E-012 — dBN heat-flow toy: two-body collision times (10^4 zeros) + full ODE check (300 zeros)
08-18-2026 · 9999 rows · script
research/numerics/scripts/E-012-dbn-heat-flow-toy.py
Metadata
Two-body Rodgers-Tao collision times from E-002 gaps (10^4 zeros) + full all-to-all backward ODE on first 300 zeros; extremal-vs-averaged mismatch
Validation checks
| V1_spread_ge_4_orders | PASS |
| V2_ode_vs_two_body_factor4 | PASS |
| V3_smallest_gap_collides_first | PASS |
Key values
| n_gaps | 9999 |
| tc_min | 0.00017764709135458984 |
| tc_median | 0.10824175495920002 |
| tc_max | 5.9293876226367646 |
| spread_orders | 4.523451741355605 |
| binding_pair_index | 6709 |
| binding_gap | 0.03769849772652378 |
| mean_gap | 0.9864634392302998 |
| min_gap | 0.03769849772652378 |
| max_gap | 6.887314497036861 |
| n_ode_zeros | 300 |
| t_collision_ode | -0.02290826416204641 |
| colliding_pair_index | 298 |
| two_body_pair_index | 298 |
| t_collision_two_body | -0.021863900791280276 |
| ratio_ode_over_two_body | 1.0477665619111591 |
| same_pair | True |
| terminated_on_event | True |
Parameters
| n_zeros | 10000 |
| n_ode | 300 |
Caveats
- toy conventions: gammas used directly as H_0 zero coordinates; absolute t_c convention-dependent — only the spread and ordering carry the argument
- two-body truncation ignores many-body forces; Part 2 ODE quantifies the correction on the binding window
Chart
Data preview (9999 rows total)
| pair_index_j | gap | two_body_collision_time_abs |
|---|---|---|
| 1 | 6.88731449703686138e+00 | 5.92938762263676455e+00 |
| 2 | 3.98881794137413337e+00 | 1.98883357117852233e+00 |
| 3 | 5.41401854571382302e+00 | 3.66394960166665218e+00 |
| 4 | 2.51018546187967928e+00 | 7.87628881629012345e-01 |
| 5 | 4.65111657108648302e+00 | 2.70411066972941061e+00 |
| 6 | 3.33254085332182370e+00 | 1.38822856738236866e+00 |
| 7 | 2.40835426876750347e+00 | 7.25021285486332046e-01 |
| 8 | 4.67807760025215913e+00 | 2.73555125424762480e+00 |
| 9 | 1.76868159650513945e+00 | 3.91029323726996114e-01 |
| 10 | 3.19648900004216330e+00 | 1.27719274092381863e+00 |
| 11 | 3.47592621934892776e+00 | 1.51025788529466620e+00 |
| 12 | 2.90079630553896095e+00 | 1.05182740077856063e+00 |
| 13 | 1.48473452200745726e+00 | 2.75554575105089072e-01 |
| 14 | 4.28076552347179273e+00 | 2.29061918336809134e+00 |
| 15 | 1.96726648141256533e+00 | 4.83767176111171926e-01 |
| 16 | 2.46659118167981717e+00 | 7.60509007192579634e-01 |
| 17 | 2.52075596330791996e+00 | 7.94276328319054925e-01 |
| 18 | 3.63753302460202121e+00 | 1.65395581313379103e+00 |
| 19 | 1.44014936979087338e+00 | 2.59253775913631246e-01 |
| 20 | 2.19253495137456866e+00 | 6.00901189124885327e-01 |
| 21 | 3.57300583383666037e+00 | 1.59579633607885119e+00 |
| 22 | 1.82511212643102283e+00 | 4.16379284255696258e-01 |
| 23 | 2.68978163260817382e+00 | 9.04365653889536603e-01 |
| 24 | 1.38383659450923346e+00 | 2.39375465037864082e-01 |
| 25 | 3.68278806292403260e+00 | 1.69536598955196860e+00 |