# Vumarii 2019: affine-Turkish control

## Scope

The image itself fixes the glyph spellings in its red `VUMARII` / `TENGRI` legend. The seven-line body could nevertheless, in principle, have been enciphered *after* that glyph alphabet was chosen. This audit tests the complete conventional affine family over the 26 Latin letters: `x -> a*x+b (mod 26)` for all 12 invertible `a` values and all 26 `b` values.

For every affine map it enumerates all `8P5 = 6,720` injective assignments of the five Vumarii glyph classes whose Latin values remain unestablished, conditional on the same seven contemporary secondary readings used by the earlier Turkish-completion control. The 312 affine maps therefore cover `2,096,640` Turkish-scored candidates. Caesar shifts and Atbash-like mappings are subsets.

## Result

- The highest-scoring mapping is the identity (`a=1`, `b=0`), with `-5.4116` bits/character and held-out Turkish z-score `-8.70`.
- The best *non-identity* affine mapping scores `-6.6174` bits/character (z `-13.10`), far below the already-unsolved identity surface.
- The identity optimum is exactly the previously reported five-class completion `{'C16': 'J', 'C17': 'Y', 'C18': 'S', 'C20': 'H', 'C21': 'K'}`; it has no full Turkish word segmentation (`None`).

Thus a simple Caesar, Atbash, or other 26-letter affine layer does not rescue the Turkish hypothesis. This is a bounded negative result, not a claim that no other language or cipher could exist.

## Highest-scoring affine cases

| Rank | a | b | Turkish 5-gram | z | C16 C17 C18 C20 C21 | Candidate |
| ---: | ---: | ---: | ---: | ---: | --- | --- |
| 1 | 1 | 0 | -5.4116 | -8.70 | J Y S H K | `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` |
| 2 | 5 | 0 | -6.6174 | -13.10 | Y L G T M | `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` |
| 3 | 17 | 4 | -6.8467 | -13.94 | Y B S N O | `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` |
| 4 | 25 | 8 | -7.1255 | -14.96 | B Y M K L | `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` |
| 5 | 9 | 4 | -7.1647 | -15.10 | M H U P K | `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` |
| 6 | 15 | 18 | -7.3729 | -15.86 | K D M O T | `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` |
| 7 | 25 | 4 | -7.4636 | -16.20 | U I H M F | `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` |
| 8 | 7 | 24 | -7.4832 | -16.27 | D K J U V | `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` |
| 9 | 23 | 20 | -7.5574 | -16.54 | G D T S A | `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` |
| 10 | 23 | 0 | -7.5663 | -16.57 | J Y Z M D | `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` |
| 11 | 11 | 8 | -7.5834 | -16.63 | H Y O M D | `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` |
| 12 | 15 | 0 | -7.5973 | -16.68 | B S U L K | `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` |

## Limits

- The primary red legend is stronger evidence than the seven secondary community readings; those readings are retained only to make this test comparable with the prior Turkish audit.
- This covers affine mappings on the standard A–Z alphabet only. It does not test Vigenere, transposition, a Turkish-specific 29-letter alphabet, a non-Latin transliteration, an artificial language, or a reading of the upper diagram.
- A language-model score is a reproducible control, not an author-selected decryption rule.

## Reproduce

```powershell
& '<bundled-python>' scripts\audit_vumarii_2019_turkish_affine.py
```

Word-class source SHA-256: `81262c1ca605c686da3acba6b4ac1ea2f11196cf74e530a9c71f607d0c5c76f8`
Transcription SHA-256: `2c6eb4492a3975c034e9fb4ba75ae676acad0fc979b76e7a0463bd77170ad6b3`