{
  "schema": 1,
  "scope": "Bounded 26-letter affine-cipher test on the Vumarii-2019 body, conditional on the existing seven secondary readings and scored by the calibrated Turkish A23 5-gram model.",
  "sources": {
    "word_classes": "archive/gaps/tr1-00-files/vumarii2019-words.json",
    "word_classes_sha256": "81262c1ca605c686da3acba6b4ac1ea2f11196cf74e530a9c71f607d0c5c76f8",
    "transcription": "archive/gaps/tr1-00-files/vumarii-2019-TRANSCRIPTION.txt",
    "transcription_sha256": "2c6eb4492a3975c034e9fb4ba75ae676acad0fc979b76e7a0463bd77170ad6b3",
    "prior_completion_audit": "scripts/audit_vumarii_2019_turkish_completion.py"
  },
  "method": {
    "cipher_family": "all x -> a*x+b (mod 26), gcd(a,26)=1; includes Caesar shifts and Atbash-like maps",
    "invertible_multipliers": [
      1,
      3,
      5,
      7,
      9,
      11,
      15,
      17,
      19,
      21,
      23,
      25
    ],
    "affine_maps": 312,
    "residual_glyph_completions_per_map": 6720,
    "total_candidates": 2096640,
    "body_only": "The red legend remains the source glyph key; only the body is hypothetically transformed."
  },
  "result": {
    "identity_map": {
      "multiplier_a": 1,
      "offset_b": 0,
      "completion_index": 1480,
      "completion": {
        "C16": "J",
        "C17": "Y",
        "C18": "S",
        "C20": "H",
        "C21": "K"
      },
      "best_char5_bits_per_character": -5.4116467891174675,
      "best_char5_z_vs_heldout_turkish": -8.695592546508015,
      "best_char5_percentile_vs_heldout_turkish": 0.0,
      "best_turkish_word_segmentation": null,
      "candidate": "TVI ULTO DA VUMARII DO CERPO TA TENGRI IGJA GENENNE NYOP SODANE DE QUINNA LANG HLANA CAUKU ABILTO DAUK CYAHAT ANDAMAH TENGRI ITHYIN MEP GENENNE TLYOH HAPIST ETMEH DE CYED JEKARU YEDOFER"
    },
    "best_non_identity": {
      "multiplier_a": 5,
      "offset_b": 0,
      "completion_index": 6133,
      "completion": {
        "C16": "Y",
        "C17": "L",
        "C18": "G",
        "C20": "T",
        "C21": "M"
      },
      "best_char5_bits_per_character": -6.617437487156906,
      "best_char5_z_vs_heldout_turkish": -13.102820752401035,
      "best_char5_percentile_vs_heldout_turkish": 0.0,
      "best_turkish_word_segmentation": null,
      "candidate": "RBO WDRS PA BWIAHOO PS KUHXS RA RUNEHO OEYA EUNUNNU NLSX GSPANU PU CWONNA DANE TDANA KAWMW AFODRS PAWM KLATAR ANPAIAT RUNEHO ORTLON IUX EUNUNNU RDLST TAXOGR URIUT PU KLUP YUMAHW LUPSZUH"
    },
    "top_affine_maps": [
      {
        "multiplier_a": 1,
        "offset_b": 0,
        "completion_index": 1480,
        "completion": {
          "C16": "J",
          "C17": "Y",
          "C18": "S",
          "C20": "H",
          "C21": "K"
        },
        "best_char5_bits_per_character": -5.4116467891174675,
        "best_char5_z_vs_heldout_turkish": -8.695592546508015,
        "best_char5_percentile_vs_heldout_turkish": 0.0,
        "best_turkish_word_segmentation": null,
        "candidate": "TVI ULTO DA VUMARII DO CERPO TA TENGRI IGJA GENENNE NYOP SODANE DE QUINNA LANG HLANA CAUKU ABILTO DAUK CYAHAT ANDAMAH TENGRI ITHYIN MEP GENENNE TLYOH HAPIST ETMEH DE CYED JEKARU YEDOFER"
      },
      {
        "multiplier_a": 5,
        "offset_b": 0,
        "completion_index": 6133,
        "completion": {
          "C16": "Y",
          "C17": "L",
          "C18": "G",
          "C20": "T",
          "C21": "M"
        },
        "best_char5_bits_per_character": -6.617437487156906,
        "best_char5_z_vs_heldout_turkish": -13.102820752401035,
        "best_char5_percentile_vs_heldout_turkish": 0.0,
        "best_turkish_word_segmentation": null,
        "candidate": "RBO WDRS PA BWIAHOO PS KUHXS RA RUNEHO OEYA EUNUNNU NLSX GSPANU PU CWONNA DANE TDANA KAWMW AFODRS PAWM KLATAR ANPAIAT RUNEHO ORTLON IUX EUNUNNU RDLST TAXOGR URIUT PU KLUP YUMAHW LUPSZUH"
      },
      {
        "multiplier_a": 17,
        "offset_b": 4,
        "completion_index": 5945,
        "completion": {
          "C16": "Y",
          "C17": "B",
          "C18": "S",
          "C20": "N",
          "C21": "O"
        },
        "best_char5_bits_per_character": -6.846673419021978,
        "best_char5_z_vs_heldout_turkish": -13.940690099347078,
        "best_char5_percentile_vs_heldout_turkish": 0.0,
        "best_turkish_word_segmentation": null,
        "candidate": "PXK GJPI DE XGAEHKK DI MUHZI PE PURCHK KCYE CURURRU RBIZ SIDERU DU QGKRRE JERC NJERE MEGOG EVKJPI DEGO MBENEP ERDEAEN PURCHK KPNBKR AUZ CURURRU PJBIN NEZKSP UPAUN DU MBUD YUOEHG BUDILUH"
      },
      {
        "multiplier_a": 25,
        "offset_b": 8,
        "completion_index": 665,
        "completion": {
          "C16": "B",
          "C17": "Y",
          "C18": "M",
          "C20": "K",
          "C21": "L"
        },
        "best_char5_bits_per_character": -7.1254559604081384,
        "best_char5_z_vs_heldout_turkish": -14.959654901203129,
        "best_char5_percentile_vs_heldout_turkish": 0.0,
        "best_turkish_word_segmentation": null,
        "candidate": "PNA OXPU FI NOWIRAA FU GERTU PI PEVCRA ACBI CEVEVVE VYUT MUFIVE FE SOAVVI XIVC KXIVI GIOLO IHAXPU FIOL GYIKIP IVFIWIK PEVCRA APKYAV WET CEVEVVE PXYUK KITAMP EPWEK FE GYEF BELIRO YEFUDER"
      },
      {
        "multiplier_a": 9,
        "offset_b": 4,
        "completion_index": 2729,
        "completion": {
          "C16": "M",
          "C17": "H",
          "C18": "U",
          "C20": "P",
          "C21": "K"
        },
        "best_char5_bits_per_character": -7.164678905526463,
        "best_char5_z_vs_heldout_turkish": -15.103016821580143,
        "best_char5_percentile_vs_heldout_turkish": 0.0,
        "best_turkish_word_segmentation": null,
        "candidate": "TLY CZTA FE LCIEBYY FA WOBJA TE TORGBY YGME GORORRO RHAJ UAFERO FO SCYRRE ZERG PZERE WECKC ENYZTA FECK WHEPET ERFEIEP TORGBY YTPHYR IOJ GORORRO TZHAP PEJYUT OTIOP FO WHOF MOKEBC HOFAXOB"
      },
      {
        "multiplier_a": 15,
        "offset_b": 18,
        "completion_index": 1825,
        "completion": {
          "C16": "K",
          "C17": "D",
          "C18": "M",
          "C20": "O",
          "C21": "T"
        },
        "best_char5_bits_per_character": -7.3728526828845,
        "best_char5_z_vs_heldout_turkish": -15.863902889777052,
        "best_char5_percentile_vs_heldout_turkish": 0.0,
        "best_turkish_word_segmentation": null,
        "candidate": "RVI GBRU LS VGQSNII LU WANJU RS RAFENI IEKS EAFAFFA FDUJ MULSFA LA YGIFFS BSFE OBSFS WSGTG SHIBRU LSGT WDSOSR SFLSQSO RAFENI IRODIF QAJ EAFAFFA RBDUO OSJIMR ARQAO LA WDAL KATSNG DALUPAN"
      },
      {
        "multiplier_a": 25,
        "offset_b": 4,
        "completion_index": 4608,
        "completion": {
          "C16": "U",
          "C17": "I",
          "C18": "H",
          "C20": "M",
          "C21": "F"
        },
        "best_char5_bits_per_character": -7.4636300279996775,
        "best_char5_z_vs_heldout_turkish": -16.19569884449639,
        "best_char5_percentile_vs_heldout_turkish": 0.0,
        "best_turkish_word_segmentation": null,
        "candidate": "LJW KTLQ BE JKSENWW BQ CANPQ LE LARYNW WYUE YARARRA RIQP HQBERA BA OKWRRE TERY MTERE CEKFK EDWTLQ BEKF CIEMEL ERBESEM LARYNW WLMIWR SAP YARARRA LTIQM MEPWHL ALSAM BA CIAB UAFENK IABQZAN"
      },
      {
        "multiplier_a": 7,
        "offset_b": 24,
        "completion_index": 130,
        "completion": {
          "C16": "D",
          "C17": "K",
          "C18": "J",
          "C20": "U",
          "C21": "V"
        },
        "best_char5_bits_per_character": -7.483170667099441,
        "best_char5_z_vs_heldout_turkish": -16.26712090467788,
        "best_char5_percentile_vs_heldout_turkish": 0.0,
        "best_turkish_word_segmentation": null,
        "candidate": "BPC IXBS TY PIEYNCC TS MANZS BY BALONC CODY OALALLA LKSZ JSTYLA TA GICLLY XYLO UXYLY MYIVI YFCXBS TYIV MKYUYB YLTYEYU BALONC CBUKCL EAZ OALALLA BXKSU UYZCJB ABEAU TA MKAT DAVYNI KATSHAN"
      },
      {
        "multiplier_a": 23,
        "offset_b": 20,
        "completion_index": 1868,
        "completion": {
          "C16": "G",
          "C17": "D",
          "C18": "T",
          "C20": "S",
          "C21": "A"
        },
        "best_char5_bits_per_character": -7.557350992465133,
        "best_char5_z_vs_heldout_turkish": -16.538253882238227,
        "best_char5_percentile_vs_heldout_turkish": 0.0,
        "best_turkish_word_segmentation": null,
        "candidate": "PJW MNPE LU JMKUVWW LE OIVBE PU PIHCVW WCGU CIHIHHI HDEB TELUHI LI YMWHHU NUHC SNUHU OUMAM URWNPE LUMA ODUSUP UHLUKUS PIHCVW WPSDWH KIB CIHIHHI PNDES SUBWTP IPKIS LI ODIL GIAUVM DILEFIV"
      },
      {
        "multiplier_a": 23,
        "offset_b": 0,
        "completion_index": 3232,
        "completion": {
          "C16": "J",
          "C17": "Y",
          "C18": "Z",
          "C20": "M",
          "C21": "D"
        },
        "best_char5_bits_per_character": -7.566301676045552,
        "best_char5_z_vs_heldout_turkish": -16.5709690998973,
        "best_char5_percentile_vs_heldout_turkish": 0.0,
        "best_turkish_word_segmentation": null,
        "candidate": "VPC STVK RA PSQABCC RK UOBHK VA VONIBC CIJA IONONNO NYKH ZKRANO RO ESCNNA TANI MTANA UASDS AXCTVK RASD UYAMAV ANRAQAM VONIBC CVMYCN QOH IONONNO VTYKM MAHCZV OVQOM RO UYOR JODABS YORKLOB"
      },
      {
        "multiplier_a": 11,
        "offset_b": 8,
        "completion_index": 2469,
        "completion": {
          "C16": "H",
          "C17": "Y",
          "C18": "O",
          "C20": "M",
          "C21": "D"
        },
        "best_char5_bits_per_character": -7.583375514072499,
        "best_char5_z_vs_heldout_turkish": -16.633374872854052,
        "best_char5_percentile_vs_heldout_turkish": 0.0,
        "best_turkish_word_segmentation": null,
        "candidate": "JFS UZJG PI FUKINSS PG EANRG JI JAVWNS SWHI WAVAVVA VYGR OGPIVA PA CUSVVI ZIVW MZIVI EIUDU ITSZJG PIUD EYIMIJ IVPIKIM JAVWNS SJMYSV KAR WAVAVVA JZYGM MIRSOJ AJKAM PA EYAP HADINU YAPGLAN"
      },
      {
        "multiplier_a": 15,
        "offset_b": 0,
        "completion_index": 574,
        "completion": {
          "C16": "B",
          "C17": "S",
          "C18": "U",
          "C20": "L",
          "C21": "K"
        },
        "best_char5_bits_per_character": -7.597268290431871,
        "best_char5_z_vs_heldout_turkish": -16.684153698672446,
        "best_char5_percentile_vs_heldout_turkish": 0.0,
        "best_turkish_word_segmentation": null,
        "candidate": "ZDQ OJZC TA DOYAVQQ TC EIVRC ZA ZINMVQ QMBA MININNI NSCR UCTANI TI GOQNNA JANM LJANA EAOKO APQJZC TAOK ESALAZ ANTAYAL ZINMVQ QZLSQN YIR MININNI ZJSCL LARQUZ IZYIL TI ESIT BIKAVO SITCXIV"
      }
    ],
    "identity_is_global_best": true
  },
  "conclusion": "Within the complete 26-letter affine family, the untransformed conditional Layer-3 surface is the global Turkish optimum and is still strongly unlike held-out Turkish. No Caesar, Atbash-like, or other affine mapping yields a Turkish plaintext.",
  "limits": [
    "The seven community readings remain secondary evidence rather than an author-selected key.",
    "The affine family does not cover arbitrary substitutions, polyalphabetic ciphers, transpositions, a 29-letter Turkish alphabet, an artificial language, or non-textual readings."
  ]
}