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4160 bytes, as of the version from 2026-10-27 01:18 (current). Recorded here, not run.
{
"table": "T533",
"skill_provenance": {
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{
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"entries_checked": 96,
"generator_default_order_matches": true,
"convolution_exact_matches": 96,
"program_exact_matches": 96,
"generator_exact_matches": 96,
"bernoulli_matches": 12,
"known_controls_passed": true,
"perturbation_rejected": true,
"new_values": 0,
"argument_uncertainty": "All orders and moment indices are exact; no rounded arguments or approximate values used.",
"versions": {
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"sage": "10.9"
},
"checked_sources": [
{
"url": "https://dlmf.nist.gov/10.21#xiii",
"checked": "Rayleigh-function definition and positive-zero indexing; no mathematical change made."
},
{
"url": "https://arxiv.org/pdf/math/9910128",
"checked": "Page 2 equations (3),(4): convolution and initial value used in exact check."
},
{
"url": "https://numberdb.org/Zeros_of_Bessel_J_functions",
"checked": "Page and API definition: positive zeros of first-kind J; valid published link."
},
{
"url": "https://numberdb.org/Values_of_Bessel_functions_of_the_first_kind",
"checked": "Page and API definition: cylindrical first-kind J; valid published link."
}
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"changed_fields": [
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"values_and_order_unchanged": true,
"fresh_independent_critique_required": true,
"reason": "Definition markup is included in the selection fingerprint; the prior critique also lacks the actual private-page inspection."
},
"browser": {
"python": "3.12.3",
"playwright": "1.64.1",
"credential_scope": "No API key or session cookies sent by browser",
"checks": [
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"math_errors": 0,
"math_elements": 1,
"links": []
},
{
"name": "definition-preview",
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"math_errors": 0,
"math_elements": 12,
"links": [
{
"text": "strictly positive zero",
"href": "Zeros_of_Bessel_J_functions"
},
{
"text": "cylindrical Bessel function J\u03bd",
"href": "Values_of_Bessel_functions_of_the_first_kind"
}
]
}
],
"chromium": "156.0.8078.4"
},
"audit": {
"tid": "T533",
"title": "Bessel Rayleigh sums",
"findings": [
"Definition links to another table; a cross-reference belongs in Similar tables or a comment"
],
"clean": false
},
"audit_adjudication": "The sole warning rejects any HREF in Definition. The matching current skill explicitly requires first-mention links once per section. These links wrap already necessary defining noun phrases; stripping markup reproduces the old definition exactly. Retained as a documented false positive; no source or skill changed.",
"initial_check_failure": "QQ(str(Fraction)) failed under named imports with missing real_mpfr; corrected only the checker to construct QQ(numerator)/QQ(denominator). Both initial artifacts retained; successful full checks followed.",
"review_scope": "Repair evidence, not independent critique or acceptance. Actual private-page inspection still unavailable without an authorized login session."
}