back to table · edit · history · where entries came from · files · download
6503 bytes, as of the version from 2026-10-27 01:01 (current). Recorded here, not run.
{
"table": "T200",
"scope": "T200-only supplement; earlier thirteen outcomes unchanged",
"baseline_revision": "3c1b6dd8444daa28cbfb0aed077adf7febe362819748e69b9f85d5bc56bb59c7",
"baseline_entries": 722,
"proposed_entries": 8,
"retained_entries": [
{
"branch": "0",
"x": "1"
}
],
"added_entries": [
{
"branch": "0",
"x": "0"
},
{
"branch": "0",
"x": "e"
},
{
"branch": "0",
"x": "-1/e"
},
{
"branch": "0",
"x": "-3*exp(-3)"
},
{
"branch": "0",
"x": "-5*exp(-5)"
},
{
"branch": "-1",
"x": "-1/e"
},
{
"branch": "-1",
"x": "-exp(-1/2)/2"
}
],
"removed_samples": 721,
"removed_samples_retained_in_website_revision_history": true,
"status": "source-justified structural/application selection with one explicit normalization reference",
"selection": [
{
"branch": "0",
"x": "0",
"kind": "intrinsic",
"reason": "Unique real zero and regular origin of the principal inverse branch.",
"source": "https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf",
"location": "Sections 1 and 4; defining equation (1.5)"
},
{
"branch": "0",
"x": "1",
"kind": "intrinsic named constant",
"reason": "Omega is the unique positive fixed point of exp(-w); the existing annotated entry is retained.",
"source": "https://oeis.org/A030178",
"location": "definition and comments"
},
{
"branch": "0",
"x": "e",
"kind": "explicit normalization reference",
"reason": "W_0(e)=1 is the inverse image of the unit output; a single exact normalization anchor, not an application or a mesh.",
"source": "https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf",
"location": "defining equation (1.5) and real-branch convention"
},
{
"branch": [
"0",
"-1"
],
"x": "-1/e",
"kind": "intrinsic branch point",
"reason": "The derivative of w*exp(w) vanishes at w=-1; the two real branches meet here.",
"source": "https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf",
"location": "Sections 1 and 4"
},
{
"branch": "0",
"x": [
"-3*exp(-3)",
"-5*exp(-5)"
],
"kind": "documented application with specified conventions",
"reason": "Planck spectral energy densities per unit linear frequency and linear wavelength fix the exponents 3 and 5. These are not a coordinate-independent peak; other dispersion variables are not automatically included.",
"source": "https://doi.org/10.1590/S1806-11172011000300008",
"location": "Section 2, equations (3)-(7), Table 2, footnote 5"
},
{
"branch": "-1",
"x": "-exp(-1/2)/2",
"kind": "derived documented application",
"reason": "For 3-XOR-SAT, degree 2 is selected by leaf stripping and arity 3 is the first nontrivial case. Minimizing lambda/(1-exp(-lambda))^2 gives exp(lambda)-1=2*lambda. With w=-lambda-1/2 this becomes w*exp(w)=-exp(-1/2)/2. Branch -1 selects the positive minimizer, while branch 0 gives the excluded zero solution.",
"source": "https://www.cs.toronto.edu/~molloy/webpapers/xorrsarevised.pdf",
"location": "Sections 1.1-1.2; equation (1) at k=3, r=2"
}
],
"every_free_parameter": {
"branch": "0 and -1 are the two real branches; each application fixes its branch by the positive solution requirement.",
"x": "Every argument is listed individually with a reason and source.",
"Planck spectral variable": "Two standard linear-coordinate spectral-energy conventions; frequency fixes 3, wavelength fixes 5, and T cancels after nondimensionalization.",
"hypergraph edge size": "3 is the first nontrivial XOR-SAT arity discussed explicitly in Section 1.1.",
"hypergraph core degree": "2 is forced by eliminating variables of occurrence degree zero or one, not chosen from a bounded integer grid."
},
"unresolved": [
"No exhaustive claim is made about other Lambert applications. Future arguments need their own problem and normalization justification."
],
"unjustified_grid_replaced": "The old positive hundredth/tenth and negative hundredth grids had no identified application-specific rationale.",
"no_quantile_table": true,
"old_numeric_identifiers_not_reassigned": true,
"nonzero_hand_metadata_preserved": true,
"primary_source_archives": [
{
"file": "dlmf-4.13.html",
"url": "https://dlmf.nist.gov/4.13",
"resolved_url": "https://dlmf.nist.gov/4.13",
"sha256": "16855dd3077e742baa3f97ad7224bf4d3fbf7249f2dcdc7662641d319dd9ef62",
"retrieved_utc": "2026-10-26T16:09:10.589193+00:00"
},
{
"file": "corless-lambert.pdf",
"url": "https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf",
"resolved_url": "https://cs.uwaterloo.ca/research/tr/1993/03/W.pdf",
"sha256": "b057325af1728ff80622a73fcff3a8654e31d495c16e780968d9f4ebc57cea34",
"retrieved_utc": "2026-10-26T16:09:11.432003+00:00"
},
{
"file": "achlioptas-molloy.pdf",
"url": "https://www.cs.toronto.edu/~molloy/webpapers/xorrsarevised.pdf",
"resolved_url": "https://www.cs.toronto.edu/~molloy/webpapers/xorrsarevised.pdf",
"sha256": "befc996679d185f3841b99acd62395e5253888b681eca7ca3c065a3ff3ce8b50",
"retrieved_utc": "2026-10-26T16:09:12.790620+00:00"
},
{
"file": "oeis-omega.html",
"url": "https://oeis.org/A030178",
"resolved_url": "https://oeis.org/A030178",
"sha256": "9f721a54a1c46db28ceb09d7c519d175b7f5fd696a6ebda455b8bda7e91b60a3",
"retrieved_utc": "2026-10-26T16:09:13.786124+00:00"
},
{
"file": "stewart-wien.web.txt",
"sha256": "85069d6c4c0021f9aec0b64d018a25f8b6dc8d11cb11ea6a982946449dc60dda",
"url": "https://www.researchgate.net/publication/256089483_Wien_peaks_and_the_Lambert_W_function",
"format": "exact browser-tool text rendering of author-uploaded primary article",
"retrieval_note": "Direct publisher PDF and proxy HTML returned HTTP 403; not claimed as an archived publisher PDF."
}
],
"skill_sha256": "b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18",
"live_skill_sha256": "b4d51ded0d52cfe3dcc0859de0845c3879b0c2363273ba7e809a7e06ded40b18",
"earlier_outcomes_sha256": "efb7e39818e8d3b4dcf3a854346e3a50dbcd4cbfd38a6cff414396112442d225",
"publication_or_approval_requested": false
}