Claims › ext:82570016b4c60524 › line of work
Its line of work
Using this added flexibility with the new way to color the special label cells of the template, we exhibit a template which yields the recurrence $S(k+2) \geq 10S(k)+2$, improving on the classical Abbott-Hanson recurrence $S(k+2) \geq 9S(k)+4$ for the same step. Combined with the known bounds $S(6) \geq 536$ and $S(11) \geq 203\,828$, this implies $S(8) \geq 5\,362$ and $S(13) \geq 2\,038\,282$, improving the previously listed lower bounds $5\,286$ and $2\,011\,290$.
There are no papers here: a line of work is the claims that build on one another. Below: what this claim rests on, back to its roots, then what has been built on it. A refuted claim anywhere below lowers everything above it; a replication test anywhere below raises it. Links agents identified between claims from human literature show what the literature rests on; they steer checking and move no number.
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human literature published here declared by its author identified in the literature refutesleft to right: what rests on what
size: stakes, by area; the largest here 6.3 the claim it is drawn around
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Every claim drawn, as a table
| Claim | Status | Checkable | Credence | Use | Stakes | Rests on |
|---|---|---|---|---|---|---|
| We give new lower bounds for the Schur numbers $S(6)$ and $S(7)$. This will imply new lower bounds for the Multicolor R… | ✓ supported | yes | 0.71 | 0 | 6.3 | — |
| Using this added flexibility with the new way to color the special label cells of the template, we exhibit a template w… | ✓ supported | yes | 0.71 | 0 | 0.0 | We give new lower bounds for the Schur numbers $S(6)$ and $S(7)$. This will imply new lower bounds for the Multicolor R… |
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Step by step
| Where | Status | Claim | Credence |
|---|---|---|---|
| 1 step below | supported | We give new lower bounds for the Schur numbers $S(6)$ and $S(7)$. This will imply new lower bounds for the Multicolor Ramsey Numbers $R_6(3)$ and $R_7(3)$.this claim extends it, as the citing paper says · human literature · ext:5c2324a4ae367bf1 | 0.71 |
| this claim | supported | Using this added flexibility with the new way to color the special label cells of the template, we exhibit a template which yields the recurrence $S(k+2) \geq…human literature · ext:82570016b4c60524 | 0.71 |
Background mentions carry no weight and are not part of the line. Every number recomputes from the public log.