files / problems / hilbert16-limit-cycles / compute / q3 / ss-cubic-l2 / certs / core.json

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{
  "L1_E_minus": "3*sqrt(2)*mu/2",
  "L1_E_plus": "3*sqrt(2)*mu/2",
  "L1_cubic_minus": "-sqrt(2)*mu/2",
  "L1_cubic_plus": "-sqrt(2)*mu/2",
  "L1_minus": "sqrt(2)*mu",
  "L1_plus": "sqrt(2)*mu",
  "L2_extra_cycles": false,
  "L2_first_nonzero": false,
  "L2_irrelevant_to_cyclicity": true,
  "L2_zero_while_L1": false,
  "V1_closed_ok": true,
  "V1_minus": "sqrt(2)*mu/8",
  "V1_mu0": "0",
  "V1_plus": "sqrt(2)*mu/8",
  "V2_closed_ok": true,
  "V2_minus": "-sqrt(2)*mu*(23*mu^2+18)/96",
  "V2_mu0": "0",
  "V2_plus": "-sqrt(2)*mu*(23*mu^2+18)/96",
  "V2_sample_mu1": "-41*sqrt(2)/96",
  "V2_sample_mu2": "-55*sqrt(2)/24",
  "V2_sample_mu_m1": "41*sqrt(2)/96",
  "centers_at_mu0": true,
  "claim": "L1 = sqrt(2)*mu at both wells of the two-well van der Pol 3-jet; V2 = -sqrt(2)*mu*(23*mu^2+18)/96 in the q1 Poincar\u00e9 gauge. Order is 1, so L2 does not add a small cycle. Not a bound on H(n).",
  "cycles_proved": 0,
  "degree": 3,
  "fourteen_from_L2": false,
  "hn_moved": false,
  "schema": "hilbert16-ss-cubic-l2-core/v1",
  "trace_at_wells": "0",
  "two_hopf_cycles": 0,
  "weak_focus_order": 1,
  "what_this_is_not": [
    "not a dent of H(n)",
    "not fourteen cycles from L2",
    "not a proved pair of Hopf cycles",
    "not L2 as the first nonzero quantity",
    "not a new H(3)"
  ]
}