{
  "nodes": [
    {
      "id": "Coalesce",
      "label": "R180: Haar absorption of every fixed shift; p_L→1",
      "state": "checked",
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      "id": "Support",
      "label": "R181: the boundary lies in one closed Haar-null set S",
      "state": "checked",
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      "id": "Uniform",
      "label": "R181: upper Banach density of the boundary is 0 — all long intervals",
      "state": "checked",
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    {
      "id": "Blocks",
      "label": "R181: synchronous merging of every fixed finite block with density 1",
      "state": "checked",
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      "id": "Time",
      "label": "R181: encounters up to any prescribed h(n)→∞ have natural density 1, for T and C",
      "state": "checked",
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      "id": "Heavy",
      "label": "R181: 1−p_L ≥ 1/√(2L+1); direct majorants are not summable",
      "state": "checked",
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    {
      "id": "Return",
      "label": "R182: tail τ−ν₂(d) ≤32√(log₂(t+2)/(t+1))",
      "state": "checked",
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      "id": "Reward",
      "label": "R182: finite expected sum 1+|a_j|^(1/32) up to absorption",
      "state": "checked",
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        -0.1323809056537267,
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    {
      "id": "Moments",
      "label": "R182: Eσ_d^r is finite exactly for 0<r<1/2, for each fixed d≠0",
      "state": "checked",
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        0.2868012460122549,
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    {
      "id": "Rate",
      "label": "R182: exact-boundary fraction ≤C_r(log N)^(-r)+N^(-1/2), 0<r<1/2",
      "state": "checked",
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        -0.2979392892971448,
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      "id": "Growing",
      "label": "R182: blocks of length (log N)^γ+1 merge with fraction→1, 0≤γ<1/2",
      "state": "checked",
      "position": [
        0.14341902208894833,
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    {
      "id": "Exact",
      "label": "R176: exact XOR boundary system is equivalent to an exact invariant",
      "state": "checked",
      "position": [
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    {
      "id": "Lower",
      "label": "R178: a nonconstant invariant requires B(X) ≥ log₂X·log₂log₂X/260 beyond a threshold",
      "state": "checked",
      "position": [
        -0.31850812278761687,
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    {
      "id": "Integer",
      "label": "R183: canonical q_k→0 at every depth ⇔ nonnegative integer start",
      "state": "checked",
      "position": [
        0.3731020068683734,
        0.9241573033707865,
        -0.08202542957661568
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      "flat": [
        8573.1,
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    },
    {
      "id": "Corridor",
      "label": "R183: exact affine-addition endpoints for all words with given k,s",
      "state": "checked",
      "position": [
        -0.22736569753140218,
        0.9185393258426966,
        0.32340430805186154
      ],
      "flat": [
        8140.2,
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    },
    {
      "id": "StepV",
      "label": "R183: exact V factors; outside input 1, factor ≤5/(3√3)<1",
      "state": "checked",
      "position": [
        -0.05244977864024951,
        0.9129213483146067,
        -0.40475132181628426
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      "flat": [
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    },
    {
      "id": "Norm",
      "label": "R183: T^k(n)/3^{s_k(n)} ≤ C_n·3^(−k/2), every natural n",
      "state": "checked",
      "position": [
        0.3215170299992344,
        0.9073033707865168,
        0.27097489326484814
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      "flat": [
        6865.3,
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    },
    {
      "id": "Minimal",
      "label": "R183: a minimal bad start requires linear escape of the parity counter",
      "state": "checked",
      "position": [
        -0.43202346526786767,
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        0.017865526646012726
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      "flat": [
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    {
      "id": "CriterionV",
      "label": "R183: reaching 1 ⇔ liminf V_k>0; equivalence only",
      "state": "checked",
      "position": [
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      "flat": [
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    },
    {
      "id": "PositiveV",
      "label": "Prove liminf V_k>0 for every natural n — open",
      "state": "unresolved",
      "position": [
        -0.02102090429407071,
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        0.45459643596047017
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      "flat": [
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    },
    {
      "id": "FixedH",
      "label": "R184: affine contraction; the only computable H≥0",
      "state": "checked",
      "position": [
        -0.2985135940266002,
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        -0.35771905230579953
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      "flat": [
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    {
      "id": "CriterionH",
      "label": "R184: H(n)>0 ⇔ n reaches 1; equivalence only",
      "state": "checked",
      "position": [
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      "flat": [
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    {
      "id": "RVBarrier",
      "label": "R184: finitely residual regularly varying h are excluded",
      "state": "checked",
      "position": [
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      "flat": [
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    },
    {
      "id": "PowerBarrier",
      "label": "R184: a common infimum gap is impossible; critical error in old iteration 1",
      "state": "checked",
      "position": [
        0.10899521052162464,
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        -0.48449463858159986
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      "flat": [
        6297.7,
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    },
    {
      "id": "Subcertificate",
      "label": "R184: a bounded h>0 with h(n)≤a(n)h(Tn) is sufficient",
      "state": "checked",
      "position": [
        0.25172086794669296,
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        0.4392864785023752
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      "flat": [
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    },
    {
      "id": "OddFlow",
      "label": "R185: exact odd equation U; all even runs included",
      "state": "checked",
      "position": [
        -0.4913474341317118,
        0.8567415730337079,
        -0.15675323284676118
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      "flat": [
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    },
    {
      "id": "OddError",
      "label": "R185: new critical error ≤βδ^L→0",
      "state": "checked",
      "position": [
        0.4765588957656841,
        0.851123595505618,
        -0.22018229729063377
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      "flat": [
        6585.1,
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    },
    {
      "id": "OddGap",
      "label": "R185: explicit convergent odd chain with U(n_j)→0",
      "state": "checked",
      "position": [
        -0.20614369455589593,
        0.8455056179775281,
        0.49256981958224333
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      "flat": [
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    },
    {
      "id": "PartialOdd",
      "label": "R185: computable nonnegative subsolution; zero at convergent 3",
      "state": "checked",
      "position": [
        -0.18369846328892572,
        0.8398876404494382,
        -0.5107285247619937
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      "flat": [
        7141.1,
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    },
    {
      "id": "NormalForm",
      "label": "R185: saturation h≤h↑≤H; full class with rational coefficients",
      "state": "checked",
      "position": [
        0.4880550619748284,
        0.8342696629213483,
        0.2565080622706552
      ],
      "flat": [
        6585.1,
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    },
    {
      "id": "RationalTail",
      "label": "R185: over odd starts liminf R=0, limsup R=3/4",
      "state": "checked",
      "position": [
        -0.541275558213141,
        0.8286516853932584,
        0.14267850004806235
      ],
      "flat": [
        7141.1,
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      ]
    },
    {
      "id": "BackLayer",
      "label": "R185: full reverse layer and 4n+1 lift for odd values; sign preserved",
      "state": "checked",
      "position": [
        0.30719179608257674,
        0.8230337078651686,
        -0.4777538237809017
      ],
      "flat": [
        7141.1,
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    },
    {
      "id": "DyadicReturn",
      "label": "R186: two finite returns in every dyadic class, growth and contraction",
      "state": "checked",
      "position": [
        0.09756883856958413,
        0.8174157303370786,
        0.5677251496434546
      ],
      "flat": [
        6006.7,
        2251.6
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    },
    {
      "id": "LocalRV",
      "label": "R186: regular asymptotic h on one class is impossible, without boundedness",
      "state": "checked",
      "position": [
        -0.46167547111641233,
        0.8117977528089888,
        -0.35754743448067783
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      "flat": [
        6585.1,
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    },
    {
      "id": "RunProfile",
      "label": "R186: regular profiles by layers ν₂(n+1) are excluded",
      "state": "checked",
      "position": [
        0.5896505037836846,
        0.8061797752808989,
        -0.04885133893442757
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      "flat": [
        7141.1,
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    },
    {
      "id": "CompletedWords",
      "label": "R187: known convergent completions of every finite word",
      "state": "checked",
      "position": [
        -0.4069384374519807,
        0.800561797752809,
        0.4398885269053182
      ],
      "flat": [
        6585.1,
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      ]
    },
    {
      "id": "CylinderEnv",
      "label": "R187: exact Q_w; in every class limsup R=(3/4)^s, liminf R=0",
      "state": "checked",
      "position": [
        0.0029595680663714913,
        0.7949438202247191,
        -0.6066758307724067
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      "flat": [
        7141.1,
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      ]
    },
    {
      "id": "PuncturedR",
      "label": "R187: punctured dyadic limit R=0 at every natural m",
      "state": "checked",
      "position": [
        0.41252037441898853,
        0.7893258426966292,
        0.45474350434115457
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      "flat": [
        7576.4,
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    },
    {
      "id": "NearOne",
      "label": "R187: explicit good starts→1 dyadically, R→0 when R1=1",
      "state": "checked",
      "position": [
        -0.6184790557225193,
        0.7837078651685393,
        -0.057320499871788194
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      "flat": [
        7576.4,
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    },
    {
      "id": "PositiveR",
      "label": "Prove R(n)>0 for all natural n — open",
      "state": "unresolved",
      "position": [
        0.5003611620142152,
        0.7780898876404494,
        -0.37975628276495593
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      "flat": [
        8140.2,
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    },
    {
      "id": "PositiveOdd",
      "label": "Construct 0<v≤1 on all odd values with v(m)≤(3m+1)v(Sm)/(4m) — open",
      "state": "unresolved",
      "position": [
        -0.11366333359505926,
        0.7724719101123596,
        0.6247942018644387
      ],
      "flat": [
        7576.4,
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    },
    {
      "id": "PositiveH",
      "label": "Prove H(n)>0 for all n or construct a sufficient h — open",
      "state": "unresolved",
      "position": [
        -0.34183780763333793,
        0.7668539325842697,
        -0.5432144690198094
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      "flat": [
        8573.1,
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      ]
    },
    {
      "id": "Trace",
      "label": "Exclude nonzero values of the exact boundary on S∩N — open",
      "state": "unresolved",
      "position": [
        0.625413384799986,
        0.7612359550561798,
        0.17139987993791153
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      "flat": [
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      ]
    },
    {
      "id": "Pair",
      "label": "Positive density of a nonempty boundary — unproved",
      "state": "unresolved",
      "position": [
        -0.5827557145719338,
        0.7556179775280899,
        0.29906061119798744
      ],
      "flat": [
        8140.2,
        2891.6
      ]
    },
    {
      "id": "PairCriterion",
      "label": "Rare boundary + positive density of a nonempty boundary imply constancy",
      "state": "checked",
      "position": [
        0.22992691347759286,
        0.75,
        -0.6201883701414173
      ],
      "flat": [
        8573.1,
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    },
    {
      "id": "Dini",
      "label": "Summability of the boundary itself — unproved",
      "state": "unresolved",
      "position": [
        0.25177174078871384,
        0.7443820224719101,
        0.6184710140021514
      ],
      "flat": [
        8140.2,
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    },
    {
      "id": "Profile",
      "label": "Strong limiting profile — not constructed",
      "state": "unresolved",
      "position": [
        -0.6090316586088863,
        0.7387640449438202,
        -0.2886314686765015
      ],
      "flat": [
        8140.2,
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    },
    {
      "id": "OldCriteria",
      "label": "Earlier Dini/profile criteria use external PD",
      "state": "checked",
      "position": [
        0.6498847187860496,
        0.7331460674157304,
        -0.2003664046721068
      ],
      "flat": [
        8573.1,
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    },
    {
      "id": "Descent",
      "label": "Descent below every odd n>1 — open",
      "state": "unresolved",
      "position": [
        -0.34689632123125896,
        0.7275280898876404,
        0.5919170725200116
      ],
      "flat": [
        9003.5,
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    },
    {
      "id": "MahlerIrr",
      "label": "M1: P(2^q/3^s) is irrational in Q₂, q≥1, 0≤s≤q",
      "state": "checked",
      "position": [
        -0.14528428374152283,
        0.7219101123595506,
        -0.676563571714243
      ],
      "flat": [
        8140.2,
        5992.6
      ]
    },
    {
      "id": "CZKnown",
      "label": "Corvaja–Zannier 2002: via 1/P and (1−z)D it covers M1–M2 values",
      "state": "checked",
      "position": [
        0.5688798261500962,
        0.7162921348314606,
        0.404105581473487
      ],
      "flat": [
        7576.4,
        6147.6
      ]
    },
    {
      "id": "TMExcluded",
      "label": "M1: exact Thue–Morse tail class from two equal blocks excluded",
      "state": "checked",
      "position": [
        -0.6981205477165434,
        0.7106741573033708,
        0.08700541935475693
      ],
      "flat": [
        8573.1,
        5925.6
      ]
    },
    {
      "id": "OtherCodes",
      "label": "Exclude the remaining bad codes of positive integers — open",
      "state": "unresolved",
      "position": [
        0.4596503317043809,
        0.7050561797752809,
        -0.5400160700615672
      ],
      "flat": [
        9003.5,
        5353.6
      ]
    },
    {
      "id": "DValue",
      "label": "M2: D(2^q/3^s) is irrational in Q₂, q≥1, 0≤s≤q",
      "state": "checked",
      "position": [
        0.026045719489700504,
        0.699438202247191,
        0.7142183291777672
      ],
      "flat": [
        8140.2,
        6137.6
      ]
    },
    {
      "id": "PDExcluded",
      "label": "M2: block tails by period doubling are excluded",
      "state": "checked",
      "position": [
        -0.5054819064405015,
        0.6938202247191011,
        -0.512934243380194
      ],
      "flat": [
        8573.1,
        6120.6
      ]
    },
    {
      "id": "TMMasks",
      "label": "M2: shifts, finite changes, and XOR masks of period 2^h",
      "state": "checked",
      "position": [
        0.7245723718888113,
        0.6882022471910112,
        0.03704787249849244
      ],
      "flat": [
        8573.1,
        6055.6
      ]
    },
    {
      "id": "HeightDomain",
      "label": "M2: sufficient domain max(a,b)<2^(2v₂(a)) for P(a/b)",
      "state": "checked",
      "position": [
        -0.5633791134733142,
        0.6825842696629214,
        0.46549187888808413
      ],
      "flat": [
        8573.1,
        5860.6
      ]
    },
    {
      "id": "MorphicCriterion",
      "label": "M3: h(TM) start is rational ⇔ uv=vu; any nonempty u,v",
      "state": "checked",
      "position": [
        0.10170250014396699,
        0.6769662921348314,
        -0.7289535244291535
      ],
      "flat": [
        8573.1,
        5990.6
      ]
    },
    {
      "id": "PDContraction",
      "label": "M4: 3^S<2^Q ⇒ two fixed grouped blocks contract",
      "state": "checked",
      "position": [
        0.4203169460867876,
        0.6713483146067416,
        0.6104302624436013
      ],
      "flat": [
        6006.7,
        6429.6
      ]
    },
    {
      "id": "PDMorphic",
      "label": "M4: when 3^S<2^Q, h(d) start is rational ⇔ uv=vu; Lucier input known",
      "state": "checked",
      "position": [
        -0.7271901700146279,
        0.6657303370786517,
        -0.16732475885905632
      ],
      "flat": [
        6585.1,
        6519.6
      ]
    },
    {
      "id": "PDGrowing",
      "label": "M5: h(d) start is rational ⇔ uv=vu; otherwise transcendental, any nonempty u,v",
      "state": "checked",
      "position": [
        0.6535617392833114,
        0.6601123595505618,
        -0.37028195434501354
      ],
      "flat": [
        7141.1,
        6584.6
      ]
    },
    {
      "id": "ScalarF",
      "label": "Exact scalar equations F,H_r; δ=0 ⇔ uv=vu",
      "state": "checked",
      "position": [
        -0.23330625367540017,
        0.6544943820224719,
        0.7191698658154223
      ],
      "flat": [
        5016.8,
        6560.6
      ]
    },
    {
      "id": "FormalH",
      "label": "H_r is not a rational function; known SML",
      "state": "checked",
      "position": [
        -0.31576262924672205,
        0.648876404494382,
        -0.6922812821835069
      ],
      "flat": [
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    {
      "id": "NishiokaKnown",
      "label": "Known Nishioka theorem: an algebraic Mahler function is rational",
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      "id": "FormalTransH",
      "label": "H_r is transcendental as a function: exact 4-Mahler equation + Nishioka",
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    {
      "id": "AuxiliaryValue",
      "label": "Mahler argument: auxiliary-series vanishing order ≥N²+2N versus height ≤9N·h(t)",
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      "id": "ScalarBarrier",
      "label": "When r is not a root of unity, rational scalar substitution yields no Laurent coefficients",
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      "id": "HValue",
      "label": "M5: all required H_r(t) are transcendental; poles and place weight checked",
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    {
      "id": "RSSystem",
      "label": "Rudin–Shapiro: exact system R(a,b),R(−a,−b); transition (a³b,ab³)",
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      "id": "RSInvert",
      "label": "Matrix invertible along the entire actual orbit; determinant checked",
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      "id": "RSNonzero",
      "label": "For a≠b, every nonzero analytic series on the orbit is eventually nonzero",
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      "id": "RSFormal",
      "label": "R(a,b) and the diagonal are formally transcendental; Nishioka input known",
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      "id": "RSJoint",
      "label": "For each admissible pair a,b in this construction, at least one of the two components is transcendental",
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      "id": "RSChoiceBarrier",
      "label": "Example of another system: invertibility does not select the transcendental component",
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      "id": "RSDiagonalKnown",
      "label": "Known DHR input: L(z),L(−z) are algebraically independent",
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      "id": "RSPairFormal",
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      "id": "RSSparse",
      "label": "Sparse support: degrees m³ allow vanishing order c·m⁷",
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      "id": "RSHermite",
      "label": "P,P_U,P_V simultaneously have order c·m⁷ at degrees m³",
      "state": "checked",
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      "id": "RSConditional",
      "label": "Nonzero resultant on an infinite orbit ⇒ selected value transcendental, a≠b",
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      "id": "RSGcd",
      "label": "Linear space: existence of a squarefree member is equivalent to a squarefree common divisor, under the stated hypotheses",
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      "id": "RSSquarefree",
      "label": "Construct the required specialization without multiple roots — open",
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      "id": "RSResultant",
      "label": "Construct the required nonzero resultant — open",
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      "id": "RSGelfondKnown",
      "label": "Known Roy–Waldschmidt criterion: small values at every large height",
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      "id": "RSGelfondCriterion",
      "label": "G1: all large heights covered; for RS, order m⁷ versus losses m⁶",
      "state": "checked",
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    {
      "id": "RSSelected",
      "label": "M6: R(a,b) itself is transcendental for all admissible a,b in this construction, including the diagonal",
      "state": "checked",
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      "id": "RSMorphic",
      "label": "M6: Rudin–Shapiro two-word image start is rational ⇔ uv=vu; otherwise transcendental",
      "state": "checked",
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      "id": "RSNorm",
      "label": "M7: norm on a fixed curve; nonzero resultant, height O(m³4^j)",
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      "id": "RSPairValues",
      "label": "M7: R(a,b),R(−a,−b) algebraically independent over Q, including the diagonal",
      "state": "checked",
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    {
      "id": "GeneralSparse",
      "label": "When E_n=o(n) and formal independence: order AL² for every fixed A",
      "state": "checked",
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    {
      "id": "FibEquation",
      "label": "Fibonacci: exact equation with transition (ab,a), invertibility, and height O(φ^j)",
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      "id": "FibNonzero",
      "label": "Irrational weight φu+v: unique leading monomial and control of the infinite tail",
      "state": "checked",
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    {
      "id": "FatouKnown",
      "label": "Known Fatou theorem + nonperiodic diagonal: formal transcendence of F",
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    {
      "id": "FibValue",
      "label": "M8: Fibonacci F(a,b) is transcendental for all admissible parameters in this construction",
      "state": "checked",
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      "id": "FibMorphic",
      "label": "M8: Fibonacci two-word image start rational ⇔ uv=vu; otherwise transcendental",
      "state": "checked",
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      "id": "AffineFree",
      "label": "Normalized 2-adic maps form a free monoid; renormalization coefficient nonzero",
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    {
      "id": "IrrationalPF",
      "label": "M9: transcendence for primitive binary substitutions with irrational PF",
      "state": "checked",
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      "id": "IntegerPF",
      "label": "M10: integer leading value, second root 0 or modulus at least 2",
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      "id": "UnitEigen",
      "label": "M11: second root ±1, exact algebraic coordinates and value transfer",
      "state": "checked",
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      "id": "PrimitiveBinary",
      "label": "M11: primitive binary substitutions, nonperiodic fixed word — all spectra",
      "state": "checked",
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      "id": "SAdic",
      "label": "M12: arbitrary directive with a common irrational matrix; compactness and uniform estimates",
      "state": "checked",
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      "id": "CompactTower",
      "label": "M13: common primitive matrix of any spectrum; explicit compact nonperiodic family",
      "state": "checked",
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    {
      "id": "IrrationalExample",
      "label": "0079: explicit family with irrational frequency; arbitrary binary directive",
      "state": "checked",
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    {
      "id": "TernaryExample",
      "label": "0080: explicit ternary family; nonperiodicity via period divisibility",
      "state": "checked",
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      "id": "CFGap",
      "label": "0082: compact irrational CF directions; separation of finite weight sets",
      "state": "checked",
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      "id": "VariableMatrix",
      "label": "M14: σ_a=(0^a1,0), a=1 or 2; arbitrary directive, varying matrices",
      "state": "checked",
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      "id": "UnboundedCF",
      "label": "M15: any positive digits; algebraicity forces them to be bounded",
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      "id": "MovingOne",
      "label": "M16: the one in any block position; two exact valuations and heights",
      "state": "checked",
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    {
      "id": "MechanicalRepresentation",
      "label": "M17: all irrational mechanical words and intercepts; exact representation",
      "state": "checked",
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      "id": "KnownComplexity",
      "label": "Dubickas: linear lower complexity bound; rational domain checked",
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      "id": "QuasiSturmian",
      "label": "Known exclusion of p(n)=n+C for nonperiodic rational codes",
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      "id": "QuasiValues",
      "label": "M18: transcendence of F for quasisturmian words; known representation and affine normalization",
      "state": "checked",
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      "id": "AlgebraicValues",
      "label": "M19: arguments algebraic over Q, any prime p, positive valuations",
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    {
      "id": "ParameterBoundary",
      "label": "0099: for arbitrary parameters from Q_p transcendence is false; explicit example F=p",
      "state": "checked",
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    {
      "id": "WordBoundary",
      "label": "0101/0103: cannot allow all nonperiodic words; F(2/3,2/3)=4",
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    {
      "id": "ThreeSystem",
      "label": "0104: three-state system; exact six-step return and nonzero determinants",
      "state": "checked",
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    {
      "id": "ThreeFormal",
      "label": "0106: formal H(w) transcendental; known Mahler dichotomy",
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    {
      "id": "ThreeComplexity",
      "label": "0107–0110: frequencies 1/3 or 2/3, complexity≤15L for all six projections",
      "state": "checked",
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    {
      "id": "FrequencyGrowth",
      "label": "0109/0110: β=max(ρlog3−log2,0); p(L)≤cL+O(1) and cβ<log2 exclude rational code",
      "state": "checked",
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    {
      "id": "AutomaticConditional",
      "label": "0111/0113: p(L)≤kD²L; with existing frequency and kD²β<log2, start is irrational",
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    {
      "id": "CyclicConditional",
      "label": "0112/0113: popcount mod m, frequency r/m; m(2m−1)β<log2 suffices",
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    {
      "id": "CyclicExplicit",
      "label": "0114/0116: explicit blocks at q and 2q; 3^(2r)<2^(3m) excludes rational start",
      "state": "checked",
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    {
      "id": "FrequencyFree",
      "label": "0115/0118: exact height deficit for repeats; unboundedness excludes rational start without frequency",
      "state": "checked",
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    {
      "id": "AutomaticDensityKnown",
      "label": "0117: existing automatic frequency is rational; small domain already known",
      "state": "checked",
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    {
      "id": "CyclicImagePeriod",
      "label": "0120–0124: h(s) images, Λ>0, periodic ⇔ all words commute pairwise; empty words allowed",
      "state": "checked",
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        -0.10850968293614095
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    {
      "id": "CyclicMorphic",
      "label": "0119–0124: different lengths, Λ>0; when 3^(2R)<2^(3Λ), rationality ⇔ pairwise commutativity",
      "state": "checked",
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      "dashed": true
    },
    {
      "from": "Descent",
      "to": "Full",
      "label": "",
      "dashed": false
    },
    {
      "from": "MahlerIrr",
      "to": "TMExcluded",
      "label": "",
      "dashed": false
    },
    {
      "from": "CZKnown",
      "to": "MahlerIrr",
      "label": "",
      "dashed": false
    },
    {
      "from": "CZKnown",
      "to": "DValue",
      "label": "",
      "dashed": false
    },
    {
      "from": "DValue",
      "to": "PDExcluded",
      "label": "",
      "dashed": false
    },
    {
      "from": "MahlerIrr",
      "to": "TMMasks",
      "label": "",
      "dashed": false
    },
    {
      "from": "MahlerIrr",
      "to": "MorphicCriterion",
      "label": "",
      "dashed": false
    },
    {
      "from": "MorphicCriterion",
      "to": "OtherCodes",
      "label": "other codes are not covered",
      "dashed": true
    },
    {
      "from": "PDContraction",
      "to": "PDMorphic",
      "label": "",
      "dashed": false
    },
    {
      "from": "PDMorphic",
      "to": "PDGrowing",
      "label": "M5 extends the M4 domain",
      "dashed": true
    },
    {
      "from": "PDGrowing",
      "to": "OtherCodes",
      "label": "other codes are not covered",
      "dashed": true
    },
    {
      "from": "ScalarF",
      "to": "FormalH",
      "label": "",
      "dashed": false
    },
    {
      "from": "ScalarF",
      "to": "ScalarBarrier",
      "label": "",
      "dashed": false
    },
    {
      "from": "ScalarBarrier",
      "to": "HValue",
      "label": "only this transformation method is covered",
      "dashed": true
    },
    {
      "from": "FormalH",
      "to": "FormalTransH",
      "label": "",
      "dashed": false
    },
    {
      "from": "NishiokaKnown",
      "to": "FormalTransH",
      "label": "",
      "dashed": false
    },
    {
      "from": "ScalarF",
      "to": "AuxiliaryValue",
      "label": "",
      "dashed": false
    },
    {
      "from": "FormalTransH",
      "to": "HValue",
      "label": "",
      "dashed": false
    },
    {
      "from": "AuxiliaryValue",
      "to": "HValue",
      "label": "",
      "dashed": false
    },
    {
      "from": "HValue",
      "to": "PDGrowing",
      "label": "",
      "dashed": false
    },
    {
      "from": "MahlerIrr",
      "to": "HeightDomain",
      "label": "extension of the same proof",
      "dashed": true
    },
    {
      "from": "PDExcluded",
      "to": "OtherCodes",
      "label": "the exclusion applies only to the stated class",
      "dashed": true
    },
    {
      "from": "TMMasks",
      "to": "OtherCodes",
      "label": "arbitrary masks are not covered",
      "dashed": true
    },
    {
      "from": "TMExcluded",
      "to": "OtherCodes",
      "label": "the exclusion applies only to the stated class",
      "dashed": true
    },
    {
      "from": "RSSystem",
      "to": "RSInvert",
      "label": "",
      "dashed": false
    },
    {
      "from": "NishiokaKnown",
      "to": "RSFormal",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSInvert",
      "to": "RSJoint",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSNonzero",
      "to": "RSJoint",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSFormal",
      "to": "RSJoint",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSJoint",
      "to": "RSSelected",
      "label": "strengthened by a separate M6 argument",
      "dashed": true
    },
    {
      "from": "RSChoiceBarrier",
      "to": "RSSelected",
      "label": "the structure of this specific system is required",
      "dashed": true
    },
    {
      "from": "RSDiagonalKnown",
      "to": "RSPairFormal",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSPairFormal",
      "to": "RSSparse",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSSparse",
      "to": "RSResultant",
      "label": "one large order is insufficient",
      "dashed": true
    },
    {
      "from": "RSSparse",
      "to": "RSHermite",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSHermite",
      "to": "RSSquarefree",
      "label": "existence of the required specialization is unproved",
      "dashed": true
    },
    {
      "from": "RSGcd",
      "to": "RSSquarefree",
      "label": "alternative certificate not constructed",
      "dashed": true
    },
    {
      "from": "RSSquarefree",
      "to": "RSResultant",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSResultant",
      "to": "RSConditional",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSConditional",
      "to": "RSSelected",
      "label": "alternative sufficient premise",
      "dashed": true
    },
    {
      "from": "RSGelfondKnown",
      "to": "RSGelfondCriterion",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSSparse",
      "to": "RSGelfondCriterion",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSInvert",
      "to": "RSGelfondCriterion",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSNonzero",
      "to": "RSGelfondCriterion",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSPairFormal",
      "to": "RSGelfondCriterion",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSGelfondCriterion",
      "to": "RSSelected",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSSelected",
      "to": "RSMorphic",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSMorphic",
      "to": "OtherCodes",
      "label": "other codes are not covered",
      "dashed": true
    },
    {
      "from": "RSSparse",
      "to": "RSNorm",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSInvert",
      "to": "RSNorm",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSNonzero",
      "to": "RSNorm",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSGelfondCriterion",
      "to": "RSNorm",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSNorm",
      "to": "RSPairValues",
      "label": "",
      "dashed": false
    },
    {
      "from": "RSPairValues",
      "to": "RSSelected",
      "label": "",
      "dashed": false
    },
    {
      "from": "GeneralSparse",
      "to": "OtherCodes",
      "label": "the formal lemma requires additional inputs",
      "dashed": true
    },
    {
      "from": "FibEquation",
      "to": "FibValue",
      "label": "",
      "dashed": false
    },
    {
      "from": "FibNonzero",
      "to": "FibValue",
      "label": "",
      "dashed": false
    },
    {
      "from": "FatouKnown",
      "to": "FibValue",
      "label": "",
      "dashed": false
    },
    {
      "from": "FibValue",
      "to": "FibMorphic",
      "label": "",
      "dashed": false
    },
    {
      "from": "FibMorphic",
      "to": "OtherCodes",
      "label": "other codes are not covered",
      "dashed": true
    },
    {
      "from": "FibNonzero",
      "to": "IrrationalPF",
      "label": "checked weight generalization",
      "dashed": true
    },
    {
      "from": "AffineFree",
      "to": "IrrationalPF",
      "label": "",
      "dashed": false
    },
    {
      "from": "FatouKnown",
      "to": "IrrationalPF",
      "label": "",
      "dashed": false
    },
    {
      "from": "IrrationalPF",
      "to": "IntegerPF",
      "label": "beyond the irrational-weight case",
      "dashed": true
    },
    {
      "from": "IntegerPF",
      "to": "OtherCodes",
      "label": "other codes are not covered",
      "dashed": true
    },
    {
      "from": "AffineFree",
      "to": "WeightedCurve",
      "label": "",
      "dashed": false
    },
    {
      "from": "WeightedCurve",
      "to": "IntegerPF",
      "label": "",
      "dashed": false
    },
    {
      "from": "RationalPFNonzero",
      "to": "IntegerPF",
      "label": "",
      "dashed": false
    },
    {
      "from": "LocalCounter",
      "to": "RationalPFNonzero",
      "label": "an exact coefficient domain is required",
      "dashed": true
    },
    {
      "from": "IrrationalPF",
      "to": "OtherCodes",
      "label": "other codes are not covered",
      "dashed": true
    },
    {
      "from": "OtherCodes",
      "to": "Full",
      "label": "a universal conclusion is required",
      "dashed": true
    },
    {
      "from": "ThetaPadicWindowDescent",
      "to": "ThetaIntegralDuality",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaIntegralDuality",
      "to": "ThetaScalarDenominatorOpen",
      "label": "global estimate remains open",
      "dashed": true
    },
    {
      "from": "ThetaIntegralDuality",
      "to": "ThetaLocalExceptions",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaExcessPeriodicity",
      "to": "ThetaLocalExceptions",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaLocalExceptions",
      "to": "ThetaScalarDenominatorOpen",
      "label": "full depth and the sum over primes remain open",
      "dashed": true
    },
    {
      "from": "ThetaLocalExceptions",
      "to": "ThetaKrylovCandidate",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaKrylovCandidate",
      "to": "ThetaScalarDenominatorOpen",
      "label": "an estimate for the actual matrices is required",
      "dashed": true
    },
    {
      "from": "ThetaFirstJet",
      "to": "ThetaJetWidth",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaSummedMultiplicity",
      "to": "ThetaJetWidth",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaJetWidth",
      "to": "ThetaDeepExcessOpen",
      "label": "explicit coefficients and their divisibility are needed",
      "dashed": true
    },
    {
      "from": "ThetaScalarMinorGcd",
      "to": "ThetaCubicLocation",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaSpecialCyclotomic",
      "to": "ThetaCubicLocation",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaOneRowResultant",
      "to": "ThetaCubicLocation",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaCubicLocation",
      "to": "ThetaDeepExcessOpen",
      "label": "possible part of the cubic contribution under D",
      "dashed": true
    },
    {
      "from": "ThetaCubicLocation",
      "to": "ThetaLargeOrderOpen",
      "label": "possible part of the cubic contribution under D",
      "dashed": true
    },
    {
      "from": "ThetaDeepExcessOpen",
      "to": "ThetaScalarDenominatorOpen",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaLargeOrderOpen",
      "to": "ThetaScalarDenominatorOpen",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaCubicLocation",
      "to": "ThetaFirstJet",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaPadicWindowDescent",
      "to": "ThetaFirstJet",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaFirstJet",
      "to": "ThetaDeepExcessOpen",
      "label": "actual unit status of the coefficient is needed",
      "dashed": true
    },
    {
      "from": "ThetaIntegralDuality",
      "to": "ThetaOneRowResultant",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaFormalKrylov",
      "to": "ThetaOneRowResultant",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaOneRowResultant",
      "to": "ThetaScalarDenominatorOpen",
      "label": "full depth and the other channels remain open",
      "dashed": true
    },
    {
      "from": "ThetaKrylovCandidate",
      "to": "ThetaFormalKrylov",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaLocalExceptions",
      "to": "ThetaFormalKrylov",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaFormalKrylov",
      "to": "ThetaScalarDenominatorOpen",
      "label": "norm height and full depth remain open",
      "dashed": true
    },
    {
      "from": "ThetaPadicWindowDescent",
      "to": "ThetaOrderFourSecond",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaOrderFourSecond",
      "to": "ThetaScalarDenominatorOpen",
      "label": "other orders and the common gcd remain open",
      "dashed": true
    },
    {
      "from": "IrrationalPF",
      "to": "PrimitiveBinary",
      "label": "",
      "dashed": false
    },
    {
      "from": "IntegerPF",
      "to": "PrimitiveBinary",
      "label": "",
      "dashed": false
    },
    {
      "from": "AffineFree",
      "to": "UnitEigen",
      "label": "",
      "dashed": false
    },
    {
      "from": "UnitEigen",
      "to": "PrimitiveBinary",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrimitiveBinary",
      "to": "OtherCodes",
      "label": "other codes are not covered",
      "dashed": true
    },
    {
      "from": "PrimitiveBinary",
      "to": "SAdic",
      "label": "variable directive",
      "dashed": true
    },
    {
      "from": "CoefficientSource",
      "to": "CompactTower",
      "label": "",
      "dashed": false
    },
    {
      "from": "SAdic",
      "to": "CompactTower",
      "label": "",
      "dashed": false
    },
    {
      "from": "SAdic",
      "to": "IrrationalExample",
      "label": "",
      "dashed": false
    },
    {
      "from": "CompactTower",
      "to": "TernaryExample",
      "label": "",
      "dashed": false
    },
    {
      "from": "CompactTower",
      "to": "VariableMatrix",
      "label": "",
      "dashed": false
    },
    {
      "from": "CFGap",
      "to": "VariableMatrix",
      "label": "",
      "dashed": false
    },
    {
      "from": "VariableMatrix",
      "to": "UnboundedCF",
      "label": "unbounded digits",
      "dashed": true
    },
    {
      "from": "UnboundedCF",
      "to": "MovingOne",
      "label": "",
      "dashed": false
    },
    {
      "from": "MovingOne",
      "to": "MechanicalRepresentation",
      "label": "",
      "dashed": false
    },
    {
      "from": "MechanicalRepresentation",
      "to": "QuasiValues",
      "label": "",
      "dashed": false
    },
    {
      "from": "MovingOne",
      "to": "AlgebraicValues",
      "label": "",
      "dashed": false
    },
    {
      "from": "MechanicalRepresentation",
      "to": "AlgebraicValues",
      "label": "",
      "dashed": false
    },
    {
      "from": "QuasiValues",
      "to": "AlgebraicValues",
      "label": "",
      "dashed": false
    },
    {
      "from": "ParameterBoundary",
      "to": "AlgebraicValues",
      "label": "parameter-domain restriction",
      "dashed": true
    },
    {
      "from": "WordBoundary",
      "to": "AlgebraicValues",
      "label": "word-family restriction",
      "dashed": true
    },
    {
      "from": "ThreeSystem",
      "to": "ThreeFormal",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThreeComplexity",
      "to": "ThreeIrrational",
      "label": "",
      "dashed": false
    },
    {
      "from": "FrequencyGrowth",
      "to": "ThreeIrrational",
      "label": "",
      "dashed": false
    },
    {
      "from": "FrequencyGrowth",
      "to": "AutomaticConditional",
      "label": "",
      "dashed": false
    },
    {
      "from": "FrequencyFree",
      "to": "FrequencyGrowth",
      "label": "",
      "dashed": false
    },
    {
      "from": "FrequencyFree",
      "to": "OtherCodes",
      "label": "unboundedness in full generality is unproved",
      "dashed": true
    },
    {
      "from": "AutomaticDensityKnown",
      "to": "AutomaticConditional",
      "label": "refinement using the known result",
      "dashed": true
    },
    {
      "from": "FrequencyGrowth",
      "to": "CyclicConditional",
      "label": "",
      "dashed": false
    },
    {
      "from": "FrequencyGrowth",
      "to": "CyclicExplicit",
      "label": "",
      "dashed": false
    },
    {
      "from": "CyclicExplicit",
      "to": "CyclicMorphic",
      "label": "",
      "dashed": false
    },
    {
      "from": "CyclicImagePeriod",
      "to": "CyclicMorphic",
      "label": "",
      "dashed": false
    },
    {
      "from": "BaseProjection",
      "to": "AllBasePhase",
      "label": "",
      "dashed": false
    },
    {
      "from": "AllBasePhase",
      "to": "PrefixSquares",
      "label": "",
      "dashed": false
    },
    {
      "from": "FrequencyFree",
      "to": "PrefixSquares",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrefixSquares",
      "to": "BaseChangeBoundary",
      "label": "other bases do not follow",
      "dashed": true
    },
    {
      "from": "AllBasePhase",
      "to": "PeriodicCycles",
      "label": "",
      "dashed": false
    },
    {
      "from": "PeriodicCycles",
      "to": "OneSymbolCycles",
      "label": "",
      "dashed": false
    },
    {
      "from": "PeriodicCycles",
      "to": "AllPositiveCycles",
      "label": "general question of integer cycles unresolved",
      "dashed": true
    },
    {
      "from": "AllPositiveCycles",
      "to": "Full",
      "label": "necessary part",
      "dashed": true
    },
    {
      "from": "PrefixSquares",
      "to": "OtherCodes",
      "label": "arbitrary codes are not covered",
      "dashed": true
    },
    {
      "from": "ThreeFormal",
      "to": "JointThreeValues",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThreeSystem",
      "to": "JointThreeValues",
      "label": "",
      "dashed": false
    },
    {
      "from": "JointThreeValues",
      "to": "ThreeTranscendence",
      "label": "earlier joint conclusion",
      "dashed": true
    },
    {
      "from": "ThreeSystem",
      "to": "ThreeGaugeBoundary",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThreeSystem",
      "to": "ThreeAffine",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThreeAffine",
      "to": "RiccatiDegree",
      "label": "",
      "dashed": false
    },
    {
      "from": "RiccatiDegree",
      "to": "RationalIrreducibility",
      "label": "",
      "dashed": false
    },
    {
      "from": "RationalIrreducibility",
      "to": "ThreeScalarOrder",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThreeAffine",
      "to": "ThreeScalarOrder",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThreeScalarOrder",
      "to": "SelectedValueBoundary",
      "label": "separate functional result",
      "dashed": true
    },
    {
      "from": "RationalIrreducibility",
      "to": "SelectedValueBoundary",
      "label": "does not itself give numerical transfer",
      "dashed": true
    },
    {
      "from": "CyclicMorphic",
      "to": "OtherCodes",
      "label": "arbitrary codes are not covered",
      "dashed": true
    },
    {
      "from": "CyclicConditional",
      "to": "CyclicExplicit",
      "label": "stronger criterion for the same family",
      "dashed": true
    },
    {
      "from": "CyclicExplicit",
      "to": "OtherCodes",
      "label": "other codes are not covered",
      "dashed": true
    },
    {
      "from": "AutomaticConditional",
      "to": "OtherCodes",
      "label": "arbitrary codes are not covered",
      "dashed": true
    },
    {
      "from": "CyclicConditional",
      "to": "OtherCodes",
      "label": "arbitrary codes are not covered",
      "dashed": true
    },
    {
      "from": "SubspaceKnown",
      "to": "SubspaceM20",
      "label": "",
      "dashed": false
    },
    {
      "from": "SubspaceKnown",
      "to": "JointRealPadicM21",
      "label": "",
      "dashed": false
    },
    {
      "from": "JointRealPadicM21",
      "to": "JointOddAffine",
      "label": "",
      "dashed": false
    },
    {
      "from": "JointRealPadicM21",
      "to": "JointWindowDrift",
      "label": "",
      "dashed": false
    },
    {
      "from": "JointRealPadicM21",
      "to": "JointPrefixOscillation",
      "label": "",
      "dashed": false
    },
    {
      "from": "JointPrefixOscillation",
      "to": "MaskZeroBanach",
      "label": "",
      "dashed": false
    },
    {
      "from": "MaskZeroBanach",
      "to": "MaskSelected",
      "label": "",
      "dashed": false
    },
    {
      "from": "FrequencyFreeSubspace",
      "to": "MaskSelected",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrimitiveHeightSubspace",
      "to": "NumeratorSubspace",
      "label": "",
      "dashed": false
    },
    {
      "from": "ActualErrorReduction",
      "to": "NumeratorSubspace",
      "label": "",
      "dashed": false
    },
    {
      "from": "PeriodPowerReduction",
      "to": "NumeratorSubspace",
      "label": "",
      "dashed": false
    },
    {
      "from": "NumeratorSubspace",
      "to": "ZeroPeriodHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "NumeratorSubspace",
      "to": "OnePeriodHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "OnePeriodHeight",
      "to": "FixedPeriodHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "FixedPeriodHeight",
      "to": "GrowingPeriodHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "GrowingPeriodHeight",
      "to": "ExpandingPeriodHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "IntegerBranchBound",
      "to": "ExpandingPeriodHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "IntegerBranchBound",
      "to": "FullPrecisionBranch",
      "label": "",
      "dashed": false
    },
    {
      "from": "FullPrecisionBranch",
      "to": "FullPrecisionValuation",
      "label": "",
      "dashed": false
    },
    {
      "from": "FullPrecisionValuation",
      "to": "FullRationalGcd",
      "label": "",
      "dashed": false
    },
    {
      "from": "FullPrecisionBranch",
      "to": "BlockDescentHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "BakerPeriodHeight",
      "to": "BlockDescentHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "BlockDescentHeight",
      "to": "OtherCodes",
      "label": "descent below the original number is unproved",
      "dashed": true
    },
    {
      "from": "FullPrecisionBranch",
      "to": "UniformActualValuation",
      "label": "",
      "dashed": false
    },
    {
      "from": "AutomaticOriginKnown",
      "to": "UniformActualValuation",
      "label": "",
      "dashed": false
    },
    {
      "from": "UniformActualValuation",
      "to": "BlockDescentHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "FullPrecisionValuation",
      "to": "LocalDenominatorGrowth",
      "label": "",
      "dashed": false
    },
    {
      "from": "FullRationalGcd",
      "to": "LocalDenominatorGrowth",
      "label": "",
      "dashed": false
    },
    {
      "from": "UniformActualValuation",
      "to": "LocalDenominatorGrowth",
      "label": "",
      "dashed": false
    },
    {
      "from": "ChainedRepeatSelection",
      "to": "OrderedRepeatSelection",
      "label": "general coverage is unproved",
      "dashed": true
    },
    {
      "from": "SturmianFixedReturns",
      "to": "OrderedRepeatSelection",
      "label": "special case",
      "dashed": true
    },
    {
      "from": "ChainedRepeatSelection",
      "to": "RepeatGraphDichotomy",
      "label": "",
      "dashed": false
    },
    {
      "from": "FixedReturnsIce",
      "to": "RepeatGraphDichotomy",
      "label": "",
      "dashed": false
    },
    {
      "from": "RepeatGraphDichotomy",
      "to": "OrderedRepeatSelection",
      "label": "existence of a positive branch is unproved",
      "dashed": true
    },
    {
      "from": "ExactLcpCounts",
      "to": "OrderedRepeatSelection",
      "label": "general transfer is open",
      "dashed": true
    },
    {
      "from": "DiscountedRepeats",
      "to": "DiscountedApplicability",
      "label": "a property of the actual graph is required",
      "dashed": true
    },
    {
      "from": "DiscountedApplicability",
      "to": "OrderedRepeatSelection",
      "label": "general coverage is open",
      "dashed": true
    },
    {
      "from": "ConstantRunGeometry",
      "to": "DiscountedApplicability",
      "label": "more general words remain open",
      "dashed": true
    },
    {
      "from": "WeightedLcpReward",
      "to": "DiscountedRepeats",
      "label": "",
      "dashed": false
    },
    {
      "from": "DiscountedRepeats",
      "to": "DiscountedGraphDuality",
      "label": "",
      "dashed": false
    },
    {
      "from": "DiscountedGraphDuality",
      "to": "DiscountedApplicability",
      "label": "exact recursion is not established",
      "dashed": true
    },
    {
      "from": "DiscountedRepeats",
      "to": "FiniteDeletionReward",
      "label": "",
      "dashed": false
    },
    {
      "from": "DiscountedGraphDuality",
      "to": "FixedPrecisionLabels",
      "label": "",
      "dashed": false
    },
    {
      "from": "FixedPrecisionLabels",
      "to": "DiscountedApplicability",
      "label": "one bounded start at growing precision has not been obtained",
      "dashed": true
    },
    {
      "from": "FixedPrecisionLabels",
      "to": "BoundedStartCompactness",
      "label": "",
      "dashed": false
    },
    {
      "from": "FixedPrecisionLabels",
      "to": "LcpRewardBoundary",
      "label": "",
      "dashed": false
    },
    {
      "from": "BoundedStartCompactness",
      "to": "DiscountedApplicability",
      "label": "existence of the required bounded family is open",
      "dashed": true
    },
    {
      "from": "GrowingPrecisionBoundary",
      "to": "BoundedStartCompactness",
      "label": "precision must be compared with height",
      "dashed": true
    },
    {
      "from": "AutomaticRepeatChains",
      "to": "ChainedRepeatSelection",
      "label": "",
      "dashed": false
    },
    {
      "from": "AutomaticRepeatChains",
      "to": "AutomaticArithmeticMargin",
      "label": "additional arithmetic estimates are needed",
      "dashed": true
    },
    {
      "from": "AutomaticArithmeticMargin",
      "to": "OtherCodes",
      "label": "general coverage is not established",
      "dashed": true
    },
    {
      "from": "AutomaticRepeatChains",
      "to": "AutomaticArithmeticRequirements",
      "label": "",
      "dashed": false
    },
    {
      "from": "AutomaticArithmeticRequirements",
      "to": "AutomaticArithmeticMargin",
      "label": "existence of a sufficient margin is open",
      "dashed": true
    },
    {
      "from": "DiscountedGraphDuality",
      "to": "FiniteValuePersistentTail",
      "label": "",
      "dashed": false
    },
    {
      "from": "ComparableSubstitutionChains",
      "to": "ChainedRepeatSelection",
      "label": "",
      "dashed": false
    },
    {
      "from": "ComparableSubstitutionChains",
      "to": "OrderedRepeatSelection",
      "label": "not all morphic words are covered",
      "dashed": true
    },
    {
      "from": "ComparableSubstitutionChains",
      "to": "PureMorphicLinearChains",
      "label": "",
      "dashed": false
    },
    {
      "from": "PureMorphicLinearChains",
      "to": "ChainedRepeatSelection",
      "label": "",
      "dashed": false
    },
    {
      "from": "IncreasingRunGeometry",
      "to": "ChainedRepeatSelection",
      "label": "under linear complexity",
      "dashed": false
    },
    {
      "from": "IncreasingRunGeometry",
      "to": "IncreasingRunPaths",
      "label": "",
      "dashed": false
    },
    {
      "from": "IncreasingRunPaths",
      "to": "RepeatGraphDichotomy",
      "label": "",
      "dashed": false
    },
    {
      "from": "IncreasingRunGeometry",
      "to": "WeightedWordWithoutChain",
      "label": "",
      "dashed": false
    },
    {
      "from": "WeightedWordWithoutChain",
      "to": "WeightedLcpReward",
      "label": "",
      "dashed": false
    },
    {
      "from": "WeightedWordWithoutChain",
      "to": "ShortRunWeightedWord",
      "label": "",
      "dashed": false
    },
    {
      "from": "ShortRunWeightedWord",
      "to": "WeightedLcpReward",
      "label": "",
      "dashed": false
    },
    {
      "from": "SubspaceM20",
      "to": "TernaryM20Application",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrimitiveBinary",
      "to": "TernaryM20Application",
      "label": "",
      "dashed": false
    },
    {
      "from": "TernaryM20Application",
      "to": "Rung1FiniteBridge",
      "label": "",
      "dashed": false
    },
    {
      "from": "Rung1FiniteBridge",
      "to": "UniformBlockReduction",
      "label": "",
      "dashed": false
    },
    {
      "from": "UniformBlockReduction",
      "to": "EqualCompletionOrbit",
      "label": "",
      "dashed": false
    },
    {
      "from": "EqualCompletionOrbit",
      "to": "PadicRationalLifting",
      "label": "",
      "dashed": false
    },
    {
      "from": "PadicLocalBound",
      "to": "PadicRationalLifting",
      "label": "",
      "dashed": false
    },
    {
      "from": "PadicAuxiliaryAlgebra",
      "to": "PadicRationalLifting",
      "label": "",
      "dashed": false
    },
    {
      "from": "PadicLocalDescent",
      "to": "PadicRationalLifting",
      "label": "",
      "dashed": false
    },
    {
      "from": "PadicRationalLifting",
      "to": "UniformBlockApplication",
      "label": "",
      "dashed": false
    },
    {
      "from": "EqualCompletionOrbit",
      "to": "UniformBlockApplication",
      "label": "",
      "dashed": false
    },
    {
      "from": "UniformBlockReduction",
      "to": "UniformBlockApplication",
      "label": "",
      "dashed": false
    },
    {
      "from": "PadicRationalLifting",
      "to": "FiniteKernelValueTransfer",
      "label": "",
      "dashed": false
    },
    {
      "from": "FiniteKernelValueTransfer",
      "to": "UniformBlockApplication",
      "label": "",
      "dashed": false
    },
    {
      "from": "FiniteKernelValueTransfer",
      "to": "BoundedDiscrepancyApplication",
      "label": "",
      "dashed": false
    },
    {
      "from": "PadicRationalLifting",
      "to": "PolynomialSystemTransfer",
      "label": "",
      "dashed": false
    },
    {
      "from": "PolynomialSystemTransfer",
      "to": "FiniteExponentOrbit",
      "label": "",
      "dashed": false
    },
    {
      "from": "PolynomialSystemTransfer",
      "to": "PrefixQuotientCriterion",
      "label": "",
      "dashed": false
    },
    {
      "from": "FiniteExponentOrbit",
      "to": "PrefixQuotientCriterion",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrefixQuotientCriterion",
      "to": "PrefixQuotientCertificate",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrefixQuotientCertificate",
      "to": "LogGrowthPowerBound",
      "label": "",
      "dashed": false
    },
    {
      "from": "LogGrowthPowerBound",
      "to": "LogGrowthQuotient",
      "label": "a new transfer is required",
      "dashed": true
    },
    {
      "from": "LogGrowthPowerBound",
      "to": "LogDiscrepancyState",
      "label": "",
      "dashed": false
    },
    {
      "from": "LogDiscrepancyState",
      "to": "SingleLogDiscrepancy",
      "label": "",
      "dashed": false
    },
    {
      "from": "SingleLogDiscrepancy",
      "to": "LogDiscrepancyPeriodicity",
      "label": "",
      "dashed": false
    },
    {
      "from": "LogDiscrepancyPeriodicity",
      "to": "AutomaticUniformFrequency",
      "label": "",
      "dashed": false
    },
    {
      "from": "AutomaticUniformFrequency",
      "to": "BeyondLogTransfer",
      "label": "",
      "dashed": false
    },
    {
      "from": "AutomaticUniformFrequency",
      "to": "MultivariateAutomaticSystem",
      "label": "",
      "dashed": false
    },
    {
      "from": "MultivariateAutomaticSystem",
      "to": "MultivariateLocalBound",
      "label": "",
      "dashed": false
    },
    {
      "from": "MultivariateLocalBound",
      "to": "BeyondLogTransfer",
      "label": "",
      "dashed": false
    },
    {
      "from": "AlgebraicBranchBoundary",
      "to": "BeyondLogTransfer",
      "label": "an algebraic equation is insufficient",
      "dashed": true
    },
    {
      "from": "MultivariateAutomaticSystem",
      "to": "MonomialProgressionCriterion",
      "label": "orbit dependencies",
      "dashed": true
    },
    {
      "from": "MonomialProgressionCriterion",
      "to": "ToricOrbitClosure",
      "label": "",
      "dashed": false
    },
    {
      "from": "ToricOrbitClosure",
      "to": "HomogeneousNonvanishing",
      "label": "passage to germs",
      "dashed": true
    },
    {
      "from": "HomogeneousNonvanishing",
      "to": "BeyondLogTransfer",
      "label": "remaining lifting conditions",
      "dashed": true
    },
    {
      "from": "ToricOrbitClosure",
      "to": "NonsingularConeReduction",
      "label": "matrix reduction",
      "dashed": true
    },
    {
      "from": "NonsingularConeReduction",
      "to": "RationalOrbitNorms",
      "label": "pointwise estimates",
      "dashed": true
    },
    {
      "from": "RationalOrbitNorms",
      "to": "AccumulatingPoles",
      "label": "fixed-disk boundary",
      "dashed": true
    },
    {
      "from": "RationalOrbitNorms",
      "to": "ShrinkingPolydisks",
      "label": "lower denominator bound",
      "dashed": true
    },
    {
      "from": "AccumulatingPoles",
      "to": "ShrinkingPolydisks",
      "label": "accounted for by shrinking the radius",
      "dashed": true
    },
    {
      "from": "ToricOrbitClosure",
      "to": "ConeAuxiliary",
      "label": "graded ring",
      "dashed": true
    },
    {
      "from": "ShrinkingPolydisks",
      "to": "ConeAuxiliary",
      "label": "high order is needed",
      "dashed": true
    },
    {
      "from": "ToricOrbitClosure",
      "to": "ConeRelationMatrix",
      "label": "avoidance of the exceptional set",
      "dashed": true
    },
    {
      "from": "ConeAuxiliary",
      "to": "ConeRelationMatrix",
      "label": "exact substitution identity is required",
      "dashed": true
    },
    {
      "from": "ConeRelationMatrix",
      "to": "ConeLocalZero",
      "label": "exact cutoff",
      "dashed": true
    },
    {
      "from": "ConeAuxiliary",
      "to": "ConeLocalZero",
      "label": "high order",
      "dashed": true
    },
    {
      "from": "ShrinkingPolydisks",
      "to": "ConeLocalZero",
      "label": "smallness of a fixed coefficient",
      "dashed": true
    },
    {
      "from": "ConeLocalZero",
      "to": "ConeConditionalDescent",
      "label": "local row",
      "dashed": true
    },
    {
      "from": "ToricOrbitClosure",
      "to": "ConeGermInjection",
      "label": "homogeneity and toric map",
      "dashed": true
    },
    {
      "from": "ConeGermInjection",
      "to": "ConeConditionalDescent",
      "label": "embedding into the germ field",
      "dashed": true
    },
    {
      "from": "BrechlerScope",
      "to": "ConeFieldRegularity",
      "label": "general transfer to the cone is unproved",
      "dashed": true
    },
    {
      "from": "ConeFieldRegularity",
      "to": "ConeConditionalDescent",
      "label": "",
      "dashed": false
    },
    {
      "from": "BrechlerScope",
      "to": "FullConeTransfer",
      "label": "full cone as a separate case",
      "dashed": true
    },
    {
      "from": "ConeConditionalDescent",
      "to": "FullConeTransfer",
      "label": "input check",
      "dashed": true
    },
    {
      "from": "FullConeTransfer",
      "to": "BeyondLogTransfer",
      "label": "",
      "dashed": false
    },
    {
      "from": "ConeConditionalDescent",
      "to": "BeyondLogTransfer",
      "label": "",
      "dashed": false
    },
    {
      "from": "BeyondLogTransfer",
      "to": "AutomaticNoFrequency",
      "label": "frequency-existence condition",
      "dashed": true
    },
    {
      "from": "FrequencyFreePadic",
      "to": "PositiveAutomatic",
      "label": "",
      "dashed": false
    },
    {
      "from": "PositiveAutomatic",
      "to": "PrimitiveWeightedGeometry",
      "label": "geometric extension",
      "dashed": true
    },
    {
      "from": "PrimitiveWeightedGeometry",
      "to": "WeightedFieldRegularity",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrimitiveWeightedGeometry",
      "to": "WeightedConeAuxiliary",
      "label": "",
      "dashed": false
    },
    {
      "from": "WeightedFieldRegularity",
      "to": "NonuniformPrimitiveSystem",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrimitiveWeightedGeometry",
      "to": "PerronPadicEstimate",
      "label": "",
      "dashed": false
    },
    {
      "from": "PerronPadicEstimate",
      "to": "WeightedLocalZero",
      "label": "",
      "dashed": false
    },
    {
      "from": "WeightedConeAuxiliary",
      "to": "WeightedLocalZero",
      "label": "",
      "dashed": false
    },
    {
      "from": "NonuniformPrimitiveSystem",
      "to": "WeightedLocalZero",
      "label": "",
      "dashed": false
    },
    {
      "from": "WeightedLocalZero",
      "to": "WeightedRationalLifting",
      "label": "",
      "dashed": false
    },
    {
      "from": "WeightedFieldRegularity",
      "to": "WeightedRationalLifting",
      "label": "",
      "dashed": false
    },
    {
      "from": "WeightedRationalLifting",
      "to": "PrimitiveCodedPeriodic",
      "label": "",
      "dashed": false
    },
    {
      "from": "NonuniformPrimitiveSystem",
      "to": "PrimitiveCodedPeriodic",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrimitiveCodedPeriodic",
      "to": "PrimitiveBlockCodes",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrimitiveCodedPeriodic",
      "to": "UniformRecurrentMorphic",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrimitiveBlockCodes",
      "to": "UniformRecurrentMorphic",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrimitiveWeightedGeometry",
      "to": "GrowingNonprimitiveGeometry",
      "label": "",
      "dashed": false
    },
    {
      "from": "GrowingNonprimitiveGeometry",
      "to": "CommonGrowthFrequency",
      "label": "",
      "dashed": false
    },
    {
      "from": "GrowingNonprimitiveGeometry",
      "to": "GrowingSystemRegularity",
      "label": "",
      "dashed": false
    },
    {
      "from": "CommonGrowthFrequency",
      "to": "CommonScalePadic",
      "label": "",
      "dashed": false
    },
    {
      "from": "CommonGrowthFrequency",
      "to": "DiscountedMorphicDensity",
      "label": "",
      "dashed": false
    },
    {
      "from": "GrowingSystemRegularity",
      "to": "CommonScaleLifting",
      "label": "",
      "dashed": false
    },
    {
      "from": "CommonScalePadic",
      "to": "CommonScaleLifting",
      "label": "",
      "dashed": false
    },
    {
      "from": "CommonScaleLifting",
      "to": "CommonGrowthRational",
      "label": "",
      "dashed": false
    },
    {
      "from": "DiscountedMorphicDensity",
      "to": "CommonGrowthRational",
      "label": "",
      "dashed": false
    },
    {
      "from": "GrowingNonprimitiveGeometry",
      "to": "IndividualGrowthTypes",
      "label": "",
      "dashed": false
    },
    {
      "from": "IndividualGrowthTypes",
      "to": "MultiscaleDensity",
      "label": "",
      "dashed": false
    },
    {
      "from": "DiscountedMorphicDensity",
      "to": "MultiscaleDensity",
      "label": "",
      "dashed": false
    },
    {
      "from": "MultiscaleDensity",
      "to": "NonerasingDensity",
      "label": "",
      "dashed": false
    },
    {
      "from": "NonerasingDensity",
      "to": "GeneralMorphicDensity",
      "label": "",
      "dashed": false
    },
    {
      "from": "IndividualGrowthTypes",
      "to": "FastFaceGrading",
      "label": "",
      "dashed": false
    },
    {
      "from": "GrowingNonprimitiveGeometry",
      "to": "FastFaceGrading",
      "label": "",
      "dashed": false
    },
    {
      "from": "FastFaceGrading",
      "to": "RelativeLatticeBase",
      "label": "",
      "dashed": false
    },
    {
      "from": "RelativeLatticeBase",
      "to": "RelativeAuxiliary",
      "label": "",
      "dashed": false
    },
    {
      "from": "FastFaceGrading",
      "to": "MaximalScalePadic",
      "label": "",
      "dashed": false
    },
    {
      "from": "CommonScalePadic",
      "to": "MaximalScalePadic",
      "label": "",
      "dashed": false
    },
    {
      "from": "RelativeAuxiliary",
      "to": "FastRelativeTail",
      "label": "",
      "dashed": false
    },
    {
      "from": "MaximalScalePadic",
      "to": "FastRelativeTail",
      "label": "",
      "dashed": false
    },
    {
      "from": "FastRelativeTail",
      "to": "RelativeLocalZero",
      "label": "",
      "dashed": false
    },
    {
      "from": "RelativeAuxiliary",
      "to": "RelativeLocalZero",
      "label": "",
      "dashed": false
    },
    {
      "from": "RelativeLocalZero",
      "to": "GrowingRationalLifting",
      "label": "",
      "dashed": false
    },
    {
      "from": "GrowingSystemRegularity",
      "to": "GrowingRationalLifting",
      "label": "",
      "dashed": false
    },
    {
      "from": "IndividualGrowthTypes",
      "to": "GrowingBanachDensity",
      "label": "",
      "dashed": false
    },
    {
      "from": "GrowingRationalLifting",
      "to": "AllGrowingRationalCodes",
      "label": "",
      "dashed": false
    },
    {
      "from": "GrowingBanachDensity",
      "to": "AllGrowingRationalCodes",
      "label": "",
      "dashed": false
    },
    {
      "from": "AllGrowingRationalCodes",
      "to": "BoundedLetterAnalytic",
      "label": "domain extension",
      "dashed": true
    },
    {
      "from": "BoundedLetterAnalytic",
      "to": "BoundedLetterGeometry",
      "label": "",
      "dashed": false
    },
    {
      "from": "BoundedLetterGeometry",
      "to": "BoundedLetterSystem",
      "label": "",
      "dashed": false
    },
    {
      "from": "BoundedLetterSystem",
      "to": "BoundedLetterFastData",
      "label": "",
      "dashed": false
    },
    {
      "from": "BoundedLetterFastData",
      "to": "BoundedLetterLocal",
      "label": "",
      "dashed": false
    },
    {
      "from": "BoundedLetterLocal",
      "to": "BoundedLetterJoin",
      "label": "",
      "dashed": false
    },
    {
      "from": "BoundedLetterJoin",
      "to": "BoundedLetterBasisValues",
      "label": "",
      "dashed": false
    },
    {
      "from": "BoundedLetterBasisValues",
      "to": "BoundedLetterRationalCodes",
      "label": "",
      "dashed": false
    },
    {
      "from": "PolynomialLetterBarrier",
      "to": "ExactWordMatrixHeight",
      "label": "separate numerical height",
      "dashed": true
    },
    {
      "from": "PolynomialLetterBarrier",
      "to": "QScalingFiniteCover",
      "label": "separate one-dimensional route",
      "dashed": true
    },
    {
      "from": "QScalingFiniteCover",
      "to": "TorusPeriodicDivisor",
      "label": "independent geometric lemma",
      "dashed": true
    },
    {
      "from": "TorusPeriodicDivisor",
      "to": "TorusCoverSources",
      "label": "checked external inputs",
      "dashed": true
    },
    {
      "from": "TorusCoverSources",
      "to": "FormalCharacterRoots",
      "label": "separate formal input",
      "dashed": true
    },
    {
      "from": "FormalCharacterRoots",
      "to": "TorusFormalRegularity",
      "label": "",
      "dashed": false
    },
    {
      "from": "TorusPeriodicDivisor",
      "to": "TorusFormalRegularity",
      "label": "",
      "dashed": false
    },
    {
      "from": "TorusCoverSources",
      "to": "TorusFormalRegularity",
      "label": "",
      "dashed": false
    },
    {
      "from": "FormalWordField",
      "to": "TorusFormalRegularity",
      "label": "input presented",
      "dashed": true
    },
    {
      "from": "BoundedFormalSpecialization",
      "to": "FormalWordField",
      "label": "formal input",
      "dashed": true
    },
    {
      "from": "PolynomialTorusGeometry",
      "to": "FormalWordField",
      "label": "geometric input",
      "dashed": true
    },
    {
      "from": "PolynomialTorusGeometry",
      "to": "PolynomialWordField",
      "label": "",
      "dashed": false
    },
    {
      "from": "BoundedFormalSpecialization",
      "to": "PolynomialWordField",
      "label": "",
      "dashed": false
    },
    {
      "from": "TorusFormalRegularity",
      "to": "PolynomialWordField",
      "label": "",
      "dashed": false
    },
    {
      "from": "PolynomialWordField",
      "to": "PolynomialActualValueStage",
      "label": "",
      "dashed": false
    },
    {
      "from": "PolynomialActualValueStage",
      "to": "PolynomialNumericTransferOpen",
      "label": "insufficient without a remainder term",
      "dashed": true
    },
    {
      "from": "QFixedOrderBarrier",
      "to": "PolynomialNumericTransferOpen",
      "label": "limit of one argument",
      "dashed": true
    },
    {
      "from": "PolynomialTorusGeometry",
      "to": "PolynomialTopDegreeTail",
      "label": "",
      "dashed": false
    },
    {
      "from": "PolynomialTopDegreeTail",
      "to": "PolynomialNumericTransferOpen",
      "label": "structural step",
      "dashed": true
    },
    {
      "from": "PolynomialTopDegreeTail",
      "to": "MultilinearThetaFormula",
      "label": "",
      "dashed": false
    },
    {
      "from": "MultilinearThetaFormula",
      "to": "PolynomialNumericTransferOpen",
      "label": "general numerical question",
      "dashed": true
    },
    {
      "from": "MultilinearThetaFormula",
      "to": "TwoGrowingBlocks",
      "label": "",
      "dashed": false
    },
    {
      "from": "TwoGrowingBlocks",
      "to": "OtherCodes",
      "label": "restricted family",
      "dashed": true
    },
    {
      "from": "MultilinearThetaFormula",
      "to": "MultilinearCancellation",
      "label": "",
      "dashed": false
    },
    {
      "from": "MultilinearCancellation",
      "to": "MultilinearArithmeticThreshold",
      "label": "",
      "dashed": false
    },
    {
      "from": "MultilinearArithmeticThreshold",
      "to": "PolynomialNumericTransferOpen",
      "label": "conditional domain",
      "dashed": true
    },
    {
      "from": "MultilinearArithmeticThreshold",
      "to": "MultilinearFullThresholdBoundary",
      "label": "",
      "dashed": false
    },
    {
      "from": "MultilinearFullThresholdBoundary",
      "to": "OtherQPrimaryScope",
      "label": "",
      "dashed": false
    },
    {
      "from": "OtherQPrimaryScope",
      "to": "PolynomialNumericTransferOpen",
      "label": "source domain",
      "dashed": true
    },
    {
      "from": "MultilinearFullThresholdBoundary",
      "to": "ThetaPadeVandermonde",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaPadeVandermonde",
      "to": "ThetaPadeCommonHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaPadeCommonHeight",
      "to": "ThetaPadeGaussianHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaPadeGaussianHeight",
      "to": "ThetaPadeOnePairDivisor",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaPadeOnePairDivisor",
      "to": "ThetaPadeType2Open",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaPadeType2Open",
      "to": "ThetaPadeType2Integral",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaPadeType2Integral",
      "to": "ThetaPadeType2Projective",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaPadeType2Projective",
      "to": "ThetaScalarHankel",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaScalarHankel",
      "to": "ThetaScalarShift",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaScalarShift",
      "to": "ThetaScalarMinorGcd",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaScalarMinorGcd",
      "to": "ThetaCyclotomicMinorDivisor",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaCyclotomicMinorDivisor",
      "to": "ThetaSpecialCyclotomic",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaSpecialCyclotomic",
      "to": "ThetaRootRank",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaRootRank",
      "to": "ThetaSummedMultiplicity",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaSummedMultiplicity",
      "to": "ThetaScalarDenominatorOpen",
      "label": "numerical gcd not estimated",
      "dashed": true
    },
    {
      "from": "ThetaSummedMultiplicity",
      "to": "ThetaThreeLayerMultiplicity",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaThreeLayerMultiplicity",
      "to": "ThetaScalarDenominatorOpen",
      "label": "numerical gcd remains open",
      "dashed": true
    },
    {
      "from": "ThetaThreeLayerMultiplicity",
      "to": "ThetaOddOrderGcd",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaOddOrderGcd",
      "to": "ThetaScalarDenominatorOpen",
      "label": "a numerical estimate is required",
      "dashed": true
    },
    {
      "from": "ThetaOddOrderGcd",
      "to": "ThetaOverlapGcdScope",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaOverlapGcdScope",
      "to": "ThetaScalarDenominatorOpen",
      "label": "full numerical gcd not estimated",
      "dashed": true
    },
    {
      "from": "ThetaRootRank",
      "to": "ThetaWeightCancellation",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaOverlapGcdScope",
      "to": "ThetaWeightCancellation",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaWeightCancellation",
      "to": "ThetaPrimeSquare",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaWeightCancellation",
      "to": "ThetaScalarDenominatorOpen",
      "label": "common growth is unproved",
      "dashed": true
    },
    {
      "from": "ThetaPrimeSquare",
      "to": "ThetaScalarDenominatorOpen",
      "label": "common growth is not established",
      "dashed": true
    },
    {
      "from": "ThetaWeightCancellation",
      "to": "ThetaRankIncrement",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaSpecialCyclotomic",
      "to": "ThetaRankIncrement",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaRankIncrement",
      "to": "ThetaScalarDenominatorOpen",
      "label": "gcd depths are unbounded",
      "dashed": true
    },
    {
      "from": "ThetaRankIncrement",
      "to": "ThetaSpectralCertificate",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaOverlapGcdScope",
      "to": "ThetaSpectralCertificate",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaSpectralCertificate",
      "to": "ThetaScalarDenominatorOpen",
      "label": "depths and short windows remain open",
      "dashed": true
    },
    {
      "from": "ThetaSpectralCertificate",
      "to": "ThetaFiniteWindow",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaFiniteWindow",
      "to": "ThetaScalarDenominatorOpen",
      "label": "shift differs from criterion D",
      "dashed": true
    },
    {
      "from": "ThetaSpecialCyclotomic",
      "to": "ThetaPadicWindowDescent",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaSummedMultiplicity",
      "to": "ThetaPadicWindowDescent",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaFiniteWindow",
      "to": "ThetaPadicWindowDescent",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaPadicWindowDescent",
      "to": "ThetaScalarDenominatorOpen",
      "label": "other primes remain open",
      "dashed": true
    },
    {
      "from": "ThetaPadicWindowDescent",
      "to": "ThetaDiagonalResidue",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaDiagonalResidue",
      "to": "ThetaScalarDenominatorOpen",
      "label": "other residues and primes remain open",
      "dashed": true
    },
    {
      "from": "ThetaPadicWindowDescent",
      "to": "ThetaExcessPeriodicity",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaExcessPeriodicity",
      "to": "ThetaScalarDenominatorOpen",
      "label": "not full depth and not all primes",
      "dashed": true
    },
    {
      "from": "ThetaPadicWindowDescent",
      "to": "ThetaDualOrderFour",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaDiagonalResidue",
      "to": "ThetaDualOrderFour",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThetaDualOrderFour",
      "to": "ThetaScalarDenominatorOpen",
      "label": "other orders and common gcd remain open",
      "dashed": true
    },
    {
      "from": "ThetaScalarDenominatorOpen",
      "to": "PolynomialNumericTransferOpen",
      "label": "a new estimate is required",
      "dashed": true
    },
    {
      "from": "BoundedLetterAnalytic",
      "to": "PolynomialLetterBarrier",
      "label": "direct-transfer boundary established",
      "dashed": true
    },
    {
      "from": "PositiveAutomatic",
      "to": "AutomaticNoFrequency",
      "label": "negative starts handled separately",
      "dashed": true
    },
    {
      "from": "ToricOrbitClosure",
      "to": "NeutralToricTwist",
      "label": "eigencones",
      "dashed": true
    },
    {
      "from": "NeutralToricTwist",
      "to": "ToricMeromorphic",
      "label": "contraction of all smaller disks",
      "dashed": true
    },
    {
      "from": "ToricMeromorphic",
      "to": "ConeFieldRegularity",
      "label": "",
      "dashed": false
    },
    {
      "from": "AlgebraicBranchBoundary",
      "to": "PositiveCoefficientBoundary",
      "label": "boundary strengthening",
      "dashed": true
    },
    {
      "from": "PositiveCoefficientBoundary",
      "to": "BeyondLogTransfer",
      "label": "structural condition is separate",
      "dashed": true
    },
    {
      "from": "MultivariateAutomaticSystem",
      "to": "BeyondLogTransfer",
      "label": "",
      "dashed": false
    },
    {
      "from": "ShortRunWeightedWord",
      "to": "DiscountedApplicability",
      "label": "arithmetic coverage is unproved",
      "dashed": true
    },
    {
      "from": "WeightedWordWithoutChain",
      "to": "DiscountedApplicability",
      "label": "general applicability is not established",
      "dashed": true
    },
    {
      "from": "OrderedRepeatSelection",
      "to": "OtherCodes",
      "label": "universal margin is also open",
      "dashed": true
    },
    {
      "from": "JointPrefixOscillation",
      "to": "JointPeriodSize",
      "label": "",
      "dashed": false
    },
    {
      "from": "JointPeriodSize",
      "to": "JointValueSelection",
      "label": "value selection is open",
      "dashed": true
    },
    {
      "from": "FullPrecisionBranch",
      "to": "BakerPeriodHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "ExpandingPeriodHeight",
      "to": "BakerPeriodHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "PeriodPowerReduction",
      "to": "PowerUniformHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "BakerPeriodHeight",
      "to": "PowerUniformHeight",
      "label": "",
      "dashed": false
    },
    {
      "from": "NumeratorSubspace",
      "to": "OtherCodes",
      "label": "required margin for all integer orbits is unproved",
      "dashed": true
    },
    {
      "from": "MaskSelected",
      "to": "OtherCodes",
      "label": "coverage of arbitrary orbits is unproved",
      "dashed": true
    },
    {
      "from": "JointPrefixOscillation",
      "to": "JointValueSelection",
      "label": "which value",
      "dashed": true
    },
    {
      "from": "JointWindowDrift",
      "to": "JointValueSelection",
      "label": "which value",
      "dashed": true
    },
    {
      "from": "AutomaticBanachDensity",
      "to": "JointWindowDrift",
      "label": "",
      "dashed": false
    },
    {
      "from": "AutomaticOriginKnown",
      "to": "JointValueSelection",
      "label": "convergence does not select a value",
      "dashed": true
    },
    {
      "from": "PeriodicPatchBoundary",
      "to": "OtherCodes",
      "label": "existence of long stretches is unproved",
      "dashed": true
    },
    {
      "from": "JointRealPadicM21",
      "to": "JointValueSelection",
      "label": "which of the two values",
      "dashed": true
    },
    {
      "from": "JointValueSelection",
      "to": "OtherCodes",
      "label": "universal coverage is also unproved",
      "dashed": true
    },
    {
      "from": "PeriodicCycles",
      "to": "FixedOddCycleBoundary",
      "label": "",
      "dashed": false
    },
    {
      "from": "PeriodicCycles",
      "to": "CyclePrimitiveCertificate",
      "label": "",
      "dashed": false
    },
    {
      "from": "CyclePrimitiveCertificate",
      "to": "AllPositiveCycles",
      "label": "divisible words still need classification",
      "dashed": true
    },
    {
      "from": "FixedOddCycleBoundary",
      "to": "AllPositiveCycles",
      "label": "no general bound in r",
      "dashed": true
    },
    {
      "from": "SubspaceM20",
      "to": "FrequencyFreeSubspace",
      "label": "",
      "dashed": false
    },
    {
      "from": "FrequencyFreeSubspace",
      "to": "PrimitiveHeightSubspace",
      "label": "",
      "dashed": false
    },
    {
      "from": "FrequencyFreeSubspace",
      "to": "LongConstantRuns",
      "label": "",
      "dashed": false
    },
    {
      "from": "LongConstantRuns",
      "to": "RationalRunBoundary",
      "label": "significance boundary",
      "dashed": true
    },
    {
      "from": "LongConstantRuns",
      "to": "OtherCodes",
      "label": "universal orbit coverage does not follow",
      "dashed": true
    },
    {
      "from": "PrimitiveHeightSubspace",
      "to": "RationalHeightLower",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrimitiveHeightSubspace",
      "to": "OtherCodes",
      "label": "independent universal upper bound not obtained",
      "dashed": true
    },
    {
      "from": "SubspaceM20",
      "to": "ComplexityBoundary",
      "label": "restriction of one consequence",
      "dashed": true
    },
    {
      "from": "FrequencyFree",
      "to": "FrequencyFreeSubspace",
      "label": "",
      "dashed": false
    },
    {
      "from": "SubspaceM20",
      "to": "OddAffineSubspace",
      "label": "",
      "dashed": false
    },
    {
      "from": "SubspaceM20",
      "to": "SparsePowerCode",
      "label": "",
      "dashed": false
    },
    {
      "from": "FrequencyFreeSubspace",
      "to": "OtherCodes",
      "label": "universal margin is not established",
      "dashed": true
    },
    {
      "from": "FrequencyGrowth",
      "to": "SubspaceM20",
      "label": "",
      "dashed": false
    },
    {
      "from": "SubspaceM20",
      "to": "ThreeTranscendence",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThreeComplexity",
      "to": "ThreeTranscendence",
      "label": "",
      "dashed": false
    },
    {
      "from": "ThreeIrrational",
      "to": "ThreeTranscendence",
      "label": "strengthened by another argument",
      "dashed": true
    },
    {
      "from": "SubspaceM20",
      "to": "DigitalTranscendence",
      "label": "",
      "dashed": false
    },
    {
      "from": "AllBasePhase",
      "to": "DigitalTranscendence",
      "label": "",
      "dashed": false
    },
    {
      "from": "PrefixSquares",
      "to": "DigitalTranscendence",
      "label": "",
      "dashed": false
    },
    {
      "from": "SubspaceM20",
      "to": "OtherCodes",
      "label": "existence of required repeats and margin for all orbits is unproved",
      "dashed": true
    },
    {
      "from": "DigitalTranscendence",
      "to": "AllPositiveCycles",
      "label": "periodic branch not excluded",
      "dashed": true
    },
    {
      "from": "ThreeIrrational",
      "to": "OtherCodes",
      "label": "other codes are not covered",
      "dashed": true
    },
    {
      "from": "AlgebraicValues",
      "to": "OtherCodes",
      "label": "arbitrary bad codes are not covered",
      "dashed": true
    },
    {
      "from": "KnownComplexity",
      "to": "QuasiSturmian",
      "label": "",
      "dashed": false
    },
    {
      "from": "QuasiSturmian",
      "to": "OtherCodes",
      "label": "other nonperiodic codes",
      "dashed": true
    },
    {
      "from": "MechanicalRepresentation",
      "to": "OtherCodes",
      "label": "other codes",
      "dashed": true
    },
    {
      "from": "UnboundedCF",
      "to": "OtherCodes",
      "label": "arbitrary bad orbit",
      "dashed": true
    },
    {
      "from": "VariableMatrix",
      "to": "OtherCodes",
      "label": "other codes are not covered",
      "dashed": true
    },
    {
      "from": "CompactTower",
      "to": "OtherCodes",
      "label": "other codes are not covered",
      "dashed": true
    }
  ],
  "snapshot": "Snapshot 2026-09-16; full conjecture unresolved; 356 nodes; 532 relationships."
}