T-120: Reported s(102) ≤ alpha_102 with a degree-8 exact side form

The case

Results on the case

10 results in the register on $n=102$$n=102$, oldest first, each with what it established and how it stands now.

1. 2005 published T-007

   s(n)≥min(⌈n​⌉,n−2⌊n​⌋+1​+1)$s(n)\ge min(\lceil \sqrt{n}\rceil ,\sqrt{n-2\lfloor \sqrt{n}\rfloor +1}+1)$ for $4\le n\le 324$$4\le n\le 324$

   S3 V0 C1 lower bound incomplete on this case, superseded by T-073 and T-080

   Nagamochi · Nagamochi 2005 · source · register

2. 2026-09-04 published T-085

   Nagamochi 2005, Lemma 1 is false for every container with $a>3$$a>3$ and $b>2$$b>2$

   S3 V3 C3 correction confirmed

   Karakuş; chelokot · Karakuş 2026 · chelokot Nagamochi counterexample 2026 · packet · register

3. 2026-09-27 published T-056

   Smaller packings for 49 counts from $n=68$$n=68$ to $307$$307$, each certified two independent ways

   S3 V3 C3 upper bound confirmed superseded by T-125

   Couzo · franciscouzo square-packing 2026-09-27 · packet · register

4. 2026-09-29 published T-083

   s(n)≥1/2+n−⌊n​⌋+1/4​$s(n)\ge 1/2+\sqrt{n-\lfloor \sqrt{n}\rfloor +1/4}$ for every nonsquare $8\le n\le 324$$8\le n\le 324$

   S3 V3 C3 lower bound confirmed on this case, superseded by T-073 and T-080

   Karakuş · Karakuş 2026 · source · register

5. 2026-10-02 published T-073

   Linear-measure lower bounds replayed at $n=83$$n=83$ and $n=101\dots 105$$n=101\dots 105$

   S3 V3 C3 lower bound confirmed

   wand125 after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 linear certificates 2026-10-02 · packet · source · review · register

6. 2026-10-02 published T-080

   Linear-measure lower bound replayed at $n=101\dots 105$$n=101\dots 105$

   S3 V3 C3 lower bound confirmed

   wand125 after Tokoharu, Levy, Stromquist, Nagamochi, Burns, Massaccesi · wand125 linear certificates 2026-10-02 · packet · source · review · register

7. 2026-10-05 published T-098

   Exact optima of 48 known-best packings: s(n) ≤ S', 3.5e-13 to 5.0e-11 below each printed side

   S2 V3 C3 upper bound confirmed on this case, superseded by T-125

   Daniel after Couzo, de Winter, Ellsworth, Levy · evand exact optima 2026-10-05 · packet · register

8. 2026-10-07 published T-120 this result

   Reported s(102) ≤ alpha_102 with a degree-8 exact side form

   S2 V0 C0 upper bound recorded superseded by T-125

   Daniel after Couzo · Daniel exact and local reports 2026 · packet · register

9. 2026-10-08 published T-125

   Complete rational construction reports at 25 counts

   S3 V3 C3 upper bound confirmed

   ry-xu · ry-xu square packing 2026 · packet · register

10. 2026-10-10 published T-146

    Exact rational certificates at fifteen counts from Evan Daniel's regularized record lists

    S2 V3 C3 upper bound confirmed

    Daniel after Xu, Chaoweeraprasit, Mishapolk, Levy · Daniel regularized lists 2026-10-10 · packet · register