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2026-08-04 |
STANDING |
Independent recomputation of axiom closure adds precision to authors' own honest declarations, and in one case shows a…
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prooftrack |
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2026-08-04 |
STANDING |
The trusted base divides into three tiers: 132 artifacts depend only on the standard kernel axioms, 1 depends on a…
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prooftrack |
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2026-08-02 |
STANDING |
The natural impossibility route is false as stated: 2-robustness does not imply that widely separated triples heal. An…
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prooftrack |
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2026-08-02 |
STANDING |
In this regime a finite horizon scan can establish healing but can never establish killing, because exceptional sets…
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prooftrack |
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2026-08-02 |
STANDING |
Sufficiently dense sequences cannot witness any pair (m,n): they remain complete after any finite removal. This follows…
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prooftrack |
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2026-08-02 |
STANDING |
Any unbounded, weakly m-robust multiset has divergent Brown slack. Consequently, for every fixed finite removal, all…
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prooftrack |
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2026-08-02 |
STANDING |
Whether a given finite removal destroys completeness is decidable for sequences on a Fibonacci-Zeckendorf backbone with…
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prooftrack |
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2026-08-02 |
RETRACTED |
The result withstood four independent adversarial verification passes, each instructed to refute rather than confirm:…
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prooftrack |
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2026-08-02 |
STANDING |
Every n-element set of reals contains a Sidon subset of size at least (sqrt(6)/9 + o(1))*sqrt(n), improving the…
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prooftrack |
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2026-08-02 |
STANDING |
The mechanism is an involution, not the retention of a discarded class: sigma(theta) = 1 - theta swaps the two…
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prooftrack |
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2026-08-02 |
STANDING |
No prior record of this constant was found. The source preprint is v1-only and uncited; the ancestry…
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prooftrack |
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2026-07-31 |
STANDING |
The scoring is reproducible as tiers but not as values: on a blind re-score of a stratified 18-problem sample by a…
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prooftrack |
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2026-07-31 |
STANDING |
Stated frontiers in problem backgrounds decay faster than the backgrounds are updated. Of the four highest-scoring…
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prooftrack |
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2026-07-31 |
STANDING |
A reliability statistic measures random variance and cannot detect a misreading shared by both scorers. The blind pass…
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prooftrack |
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2026-07-31 |
STANDING |
A recurring corpus defect is paraphrase drift rather than mathematical error: problem backgrounds are paraphrases of…
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prooftrack |
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2026-07-31 |
STANDING |
Across 370 proof-shaped Erdos problems scored against each problem's own stated ADVANCES condition, mean reachability…
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prooftrack |
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2026-07-28 |
STANDING |
The minimal linear recurrence of the odd branch has order 8 with integer coefficients $[4, -2, -3, -5, 3, 4, 1, -1]$…
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astro-catalogs |
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2026-07-28 |
STANDING |
Lopez-Bonilla's closed form for odd $n$, $a(n) = L_n + 2\cos(2\pi n/3) + 2 s_n + 2$ with $s_{n+3} = -s_{n+2} - s_n$,…
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astro-catalogs |
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2026-07-28 |
STANDING |
Definition-level enumeration (backtracking on the literal edge set) reproduces ALL 15 published b-file terms of A383733…
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astro-catalogs |
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2026-07-28 |
STANDING |
The odd-branch zero set is $\{7\}$ for ALL odd $n$ (not just the computed range): in the closed form, $L_n \sim…
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astro-catalogs |
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2026-07-28 |
STANDING |
Within $6 \le n \le 3000$ the zero set of A383733 is exactly $\{7, 8, 12, 16\}$: bigint-exact for $n \le 400$ via two…
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astro-catalogs |
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2026-07-28 |
STANDING |
The OEIS entry's comment 'the sequence displays ... recurring zeros for even values of n divisible by 4…
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astro-catalogs |
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2026-07-28 |
STANDING |
This confirms Barker's conjecture decisively over the computed range and establishes minimality there, but is not a…
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astro-catalogs |
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2026-07-28 |
STANDING |
Berlekamp–Massey over $\mathbb{Q}$ applied to the extended sequence yields a minimal recurrence of order exactly 10…
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astro-catalogs |
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2026-07-28 |
STANDING |
The sequence extends to $n = 5000$ ($a(5000)$: 2390 decimal digits) via an $O(N)$ single-sweep evaluation of all four…
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astro-catalogs |
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2026-07-28 |
STANDING |
An independent implementation of A321614's definition (Burnside over the rectangle's Klein four-group on maximum king…
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astro-catalogs |
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2026-07-28 |
STANDING |
Correctness is certified by independent layers: definition-level raw-grid brute force agrees at $n \le 2$; a no-DP…
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astro-catalogs |
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2026-07-28 |
STANDING |
Noe's 2006 record computation is independently re-verified in full: cumulative counts of cluster primes, odd…
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roman-cc |
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2026-07-28 |
STANDING |
The verification chain passes end-to-end at write-up time: './verify.sh' exited 0 — rebuild from source; term-by-term…
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roman-cc |
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2026-07-28 |
STANDING |
The prior published frontier for exhaustive cluster-prime classification was 10^13 (T. D. Noe, 2006: A039506/A039507…
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roman-cc |
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2026-07-28 |
STANDING |
The exhaustive-classification record is extended 15.2% past 10^13 to the certified contiguous frontier…
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roman-cc |
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2026-07-28 |
STANDING |
The artifact is a standing relay (RELAY.md, in the SETI@home spirit): any third party can extend the certified frontier…
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roman-cc |
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2026-07-28 |
STANDING |
For every even m < 1.152e13, the least odd prime k with m + k prime satisfies k(m) <= 4093, with the maximum attained…
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roman-cc |
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2026-07-28 |
STANDING |
Cluster primes remain plentiful but slowly thinning at record heights: per-decade cluster fractions among odd primes…
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roman-cc |
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2026-07-28 |
STANDING |
Every odd prime p < 11,520,000,000,000 was deterministically classified as cluster or non-cluster: 396,722,129,482 odd…
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roman-cc |
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2026-07-28 |
STANDING |
Exhaustive enumeration: for all $4\le n\le 5\times10^6$ and all $2\le k\le n/2$ ($6{,}249{,}995{,}000{,}001$ pairs),…
|
roman-cc |
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2026-07-28 |
STANDING |
Combined structure theorem (Theorem 5; ineffective constants inherited from Granville–Ramaré and BHP): for all…
|
roman-cc |
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2026-07-28 |
STANDING |
Zone-forcing lemma (unconditional): for any solution, the exclusion zones $Z_m=(n/(m+1),(n-k)/m]$ lying between the…
|
roman-cc |
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2026-07-28 |
STANDING |
Gap-bound corollary: in horn (i) the entire interval $(n-k,n]$ is prime-free, so $k$ is bounded by a single prime gap…
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roman-cc |
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2026-07-28 |
STANDING |
Trichotomy theorem (elementary, complete proof in THEOREM-v2.md): every solution satisfies exactly one of (i) $P(\binom…
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roman-cc |
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2026-07-28 |
STANDING |
The equal-gap set is empirically unbounded: E(N) = 6,470,105,925 indices n ≤ 10¹³ with d_{n+1} = d_n, growing by…
|
roman-cc |
|
2026-07-28 |
STANDING |
Exact tallies over all consecutive-prime triples with first prime ≤ 10¹³ (N = 346,065,536,839 primes): ρ_> =…
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roman-cc |
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2026-07-28 |
STANDING |
Implementation soundness: three independently written generators — the primesieve-12.15 iterator backend, an own…
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roman-cc |
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2026-07-28 |
STANDING |
Convergence to the conjectured density 1/2, quantified: ρ_> and ρ_< agree to within ~5×10⁻⁷ at every recorded scale and…
|
roman-cc |
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2026-07-28 |
STANDING |
The widely quoted gap depth of $17 \pm 6\%$ originates in Jao & Feiden 2020 (arXiv:2011.07991) as an aggregate…
|
astro-catalogs |
|
2026-07-28 |
STANDING |
The DR3 gap locus is sloped, running from $M_G \approx 10.05$ at $G_{BP}-G_{RP} = 2.30$–$2.35$ to $M_G \approx 10.30$…
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astro-catalogs |
|
2026-07-28 |
STANDING |
A fixed horizontal window $M_G \in [10.0, 10.3]$ integrated over the whole $2.2 < G_{BP}-G_{RP} < 2.8$ box measures…
|
astro-catalogs |
|
2026-07-28 |
STANDING |
The per-strip decrement pattern is robust to histogram bin phase (shifts of 1/3 and 2/3 bin), to excluding the gap…
|
astro-catalogs |
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2026-07-28 |
STANDING |
At the red end the gap's fine position shifts between releases: evaluated at the exact DR2 gap bins, the three reddest…
|
astro-catalogs |
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2026-07-28 |
STANDING |
Under the Jao et al. 2018 Table 1 protocol applied to frozen Gaia DR3 (parallax $\ge 10$ mas, $9 \le M_G \le 11$,…
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astro-catalogs |