Sam Burns

Years active
2026

Resources

WebsiteProposing a Better Lower Bound for n=17 Square Packing

By Burns

sam-burns.com/posts/proposing-better-lower-bound-for-n17-square-packingA weighted certificate for s(17) ≥ 4.4811, the method Massaccesi’s bound builds on.

0 results · 14 credits (3 at S5, 3 at S4, 8 at S3)

0 results · 0 records · 68 credits (3 at S5, 8 at S4, 55 at S3, 2 at S2)

Credited work

Credits: 68
  • T-006 (optimality, n = 13): prerequisite — Burns, in [evand square-packing 2026-09-28]
  • T-015 (lower bound, n = 17): source author, prerequisite — Burns, in [Burns–Massaccesi n17]
  • T-016 (lower bound, n = 18, 19): source author, prerequisite — Burns, in [Burns–Massaccesi n17]
  • T-017 (lower bound, n = 12): prerequisite — Burns
  • T-018 (lower bound, n = 11): prerequisite — Burns
  • T-019 (lower bound, n = 17, 18, 19): prerequisite — Burns
  • T-020 (lower bound, n = 19, 20, 21): prerequisite — Burns
  • T-021 (lower bound, n = 20, 21): prerequisite — Burns
  • T-022 (lower bound, n = 11): prerequisite — Burns
  • T-024 (lower bound, n = 11): prerequisite — Burns
  • T-027 (lower bound, n = 18): prerequisite — Burns
  • T-028 (lower bound, n = 18): prerequisite — Burns
  • T-029 (lower bound, n = 18): prerequisite — Burns
  • T-030 (lower bound, n = 18): prerequisite — Burns
  • T-032 (lower bound, n = 17): prerequisite — Burns, in [n17 weighted certificates 2026-09-20]
  • T-034 (lower bound, n = 21): prerequisite — Burns
  • T-044 (lower bound, 17 cases, n = 26 to 73): prerequisite — Burns, in [wand125 point bounds 2026]
  • T-045 (lower bound, 15 cases, n = 18 to 78): prerequisite — Burns, in [wand125 rectangle bounds 2026]
  • T-046 (lower bound, 48 cases, n = 18 to 95): prerequisite — Burns, in [wand125 rectangle bounds 2026]; [wand125 rectangle bounds 2026-09-28]
  • T-047 (lower bound, 7 cases, n = 11 to 31): prerequisite — Burns, in [Tokoharu density 2026]
  • T-048 (lower bound, n = 50, 51): prerequisite — Burns, in [wand125 point and mixed bounds 2026-09-28]
  • T-049 (lower bound, n = 12): prerequisite — Burns, in [evand square-packing 2026]
  • T-050 (lower bound, n = 21): prerequisite — Burns, in [evand square-packing 2026]
  • T-051 (optimality, n = 32): prerequisite — Burns, in [evand square-packing 2026]
  • T-052 (optimality, n = 21): prerequisite — Burns, in [evand square-packing 2026-09-28]
  • T-053 (optimality, n = 45): prerequisite — Burns, in [evand square-packing 2026-09-28] (Registered in: #563)
  • T-054 (simplification, n = 45): prerequisite — Burns, in [wand125 point and mixed bounds 2026-09-28]
  • T-055 (simplification, n = 21): prerequisite — Burns, in [wand125 point and mixed bounds 2026-09-28]
  • T-062 (optimality, n = 60): prerequisite — Burns, in [evand square-packing 2026-10-01] (Registered in: #508)
  • T-063 (optimality, n = 61): prerequisite — Burns, in [evand square-packing 2026-10-01] (Registered in: #563)
  • T-064 (optimality, 13 cases, n = 33 to 321): prerequisite — Burns, in [evand square-packing 2026-10-01] (Registered in: #508)
  • T-066 (optimality, n = 59): prerequisite — Burns, in [wand125 exact covers 2026-10-01]
  • T-067 (optimality, n = 77, 78): prerequisite — Burns, in [wand125 exact covers 2026-10-01]
  • T-068 (lower bound, 34 cases, n = 19 to 95): prerequisite — Burns, in [wand125 rectangle bounds 2026-10-01]
  • T-069 (lower bound, 5 cases, n = 37 to 92): prerequisite — Burns, in [wand125 mixed bounds 2026-10-01]
  • T-070 (lower bound, 25 cases, n = 29 to 95): prerequisite — Burns, in [wand125 rectangle bounds 2026-09-28]
  • T-071 (lower bound, n = 84, 85, 86, 87): prerequisite — Burns, in [wand125 mixed bounds 2026-10-02]
  • T-072 (lower bound, n = 76): prerequisite — Burns, in [wand125 mixed bounds n76 2026-10-02]
  • T-073 (lower bound, 6 cases, n = 83 to 105): prerequisite — Burns, in [wand125 linear certificates 2026-10-02]
  • T-074 (lower bound, 31 cases, n = 19 to 95): prerequisite — Burns, in [wand125 rectangle bounds 2026-10-01]
  • T-075 (lower bound, 9 cases, n = 83 to 96): prerequisite — Burns, in [wand125 mixed bounds afternoon 2026-10-02]
  • T-076 (lower bound, n = 82): prerequisite — Burns, in [wand125 linear n82 2026-10-02]
  • T-077 (lower bound, n = 20, 42, 70): prerequisite — Burns, in [wand125 rectangle bounds 2026-10-02]
  • T-080 (lower bound, 5 cases, n = 101 to 105): prerequisite — Burns, in [wand125 linear certificates 2026-10-02]
  • T-081 (optimality, 14 cases, n = 21 to 320): prerequisite — Burns, in [evand square-packing 2026-10-03] (Registered in: #508)
  • T-082 (lower bound, 22 cases, n = 51 to 96): prerequisite — Burns, in [wand125 mixed bounds 2026-10-03]
  • T-090 (lower bound, 17 cases, n = 42 to 96): prerequisite — Burns, in [wand125 mixed bounds 2026-10-04]
  • T-091 (lower bound, 17 cases, n = 53 to 95): prerequisite — Burns, in [wand125 mixed bounds evening 2026-10-04]
  • T-094 (lower bound, n = 67, 84): prerequisite — Burns, in [wand125 mixed bounds 2026-10-05]
  • T-096 (lower bound, n = 18): prerequisite — Burns, in [wand125 mixed bounds finer net 2026-10-05]
  • T-097 (lower bound, n = 66): prerequisite — Burns, in [wand125 mixed bounds finer net 2026-10-05]
  • T-099 (lower bound, n = 18): prerequisite — Burns, in [wand125 mixed bounds finer net 2026-10-06]
  • T-100 (lower bound, n = 19): prerequisite — Burns, in [wand125 mixed bounds finer net 2026-10-06]
  • T-102 (lower bound, n = 18): prerequisite — Burns, in [wand125 mixed bounds check2 2026-10-06]
  • T-103 (lower bound, n = 19): prerequisite — Burns, in [wand125 mixed bounds check2 2026-10-06]
  • T-104 (lower bound, n = 20): prerequisite — Burns, in [wand125 mixed bounds check2 2026-10-06]
  • T-105 (lower bound, n = 26): prerequisite — Burns, in [wand125 mixed bounds check2 2026-10-06]
  • T-106 (lower bound, n = 27): prerequisite — Burns, in [wand125 mixed bounds check2 2026-10-06]
  • T-107 (lower bound, n = 28): prerequisite — Burns, in [wand125 mixed bounds check2 2026-10-06]
  • T-108 (lower bound, n = 29): prerequisite — Burns, in [wand125 mixed bounds check2 2026-10-06]
  • T-109 (lower bound, n = 30): prerequisite — Burns, in [wand125 mixed bounds check2 2026-10-06]
  • T-110 (lower bound, n = 39): prerequisite — Burns, in [wand125 mixed bounds check2 2026-10-06]
  • T-111 (lower bound, n = 41): prerequisite — Burns, in [wand125 mixed bounds check2 2026-10-06]
  • T-133 (lower bound, n = 40): prerequisite — Burns, in [Guzhou0806 n40 clipped corner 2026-10-10] (Registered in: #487)
  • T-144 (lower bound, 5 cases, n = 122 to 126): prerequisite — Burns, in [wand125 linear n122 2026-10-10] (Registered in: #487)
  • T-145 (lower bound, n = 40): prerequisite — Burns, in [Guzhou0806 n40 continuous pose 2026-10-10] (Registered in: #487)
  • T-157 (lower bound, n = 40): prerequisite — Burns, in [Guzhou0806 n40 new supports 2026-10-11] (Registered in: #598)
  • T-179 (lower bound, 5 cases, n = 145 to 149): prerequisite — Burns, in [wand125 linear n145 2026-10-13] (Registered in: #602)

Other reviewed records

Sources
  1. primary-byline: First-party title and meta author attribute name Sam Burns.
  2. bibliography: Source author, credit and credited_names fields retain the printed attribution labels.

Identity evidence