about this, but as you noted, that still wouldn't make it suitable for Wikipedia. Your argument relies on combining two different rules, which is a textbook example of WP:SYNTH. As long as the rulebook doesn't explicitly state that those two rules can actually apply together (and that the result may be as described), we can't be sure that's even true in practice (not to mention the issue of verifiability).
 * The example presented by Nigej is indeed absurd, and not really relevant to the question. It is quite different from the example of an accidentally added 16th red ball, as described in the section removed by Nigej. You don't need mass delusion for that. Color blindness would suffice. I don't know if something like this could ever conceivably happen, but the more interesting question is how it would be dealt with. Alas, Wikipedia is not a snooker forum, so if we can't establish that this is relevant, we better discuss it somewhere else. Renerpho (talk) 14:27, 17 December 2023 (UTC)

Mark Williams 151 in practice play?
The article mentions breaks higher than 147 that were achieved in practice. The breakboard at the Mark Williams Snooker Club in Tredegar states that Mark Williams holds the record for the highest break achieved at the club, a 151. Renerpho (talk) 14:12, 17 December 2023 (UTC)

 * This section seems to be growing such that it's probably time to remove such instances in practice frames (retaining the 155s). Really no encyclopedic value. Nigej (talk) 14:22, 17 December 2023 (UTC)
 * Could you provide evidence that the section has considerably expanded recently? Renerpho (talk) 14:28, 17 December 2023 (UTC)
 * Outside of a true maximum, practice frames are rarely important, unless it's something specific  Lee Vilenski (talk • contribs) 12:13, 31 December 2023 (UTC)
 * I didn't say it had "considerably expanded recently". However its the nature of these that they do grow over time, or maybe instances just get left out (as here). I really don't see the point in wasting effort maintaining such a list for practice frames. Nigej (talk) 14:54, 31 December 2023 (UTC)

167
Rules have changed for some tournaments. This page needs to reflect this. https://www.bbc.co.uk/sport/snooker/68027678 146.90.251.136 (talk) 19:45, 19 January 2024 (UTC)

 * The source you provide clearly refers in the headline to a "167 break possible" (no mention of maximum) and later says "Games will follow current rules but with a 23rd "Riyadh Season ball" pottable on completing a maximum break.". In order words the "maximum break" comes first and the 20 point "Riyadh Seaon ball" comes after that. We already have situations where breaks of over 147 are possible and indeed do happen occasionally but the "maximum break" remains at 147. 19:51, 19 January 2024 (UTC) Nigej (talk) 19:51, 19 January 2024 (UTC)
 * No source to my knowledge mentions this being a maximum break, and more to the point, this ridiculous 167 is actually being referred to as a different set of rules (similar to power snooker) than being part of the official ruleset.  Lee Vilenski (talk • contribs) 19:54, 19 January 2024 (UTC)
 * The BBC reference says: "It is not clear at this stage if the ball will be on the table throughout the game, if there will be any penalty for hitting it too early or what a player gains for potting it other than extra points in an already-won frame." At best it's a "maximum break" under varied rules and outside of the scope of this article (similarly, we do not include the maximum break in Snooker Plus). It does not change the fact that a "maximum break" is 147, not 167. AmethystZhou (talk) 19:55, 19 January 2024 (UTC)

Multiple maximum breaks during a tournament
Seems to me that this section is getting ludicrously large and has very little interest. I'd suggest reducing the list to those events with 3 maximums, together with an introductory sentence about the first event to have 2. Nigej (talk) 17:24, 29 February 2024 (UTC)

 * Agreed. Maybe also mention Mark Davis making two maximums at the 2017 Championship League. AmethystZhou (talk) 20:53, 29 February 2024 (UTC)
 * It is already mentioned at Maximum_break. I'm not sure we need to say it twice, to be honest.. Betty Logan (talk) 04:55, 2 March 2024 (UTC)
 * Indeed, pretty much all the "Multiple maximum breaks during a tournament" section is a duplicate of that one, perhaps indicating that it could go completely, with suitable additions to the ."Multiple maximums" section. Nigej (talk) 08:49, 2 March 2024 (UTC)
 * Good point - but I like the table. Maybe move the table into the "Multiple maximums" section, and delete the "Multiple maximum breaks during a tournament" section.  Alan   (talk) 10:14, 2 March 2024 (UTC)
 * Also agreed. Much better.  Alan   (talk) 12:34, 1 March 2024 (UTC)
 * Now that I've added the three 147s made at the Championship League to the "Multiple maximums" section, it seems to me that you are right and the "Multiple maximum breaks during a tournament" section should be deleted. The table is nice, but since it only has three rows it's probably better in prose. The text about John Parrott and Stephen Hendry at the 1992 Matchroom League would need to be retained though, perhaps moved into the "Multiple maximums" section.  Alan   (talk) 11:29, 17 March 2024 (UTC)
 * Agreed. Nigej (talk) 14:27, 17 March 2024 (UTC)
 * Done.  Alan   (talk) 15:11, 17 March 2024 (UTC)

Standardised reference names
For information: I have renamed all of the citations in the main table to try to standardise them. Most of them are not re-used but it makes sense to have them named anyway. The ones that are re-used makes it easy to find cross-references. For instance, all of the citations in the "Match-winning maximum breaks" section are now re-used from the main table, as are many in the article's prose. Some entries (15 as of 29 March) still need suitable citations. For these I have used as a default, which points to this archive. These 15 entries are numbers: 3, 15, 21, 24, 27, 28, 33, 35, 36, 45, 57, 64, 65, 66, and 69. If anyone can find suitable citations for any of these, please put them in place of the default. All of the names use the form  except where two entries use the same citation, in which case I have used . Alan  (talk) 15:29, 29 March 2024 (UTC)

 * ...also note that there is an archived citation at the top of the main table called "WPBSA_Official_List", which points to this list. The WPBSA keep this list pretty-much up-to-date and so the archived version will become out-of-date and will need to be re-archived from time to time. It was last archived on 27 March and is therefore up-to-date for now.  Alan   (talk) 16:23, 29 March 2024 (UTC)
 * Both WPBSA and WST archives updated on 16 April.  Alan   (talk) 08:30, 16 April 2024 (UTC)
 * ...also, please do not be tempted to use the brilliant scripts Reference Renamer or Reference Organizer, both of which will want to remove all of the names which have not yet been re-used.  Alan   (talk) 21:11, 29 March 2024 (UTC)

title: Talk:Maximum break


text:
Talk:Locomotion

Do skiing or skating count here? Does it matter whether you actually use ski or not (you can ski or skate without ski or skates, it's just difficult). If ski were vehicles, skiing would be a form of transport, not locomotion. No.

Science what part biological body conductive locomotion
Saan po bang parti ng katawan nabilang ang locomotion 120.28.192.56 (talk) 09:13, 20 January 2022 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Locomotion


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Hilbert–Pólya conjecture

In mathematics, the Hilbert–Pólya conjecture states that the non-trivial zeros of the Riemann zeta function correspond to eigenvalues of a self-adjoint operator. It is a possible approach to the Riemann hypothesis, by means of spectral theory.

History
In a letter to Andrew Odlyzko, dated January 3, 1982, George Pólya said that while he was in Göttingen around 1912 to 1914 he was asked by Edmund Landau for a physical reason that the Riemann hypothesis should be true, and suggested that this would be the case if the imaginary parts t of the zeros
 * $$ \tfrac12 + it $$

of the Riemann zeta function corresponded to eigenvalues of a self-adjoint operator. The earliest published statement of the conjecture seems to be in.

David Hilbert did not work in the central areas of analytic number theory, but his name has become known for the Hilbert–Pólya conjecture due to a story told by Ernst Hellinger, a student of Hilbert, to André Weil. Hellinger said that Hilbert announced in his seminar in the early 1900s that he expected the Riemann Hypothesis would be a consequence of Fredholm's work on integral equations with a symmetric kernel.

1950s and the Selberg trace formula
At the time of Pólya's conversation with Landau, there was little basis for such speculation. However Selberg in the early 1950s proved a duality between the length spectrum of a Riemann surface and the eigenvalues of its Laplacian. This so-called Selberg trace formula bore a striking resemblance to the explicit formulae, which gave credibility to the Hilbert–Pólya conjecture.

1970s and random matrices
Hugh Montgomery investigated and found that the statistical distribution of the zeros on the critical line has a certain property, now called Montgomery's pair correlation conjecture. The zeros tend not to cluster too closely together, but to repel. Visiting at the Institute for Advanced Study in 1972, he showed this result to Freeman Dyson, one of the founders of the theory of random matrices.

Dyson saw that the statistical distribution found by Montgomery appeared to be the same as the pair correlation distribution for the eigenvalues of a random Hermitian matrix. These distributions are of importance in physics — the eigenstates of a Hamiltonian, for example the energy levels of an atomic nucleus, satisfy such statistics. Subsequent work has strongly borne out the connection between the distribution of the zeros of the Riemann zeta function and the eigenvalues of a random Hermitian matrix drawn from the Gaussian unitary ensemble, and both are now believed to obey the same statistics. Thus the Hilbert–Pólya conjecture now has a more solid basis, though it has not yet led to a proof of the Riemann hypothesis.

Later developments
In 1998, Alain Connes formulated a trace formula that is actually equivalent to the Riemann hypothesis. This strengthened the analogy with the Selberg trace formula to the point where it gives precise statements. He gives a geometric interpretation of the explicit formula of number theory as a trace formula on noncommutative geometry of Adele classes.

Possible connection with quantum mechanics
A possible connection of Hilbert–Pólya operator with quantum mechanics was given by Pólya. The Hilbert–Pólya conjecture operator is of the form $$\tfrac{1}{2}+iH$$ where $$H$$ is the Hamiltonian of a particle of mass $$m$$ that is moving under the influence of a potential $$V(x)$$. The Riemann conjecture is equivalent to the assertion that the Hamiltonian is Hermitian, or equivalently that $$V$$ is real.

Using perturbation theory to first order, the energy of the nth eigenstate is related to the expectation value of the potential:

 * $$ E_{n}=E_{n}^{0}+ \left. \left \langle \varphi^{0}_n \right | V \left | \varphi^{0}_n \right. \right \rangle $$

where $$E^{0}_n$$ and $$\varphi^{0}_n$$ are the eigenvalues and eigenstates of the free particle Hamiltonian. This equation can be taken to be a Fredholm integral equation of first kind, with the energies $$E_n$$. Such integral equations may be solved by means of the resolvent kernel, so that the potential may be written as

 * $$ V(x)=A\int_{-\infty}^{\infty} \left (g(k)+\overline{g(k)}-E_{k}^{0} \right )\,R(x,k)\,dk $$

where $$R(x,k)$$ is the resolvent kernel, $$A$$ is a real constant and

 * $$ g(k)=i \sum_{n=0}^{\infty} \left(\frac{1}{2}-\rho_n \right)\delta(k-n) $$

where $$\delta(k-n)$$ is the Dirac delta function, and the $$\rho_n$$ are the "non-trivial" roots of the zeta function $$\zeta (\rho_n)=0 $$.

Michael Berry and Jonathan Keating have speculated that the Hamiltonian H is actually some quantization of the classical Hamiltonian xp, where p is the canonical momentum associated with x The simplest Hermitian operator corresponding to xp is
 * $$\hat{H} = \tfrac1{2} (\hat{x}\hat{p}+\hat{p}\hat{x}) = - i \left( x \frac{\mathrm{d}}{\mathrm{d} x} + \frac1{2} \right).$$

This refinement of the Hilbert–Pólya conjecture is known as the Berry conjecture (or the Berry–Keating conjecture). As of 2008, it is still quite far from being concrete, as it is not clear on which space this operator should act in order to get the correct dynamics, nor how to regularize it in order to get the expected logarithmic corrections. Berry and Keating have conjectured that since this operator is invariant under dilations perhaps the boundary condition f(nx) = f(x) for integer n may help to get the correct asymptotic results valid for large n
 * $$ \frac{1}{2} + i \frac{ 2\pi n}{\log n}. $$

A paper was published in March 2017, written by Carl M. Bender, Dorje C. Brody, and Markus P. Müller, which builds on Berry's approach to the problem. There the operator

 * $$\hat{H} = \frac{1}{1-e^{-i\hat{p}}} \left (\hat{x}\hat{p}+\hat{p}\hat{x} \right ) \left (1-e^{-i\hat{p}} \right )$$

was introduced, which they claim satisfies a certain modified versions of the conditions of the Hilbert–Pólya conjecture. Jean Bellissard has criticized this paper, and the authors have responded with clarifications. Moreover, Frederick Moxley has approached the problem with a Schrödinger equation.

title: Hilbert–Pólya conjecture


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Die (manufacturing)

A die is a specialized machine tool used in manufacturing industries to cut and/or form material to a desired shape or profile. Stamping dies are used with a press, as opposed to drawing dies (used in the manufacture of wire) and casting dies (used in molding) which are not. Like molds, dies are generally customized to the item they are used to create.

Products made with dies range from simple paper clips to complex pieces used in advanced technology. Continuous-feed laser cutting may displace the analogous die-based process in the automotive industry, among others.

Die stamping
Blanking and piercing are two die cutting operations, and bending is an example of a die forming operation.

Die forming
Forming operations work by deforming materials like sheet metal or plastic using force (compression, tension, or both) and rely on the material's mechanical properties. Forming dies are typically made by tool and die makers and put into production after mounting into a press.

Differences between materials
For the vacuum forming of plastic sheet only a single form is used, typically to form transparent plastic containers (called blister packs) for merchandise. Vacuum forming is considered a simple molding thermoforming process but uses the same principles as die forming.

For the forming of sheet metal, such as automobile body parts, two parts may be used: one, called the punch, performs the stretching, bending, and/or blanking operation, while another part that is called the die block securely clamps the workpiece and provides a similar stretching, bending, and/or blanking operation. The workpiece may pass through several stages using different tools or operations to obtain the final form. In the case of an automotive component, there will usually be a shearing operation after the main forming is done. Additional crimping or rolling operations may be performed to ensure that all sharp edges are hidden and/or to add rigidity to the panel.

Die components
The main components of a die set (including press mounting) are as follows. Note that because nomenclature varies between sources, alternate names are in parentheses:

 * Die shoes (holders) – the set of flat, parallel plates that serve as the foundation for mounting die components.
 * Guide pins (pillars) – together with guide bushings, the pins align the die shoes precisely during each press stroke.
 * Die set (plates). Note: placement can be inverted depending on the operation, such as use of a knock-out:
 * Die block – the lower (bottom) half of the die set. Machined to conform to the desired shape of the workpiece being formed or cut.
 * Punch plate – the upper (top) half of the die set. Holds and supports the different punches in place.
 * Punch – male portion of the die which punches through the sheet metal and into the corresponding (female) section of the die block. More specifically:
 * Blanking punch – performs a dual-purpose operation where either a profiled slug, called the blank, is cut out and used for further working, or where a finished piece is cut free from the sheet metal.
 * Pierce punch – cuts a desired shape (circular, polygonal, etc.) out of the workpiece. The slug is discarded.
 * Stripper plate (pad) – spring-loaded plate that separates (i.e., strips) the workpiece from the withdrawing punch after each press stroke.
 * Pilot – This will help to place the sheet accurately for the next stage of operation.
 * Stock guide – ensures that the material being worked on always goes in the same position, within the die, as the last one.
 * Setting (stop) block – This part is used to control the depth that the punch goes into the die.
 * Shank – installs the punch plate to the press. It should be aligned and situated at the center of gravity of the plate.

Process

 * Blanking: A blanking die produces a flat piece of material by cutting the desired shape in one operation. The finished part is referred to as a blank. Generally a blanking die may only cut the outside contour of a part, often used for parts with no internal features. Three benefits to die blanking are:
 * 1) Accuracy. A properly sharpened die, with the correct amount of clearance between the punch and die, will produce a part that holds close dimensional tolerances in relationship to the part's edges.
 * 2) Appearance. Since the part is blanked in one operation, the finish edges of the part produces a uniform appearance as opposed to varying degrees of burnishing from multiple operations.
 * 3) Flatness. Due to the even compression of the blanking process, the result is a flat part that may retain a specific level of flatness for additional manufacturing operations.
 * Broaching: The process of removing material through the use of multiple cutting teeth, with each tooth cutting behind the other. A broaching die is often used to remove material from parts that are too thick for shaving.
 * Bulging: A bulging die expands the closed end of tube through the use of two types of bulging dies. Similar to the way a chef's hat bulges out at the top from the cylindrical band around the chef's head.
 * 1) Bulging fluid dies: Uses water or oil as a vehicle to expand the part.
 * 2) Bulging rubber dies: Uses a rubber pad or block under pressure to move the wall of a workpiece.
 * Coining: is similar to forming with the main difference being that a coining die may form completely different features on either face of the blank, these features being transferred from the face of the punch or die respectively. The coining die and punch flow the metal by squeezing the blank within a confined area, instead of bending the blank. For example, an Olympic medal that was formed from a coining die may have a flat surface on the back and a raised feature on the front. If the medal was formed (or embossed), the surface on the back would be the reverse image of the front.
 * Compound operations: Compound dies perform multiple operations on the part. The compound operation is the act of implementing more than one operation during the press cycle.
 * Compound die: A type of die that has the die block (matrix) mounted on a punch plate with perforators in the upper die with the inner punch mounted in the lower die set. An inverted type of blanking dies that punches upwards, leaving the part sitting on the lower punch (after being shed from the upper matrix on the press return stroke) instead of blanking the part through. A compound die allows the cutting of internal and external part features on a single press stroke.
 * Curling: The curling operation is used to roll the material into a curved shape. A door hinge is an example of a part created by a curling die.
 * Cut off: Cut off dies are used to cut off excess material from a finished end of a part or to cut off a predetermined length of material strip for additional operations.
 * Drawing: The drawing operation is very similar to the forming operation except that the drawing operation undergoes severe plastic deformation and the material of the part extends around the sides. A metal cup with a detailed feature at the bottom is an example of the difference between formed and drawn. The bottom of the cup was formed while the sides were drawn.
 * Extruding: Extruding is the act of severely deforming blanks of metal called slugs into finished parts such as an aluminum I-beam. Extrusion dies use extremely high pressure from the punch to squeeze the metal out into the desired form. The difference between cold forming and extrusion is extruded parts do not take shape of the punch.
 * Forming: Forming dies to bend the blank along a curved surface. An example of a part that has been formed would be the positive end(+) of a AA battery.
 * Cold forming (cold heading): Cold forming is similar to extruding in that it squeezes the blank material but cold forming uses the punch and the die to create the desired form, extruding does not.
 * Roll forming: a continuous bending operation in which sheet or strip metal is gradually formed in tandem sets of rollers until the desired cross-sectional configuration is obtained. Roll forming is ideal for producing parts with long lengths or in large quantities.
 * Horning: A horning die provides an arbor or horn in which the parts are placed for secondary operations.
 * Hydroforming: Forming of tubular part from simpler tubes with high water pressure.
 * Pancake die: A Pancake die is a simple type of manufacturing die that performs blanking and/or piercing. While many dies perform complex procedures simultaneously, a pancake die may only perform one simple procedure with the finished product being removed by hand.
 * Piercing: The piercing operation is used to pierce holes in stampings.
 * Transfer die: Transfer dies provide different stations for operations to be performed. A common practice is to move the material through the die so it is progressively modified at each station until the final operation ejects a finished part.
 * Progressive die: The sheet metal is fed through as a coil strip, and a different operation (such as punching, blanking, and notching) is performed at the same station of the machine with each stroke of a series of punches.
 * Punching:
 * Shaving: The shaving operation removes a small amount of material from the edges of the part to improve the edges finish or part accuracy. (Compare to Trimming).
 * Side cam die: Side cams transform vertical motion from the press ram into horizontal or angular motion.
 * Sub press operation: Sub-press dies blank and/or form small watch, clock, and instrument parts.
 * Swaging: Swaging (necking) is the process of "necking down" a feature on a part. Swaging is the opposite of bulging as it reduces the size of the part. The end of a shell casing that captures the bullet is an example of swaging.
 * Trimming: Trimming dies cut away excess or unwanted irregular features from a part, they are usually the last operation performed.
 * Pillar set: Pillar set are used for alignment of dies in press movement.

Steel-rule die
Steel-rule die, also known as cookie cutter dies, are used for cutting sheet metal and softer materials, such as plastics, wood, cork, felt, fabrics, and paperboard. The cutting surface of the die is the edge of hardened steel strips, known as steel rule. These steel rules are usually located using saw or laser-cut grooves in plywood. The mating die can be a flat piece of hardwood or steel, a male shape that matches the workpiece profile, or it can have a matching groove that allows the rule to nest into. Rubber strips are wedged in with the steel rule to act as the stripper plate; the rubber compresses on the down-stroke and on the up-stroke it pushes the workpiece out of the die. The main advantage of steel-rule dies is the low cost to make them, as compared to solid dies; however, they are not as robust as solid dies, so they are usually only used for short production runs.

Rotary die
In the broadest sense, a rotary die is a cylindrical shaped die that may be used in any manufacturing field. However, it most commonly refers to cylindrical shaped dies used to process soft materials, such as paper or cardboard. Two rules are used, cutting and creasing rules. This is for corrugated boards whose thickness is more than 2 mm. Rotary dies are faster than flat dies.

The term also refers to dies used in the roll forming process.

Wire pulling
Wire-making dies have a hole through the middle of them. A wire or rod of steel, copper, other metals, or alloy enters into one side and is lubricated and reduced in size. The leading tip of the wire is usually pointed in the process. The tip of the wire is then guided into the die and rolled onto a block on the opposite side. The block provides the power to pull the wire through the die.

The die is divided into several different sections. First is an entrance angle that guides the wire into the die. Next is the approach angle, which brings the wire to the nib, which facilitates the reduction. Next is the bearing and the back relief. Lubrication is added at the entrance angle. The lube can be in powdered soap form. If the lubricant is soap, the friction of the drawing of wire heats the soap to liquid form and coats the wire. The wire should never actually come in contact with the die. A thin coat of lubricant should prevent the metal to metal contact.

For pulling a substantial rod down to a fine wire a series of several dies is used to obtain progressive reduction of diameter in stages.

Standard wire gauges used to refer to the number of dies through which the wire had been pulled. Thus, a higher-numbered wire gauge meant a thinner wire. Typical telephone wires were 22-gauge, while main power cables might be 3- or 4-gauge.

title: Die (manufacturing)


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Asymptotic freedom

In quantum field theory, asymptotic freedom is a property of some gauge theories that causes interactions between particles to become asymptotically weaker as the energy scale increases and the corresponding length scale decreases. (Alternatively, and perhaps contrarily, in applying an S-matrix, asymptotically free refers to free particles states in the distant past or the distant future.)

Asymptotic freedom is a feature of quantum chromodynamics (QCD), the quantum field theory of the strong interaction between quarks and gluons, the fundamental constituents of nuclear matter. Quarks interact weakly at high energies, allowing perturbative calculations. At low energies, the interaction becomes strong, leading to the confinement of quarks and gluons within composite hadrons.

The asymptotic freedom of QCD was discovered in 1973 by David Gross and Frank Wilczek, and independently by David Politzer in the same year. For this work all three shared the 2004 Nobel Prize in Physics.

Discovery
Asymptotic freedom in QCD was discovered in 1973 by David Gross and Frank Wilczek, and independently by David Politzer in the same year. The same phenomenon had previously been observed (in quantum electrodynamics with a charged vector field, by V.S. Vanyashin and M.V. Terent'ev in 1965; and Yang–Mills theory by Iosif Khriplovich in 1969 and Gerard 't Hooft in 1972 ), but its physical significance was not realized until the work of Gross, Wilczek and Politzer, which was recognized by the 2004 Nobel Prize in Physics.

Experiments at the Stanford Linear Accelerator showed that inside protons, quarks behaved as if they were free. This was a great surprise, as many believed quarks to be tightly bound by the strong interaction, and so they should rapidly dissipate their motion by strong interaction radiation when they got violently accelerated, much like how electrons emit electromagnetic radiation when accelerated.

The discovery was instrumental in "rehabilitating" quantum field theory. Prior to 1973, many theorists suspected that field theory was fundamentally inconsistent because the interactions become infinitely strong at short distances. This phenomenon is usually called a Landau pole, and it defines the smallest length scale that a theory can describe. This problem was discovered in field theories of interacting scalars and spinors, including quantum electrodynamics (QED), and Lehmann positivity led many to suspect that it is unavoidable. Asymptotically free theories become weak at short distances, there is no Landau pole, and these quantum field theories are believed to be completely consistent down to any length scale.

Electroweak theory within the Standard Model is not asymptotically free. So a Landau pole exists in the Standard Model. With the Landau pole a problem arises when Higgs boson is being considered. Quantum triviality can be used to bound or predict parameters such as the Higgs boson mass. This leads to a predictable Higgs mass in asymptotic safety scenarios. In other scenarios, interactions are weak so that any inconsistency arises at distances shorter than the Planck length.

Screening and antiscreening

The variation in a physical coupling constant under changes of scale can be understood qualitatively as coming from the action of the field on virtual particles carrying the relevant charge. The Landau pole behavior of QED (related to quantum triviality) is a consequence of screening by virtual charged particle–antiparticle pairs, such as electron–positron pairs, in the vacuum. In the vicinity of a charge, the vacuum becomes polarized: virtual particles of opposing charge are attracted to the charge, and virtual particles of like charge are repelled. The net effect is to partially cancel out the field at any finite distance. Getting closer and closer to the central charge, one sees less and less of the effect of the vacuum, and the effective charge increases.

In QCD the same thing happens with virtual quark-antiquark pairs; they tend to screen the color charge. However, QCD has an additional wrinkle: its force-carrying particles, the gluons, themselves carry color charge, and in a different manner. Each gluon carries both a color charge and an anti-color magnetic moment. The net effect of polarization of virtual gluons in the vacuum is not to screen the field but to augment it and change its color. This is sometimes called antiscreening. Getting closer to a quark diminishes the antiscreening effect of the surrounding virtual gluons, so the contribution of this effect would be to weaken the effective charge with decreasing distance.

Since the virtual quarks and the virtual gluons contribute opposite effects, which effect wins out depends on the number of different kinds, or flavors, of quark. For standard QCD with three colors, as long as there are no more than 16 flavors of quark (not counting the antiquarks separately), antiscreening prevails and the theory is asymptotically free. In fact, there are only 6 known quark flavors.

Calculating asymptotic freedom
Asymptotic freedom can be derived by calculating the beta-function describing the variation of the theory's coupling constant under the renormalization group. For sufficiently short distances or large exchanges of momentum (which probe short-distance behavior, roughly because of the inverse relationship between a quantum's momentum and De Broglie wavelength), an asymptotically free theory is amenable to perturbation theory calculations using Feynman diagrams. Such situations are therefore more theoretically tractable than the long-distance, strong-coupling behavior also often present in such theories, which is thought to produce confinement.

Calculating the beta-function is a matter of evaluating Feynman diagrams contributing to the interaction of a quark emitting or absorbing a gluon. Essentially, the beta-function describes how the coupling constants vary as one scales the system $$x \rightarrow bx$$. The calculation can be done using rescaling in position space or momentum space (momentum shell integration). In non-abelian gauge theories such as QCD, the existence of asymptotic freedom depends on the gauge group and number of flavors of interacting particles. To lowest nontrivial order, the beta-function in an SU(N) gauge theory with $$n_f$$ kinds of quark-like particle is

 * $$\beta_1(\alpha) = { \alpha^2 \over \pi} \left( -{11N \over 6} + {n_f \over 3} \right) $$

where $$\alpha$$ is the theory's equivalent of the fine-structure constant, $$g^2/(4 \pi)$$ in the units favored by particle physicists. If this function is negative, the theory is asymptotically free. For SU(3), one has $$N = 3,$$ and the requirement that $$\beta_1 < 0 $$ gives
 * $$n_f < {33 \over 2}.$$

Thus for SU(3), the color charge gauge group of QCD, the theory is asymptotically free if there are 16 or fewer flavors of quarks.

Besides QCD, asymptotic freedom can also be seen in other systems like the nonlinear $$\sigma$$-model in 2 dimensions, which has a structure similar to the SU(N) invariant Yang–Mills theory in 4 dimensions.

Finally, one can find theories that are asymptotically free and reduce to the full Standard Model of electromagnetic, weak and strong forces at low enough energies.

title: Asymptotic freedom