History of Minimal polynomials of the Salem numbers less than 1.3

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2026-09-17 12:51 zeta3 table-repair@2.0+dc0f96a0 keep Salem definition concise after audit current reviewed
2026-09-17 12:50 zeta3 table-repair@2.0+dc0f96a0 define Salem polynomial index and cite completeness
2026-09-17 12:38 zeta3 table-build@2.0+395f185d shorten definition and move root-table link
2026-09-17 12:37 zeta3 with Codex CLI table-build@2.0+395f185d computed Salem minimal polynomials from half-lists
2026-09-17 12:34 zeta3 table-build@2.0+395f185d claim Salem minimal polynomial table

What changed between 2026-09-17 12:34 and 2026-09-17 12:37

from line 84 (264 lines, 261 more than before) @@ -84,3 +84,264 @@
 Display properties:   number-header: $m_a(x)$-Numbers: []+Numbers:+- params:+    coefficients: 1,1,0,-1,-1,-1+  number: x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,1,0,-1,-1,-1}[$\tau$] is the real root+    greater than $1$.+- params:+    coefficients: 1,-1,1,-1,0,0,-1,1,-1,1+  number: x^18 - x^17 + x^16 - x^15 - x^12 + x^11 - x^10 + x^9 - x^8 + x^7 - x^6 -+    x^3 + x^2 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,1,-1,0,0,-1,1,-1,1}[$\tau$] is the+    real root greater than $1$.+- params:+    coefficients: 1,0,0,-1,-1,0,0,1+  number: x^14 - x^11 - x^10 + x^7 - x^4 - x^3 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,0,-1,-1,0,0,1}[$\tau$] is the real+    root greater than $1$.+- params:+    coefficients: 1,0,-1,0,0,0,0,-1+  number: x^14 - x^12 - x^7 - x^2 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,-1,0,0,0,0,-1}[$\tau$] is the real+    root greater than $1$.+- params:+    coefficients: 1,0,0,0,-1,-1+  number: x^10 - x^6 - x^5 - x^4 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,0,0,-1,-1}[$\tau$] is the real root+    greater than $1$.+- params:+    coefficients: 1,-1,0,0,0,0,0,0,-1,1+  number: x^18 - x^17 - x^10 + x^9 - x^8 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,0,0,0,0,-1,1}[$\tau$] is the+    real root greater than $1$.+- params:+    coefficients: 1,0,0,-1,0,-1+  number: x^10 - x^7 - x^5 - x^3 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,0,-1,0,-1}[$\tau$] is the real root+    greater than $1$.+- params:+    coefficients: 1,-1,0,0,0,-1,1,0,0,-1,1+  number: x^20 - x^19 - x^15 + x^14 - x^11 + x^10 - x^9 + x^6 - x^5 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,0,-1,1,0,0,-1,1}[$\tau$] is the+    real root greater than $1$.+- params:+    coefficients: 1,0,-1,-1,0,0,0,1,1,0,-1,-1+  number: x^22 - x^20 - x^19 + x^15 + x^14 - x^12 - x^11 - x^10 + x^8 + x^7 - x^3+    - x^2 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,-1,-1,0,0,0,1,1,0,-1,-1}[$\tau$] is+    the real root greater than $1$.+- params:+    coefficients: 1,-1,0,0,0,0,0,0,-1+  number: x^16 - x^15 - x^8 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,0,0,0,0,-1}[$\tau$] is the real+    root greater than $1$.+- params:+    coefficients: 1,0,-1,0,0,-1,0,0,-1,0,1,0,0,1+  number: x^26 - x^24 - x^21 - x^18 + x^16 + x^13 + x^10 - x^8 - x^5 - x^2 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,-1,0,0,-1,0,0,-1,0,1,0,0,1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,-1,1,-1,0,0,-1+  number: x^12 - x^11 + x^10 - x^9 - x^6 - x^3 + x^2 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,1,-1,0,0,-1}[$\tau$] is the real+    root greater than $1$.+- params:+    coefficients: 1,0,0,0,0,0,-1,-1,-1,-1+  number: x^18 - x^12 - x^11 - x^10 - x^9 - x^8 - x^7 - x^6 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,0,0,0,0,-1,-1,-1,-1}[$\tau$] is the+    real root greater than $1$.+- params:+    coefficients: 1,0,-1,0,0,-1,0,0,0,0,0+  number: x^20 - x^18 - x^15 - x^5 - x^2 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,-1,0,0,-1,0,0,0,0,0}[$\tau$] is the+    real root greater than $1$.+- params:+    coefficients: 1,0,-1,-1,0,1,0,-1+  number: x^14 - x^12 - x^11 + x^9 - x^7 + x^5 - x^3 - x^2 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,-1,-1,0,1,0,-1}[$\tau$] is the real+    root greater than $1$.+- params:+    coefficients: 1,-1,0,0,-1,1,0,0,0,-1+  number: x^18 - x^17 - x^14 + x^13 - x^9 + x^5 - x^4 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,-1,1,0,0,0,-1}[$\tau$] is the+    real root greater than $1$.+- params:+    coefficients: 1,-1,0,0,-1,1,0,-1,1,-1,0,1,-1+  number: x^24 - x^23 - x^20 + x^19 - x^17 + x^16 - x^15 + x^13 - x^12 + x^11 - x^9+    + x^8 - x^7 + x^5 - x^4 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,-1,1,0,-1,1,-1,0,1,-1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,-1,0,-1,1,0,0,0,-1,1,-1,1+  number: x^22 - x^21 - x^19 + x^18 - x^14 + x^13 - x^12 + x^11 - x^10 + x^9 - x^8+    + x^4 - x^3 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,-1,1,0,0,0,-1,1,-1,1}[$\tau$] is+    the real root greater than $1$.+- params:+    coefficients: 1,0,-1,0,0,-1+  number: x^10 - x^8 - x^5 - x^2 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,-1,0,0,-1}[$\tau$] is the real root+    greater than $1$.+- params:+    coefficients: 1,-1,0,0,0,0,-1,0,0,0,0,0,0,1+  number: x^26 - x^25 - x^20 + x^13 - x^6 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,0,0,-1,0,0,0,0,0,0,1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,-1,0,0,0,0,-1,1+  number: x^14 - x^13 - x^8 + x^7 - x^6 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,0,0,-1,1}[$\tau$] is the real+    root greater than $1$.+- params:+    coefficients: 1,-1,-1,1,0,0,0,0,0,-1,0,1+  number: x^22 - x^21 - x^20 + x^19 - x^13 + x^11 - x^9 + x^3 - x^2 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,-1,1,0,0,0,0,0,-1,0,1}[$\tau$] is+    the real root greater than $1$.+- params:+    coefficients: 1,0,0,-1,-1+  number: x^8 - x^5 - x^4 - x^3 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,0,-1,-1}[$\tau$] is the real root+    greater than $1$.+- params:+    coefficients: 1,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1+  number: x^26 - x^20 - x^19 - x^18 - x^17 - x^16 - x^15 - x^14 - x^13 - x^12 - x^11+    - x^10 - x^9 - x^8 - x^7 - x^6 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,0,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,-2,2,-2,2,-2,1,0,-1,1,-1+  number: x^20 - 2*x^19 + 2*x^18 - 2*x^17 + 2*x^16 - 2*x^15 + x^14 - x^12 + x^11 -+    x^10 + x^9 - x^8 + x^6 - 2*x^5 + 2*x^4 - 2*x^3 + 2*x^2 - 2*x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-2,2,-2,2,-2,1,0,-1,1,-1}[$\tau$] is+    the real root greater than $1$.+- params:+    coefficients: 1,0,0,0,-1,0,-1,-1,0,-1+  number: x^18 - x^14 - x^12 - x^11 - x^9 - x^7 - x^6 - x^4 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,0,0,-1,0,-1,-1,0,-1}[$\tau$] is the+    real root greater than $1$.+- params:+    coefficients: 1,-2,1,1,-2,1,0,0,-1,1,0,-1,1,-1+  number: x^26 - 2*x^25 + x^24 + x^23 - 2*x^22 + x^21 - x^18 + x^17 - x^15 + x^14+    - x^13 + x^12 - x^11 + x^9 - x^8 + x^5 - 2*x^4 + x^3 + x^2 - 2*x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-2,1,1,-2,1,0,0,-1,1,0,-1,1,-1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,0,0,1+  number: x^30 - x^25 - x^24 - x^23 - x^22 - x^21 - x^20 + x^15 - x^10 - x^9 - x^8+    - x^7 - x^6 - x^5 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,0,0,0,-1,-1,-1,-1,-1,-1,0,0,0,0,1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,-2,2,-2,1,0,-1,2,-2,1,0,-1,1,-1,1,-1+  number: x^30 - 2*x^29 + 2*x^28 - 2*x^27 + x^26 - x^24 + 2*x^23 - 2*x^22 + x^21 -+    x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^9 - 2*x^8 + 2*x^7+    - x^6 + x^4 - 2*x^3 + 2*x^2 - 2*x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-2,2,-2,1,0,-1,2,-2,1,0,-1,1,-1,1,-1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,-1,0,0,0,0,0,0,-1,0,0,0,-1,0,0,-1+  number: x^30 - x^29 - x^22 - x^18 - x^15 - x^12 - x^8 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,0,0,0,0,-1,0,0,0,-1,0,0,-1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,0,-1,-1,0,0,0,1,0,-1,-1,0,1,1+  number: x^26 - x^24 - x^23 + x^19 - x^17 - x^16 + x^14 + x^13 + x^12 - x^10 - x^9+    + x^7 - x^3 - x^2 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,-1,-1,0,0,0,1,0,-1,-1,0,1,1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,-1,0,0,0,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,1+  number: x^44 - x^43 - x^37 - x^33 + x^25 + x^22 + x^19 - x^11 - x^7 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,0,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,0,-1,0,0,-1,-1,0,0,0,1,0,0,1,0,-1+  number: x^30 - x^28 - x^25 - x^24 + x^20 + x^17 - x^15 + x^13 + x^10 - x^6 - x^5+    - x^2 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,-1,0,0,-1,-1,0,0,0,1,0,0,1,0,-1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,-1,0,0,-1,1,-1,0,1,-1,1,0,-1,1,-1,0,1,-1+  number: x^34 - x^33 - x^30 + x^29 - x^28 + x^26 - x^25 + x^24 - x^22 + x^21 - x^20+    + x^18 - x^17 + x^16 - x^14 + x^13 - x^12 + x^10 - x^9 + x^8 - x^6 + x^5 - x^4+    - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,-1,1,-1,0,1,-1,1,0,-1,1,-1,0,1,-1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,-2,2,-2,2,-2,2,-3,3,-3+  number: x^18 - 2*x^17 + 2*x^16 - 2*x^15 + 2*x^14 - 2*x^13 + 2*x^12 - 3*x^11 + 3*x^10+    - 3*x^9 + 3*x^8 - 3*x^7 + 2*x^6 - 2*x^5 + 2*x^4 - 2*x^3 + 2*x^2 - 2*x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-2,2,-2,2,-2,2,-3,3,-3}[$\tau$] is the+    real root greater than $1$.+- params:+    coefficients: 1,-1,0,0,-1,1,-1,0,1,-1,1,0,-1,1+  number: x^26 - x^25 - x^22 + x^21 - x^20 + x^18 - x^17 + x^16 - x^14 + x^13 - x^12+    + x^10 - x^9 + x^8 - x^6 + x^5 - x^4 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,-1,1,-1,0,1,-1,1,0,-1,1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,-1,0,0,0,0,-1,0,0,0,0,0,0+  number: x^24 - x^23 - x^18 - x^6 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,0,0,-1,0,0,0,0,0,0}[$\tau$] is+    the real root greater than $1$.+- params:+    coefficients: 1,0,-1,0,0,-1,0,0,-1,0,1+  number: x^20 - x^18 - x^15 - x^12 + x^10 - x^8 - x^5 - x^2 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,-1,0,0,-1,0,0,-1,0,1}[$\tau$] is the+    real root greater than $1$.+- params:+    coefficients: 1,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,1,0,1,0,1,0,1+  number: x^40 - x^37 - x^35 - x^33 - x^31 - x^29 + x^26 + x^24 + x^22 + x^20 + x^18+    + x^16 + x^14 - x^11 - x^9 - x^7 - x^5 - x^3 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,0,-1,0,-1,0,-1,0,-1,0,-1,0,0,1,0,1,0,1,0,1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1+  number: x^46 - x^42 - x^41 - x^40 - x^39 + x^25 + x^24 + x^23 + x^22 + x^21 - x^7+    - x^6 - x^5 - x^4 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,0,0,-1,-1,-1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,0,-1,-1,0,1+  number: x^10 - x^8 - x^7 + x^5 - x^3 - x^2 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,-1,-1,0,1}[$\tau$] is the real root+    greater than $1$.+- params:+    coefficients: 1,-1,0,0,-1,1,-1,0,1,-1+  number: x^18 - x^17 - x^14 + x^13 - x^12 + x^10 - x^9 + x^8 - x^6 + x^5 - x^4 -+    x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,-1,1,-1,0,1,-1}[$\tau$] is the+    real root greater than $1$.+- params:+    coefficients: 1,-1,0,-1,0,1,0,1,-2,0,0,1,1,-1,-1,-1,1,1+  number: x^34 - x^33 - x^31 + x^29 + x^27 - 2*x^26 + x^23 + x^22 - x^21 - x^20 -+    x^19 + x^18 + x^17 + x^16 - x^15 - x^14 - x^13 + x^12 + x^11 - 2*x^8 + x^7 + x^5+    - x^3 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,-1,0,1,0,1,-2,0,0,1,1,-1,-1,-1,1,1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,-1,0,0,0,-1,0,0,0,0,0,1+  number: x^22 - x^21 - x^17 + x^11 - x^5 - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,0,0,0,-1,0,0,0,0,0,1}[$\tau$] is+    the real root greater than $1$.+- params:+    coefficients: 1,0,0,0,-1,-1,-1,-1,-1,0,0,0,1,1,1+  number: x^28 - x^24 - x^23 - x^22 - x^21 - x^20 + x^16 + x^15 + x^14 + x^13 + x^12+    - x^8 - x^7 - x^6 - x^5 - x^4 + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,0,0,0,-1,-1,-1,-1,-1,0,0,0,1,1,1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,1,0,-1,-2,-2,-1,0,1,1,0,-1,-1,0,1,1,0,-1,-1+  number: x^36 + x^35 - x^33 - 2*x^32 - 2*x^31 - x^30 + x^28 + x^27 - x^25 - x^24+    + x^22 + x^21 - x^19 - x^18 - x^17 + x^15 + x^14 - x^12 - x^11 + x^9 + x^8 - x^6+    - 2*x^5 - 2*x^4 - x^3 + x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,1,0,-1,-2,-2,-1,0,1,1,0,-1,-1,0,1,1,0,-1,-1}[$\tau$]+    is the real root greater than $1$.+- params:+    coefficients: 1,-1,-1,0,2,0,-2,-1,2,2,-2,-2,0,3+  number: x^26 - x^25 - x^24 + 2*x^22 - 2*x^20 - x^19 + 2*x^18 + 2*x^17 - 2*x^16 -+    2*x^15 + 3*x^13 - 2*x^11 - 2*x^10 + 2*x^9 + 2*x^8 - x^7 - 2*x^6 + 2*x^4 - x^2+    - x + 1+  comment: HREF{Salem_numbers_less_than_1_3#1,-1,-1,0,2,0,-2,-1,2,2,-2,-2,0,3}[$\tau$]+    is the real root greater than $1$. 

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