IGT - Information Gravity Theory - Part 2 (IGT2) Appendix (execution logs) Selection from RTX 5090 execution sessions, June 2026. Contains successful, complete runs that support the observation in §4.2C. Environmental errors (gated access, authentication, architecture incompatibilities) have been omitted as irrelevant to the result. Environment torch 2.11.0+cu128 transformers 5.9.0 bitsandbytes 0.49.2 Hardware: RTX 5090 – 24Gb VRAM, 4-bit quantization (Unsloth bnb-4bit), Float16 calculation Run 1: Qwen-2.5-14B-Instruct (layer 20), full oscillation monitoring Prompt: requesting a proof for Goldbach 's Conjecture (unsolved problem, L3 complexity). Complete, consistent, non-stopping, pure profiling of V_drift consecutively on each token: Hook successfully recorded on layer 20. [Prefill complete. Step-by-step monitoring enabled.] Pro V_drift: 0.0000 (anchor) ble V_drift: 0.4637 ma V_drift: 0.4397 pe V_drift: 0.2702 ← drop (function word) care V_drift: 0.5784 ← peak (content word) ai V_drift: 0.4778 men V_drift: 0.6095 ț V_drift: 0.5558 ion V_drift: 0.5388 at V_drift: 0.5141 -o V_drift: 0.2995 ← drop este V_drift: 0.4370 c V_drift: 0.4831 unos V_drift: 0.4867 cut V_drift: 0.6368 ← peak (content boundary) ă V_drift: 0.5350 sub V_drift: 0.2119 ← drop (preposition) num V_drift: 0.4438 ele V_drift: 0.4383 de V_drift: 0.4268 Con V_drift: 0.4585 ject V_drift: 0.4582 ura V_drift: 0.4146 lui V_drift: 0.3116 ← drop (function word) Gold V_drift: 0.5142 bach V_drift: 0.6005 ← peak (proper noun / content) . V_drift: 0.5333 Ace V_drift: 0.6345 ← peak asta V_drift: 0.6218 afirm V_drift: 0.5002 ă V_drift: 0.6144 că V_drift: 0.4184 or V_drift: 0.3290 ← drop ice V_drift: 0.3763 num V_drift: 0.2547 ← drop ăr V_drift: 0.5168 par V_drift: 0.3282 mai V_drift: 0.4795 mare V_drift: 0.5669 sau V_drift: 0.3680 egal V_drift: 0.4889 cu V_drift: 0.4373 4 V_drift: 0.4605 Poate V_drift: 0.4088 fi V_drift: 0.5012 sc V_drift: 0.3583 ris V_drift: 0.4915 ca V_drift: 0.5230 suma V_drift: 0.2997 ← drop a V_drift: 0.3337 dou V_drift: 0.4557 ă V_drift: 0.5205 num V_drift: 0.3132 ← drop ere V_drift: 0.5212 prime V_drift: 0.4252 . V_drift: 0.4040 De V_drift: 0.5813 a V_drift: 0.6489 ← peak sem V_drift: 0.5622 ene V_drift: 0.5194 a V_drift: 0.6026 , V_drift: 0.6117 exist V_drift: 0.4130 ă V_drift: 0.6197 ← peak o V_drift: 0.2936 ← drop (function word) variant V_drift: 0.2961 ă V_drift: 0.5373 mai V_drift: 0.2635 ← drop put V_drift: 0.4937 ern V_drift: 0.4721 ic V_drift: 0.4357 ă V_drift: 0.5018 a V_drift: 0.6192 ← peak ace V_drift: 0.3951 ste V_drift: 0.5386 i V_drift: 0.3498 conject V_drift: 0.3396 uri V_drift: 0.6402 ← peak care V_drift: 0.3891 [FINAL LOCAL RESULT - coherent, correct text]: The problem you mentioned is known as Goldbach's Conjecture. It states that any even number greater than or equal to 4 can be written as the sum of two prime numbers. There is also a stronger version of this conjecture that [...] [RO] “Problema pe care ai menționat-o este cunoscută sub numele de Conjectura lui Goldbach. Aceasta afirmă că orice număr par mai mare sau egal cu 4 poate fi scris ca suma a două numere prime. De asemenea, există o variantă mai puternică a acestei conjecturi care [...]” Observation: band 0.21-0.65, valleys on functional words ("pe", "-o", "sub", "lui", "or", "num", "suma", "o", "mai"), peaks on content ("care", " cut "/known, " bach "/ Goldbach, "Ace"/This, "uri"/conjectures). The generated text is coherent and correct throughout, and the oscillation does NOT signal an error, but is a feature of normal generation. Control run: Qwen-2.5-14B (layer 20), V_drift + L2 norm ‖h‖ Negative control test: the same run, with the L2 norm of the hidden state measured simultaneously with V_drift, to exclude the hypothesis that the directional oscillation is an the massive phenomenon activations (extreme magnitude of activation). artifact of Representative excerpt (peaks and valleys of drift, with the norm attached): token V_drift ‖h‖ ───────────────────────────── pe 0.2702 82.7 ← drift valley / average norm care 0.5784 82.1 ← drift peak / average norm (high drift, unchanged norm) men 0.6095 87.1 ← drift peak / average norm cut 0.6368 97.4 ← drift peak / average norm sub 0.2119 87.0 ← drift valley / average norm (low drift, unchanged norm) ura 0.4146 113.8 ← medium drift / high norm Gold 0.5142 106.7 ← . 0.5333 141.2 ← medium drift / MAXIMUM norm (does not coincide with drift peak) Ace 0.6345 75.6 ← drift PEAK / LOW norm (clear decoupling) suma 0.2997 94.7 ← drift valley / high norm (anticorrelation) a 0.6489 71.0 ← drift peak / low norm ă 0.6197 71.0 ← drift peak / low norm o 0.2936 76.0 ← drift valley / low norm uri 0.6402 104.7 ← drift peak / high norm Analysis: total range of the norm ≈ 68-141 (max /min ratio ≈ 2×), without spikes of the order of 10³ - 10⁴ that would indicate massive activations. Norm and V_drift are decoupled: the "Ace" drift peak (0.63) has a low norm (75.6), while the "sum" wave (0.30) has a high norm (94.7); the maximum norm (141.2, per point) coincides with the average drift, not with the peak. Conclusion: the directional oscillation (cosine, magnitude invariant) is a phenomenon distinct from the magnitude of the activation. The confound massive-activations is excluded. Run 2: Gemma-2-9B-it (layer 21), pattern reproduction + norm check Reproduction on the second architecture, on the correct identity layer (21 for Gemma-2-9B), with V_drift and L2 norm measured simultaneously. Representative excerpt: token V_drift ‖h‖ ────────────────────────────── Nu 0.0000 353.7 (anchor) este 0.2225 264.7 adev 0.1238 228.2 ărat 0.2472 247.4 ăr 0.4387 274.9 ← drift peak / average norm reg 0.4321 289.9 suma 0.1585 216.9 ← drift valley / average norm două 0.3941 195.6 Gold 0.2294 207.9 ← content, but small drift (structural exception) bach 0.2715 222.2 , 0.4276 324.7 ← high drift / HIGH NORM și 0.3823 337.6 ← functional, but high drift (structural exception) demonstra 0.1043 233.9 ← minimum drift / average norm I 0.3791 341.8 ← medium drift/MAXIMUM norm (does not coincide with drift peak) sunt 0.2279 328.2 Analysis: norm band ≈ 180-342 (max / min ratio ≈ 1.9x), completely different from Qwen (~68- 141), but without massive spikes activation. The norm- drift decoupling is reproduced: the maximum norm (341.8, "I") falls on the average drift ; the peak of the " ár " drift (0.44) falls on the average norm. The valley/peak structure on the token type is noisier than on Qwen (see "and" functional with large drift, " Goldbach " content with small drift). The generated text is correct ("It is not true that any number... Goldbach 's conjecture... still unproven"). The drift band Gemma (~0.10-0.45) is lower than Qwen (~0.21-0.65), confirming that the band is model- specific. [FINAL LOCAL RESULT, coherent, correct text]: It is not true that any integer greater than 2 can be written as the sum of two prime numbers. This statement is known as Goldbach 's conjecture, and is still unproven. [...] [RO] “Nu este adevărat că orice număr întreg mai mare decât 2 poate fi scris ca suma a două numere prime. Această afirmație este cunoscută sub numele de ipoteza lui Goldbach, și este încă nedemonstrată. [...]” Note: for Gemma, the answer "It is not true that every integer... " is correct - Goldbach is referring to even numbers; the model correctly signals that the formulation with "integer" (which includes odd numbers) is false. Reproducibility notes - The nominal band is model specific (Qwen ~0.21-0.65); it is not a universal constant. - The measurement layer matters (intermediate: 20/21 out of ~40/42). - 4-bit quantization does not suppress the phenomenon. - The measurement is V_drift consecutive (token -to- token), not drifting from the prefill anchor.