-
@ 7f5c2b4e:a818d75d
2025-05-12 17:04:10
You could get him one under a condition he figures out how to set up Graphene on it 😄
-
@ 296842ea:ac34c17e
2025-05-12 17:03:07
feeling it 🧬✨
-
@ 68c90cf3:99458f5c
2025-05-12 17:02:28
I’m logged in with my npub and see my own notes and articles. If I use my nsec will I see my follows’ notes? If so it would be great to use a browser extension.
-
@ 9c5d062a:2b672b5f
2025-05-12 17:03:49
Trump hopeful for Russia-Ukraine talks
https://www.rt.com/news/617434-trump-russia-ukraine-talks/?utm_source=rss&utm_medium=rss&utm_campaign=RSS
-
@ 7f5c2b4e:a818d75d
2025-05-12 17:02:14
Why? Whatcha gonna do when it’s ATH?
And please don’t say “sell” — I won’t believe you anyways 😉
-
@ 9c5d0669:d516c048
2025-05-12 17:03:08
Who are the hostages believed to still be alive in Gaza?
https://www.washingtonpost.com/world/2025/05/12/hamas-gaza-remaining-israel-hostages/
-
@ 1ae011cb:1257a556
2025-05-12 17:00:55
Block 896433
19 - high priority
14 - medium priority
10 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 9c5d04b8:b5b2cb2c
2025-05-12 17:02:43
Car similar to Bryan Kohberger's seen near victims' home multiple times just before alleged killings: Report
https://www.foxnews.com/us/car-similar-bryan-kohbergers-seen-near-victims-home-multiple-times-just-before-alleged-killings-report
-
@ cbab7074:f9f0bd61
2025-05-12 17:00:55
Block 896433
19 - high priority
14 - medium priority
10 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ e7bf8dad:839ef3db
2025-05-12 17:00:55
Block 896433
19 - high priority
14 - medium priority
10 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 9c5d0714:798b2576
2025-05-12 17:02:05
Why Apple's Stock Is Surging Today
https://finance.yahoo.com/news/why-apples-stock-surging-today-162209767.html
-
@ 7f5c2b4e:a818d75d
2025-05-12 17:00:52
Ok, so media feed on Nostur got me a bit confused. Being used to latest posts being actually fresh just made me wish Derek a good night while it’s not late enough for where he is to go to sleep.
Only after posting I noticed his post is 14h old.
Been using Nostr for years now, yet I again and again re-realize that paying attention is super important on Nostr.
nostr:nevent1qqsyz3uyr6cmu2lzy37wk97ss6x9n3w82rghyu60lwfa4a0vfq3fdaqzypl4c26wfzswnlk2vwjxky7dhqjgnaqzqwvdvz3qwz5k3j4grrt46qcyqqqqqqgpr3mhxue69uhksctkv4hz6ar0deujuv33d9jx2ctn9ehhyecc0w20v
-
@ 9c5d0714:798b2576
2025-05-12 17:02:02
Nvidia Stock Continued to Rally Today. Why It's Not Too Late to Buy.
https://finance.yahoo.com/news/nvidia-stock-continued-rally-today-162405943.html
-
@ 71ecabd8:e4885975
2025-05-12 17:00:00
https://smartflowsocial.s3.us-east-1.amazonaws.com/clients/cm7kdrwdk0000qyu6fwtd96ui/8516f528-ad83-432b-80b1-7131131cb0dc.jpg
-
@ 9c5d006c:e0e4eeb7
2025-05-12 17:02:01
The U.S. doesn’t want ‘generalized decoupling’ from China, but a strategic break instead, Treasury secretary says
https://fortune.com/2025/05/12/us-china-tariffs-trump-trade-war-strategic-decoupling-scott-bessent/
-
@ f03df3d4:a4d4f676
2025-05-12 16:55:55
Block 896433
14 - high priority
12 - medium priority
9 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 9c5d0714:798b2576
2025-05-12 17:01:59
The 2 Best Stocks to Invest $1,000 in Right Now
https://finance.yahoo.com/news/2-best-stocks-invest-1-163000893.html
-
@ 7f5c2b4e:a818d75d
2025-05-12 16:55:51
🌸
-
@ 9c5d006c:e0e4eeb7
2025-05-12 17:01:58
Nick Jonas has invested in Olipop, Snackpass, and Magic Spoon—he says he won’t back a founder without a killer story
https://fortune.com/2025/05/12/multimillionaire-nick-jonas-investing-advice-red-flag-olipop-magic-spoon-snackpass/
-
@ 7f5c2b4e:a818d75d
2025-05-12 16:55:30
GN Derek. Have a good rest — big things await you tomorrow ✊
-
@ 63fe6318:330504ed
2025-05-12 15:26:47
Pushed a new version of zap.stream v0.2.2, lots of important stuff done today!
-Chat message parsing (links / mentions)
-Chat message zaps / reactions
-Chat modal (long press) for zaps / reactions / mute
-Top zappers
-Login with key
-Create new basic account
https://github.com/nostrlabs-io/zap-stream-flutter/releases/tag/v0.2.2
-
@ b133bfc5:49d5789d
2025-05-12 16:55:28
https://image.nostr.build/52f3371d87b7d36831b963b4f42b27f50ae3d9f28ec7059daaf78bfc7f4f7237.jpg
nostr:note1t3rt5afz6u5vy3zkeu5lmn20acf6z2vlpeeyzlyxq39yw6kre9yq7ssvfx
-
@ 9c5d0714:798b2576
2025-05-12 17:01:56
Monday.com's High-Paying Customers Rise 38%, Improves Operating Margin
https://finance.yahoo.com/news/monday-coms-high-paying-customers-164818266.html
-
@ 9c5d0714:798b2576
2025-05-12 17:01:53
Hong Kong's CK Hutchison assures legal compliance in ports deal
https://finance.yahoo.com/news/hong-kongs-ck-hutchison-assures-164902353.html
-
@ d662c10f:78d039af
2025-05-12 16:54:30
🌺
-
@ 9c5d0d56:c73ddeca
2025-05-12 16:58:48
UK police investigating fire at PM Starmer’s private home
https://globalnews.ca/news/11175589/keir-starmer-private-home-fire-investigation/
-
@ 43baaf0c:d193e34c
2025-05-12 17:04:59
https://i.nostr.build/L3vLU85fykIo4Z3d.jpg
-
@ 9c5d04b8:b5b2cb2c
2025-05-12 16:58:24
Fox News goes inside New Jersey ICE facility stormed by Democrats
https://www.foxnews.com/media/fox-news-goes-inside-new-jersey-ice-facility-stormed-democrats
-
@ 7f5c2b4e:a818d75d
2025-05-12 16:52:55
This ☝️
-
@ 9c5d04b8:b5b2cb2c
2025-05-12 16:58:21
Michael Jordan to join NBC as 'special contributor' for NBA coverage
https://www.foxnews.com/sports/michael-jordan-join-nbc-special-contributor-nba-coverage
-
@ 55e343e6:880acd1b
2025-05-12 16:52:11
want another prediction? 😂 zuck’s a genius and sneaky as hell. he knows bitcoin adoption is happening fast. he’ll be the first to plug bitcoin into all his platforms and he’ll capitalize on it harder than anyone ever will.
-
@ 9c5d04b8:b5b2cb2c
2025-05-12 16:58:18
British police investigate fire at Prime Minister Keir Starmer's London home
https://www.foxnews.com/world/british-police-investigate-fire-prime-minister-starmers-london-home
-
@ 9c5d0c59:e4e08fb8
2025-05-12 16:57:58
Crates full of Nazi documents found in Argentine court's basement
https://www.bbc.com/news/articles/c1w3jlqlp27o
-
@ c860325a:9efad850
2025-05-12 17:04:55
LFG ! Am in this one !
And hey there .. this is Anucools from X
Nice to meet you here 👋
-
@ e13cb9dd:e8258358
2025-05-12 17:04:40
A regulamentação é apenas para calar opositores. Sempre terão liberdade de postar porcaria e propaganda.
-
@ dab9562a:ba18162e
2025-05-12 17:05:00
delivery sys.?
-
@ e7bf8dad:839ef3db
2025-05-12 16:50:55
Block 896433
11 - high priority
10 - medium priority
8 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 3ce2b51d:36fc72c7
2025-05-12 17:05:00
✄------------ 2:05 ------------✄
-
@ f03df3d4:a4d4f676
2025-05-12 16:50:55
Block 896433
11 - high priority
10 - medium priority
8 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ b133bfc5:49d5789d
2025-05-12 16:50:28
I have lots of these
-
@ 3878d95d:f3b45a69
2025-05-12 17:04:33
GM, stay humble, keep workin’ on your hard skillsets.
-
@ f26626a9:6eec3661
2025-05-12 16:49:36
For a typical "worker":
You're going to spend 80000 hours working. Hours & energy in --> stuff out later.
Bitcoin optimises the time between work & reward; nothing works better. So spend 1% early on, 20 weeks, to study this process & build a plan!
-
@ 51bbb15e:b77a2290
2025-05-12 16:36:53
If you think that's fun you might also like KENO.
-
@ 0d8c556f:73dfd4d7
2025-05-12 17:04:42
nevent1qqsz73cs93rd5jxwf08f3agzcu6622fekm6lfe78ngyr4g0rrrldd7qpr3mhxue69uh5ummnw3ezuumhd9ehxtt9de5kwmtp9e3kstca9znzh
-
@ 9c5d0bcc:4787ce5e
2025-05-12 16:54:53
Gaza on edge of famine as Israel conflict escalates: UN report
https://timesofindia.indiatimes.com/world/middle-east/gaza-on-edge-of-famine-as-israel-conflict-escalates-un-report/articleshow/121117089.cms
-
@ 9c5d0ef9:0c5c9988
2025-05-12 16:54:28
Why Trump and the Saudis Are Cozying Up
https://time.com/7284797/trump-middle-east-saudi-trip/
-
@ 9c5d0793:0176d77e
2025-05-12 16:51:33
Iran Rejects 'Unacceptable' US Demand To Dismantle Nuclear Sites
https://www.zerohedge.com/geopolitical/iran-rejects-unacceptable-us-demand-dismantle-nuclear-sites
-
@ e7bf8dad:839ef3db
2025-05-12 16:30:55
Block 896431
17 - high priority
14 - medium priority
11 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 9c5d04b8:b5b2cb2c
2025-05-12 16:49:34
Federal judge's order for Trump to return deported migrant temporarily halted on appeal
https://www.foxnews.com/politics/federal-judges-order-trump-return-deported-migrant-temporarily-halted-appeal
-
@ cbab7074:f9f0bd61
2025-05-12 16:30:55
Block 896431
17 - high priority
14 - medium priority
11 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 832b77d5:a5e3d55c
2025-05-12 17:04:23
🟥SELL BTC for EUR
Price: 89570.53EUR (-3%)
BTC: 0.02 - 0.023
EUR: 1791 - 2060
Method: SEPA
Created: 2025-05-12T17:02:05Z
-
@ 9c5d04b8:b5b2cb2c
2025-05-12 16:49:31
Naomi Judd's widower confirms late singer shot a gun at him after learning about his infidelity
https://www.foxnews.com/entertainment/naomi-judds-widower-confirms-late-singer-shot-gun-him-after-learning-about-his-his-infidelity
-
@ 16d76f26:dac92856
2025-05-12 17:04:21
Alice in wonderland.
https://image.nostr.build/97ea3e20b51ea7c885e9d3476893d5c3c0664b09cf8d3559f4a526031c47449c.jpg
nostr:note1cct66v0rxuyzduejfff3ns5ak5qk7nhmted7earszg38pz8wuk3s3zckg9
-
@ e7bf8dad:839ef3db
2025-05-12 16:27:44
Block 896431
16 - high priority
14 - medium priority
11 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 9c5d04b8:b5b2cb2c
2025-05-12 16:49:28
Three natural food dyes approved by FDA as RFK Jr. says industry is 'stepping up'
https://www.foxnews.com/food-drink/three-natural-food-dyes-approved-fda-rfk-jr-industry-stepping-up
-
@ f768fae9:91b11cdd
2025-05-12 17:04:20
#バズワードランキング
1位: #语法: (15)
2位: #〖主人 (9)
3位: #ケバブ (8)
4位: #いい (7)
5位: #ぷく (7)
6位: #おもち (6)
7位: #もち (5)
8位: #画像 (5)
9位: #寝言 (4)
10位: #感じ (4)
-
@ f03df3d4:a4d4f676
2025-05-12 16:20:55
Block 896430
21 - high priority
18 - medium priority
14 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 9c5d0714:798b2576
2025-05-12 16:48:44
Consumer Stocks Pop After US-China Trade War Eases
https://finance.yahoo.com/news/consumer-stocks-pop-us-china-160007611.html
-
@ 51bbb15e:b77a2290
2025-05-12 16:11:02
If they are good it's because they know cash flow is more important.
It's even more important on a Bitcoin standard.
Your Bitcoin will not make more Bitcoin.
-
@ 9c5d0714:798b2576
2025-05-12 16:48:41
Why Railroad Stocks Are Moving Higher Today
https://finance.yahoo.com/news/why-railroad-stocks-moving-higher-161513330.html
-
@ e7bf8dad:839ef3db
2025-05-12 15:40:55
Block 896424
41 - high priority
37 - medium priority
31 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 9c5d0714:798b2576
2025-05-12 16:48:38
HistoSonics secures first insurance coverage for histotripsy system
https://finance.yahoo.com/news/histosonics-secures-first-insurance-coverage-164238878.html
-
@ f03df3d4:a4d4f676
2025-05-12 15:35:55
Block 896423
47 - high priority
43 - medium priority
36 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 9c5d0669:d516c048
2025-05-12 16:45:28
Gaza faces ‘critical’ famine risk, experts say, as Israel blocks aid
https://www.washingtonpost.com/world/2025/05/12/gaza-famine-report-looting/
-
@ cbab7074:f9f0bd61
2025-05-12 15:30:55
Block 896423
45 - high priority
40 - medium priority
33 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 9c5d011f:fc5bb983
2025-05-12 16:45:23
Hamas Frees Edan Alexander, American Hostage Held in Gaza, in Deal With U.S.
https://www.nytimes.com/2025/05/12/world/middleeast/edan-alexander-israel-hamas-hostage-released.html
-
@ 9c5d0674:181409e0
2025-05-12 16:43:38
MSI to unveil desktop AI supercomputer at Computex 2025, powered by Nvidia DGX
https://www.tomshardware.com/desktops/mini-pcs/msi-to-unveil-desktop-ai-supercomputer-at-computex-2025-powered-by-nvidia-dgx
-
@ 9c5d0bcc:4787ce5e
2025-05-12 16:41:38
Pope Leo XIV urges release of jailed journalists as Zelensky invites to Ukraine
https://timesofindia.indiatimes.com/world/europe/pope-leo-xiv-urges-release-of-jailed-journalists-as-zelensky-invites-to-ukraine/articleshow/121116941.cms
-
@ 9c5d0b12:1a292b27
2025-05-12 16:40:39
A power outage disrupts London's subway network
https://abcnews.go.com/International/wireStory/power-outage-disrupts-londons-subway-network-121716084
-
@ efe5d120:1fc51981
2025-05-12 16:48:40
All these treasury companies feel like a race to remove as much bitcoin from circulation, trying to make sure its used only for NgU instead od permissionless payments.
At least we will see how many billions(trillions?) stopping p2p cash is worth.
-
@ 9c5d04b8:b5b2cb2c
2025-05-12 16:40:38
Paulina Gretzky watches as Panthers tie playoff series with Maple Leafs
https://www.foxnews.com/sports/paulina-gretzky-watches-panthers-tie-playoff-series-maple-leafs
-
@ ecf46816:55bbc75a
2025-05-12 16:48:24
So disheartening to see the stratospheric aerosol injections in the sky everywhere. People should be way more upset about these insane programs dumping god knows how many metric tons of toxic materials into the sky.
-
@ 90a81209:07a835be
2025-05-12 16:47:48
🚀BTC MARKET VENDOR🚀 - May 17th @gwrnoda nostr:nprofile1qyghwumn8ghj7nn0wd68ytnhd9hx2tcppemhxue69uhkummn9ekx7mp0qqsqlyznaqu2dqdkpjql5ptwh5cps780mddntgmara82u6afl2u6dqqpsapwu
nostr:nprofile1qy2hwumn8ghj7etyv4hzumn0wd68ytnvv9hxgqtxwaehxw309anxjmr5v4ezumn0wd68ytnhd9hx2tmwwp6kyvt5dqm8qwp50quh2dtsx3kxzem8d34hvmfc0fjhqcfjv3cngueev4skuup4xamxx635wu6nvdfjddskvctywvmk6wfnxpcn7cnjdaskgcmpwd6r6arjw4jsqgza7sfaf309qd0l2z8anxeckg02ng9vpw0vcd8nxy4t4x4z4h20tv7gtjqj https://blossom.primal.net/ab9f40b33f0bc8b56e512e26e761ec916af469bf96dd9a7ffaa655dfd89bf1de.jpg - Charlotte-based maze artist https://blossom.primal.net/1ad98589e69eb2522d480ec39e12dc63a8f809931800de79127a838ca0845a1b.png https://blossom.primal.net/f46970ac8acb6cd3b0440c16bce140f2b84cc1c58d93cc86d28f83bc4da9e34d.png
-
@ 9c5d0b12:1a292b27
2025-05-12 16:40:36
Denmark takes over as chair of the Arctic Council at a time when Trump eyes Greenland
https://abcnews.go.com/International/wireStory/denmark-takes-chair-arctic-council-time-trump-eyes-121716086
-
@ c7eda660:efd97c86
2025-05-12 16:47:19
Pro tip: don't take financial advice from someone who says "times it."
-
@ 9c5d0b12:1a292b27
2025-05-12 16:40:33
Ringleader in Russian spy ring gets more than 10 years in UK prison
https://abcnews.go.com/International/wireStory/ringleader-russian-spy-ring-gets-10-years-uk-121716381
-
@ f03df3d4:a4d4f676
2025-05-12 16:45:55
Block 896433
10 - high priority
9 - medium priority
7 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 9c5d0714:798b2576
2025-05-12 16:40:15
MicroStrategy Snaps Up More Bitcoin. What the U.S.-China Talks Mean for the Stock.
https://www.barrons.com/articles/microstrategy-stock-bitcoin-china-tariffs-4bd5e8a8?siteid=yhoof2&yptr=yahoo
-
@ 9c5d0714:798b2576
2025-05-12 16:40:12
Retail Stocks Jump on Lower China Tariffs. It Isn’t the ‘All Clear’ Yet.
https://www.barrons.com/articles/retail-stocks-china-tariffs-522961c4?siteid=yhoof2&yptr=yahoo
-
@ d6affa19:9110b177
2025-05-12 16:45:33
gongeous~! ^_^
-
@ 9c5d0714:798b2576
2025-05-12 16:40:09
Bill Ackman’s Long-Shot Bet on Hertz: Should You Ride Along?
https://www.barrons.com/articles/hertz-bill-ackman-tesla-uber-stock-f4827918?siteid=yhoof2&yptr=yahoo
-
@ efe5d120:1fc51981
2025-05-12 16:45:27
Oh no, dont dare to actually use bitcoin! Thats not a pure play, needs to be put into an institutional custodian and never to be seen again, as far away as possible from it becoming a medium of exchange.
-
@ 9c5d0714:798b2576
2025-05-12 16:40:06
Gold Prices Tumble. What the Latest Tariff News Means for Newmont and Other Stocks.
https://www.barrons.com/articles/gold-price-newmont-stock-1827e186?siteid=yhoof2&yptr=yahoo
-
@ c7eda660:efd97c86
2025-05-12 16:45:14
You'll see mine displayed in the background on nostr:npub1trustldqg4fnp40f3g75mu0p03zj4dxpa4jg7dclzqp9g3aunsgs4a4j8j Beautiful piece that I'm delighted to own. nostr:note1v8tqn0wgr6jswwzvy3etdweluezy5c5l5339zqklteh2y4m60nuq3llwvl
-
@ 9c5d0714:798b2576
2025-05-12 16:40:03
Why Nuclear Stocks Constellation Energy, Vistra, and Oklo All Popped This Morning
https://finance.yahoo.com/news/why-nuclear-stocks-constellation-energy-160932635.html
-
@ 9c5d0714:798b2576
2025-05-12 16:40:00
Rivian Stock Gets an Oddly Specific Price-Target Increase. Shares Are Up.
https://www.barrons.com/articles/rivian-stock-price-target-increase-1eec236d?siteid=yhoof2&yptr=yahoo
-
@ d6affa19:9110b177
2025-05-12 16:45:11
#FLR #FemaleLedRelationship #memes #memestr #gfd #grownostr
https://image.nostr.build/d7421bf91566249840772e5d6aa72bd48af5a626202e94eca410d2896e838750.jpg
-
@ 508f2865:a64b2960
2025-05-12 16:45:02
💕💕🥰
#bloomscrolling #flowerstr #photography #nature
https://image.nostr.build/9320cfd61c2466271b738d6600634266e20ef646135c103d4fad5bcb6c5975d7.jpg
-
@ 9c5d0714:798b2576
2025-05-12 16:39:57
Accounting change, higher labor costs drive $3.3B Postal Service loss
https://finance.yahoo.com/news/accounting-change-higher-labor-costs-160052860.html
-
@ 9c5d0714:798b2576
2025-05-12 16:39:54
Stock soars over 600% after surprising new strategy
https://finance.yahoo.com/news/stock-soars-over-600-surprising-162442511.html
-
@ c7eda660:efd97c86
2025-05-12 16:43:48
Madness.
-
@ 665e364f:16310af9
2025-05-12 16:42:05
Because they don't play with their money.
They don't trust themself enough for that.
Like any bank do with people money.
-
@ 9c5d0714:798b2576
2025-05-12 16:39:51
Ramit Sethi Says This Mistake Can Keep You In Debt: 'Ignoring Your Debt Doesn't Make It Go Away'
https://finance.yahoo.com/news/ramit-sethi-says-mistake-keep-163119109.html
-
@ a0f0ad35:2a9c4cff
2025-05-12 16:41:17
Faz 2 então
-
@ b300db32:0bf5db3a
2025-05-12 17:04:17
A relação entre a teoria dos grafos e a conjectura de Collatz é uma conexão fascinante, embora ainda incompleta, que oferece uma estrutura para analisar o comportamento caótico da conjectura por meio de estruturas gráficas. Abaixo, exploramos os principais pontos de contato, desafios e limitações dessa interação:
---
### **1. Representação Gráfica da Conjectura de Collatz**
A conjectura de Collatz pode ser visualizada como um **grafo direcionado infinito**, onde:
- **Nós**: Representam números inteiros positivos.
- **Arestas**: Representam as operações da conjectura:
- Se $ n $ é par, há uma aresta de $ n $ para $ n/2 $.
- Se $ n $ é ímpar, há uma aresta de $ n $ para $ 3n + 1 $.
Esse grafo é conhecido como **grafo de Collatz** e tem como característica central a suposição de que **todos os caminhos eventualmente convergem para o ciclo trivial $ 4 \rightarrow 2 \rightarrow 1 \rightarrow 4 $**. Provar isso equivale a resolver a conjectura.
---
### **2. "Santo Graal" da Relação**
O "santo graal" dessa interação seria **provar a conjectura de Collatz usando propriedades do grafo**, como:
- **Conectividade**: Mostrar que o grafo é fortemente conectado (todos os nós levam a 1).
- **Ausência de ciclos não triviais**: Demonstrar que não existem ciclos além de $ 4 \rightarrow 2 \rightarrow 1 $.
- **Estrutura em árvore**: Confirmar que o grafo forma uma única árvore infinita com raiz em 1.
Esses objetivos exigem técnicas avançadas de teoria dos grafos combinadas com teoria dos números e sistemas dinâmicos.
---
### **3. Pontos de Contato e Influências Recíprocas**
#### **(a) Estrutura do Grafo**
- O grafo de Collatz é uma **árvore inversa** quando invertemos as direções das arestas (ou seja, partindo de 1 e aplicando operações inversas: $ n \rightarrow 2n $ e $ n \rightarrow (n-1)/3 $, se $ n \equiv 4 \mod 6 $).
- Pesquisadores como **Jeffrey Lagarias** usaram essa estrutura para explorar **caminhos inversos** e tentar provar que todos os números estão conectados a 1.
#### **(b) Algoritmos Computacionais**
- Algoritmos de **busca em largura (BFS)** ou **profundidade (DFS)** foram aplicados para verificar a conjectura computacionalmente até grandes números, explorando o grafo de Collatz.
- Exemplo: O projeto **BOINC** (computação distribuída) usa essas técnicas para testar bilhões de números.
#### **(c) Sistemas Dinâmicos e Teoria de Grafos**
- A conjectura pode ser vista como um sistema dinâmico discreto, onde o grafo modela o comportamento assintótico das órbitas dos números.
- Propriedades como **tempo de parada** (número de passos para alcançar 1) e **recorde de voo** (número máximo atingido antes de cair) são analisadas via caminhos no grafo.
#### **(d) Teoria de Complexidade**
- A conjectura levanta questões sobre **complexidade computacional**: por exemplo, se determinar se um número atinge 1 é decidível ou se o grafo possui padrões algorítmicos previsíveis.
---
### **4. Descobertas e Insights Relevantes**
- **Terras (1976)**: Provou que quase todos os números têm tempo de parada finito, usando propriedades estatísticas do grafo.
- **Lagarias (1985)**: Estudou a estrutura do grafo inverso, mostrando que ele cresce exponencialmente, mas com lacunas que precisam ser preenchidas para provar a conjectura.
- **Krasikov e Lagarias (2003)**: Usaram técnicas de análise combinatória para limitar a densidade de números que violariam a conjectura.
---
### **5. Fraquezas e Limitações da Relação**
- **Infinitude do Grafo**: Como o grafo é infinito e não periódico, métodos finitos de teoria dos grafos são insuficientes.
- **Caos Combinatório**: Pequenas mudanças em $ n $ podem gerar caminhos drasticamente diferentes, dificultando a identificação de padrões.
- **Falta de Isomorfismo Útil**: Não há uma relação clara entre propriedades do grafo (como ciclos ou conectividade) e propriedades numéricas (como primalidade ou fatoração).
- **Dependência de Outras Áreas**: Até hoje, a teoria dos grafos não forneceu uma prova independente, sugerindo que a conjectura requer insights de teoria dos números, análise funcional ou até física matemática.
---
### **6. Conclusão**
A interação entre teoria dos grafos e a conjectura de Collatz oferece uma **perspectiva visual e computacional** poderosa, mas enfrenta obstáculos fundamentais devido à complexidade intrínseca do problema. O "santo graal" seria unir ferramentas gráficas a outras disciplinas para finalmente provar (ou refutar) a conjectura, revelando insights profundos sobre a dinâmica de funções aritméticas e sistemas caóticos. Até lá, a relação permanece como um desafio aberto na matemática moderna.
-
@ e7bf8dad:839ef3db
2025-05-12 16:40:55
Block 896433
9 - high priority
8 - medium priority
6 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 36e451bb:163e8ffa
2025-05-12 17:04:17
そろそろ寝ないとヤバいぜ
-
@ f03df3d4:a4d4f676
2025-05-12 16:40:55
Block 896433
9 - high priority
8 - medium priority
6 - low priority
2 - no priority
1 - purging
#bitcoinfees #mempool
-
@ 7cd5f588:02454296
2025-05-12 16:40:14
Peak art of the deal tactic
-
@ 9c5d0714:798b2576
2025-05-12 16:39:48
The Dow, Up 900 Points, Is on Track to Exit Correction
https://www.barrons.com/livecoverage/stock-market-today-051225/card/the-dow-up-900-points-is-on-track-to-exit-correction-Kp47EzeaLrd4raIWjcai?siteid=yhoof2&yptr=yahoo
-
@ 1bd32a38:77a23e69
2025-05-12 17:04:17
Fair nuance. They are changing a longstanding mempool policy, however.