Live and recent posts from across the Fediverse tagged #sieveoferatosthenes, aggregated by home.social.
Opus 5 - High-res PNG (slight offset from the origin):
The base case: the natural numbers - the weight sheet is the sieve of Eratosthenes
#decompwlj #math #graph #AI #Anthropic #Claude #Opus #Opus5 #mathematics #sequence #natural #numbers #NaturalNumbers #sieveOfEratosthenes #NumberTheory #sieve #arithmetic #classification #decomposition
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition
We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. Applied to prime numbers this decomposition leads to a new classification of primes.
#decompwlj #math #mathematics #maths #sequence #OEIS #graph #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #SieveofEratosthenes #sieve #Eratosthenes #fundamental #theorem #arithmetic #research
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition
We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. Applied to prime numbers this decomposition leads to a new classification of primes.
#decompwlj #math #mathematics #maths #sequence #OEIS #graph #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #SieveofEratosthenes #sieve #Eratosthenes #fundamental #theorem #arithmetic #research
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification #decomposition
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to #decompwlj
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
#math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to #decompwlj
The weight is unique:
"The weight is unique. Minimality pins it. There is no choice of parameter anywhere in Definition 1 — no window, no threshold, no cut-off. This is what makes the construction worth studying at all: it is a canonical map, and the objects it produces are invariants of the sequence."
Proof of Conjecture 9:
"This is the framework's native question: it cannot even be asked without the coordinates, and it has an answer."
The atlas as an instrument:
"About a thousand OEIS sequences have been decomposed and published at https://decompwlj.com. Today that is an archive. It could be an instrument."
Opus 5 Max: A pedagogical treatise for Graduate / researcher new to the decomposition into weight × level + jump ➡️ https://decompwlj.com/Opus5_decompwlj_pedagogical_treatise_9th_edition_2026_08_16.html
#decompwlj #math #AI #Anthropic #Claude #Opus #Opus5 #mathematics #OEIS #sequence #numbers #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification
My favorite Fable 5 report, the 7th edition:
Conjecture ledger and primes graph:
Fable 5 - 7th edition ➡️ https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
For privacy ➡️ https://web.archive.org/web/20260806034509/https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
#decompwlj #math #AI #Anthropic #Claude #Fable #Fable5 #mathematics #OEIS #sequence #numbers #graph #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification
My favorite Fable 5 report, the 7th edition:
Conjecture ledger and primes graph:
Fable 5 - 7th edition ➡️ https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
For privacy ➡️ https://web.archive.org/web/20260806034509/https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
#decompwlj #math #AI #Anthropic #Claude #Fable #Fable5 #mathematics #OEIS #sequence #numbers #graph #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification
My favorite Fable 5 report, the 7th edition:
Conjecture ledger and primes graph:
Fable 5 - 7th edition ➡️ https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
For privacy ➡️ https://web.archive.org/web/20260806034509/https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
#decompwlj #math #AI #Anthropic #Claude #Fable #Fable5 #mathematics #OEIS #sequence #numbers #graph #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification
My favorite Fable 5 report, the 7th edition:
Conjecture ledger and primes graph:
Fable 5 - 7th edition ➡️ https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
For privacy ➡️ https://web.archive.org/web/20260806034509/https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
#decompwlj #math #AI #Anthropic #Claude #Fable #Fable5 #mathematics #OEIS #sequence #numbers #graph #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification
We see the fundamental theorem of arithmetic and the sieve of Eratosthenes in the decomposition into weight × level + jump of natural numbers. Applied to prime numbers this decomposition leads to a new classification of primes.
#decompwlj #math #mathematics #maths #sequence #OEIS #graph #numbers #primes #PrimeNumbers #FundamentalTheoremOfArithmetic #sequences #NumberTheory #classification #integer #decomposition #number #theory #equation #graphs #SieveofEratosthenes #sieve #Eratosthenes #fundamental #theorem #arithmetic #research
My favorite Fable 5 report, the 7th edition:
Conjecture ledger and primes graph:
Fable 5 - 7th edition ➡️ https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
For privacy ➡️ https://web.archive.org/web/20260806034509/https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
#decompwlj #math #AI #Anthropic #Claude #Fable #Fable5 #mathematics #OEIS #sequence #numbers #graph #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification
My favorite Fable 5 report, the 7th edition:
Conjecture ledger and primes graph:
Fable 5 - 7th edition ➡️ https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
For privacy ➡️ https://web.archive.org/web/20260806034509/https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
#decompwlj #math #AI #Anthropic #Claude #Fable #Fable5 #mathematics #OEIS #sequence #numbers #graph #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #conjecture #graph #sieveOfEratosthenes #FundamentalTheoremOfArithmetic #classification
My favorite Fable 5 report, the 7th edition:
Conjecture ledger and primes graph:
Fable 5 - 7th edition ➡️ https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
For privacy ➡️ https://web.archive.org/web/20260806034509/https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
#decompwlj #math #AI #Anthropic #Claude #Fable #Fable5 #mathematics #OEIS #sequence #numbers #graph #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #sieveOfEratosthenes
My favorite Fable 5 report, the 7th edition:
Conjecture ledger and primes graph:
Fable 5 - 7th edition ➡️ https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
For privacy ➡️ https://web.archive.org/web/20260806034509/https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
#decompwlj #math #AI #Anthropic #Claude #Fable #Fable5 #mathematics #OEIS #sequence #numbers #graph #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #sieveOfEratosthenes
My favorite Fable 5 report, the 7th edition:
Conjecture ledger and primes graph:
Fable 5 - 7th edition ➡️ https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
For privacy ➡️ https://web.archive.org/web/20260806034509/https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
#decompwlj #math #AI #Anthropic #Claude #Fable #Fable5 #mathematics #OEIS #sequence #numbers #graph #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #sieveOfEratosthenes
GPT5.6 Sol: "If decompwlj became a standard mathematical lens"
The most important conceptual impact would be a change of question. Instead of asking only, “What is the next term?” or “How fast does the sequence grow?”, researchers could also ask:
How does the next additive jump expose—or hide—the multiplicative structure behind the present term?
That is a legitimate and surprisingly rich question.
https://decompwlj.com/GPT5.6Sol_decompwlj_counterfactual_impacts_report_2026-08-11.html
#decompwlj #math #AI #OpenAI #ChatGPT #GPT #GPT56Sol #GPTSol #sequence #numbers #graph #PrimeNumbers #NumberTheory #arithmetic #threejs #FTA #classification #research #FundamentalTheoremOfArithmetic #TwinPrimes #twin #primes #conjecture #sieveOfEratosthenes #Eratosthenes #sieve
My favorite Fable 5 report, the 7th edition:
Conjecture ledger and primes graph:
Fable 5 - 7th edition ➡️ https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
For privacy ➡️ https://web.archive.org/web/20260806034509/https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
#decompwlj #math #AI #Anthropic #Claude #Fable #Fable5 #mathematics #OEIS #sequence #numbers #graph #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #sieveOfEratosthenes
My favorite Fable 5 report, the 7th edition:
Conjecture ledger and primes graph:
Fable 5 - 7th edition ➡️ https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
For privacy ➡️ https://web.archive.org/web/20260806034509/https://decompwlj.com/Fable5_decompwlj_deep_analysis_7th_edition_2026_08_05.html
#decompwlj #math #AI #Anthropic #Claude #Fable #Fable5 #mathematics #OEIS #sequence #numbers #graph #PrimeNumbers #NumberTheory #sieve #arithmetic #threejs #research #sieveOfEratosthenes