{
  "classification": "CERTIFIED COMPUTATION: fresh strict interval gates at two precisions",
  "scope": "Existing lambda=5 N=25 partition; first three blocks 26:50,51:100,101:200, both parities; failure of the norm comparison only",
  "not_original_recovery": true,
  "full_block_inertia_not_asserted": true,
  "logic": "If 0<M_j<=T_jj exist, each T_jj is positive definite and the verified positive-energy pair ratios lower-bound beta_jk(T); the exact rational H has Rayleigh quotient >1. Otherwise the prerequisite metrics do not exist. In either case the specified criterion cannot hold.",
  "analytic_series_terms": 96,
  "fresh_assembly": true,
  "witness_sha256": "2a8725849e1cb8b363bd0d79bdb07b1d0b17b22a856f0fdd01fb72145a1e1a64",
  "source_sha256": {
    "evidence/v124/g2_schur_cancellation/assembly_general.py": "4da2e6805e92a2850fe28bd51cd2450d1f2ef0566e9f4f5b5b5fb50db2825b58",
    "evidence/ns45_block_replay/replay.py": "77aa0b462347380193594473504e0c299fe036ab813a7e4c1690f4300527435e"
  },
  "runs": [
    {
      "bits": 320,
      "parity": "even",
      "pairs": [
        {
          "blocks": [
            0,
            1
          ],
          "H_numerator": 997,
          "H_denominator": 1000,
          "energy_x": "[0.017436702631273928142033815566194262851971227171825487119972829708436284828448514090773 +/- 3.64e-88]",
          "energy_y": "[1.2792737555709723158114402514964973917147649565346556361340901066509298305169046362066 +/- 1.14e-86]",
          "cross_pairing": "[0.14935299145737902327141892577495979878703438887858615436177468029043734961120538246621 +/- 1.84e-87]",
          "coupling_ratio": "[0.99999999994135917690932306223824537873409398805942245424221349209224508543013339475871 +/- 1.32e-87]",
          "squared_gate_gap": "[0.00013363713689864389367133049401856472334254115654475780844090430187112807477532145809820 +/- 2.77e-90]",
          "signed_energy_x": "[0.017436702631273928142033815566194262851971227171825487119972829708436284828448514090773 +/- 3.64e-88]",
          "signed_energy_y": "[1.2792737555709723158114402514964973917147649565346556361340901066509298305169046362066 +/- 1.14e-86]",
          "signed_cross_pairing": "[0.14935299145737902327141892577495979878703438887858615436177468029043734961120538246621 +/- 1.84e-87]",
          "signed_squared_gate_gap": "[0.00013363713689864389367133049401856472334254115654475780844090430187112807477532145809820 +/- 2.77e-90]",
          "energy_x_assembly_difference": "[+/- 2.35e-92]",
          "energy_y_assembly_difference": "[+/- 2.06e-92]",
          "cross_assembly_difference": "[+/- 4.75e-93]",
          "gates": {
            "both_energies_strictly_positive": true,
            "normalized_coupling_strictly_above_H": true,
            "signed_index_energies_strictly_positive": true,
            "signed_index_squared_gate_positive": true,
            "all_three_assemblies_overlap": true
          }
        },
        {
          "blocks": [
            0,
            2
          ],
          "H_numerator": 71,
          "H_denominator": 125,
          "energy_x": "[1.299150285617730118415822960555965140140231664931258514191224281256436816876262755469e-7 +/- 4.00e-92]",
          "energy_y": "[1.7588657905269351062490370181816638640421141234850398515083993500769699409804147038485 +/- 3.80e-86]",
          "cross_pairing": "[0.00027276345871558055827371483686938363921061425383476978494815149010231837632310429644772 +/- 4.68e-90]",
          "coupling_ratio": "[0.5706110021376908530327748151752518328568732565394712577059286905757285366968160300972 +/- 4.23e-86]",
          "squared_gate_gap": "[6.7932046558515528594877566901378183243264475609475476547671982663572938142788164063e-10 +/- 7.76e-93]",
          "signed_energy_x": "[1.299150285617730118415822960555965140140231664931258514191224281256436816876262755469e-7 +/- 4.00e-92]",
          "signed_energy_y": "[1.7588657905269351062490370181816638640421141234850398515083993500769699409804147038485 +/- 3.80e-86]",
          "signed_cross_pairing": "[0.00027276345871558055827371483686938363921061425383476978494815149010231837632310429644772 +/- 4.68e-90]",
          "signed_squared_gate_gap": "[6.7932046558515528594877566901378183243264475609475476547671982663572938142788164063e-10 +/- 7.77e-93]",
          "energy_x_assembly_difference": "[+/- 1.92e-92]",
          "energy_y_assembly_difference": "[+/- 1.11e-91]",
          "cross_assembly_difference": "[+/- 3.12e-93]",
          "gates": {
            "both_energies_strictly_positive": true,
            "normalized_coupling_strictly_above_H": true,
            "signed_index_energies_strictly_positive": true,
            "signed_index_squared_gate_positive": true,
            "all_three_assemblies_overlap": true
          }
        },
        {
          "blocks": [
            1,
            2
          ],
          "H_numerator": 481,
          "H_denominator": 1000,
          "energy_x": "[0.68388877768123705910260270799044516964439307968441367952745463135565853211269450179961 +/- 4.46e-87]",
          "energy_y": "[1.3656890847761734743962434329627191249189463683496249586854323805348479829404416082027 +/- 3.81e-86]",
          "cross_pairing": "[0.46757899614259463213815284800971936579635229469740154940027337955086342417579743458528 +/- 1.48e-87]",
          "coupling_ratio": "[0.48382280663024154622009439310711876842615358207055751037182484173679180006405067566468 +/- 3.91e-87]",
          "squared_gate_gap": "[0.0025437006749581338854120241861484407356882873953648064755422972115203801228754733919284 +/- 2.63e-89]",
          "signed_energy_x": "[0.68388877768123705910260270799044516964439307968441367952745463135565853211269450179961 +/- 4.46e-87]",
          "signed_energy_y": "[1.3656890847761734743962434329627191249189463683496249586854323805348479829404416082027 +/- 3.81e-86]",
          "signed_cross_pairing": "[0.46757899614259463213815284800971936579635229469740154940027337955086342417579743458528 +/- 1.48e-87]",
          "signed_squared_gate_gap": "[0.0025437006749581338854120241861484407356882873953648064755422972115203801228754733919284 +/- 2.63e-89]",
          "energy_x_assembly_difference": "[+/- 3.44e-92]",
          "energy_y_assembly_difference": "[+/- 8.94e-92]",
          "cross_assembly_difference": "[+/- 1.32e-92]",
          "gates": {
            "both_energies_strictly_positive": true,
            "normalized_coupling_strictly_above_H": true,
            "signed_index_energies_strictly_positive": true,
            "signed_index_squared_gate_positive": true,
            "all_three_assemblies_overlap": true
          }
        }
      ],
      "exact_rayleigh_numerator": 341,
      "exact_rayleigh_denominator": 250,
      "exact_rayleigh_strictly_above_one": true
    },
    {
      "bits": 320,
      "parity": "odd",
      "pairs": [
        {
          "blocks": [
            0,
            1
          ],
          "H_numerator": 997,
          "H_denominator": 1000,
          "energy_x": "[0.016877555264046884387326612803688310799361654431494089383555951467297993697601451029859 +/- 2.25e-88]",
          "energy_y": "[1.3234634948432278331289525179052252612404373981571264947664332545619209870040626728241 +/- 1.30e-86]",
          "cross_pairing": "[0.14945510454205045454973490439675965307854825152832163358989911953410874750501238775409 +/- 3.58e-87]",
          "coupling_ratio": "[0.99999999998903210140007611155318657371626779448819801514244232109100750256660041831912 +/- 1.73e-87]",
          "squared_gate_gap": "[0.00013381993770054761730315965212718129611024015429696210066443004555316665079530591939020 +/- 4.98e-90]",
          "signed_energy_x": "[0.016877555264046884387326612803688310799361654431494089383555951467297993697601451029859 +/- 2.25e-88]",
          "signed_energy_y": "[1.3234634948432278331289525179052252612404373981571264947664332545619209870040626728241 +/- 1.30e-86]",
          "signed_cross_pairing": "[0.14945510454205045454973490439675965307854825152832163358989911953410874750501238775409 +/- 3.58e-87]",
          "signed_squared_gate_gap": "[0.00013381993770054761730315965212718129611024015429696210066443004555316665079530591939020 +/- 4.98e-90]",
          "energy_x_assembly_difference": "[+/- 2.34e-92]",
          "energy_y_assembly_difference": "[+/- 2.05e-92]",
          "cross_assembly_difference": "[+/- 4.72e-93]",
          "gates": {
            "both_energies_strictly_positive": true,
            "normalized_coupling_strictly_above_H": true,
            "signed_index_energies_strictly_positive": true,
            "signed_index_squared_gate_positive": true,
            "all_three_assemblies_overlap": true
          }
        },
        {
          "blocks": [
            0,
            2
          ],
          "H_numerator": 121,
          "H_denominator": 250,
          "energy_x": "[1.1956398243367374915227033482177788670491362978217625708637624755806485142340372525494e-6 +/- 3.75e-92]",
          "energy_y": "[1.6807327892795970143561918558561739731759313070378135536107382213729886979256667131041 +/- 4.93e-87]",
          "cross_pairing": "[0.00068931930327491390209943122213222944640746605420164845476917945837134753236647689430763 +/- 9.11e-92]",
          "coupling_ratio": "[0.48626265606385695559155846843695375193371274316398781340792450780137466338615214386388 +/- 2.94e-87]",
          "squared_gate_gap": "[4.41170947492531143787809782839741346584155316983554439662242324687512997051334828872e-9 +/- 4.90e-93]",
          "signed_energy_x": "[1.1956398243367374915227033482177788670491362978217625708637624755806485142340372525494e-6 +/- 3.75e-92]",
          "signed_energy_y": "[1.6807327892795970143561918558561739731759313070378135536107382213729886979256667131041 +/- 4.93e-87]",
          "signed_cross_pairing": "[0.00068931930327491390209943122213222944640746605420164845476917945837134753236647689430763 +/- 9.11e-92]",
          "signed_squared_gate_gap": "[4.41170947492531143787809782839741346584155316983554439662242324687512997051334828872e-9 +/- 4.90e-93]",
          "energy_x_assembly_difference": "[+/- 2.00e-92]",
          "energy_y_assembly_difference": "[+/- 1.14e-91]",
          "cross_assembly_difference": "[+/- 3.31e-93]",
          "gates": {
            "both_energies_strictly_positive": true,
            "normalized_coupling_strictly_above_H": true,
            "signed_index_energies_strictly_positive": true,
            "signed_index_squared_gate_positive": true,
            "all_three_assemblies_overlap": true
          }
        },
        {
          "blocks": [
            1,
            2
          ],
          "H_numerator": 153,
          "H_denominator": 250,
          "energy_x": "[0.030357036451663799514864258122436560602658893043084917121052968085343055257272079764279 +/- 2.77e-89]",
          "energy_y": "[1.5982118447567420693298499848289254582437873677130319660964312927900956708574709668052 +/- 4.12e-86]",
          "cross_pairing": "[0.13540902219330760527061120604427165902544588149604783940463638371799306688441907161098 +/- 2.36e-87]",
          "coupling_ratio": "[0.61475312267370076206018327665243198693472484880828063341936793240524797292924050055162 +/- 2.76e-87]",
          "squared_gate_gap": "[0.00016386132126651254598470086090975449367485693764712529924242464947968220861609122678047 +/- 2.86e-91]",
          "signed_energy_x": "[0.030357036451663799514864258122436560602658893043084917121052968085343055257272079764279 +/- 2.77e-89]",
          "signed_energy_y": "[1.5982118447567420693298499848289254582437873677130319660964312927900956708574709668052 +/- 4.12e-86]",
          "signed_cross_pairing": "[0.13540902219330760527061120604427165902544588149604783940463638371799306688441907161098 +/- 2.36e-87]",
          "signed_squared_gate_gap": "[0.00016386132126651254598470086090975449367485693764712529924242464947968220861609122678047 +/- 2.86e-91]",
          "energy_x_assembly_difference": "[+/- 2.45e-92]",
          "energy_y_assembly_difference": "[+/- 1.01e-91]",
          "cross_assembly_difference": "[+/- 7.26e-93]",
          "gates": {
            "both_energies_strictly_positive": true,
            "normalized_coupling_strictly_above_H": true,
            "signed_index_energies_strictly_positive": true,
            "signed_index_squared_gate_positive": true,
            "all_three_assemblies_overlap": true
          }
        }
      ],
      "exact_rayleigh_numerator": 2093,
      "exact_rayleigh_denominator": 1500,
      "exact_rayleigh_strictly_above_one": true
    },
    {
      "bits": 448,
      "parity": "even",
      "pairs": [
        {
          "blocks": [
            0,
            1
          ],
          "H_numerator": 997,
          "H_denominator": 1000,
          "energy_x": "[0.01743670263127392814203381556619426285197122717182548711997282970843628482844851409077336323289647969550410593838667063234033 +/- 4.90e-127]",
          "energy_y": "[1.279273755570972315811440251496497391714764956534655636134090106650929830516904636206611363317896802291797255871334656390913 +/- 7.61e-126]",
          "cross_pairing": "[0.1493529914573790232714189257749597987870343888785861543617746802904373496112053824662118328533754965640052153332419465162458 +/- 2.76e-125]",
          "coupling_ratio": "[0.9999999999413591769093230622382453787340939880594224542422134920922450854301333947587113118025713813223944640993417221374605 +/- 1.33e-125]",
          "squared_gate_gap": "[0.0001336371368986438936713304940185647233425411565447578084409043018711280747753214580981972483307091538068324994763393936314108 +/- 3.10e-128]",
          "signed_energy_x": "[0.01743670263127392814203381556619426285197122717182548711997282970843628482844851409077336323289647969550410593838667063234033 +/- 4.90e-127]",
          "signed_energy_y": "[1.279273755570972315811440251496497391714764956534655636134090106650929830516904636206611363317896802291797255871334656390913 +/- 7.61e-126]",
          "signed_cross_pairing": "[0.1493529914573790232714189257749597987870343888785861543617746802904373496112053824662118328533754965640052153332419465162458 +/- 2.76e-125]",
          "signed_squared_gate_gap": "[0.0001336371368986438936713304940185647233425411565447578084409043018711280747753214580981972483307091538068324994763393936314108 +/- 3.10e-128]",
          "energy_x_assembly_difference": "[+/- 1.93e-130]",
          "energy_y_assembly_difference": "[+/- 7.98e-131]",
          "cross_assembly_difference": "[+/- 2.26e-131]",
          "gates": {
            "both_energies_strictly_positive": true,
            "normalized_coupling_strictly_above_H": true,
            "signed_index_energies_strictly_positive": true,
            "signed_index_squared_gate_positive": true,
            "all_three_assemblies_overlap": true
          }
        },
        {
          "blocks": [
            0,
            2
          ],
          "H_numerator": 71,
          "H_denominator": 125,
          "energy_x": "[1.29915028561773011841582296055596514014023166493125851419122428125643681687626275546930428749126784124589079884323240030396e-7 +/- 6.05e-130]",
          "energy_y": "[1.758865790526935106249037018181663864042114123485039851508399350076969940980414703848537973612072984209040474880741338243248 +/- 1.24e-124]",
          "cross_pairing": "[0.0002727634587155805582737148368693836392106142538347697849481514901023183763231042964477246709553387849406541722934761858024206 +/- 1.99e-128]",
          "coupling_ratio": "[0.570611002137690853032774815175251832856873256539471257705928690575728536696816030097220906173770264209005294367594311479099 +/- 4.12e-124]",
          "squared_gate_gap": "[6.79320465585155285948775669013781832432644756094754765476719826635729381427881640632248275353571953349509479815687317099e-10 +/- 4.12e-130]",
          "signed_energy_x": "[1.29915028561773011841582296055596514014023166493125851419122428125643681687626275546930428749126784124589079884323240030396e-7 +/- 6.05e-130]",
          "signed_energy_y": "[1.758865790526935106249037018181663864042114123485039851508399350076969940980414703848537973612072984209040474880741338243248 +/- 1.24e-124]",
          "signed_cross_pairing": "[0.0002727634587155805582737148368693836392106142538347697849481514901023183763231042964477246709553387849406541722934761858024206 +/- 1.99e-128]",
          "signed_squared_gate_gap": "[6.79320465585155285948775669013781832432644756094754765476719826635729381427881640632248275353571953349509479815687317099e-10 +/- 4.12e-130]",
          "energy_x_assembly_difference": "[+/- 3.52e-130]",
          "energy_y_assembly_difference": "[+/- 3.24e-130]",
          "cross_assembly_difference": "[+/- 1.73e-131]",
          "gates": {
            "both_energies_strictly_positive": true,
            "normalized_coupling_strictly_above_H": true,
            "signed_index_energies_strictly_positive": true,
            "signed_index_squared_gate_positive": true,
            "all_three_assemblies_overlap": true
          }
        },
        {
          "blocks": [
            1,
            2
          ],
          "H_numerator": 481,
          "H_denominator": 1000,
          "energy_x": "[0.6838887776812370591026027079904451696443930796844136795274546313556585321126945017996144554432922234448995263824366252582046 +/- 4.02e-125]",
          "energy_y": "[1.365689084776173474396243432962719124918946368349624958685432380534847982940441608202661935250756459626747305258679243374771 +/- 3.19e-124]",
          "cross_pairing": "[0.4675789961425946321381528480097193657963522946974015494002733795508634241757974345852785273941108770565777999835567500219489 +/- 2.09e-125]",
          "coupling_ratio": "[0.4838228066302415462200943931071187684261535820705575103718248417367918000640506756646760932722538911573077053254972066536691 +/- 4.07e-125]",
          "squared_gate_gap": "[0.002543700674958133885412024186148440735688287395364806475542297211520380122875473391928373722617155339783366934563324785940318 +/- 3.07e-127]",
          "signed_energy_x": "[0.6838887776812370591026027079904451696443930796844136795274546313556585321126945017996144554432922234448995263824366252582046 +/- 4.02e-125]",
          "signed_energy_y": "[1.365689084776173474396243432962719124918946368349624958685432380534847982940441608202661935250756459626747305258679243374771 +/- 3.19e-124]",
          "signed_cross_pairing": "[0.4675789961425946321381528480097193657963522946974015494002733795508634241757974345852785273941108770565777999835567500219489 +/- 2.09e-125]",
          "signed_squared_gate_gap": "[0.002543700674958133885412024186148440735688287395364806475542297211520380122875473391928373722617155339783366934563324785940318 +/- 3.07e-127]",
          "energy_x_assembly_difference": "[+/- 1.85e-130]",
          "energy_y_assembly_difference": "[+/- 2.62e-130]",
          "cross_assembly_difference": "[+/- 4.27e-131]",
          "gates": {
            "both_energies_strictly_positive": true,
            "normalized_coupling_strictly_above_H": true,
            "signed_index_energies_strictly_positive": true,
            "signed_index_squared_gate_positive": true,
            "all_three_assemblies_overlap": true
          }
        }
      ],
      "exact_rayleigh_numerator": 341,
      "exact_rayleigh_denominator": 250,
      "exact_rayleigh_strictly_above_one": true
    },
    {
      "bits": 448,
      "parity": "odd",
      "pairs": [
        {
          "blocks": [
            0,
            1
          ],
          "H_numerator": 997,
          "H_denominator": 1000,
          "energy_x": "[0.01687755526404688438732661280368831079936165443149408938355595146729799369760145102985877517130910086245024352015810474088288 +/- 5.24e-127]",
          "energy_y": "[1.323463494843227833128952517905225261240437398157126494766433254561920987004062672824112922034281467171304005989714167146433 +/- 7.29e-125]",
          "cross_pairing": "[0.1494551045420504545497349043967596530785482515283216335898991195341087475050123877540935728026629091360984011207244195825192 +/- 4.35e-126]",
          "coupling_ratio": "[0.9999999999890321014000761115531865737162677944881980151424423210910075025666004183191217196925962797293340761725076532636632 +/- 4.01e-125]",
          "squared_gate_gap": "[0.0001338199377005476173031596521271812961102401542969621006644300455531666507953059193901950446376283694724510172724737154491772 +/- 3.18e-129]",
          "signed_energy_x": "[0.01687755526404688438732661280368831079936165443149408938355595146729799369760145102985877517130910086245024352015810474088288 +/- 5.24e-127]",
          "signed_energy_y": "[1.323463494843227833128952517905225261240437398157126494766433254561920987004062672824112922034281467171304005989714167146433 +/- 7.29e-125]",
          "signed_cross_pairing": "[0.1494551045420504545497349043967596530785482515283216335898991195341087475050123877540935728026629091360984011207244195825192 +/- 4.35e-126]",
          "signed_squared_gate_gap": "[0.0001338199377005476173031596521271812961102401542969621006644300455531666507953059193901950446376283694724510172724737154491772 +/- 3.18e-129]",
          "energy_x_assembly_difference": "[+/- 1.91e-130]",
          "energy_y_assembly_difference": "[+/- 7.93e-131]",
          "cross_assembly_difference": "[+/- 2.24e-131]",
          "gates": {
            "both_energies_strictly_positive": true,
            "normalized_coupling_strictly_above_H": true,
            "signed_index_energies_strictly_positive": true,
            "signed_index_squared_gate_positive": true,
            "all_three_assemblies_overlap": true
          }
        },
        {
          "blocks": [
            0,
            2
          ],
          "H_numerator": 121,
          "H_denominator": 250,
          "energy_x": "[1.195639824336737491522703348217778867049136297821762570863762475580648514234037252549372626288751487837178323743152123526538e-6 +/- 2.59e-130]",
          "energy_y": "[1.680732789279597014356191855856173973175931307037813553610738221372988697925666713104095074923323733815668665106789207005958 +/- 3.52e-124]",
          "cross_pairing": "[0.0006893193032749139020994312221322294464074660542016484547691794583713475323664768943076300893381010496248532276262181209111040 +/- 2.20e-128]",
          "coupling_ratio": "[0.4862626560638569555915584684369537519337127431639878134079245078013746633861521438638808887244324701378813723621466231903930 +/- 5.34e-125]",
          "squared_gate_gap": "[4.4117094749253114378780978283974134658415531698355443966224232468751299705133482887209295074075853655611740555186192597114e-9 +/- 6.69e-131]",
          "signed_energy_x": "[1.195639824336737491522703348217778867049136297821762570863762475580648514234037252549372626288751487837178323743152123526538e-6 +/- 2.59e-130]",
          "signed_energy_y": "[1.680732789279597014356191855856173973175931307037813553610738221372988697925666713104095074923323733815668665106789207005958 +/- 3.52e-124]",
          "signed_cross_pairing": "[0.0006893193032749139020994312221322294464074660542016484547691794583713475323664768943076300893381010496248532276262181209111040 +/- 2.20e-128]",
          "signed_squared_gate_gap": "[4.4117094749253114378780978283974134658415531698355443966224232468751299705133482887209295074075853655611740555186192597114e-9 +/- 6.69e-131]",
          "energy_x_assembly_difference": "[+/- 2.95e-130]",
          "energy_y_assembly_difference": "[+/- 3.35e-130]",
          "cross_assembly_difference": "[+/- 1.67e-131]",
          "gates": {
            "both_energies_strictly_positive": true,
            "normalized_coupling_strictly_above_H": true,
            "signed_index_energies_strictly_positive": true,
            "signed_index_squared_gate_positive": true,
            "all_three_assemblies_overlap": true
          }
        },
        {
          "blocks": [
            1,
            2
          ],
          "H_numerator": 153,
          "H_denominator": 250,
          "energy_x": "[0.03035703645166379951486425812243656060265889304308491712105296808534305525727207976427902762480674860550188627452358647672998 +/- 8.14e-127]",
          "energy_y": "[1.598211844756742069329849984828925458243787367713031966096431292790095670857470966805241121189616898372060075024514349770892 +/- 1.26e-125]",
          "cross_pairing": "[0.1354090221933076052706112060442716590254458814960478394046363837179930668844190716109776493841299103764204050688783921140004 +/- 3.51e-125]",
          "coupling_ratio": "[0.6147531226737007620601832766524319869347248488082806334193679324052479729292405005516227587888345707987681298352367248561978 +/- 4.29e-125]",
          "squared_gate_gap": "[0.0001638613212665125459847008609097544936748569376471252992424246494796822086160912267804702767246064122228833138697494165014770 +/- 3.28e-128]",
          "signed_energy_x": "[0.03035703645166379951486425812243656060265889304308491712105296808534305525727207976427902762480674860550188627452358647672998 +/- 8.14e-127]",
          "signed_energy_y": "[1.598211844756742069329849984828925458243787367713031966096431292790095670857470966805241121189616898372060075024514349770892 +/- 1.26e-125]",
          "signed_cross_pairing": "[0.1354090221933076052706112060442716590254458814960478394046363837179930668844190716109776493841299103764204050688783921140004 +/- 3.51e-125]",
          "signed_squared_gate_gap": "[0.0001638613212665125459847008609097544936748569376471252992424246494796822086160912267804702767246064122228833138697494165014770 +/- 3.28e-128]",
          "energy_x_assembly_difference": "[+/- 1.23e-130]",
          "energy_y_assembly_difference": "[+/- 2.95e-130]",
          "cross_assembly_difference": "[+/- 2.44e-131]",
          "gates": {
            "both_energies_strictly_positive": true,
            "normalized_coupling_strictly_above_H": true,
            "signed_index_energies_strictly_positive": true,
            "signed_index_squared_gate_positive": true,
            "all_three_assemblies_overlap": true
          }
        }
      ],
      "exact_rayleigh_numerator": 2093,
      "exact_rayleigh_denominator": 1500,
      "exact_rayleigh_strictly_above_one": true
    }
  ]
}