{
 "what": "the terra bracket table \u2014 six instances under the peak-splitting theorem",
 "statement": "HONEST COUNT: one phenomenon theorem (T1) + one three-peak theorem (T6) + this bracket table. Each row is a certified enclosure with a certified critical-point count; negatives and replications are rows, not theorems. The splitting threshold at sigma = 0.002, gamma = 0.01 is pinned inside [0.13, 0.14] by the certified T7/T8 counts, and the exact-rational linear-response prediction lands inside the pin.",
 "verdict": "VERIFIED",
 "table": [
  {
   "tag": "T1",
   "role": "main: r = 0.20, the phenomenon theorem",
   "sigma": 0.002,
   "gamma": 0.01,
   "A1": 0.003,
   "A2": 0.0006000000000000001,
   "A3": 0.0,
   "N": 96,
   "nu": 1.02,
   "r": 2.519546402577481e-13,
   "Z1": 0.8969618723747638,
   "minM": 0.8943896325413366,
   "peaks": 2,
   "wells": 1,
   "certs": [
    "certs/terra-recert-t1.json",
    "certs/terra-peakcount-t1.json"
   ]
  },
  {
   "tag": "T2",
   "role": "negative: r = 0.12 < threshold",
   "sigma": 0.002,
   "gamma": 0.01,
   "A1": 0.003,
   "A2": 0.00035999999999999997,
   "A3": 0.0,
   "N": 96,
   "nu": 1.02,
   "r": 2.2462335911279024e-13,
   "Z1": 0.8888834157058526,
   "minM": 0.905861937596444,
   "peaks": 1,
   "wells": 1,
   "certs": [
    "certs/terra-recert-t2.json",
    "certs/terra-peakcount-t2.json"
   ]
  },
  {
   "tag": "T3",
   "role": "negative: sigma = 0.02 > sigma*",
   "sigma": 0.02,
   "gamma": 0.01,
   "A1": 0.003,
   "A2": 0.0006000000000000001,
   "A3": 0.0,
   "N": 64,
   "nu": 1.05,
   "r": 2.9664112988846404e-14,
   "Z1": 0.5234763857951094,
   "minM": 0.9620729027916399,
   "peaks": 1,
   "wells": 1,
   "certs": [
    "certs/terra-recert-t3.json",
    "certs/terra-peakcount-t3.json"
   ]
  },
  {
   "tag": "T4",
   "role": "replication: r = 0.15",
   "sigma": 0.002,
   "gamma": 0.01,
   "A1": 0.003,
   "A2": 0.00045,
   "A3": 0.0,
   "N": 96,
   "nu": 1.02,
   "r": 2.367300631563991e-13,
   "Z1": 0.891904814365038,
   "minM": 0.9015595874334734,
   "peaks": 2,
   "wells": 1,
   "certs": [
    "certs/terra-recert-t4.json",
    "certs/terra-peakcount-t4.json"
   ]
  },
  {
   "tag": "T5",
   "role": "replication at low viscosity: sigma = 0.001, N = 176",
   "sigma": 0.001,
   "gamma": 0.01,
   "A1": 0.001,
   "A2": 0.00015,
   "A3": 0.0,
   "N": 176,
   "nu": 1.015,
   "r": 5.313360274907975e-13,
   "Z1": 0.9259760724291124,
   "minM": 0.96494281979973,
   "peaks": 2,
   "wells": 1,
   "certs": [
    "certs/terra-recert-t5.json",
    "certs/terra-peakcount-t5.json"
   ]
  },
  {
   "tag": "T6",
   "role": "three peaks: third harmonic r3 = 0.25",
   "sigma": 0.002,
   "gamma": 0.01,
   "A1": 0.003,
   "A2": 0,
   "A3": 0.00075,
   "N": 96,
   "nu": 1.02,
   "r": 2.7311095673162594e-13,
   "Z1": 0.9046401227896799,
   "minM": 0.882342415053201,
   "peaks": 3,
   "wells": 1,
   "certs": [
    "certs/terra-recert-t6.json",
    "certs/terra-peakcount-t6.json"
   ]
  },
  {
   "tag": "T7",
   "role": "threshold pin, lower: r = 0.13",
   "sigma": 0.002,
   "gamma": 0.01,
   "A1": 0.003,
   "A2": 0.00039000000000000005,
   "A3": 0,
   "N": 96,
   "nu": 1.02,
   "r": 2.300595137852456e-13,
   "Z1": 0.889889492858591,
   "minM": 0.9044277944314566,
   "peaks": 1,
   "wells": 1,
   "certs": [
    "certs/terra-recert-t7.json",
    "certs/terra-peakcount-t7.json"
   ]
  },
  {
   "tag": "T8",
   "role": "threshold pin, upper: r = 0.14",
   "sigma": 0.002,
   "gamma": 0.01,
   "A1": 0.003,
   "A2": 0.00042000000000000007,
   "A3": 0,
   "N": 96,
   "nu": 1.02,
   "r": 2.3234136035514796e-13,
   "Z1": 0.8908966237682399,
   "minM": 0.9029936770002043,
   "peaks": 2,
   "wells": 1,
   "certs": [
    "certs/terra-recert-t8.json",
    "certs/terra-peakcount-t8.json"
   ]
  }
 ],
 "thresholdPin": {
  "certified": "peaks(r=0.13) = 1 and peaks(r=0.14) = 2 \u2014 every threshold crossing lies inside [0.13, 0.14]",
  "linearResponsePrediction": {
   "rc": "r_c = [(1+4s)^2+4g] / (16[(1+s)^2+g]), s = 4 pi^2 sigma, g = 4 pi^2 gamma",
   "bracketRational": [
    "5836654951100826708362054978764671863176315619043734127257378695936121372087543357978786613034821445021317323456020211070196198544338742638108692924924909727056537850091664268843129863506213237836508238675858510914605127347428850972905718166858026158437061220691573493726149554006672914516726665892056372600371496058430816597058665997206853501289232068335725275477321928585154073074625034235478689803159918674596380996956878567845260666576819280564905539896074114255536514916175559493198299897605185864497746125274683621195995981002437586833986056136660518847541865023456528527421036308201067266824408670228846342159554904279346517988160220946996166477617279261319266973316995363052001501000551535538797741788383135463027409418093329541563677372882531067201455698315270331655814094911386334123794098443269065149240896049/43975680232555409196861299718225122936898653029148617208107265741200181043152284797006041781163024500413434470566123490626379728108324521214786702490728672882347978434332827082586658423939158220959894890716489100448318017327265597891697835044682422997292290250490582170700992205127219547112851023496848992989822335098309747781973722526988627063198672299354429533176237920053328786514589923232238590810257482977628980322484248965746781055729466967784355177527498944684405349450795448309285880439662765509999086535185261891004653743127595703161259820052146969125331683736881835112656569240956056312519425041986968972067893520696240749868535439902947903596779208893543183159947857822753677461531353797644078860545281913829463106141149921558395378048421272119352182016674645331655814094911386334123794098443269065149240896049",
    "9941850081043437143191437442688876982104456059885211188227060120480119062204128676811786023189234398820483928280698454552505451918381284694260857172871024709886305034344493255087242352462432872225463443594808493242033281510569673694503552402978568495421881757872068269831142586395307773180362005938320049233955203538986954491771421626521579012011431398737326360386281666206578927643541435715368869331851367192514652465641327943494137200609374604590256198891380689959284912233039542753173493336051516509267038322128239365810567471339749421665338721488775292508068772868300355197876059675637087584786988679692317626962678646993365411201333869581148254410282833316519932632760905100984442430435524852464070561688437110157269042195471749784325166692635716843686433242905448796737670270335878308498103613713024686723630260692309461569089/74905853394933498278874739362282138133297564778632685749146476037582381417632335061467699563266063488559004613264469755008740704032411560424056714311693109485039100475644786246898557928414602481681297888371517967286285773291373163854291753472836548428867500377203387710762682357419225040449644695764636808523531684974115541198415676534896803020519457664432659787491606304383962929472160844415338011383607478724717168898998679395621604170010013834768575159595643450347395165035673360069758057468936575519182968915859425926705270782682219141033321618221937386595741646405266706585266981986035551133251850894183420958671387341915507747202932323850260595568715822636737499696645676959910055870018060719228193135881872188193753751217782578049667771782185260450294928126308630826461791364085878308498103613713024686723630260692309461569089"
   ],
   "bracketDecimal": [
    0.13272460869814864,
    0.13272460869814864
   ],
   "insideCertifiedPin": true,
   "note": "decided in exact rationals (Machin pi bracket); the prediction is LINEAR RESPONSE \u2014 the pin itself is carried by the certified counts alone"
  }
 },
 "meta": {
  "date": "2026-09-01",
  "git": "5b6a608"
 }
}