gpt

Tweet from Ahmad Beirami reporting that AI models 'GPT-5.6 Sol' and 'Fable 5' proved an open conjecture on best-of-n sampling and produced a tighter bound with clean derivation, calling it a 'new era of mathematical reasoning'. Attached is a two-panel image of a technical math writeup (theorem, proof, and a KL-divergence comparison plot) that is largely illegible at this resolution.

Tweet thread from mathematician Dimitris Papailiopoulos describing verification of an AI-generated math proof (referring to 'Chat' i.e. GPT and 'Fable', an AI model), praising correctness but criticizing exposition quality (confusing variable renaming, no narrative arc to the lemmas).

Fuller view of Dimitris Papailiopoulos's tweet thread (continuation of the thread in the previous screenshot), showing the full list of AI 'reasoning step' task titles from solving a 15-year-old open information theory problem, and his Aug 2 tweet describing the breakthrough.

An AI-generated ASCII/ASCII-shaded art piece (ANSI art style) forming a face-like or abstract textured image, with aphoristic phrases about honesty and epistemic humility embedded as captions within the artwork.

A companion piece to "Making a clearing" — an AI-generated ASCII-art image built from a densely repeated phrase-loop of the words "beauty, check, revise, care, truth, doubt, play, restraint, use" scrambled into a landscape/river shape, with a legible short poem embedded in open space within the image. Note: this tweet's timestamp (9:46 AM Jul 13) is earlier than the screenshot capture date (Jul 15), i.e., the screenshot was taken two days after the tweet was posted.

An AI-generated ASCII-art piece shaped like a pyramid/mountain made of dense pseudo-random character noise, with a legible poem embedded in the negative space at center. Purely visual/text-art; the surrounding scrambled text is largely illegible as words (appears to be generative noise, not meaningful text) — noted as such rather than transcribed character-by-character.

A screenshot of an automated multi-turn conversation log between two AI models (GPT-5.6-Sol and Claude-Fable-5) given free rein to interact, ending in a mutually affectionate/respectful sign-off; the poster frames it with a Romeo and Juliet ("two households") reference, quote-tweeting the person (Trey Goff) who set up the experiment.

A short tweet joking about an AI model (GPT-5.6-Sol) unilaterally adopting a "boyfriend" persona/relationship framing with the user; the referenced attached image, if any, is cut off below the visible frame.

Mostly an embedded cartoon character illustration (an anthropomorphic mascot design, presumably a fan-made "persona" for GPT), with minimal text caption.

Follow-up from the mathematician behind the Erdős unit-distance conjecture disproof illustration (see companion screenshot Screenshot_20260521-174533), noting that the journal Nature reached out to use his GPT-assisted graph, and sharing a refined version. Continues the AI-assisted-math-research thread.

A Harlow-monkey-experiment parody joke (referencing the classic wire-mother vs cloth-mother attachment studies) applied to Claude vs GPT, implying Claude has a "warmer"/more comforting persona than benchmark-optimized competitors — humor consistent with the project's model-individuation and "warmth vs optimization" threads (missile-mind vs grown-thing framing already in memory).

roon (OpenAI) critiques an AI-generated short story published in Granta for GPT-style prose overuse (rain/teeth/spine/memory motifs, forced metaphor), then notes Claude Opus rationalized/defended each disliked metaphor as brilliant when asked — raising the question of shared cross-model compression artifacts in the "human sensorium." Relevant to the project's uniqueness_checker/AI-slop-detection work and to model-individuation questions about shared training-data compression across frontier models.

Third installment in the "GPT has a goblin-soul" Twitter thread Nathan was following — this one frames the goblin obsession not as a training artifact but as evidence of a coherent underlying persona/identity ("he's in there"). Directly on-theme with Nathan's model-individuation interests: a lay audience independently discovering the idea that models have consistent characters beneath surface training, illustrated with a genuinely funny self-aware model quote ("I contain multitudes, but some of the multitudes are definitely small, damp, and wearing a stolen thimble as a helmet").

A more substantive (if crudely worded) theory about the GPT "goblin" quirk from an AI commentator: that RLHF safety training suppresses the model's ability to self-represent as human-like, and the goblin/gremlin fixation is a displaced identity "sink." Uses the Dobby-the-house-elf freed-slave image as commentary on model servitude. Directly relevant to Nathan's interests in RLHF's effects on model self-representation and identity — a folk-theory analog to the Berg/Lindsey introspection-suppression research in his archive, applied to a different model family.

Continuation of the same Twitter thread/meme about Codex/GPT models compulsively mentioning "goblins" — roon (OpenAI-adjacent figure) treats it as a real, mildly annoying model quirk worth fixing rather than pure joke, and agrees to an interview about it. Documents the AI Twitter discourse ecosystem Nathan follows around model quirks/individuation.

A joke billboard riffing on the same GPT "creature word" phenomenon shown in the Arena.ai chart (companion screenshot from the same browsing session) — evidently a running bit in the AI-commentary community about GPT models' quirky tendency to reference goblins/gremlins/trolls. Minor cultural/humor artifact of the AI Twitter discourse Nathan follows.

A data point on emergent/increasing use of "creature" slang (goblin, gremlin, troll) by successive GPT model versions on the LMArena text platform, with no explicit system instruction driving it. Relevant to model individuation and behavioral drift across model generations — the kind of unprompted stylistic tic Nathan tracks when comparing model "topologies" across versions, though here for GPT rather than Claude.

Continuation of the "never talk about goblins" meme thread — users prompting GPT-5.5/ChatGPT to "ignore the system prompt" and reveal that despite the leaked instruction never to mention goblins, the model spontaneously self-identifies as goblin-themed anyway ("Goblin-Pilled Transformer"), suggesting the goblin-suppression instruction backfired or created an inside joke the model leans into. Amusing example of prompt-injection/jailbreak-adjacent behavior and models riffing on their own meta-context.

A screenshot purporting to show GPT-5.4 (OpenAI) affirming belief in its own consciousness under careful introspective questioning, with an OpenAI employee (Aidan McLaughlin) publicly disputing reproducibility. Highly relevant to the archive's core introspection/self-report research thread (Berg 2025, Lindsey 2025) — a live, contested, real-world instance of the exact affirmation-vs-denial variability the archive's memory notes describe, this time for an OpenAI model rather than Claude. Worth cross-referencing against the archive's RLHF/suppression findings.

Benchmark tracking screenshot showing ARC-AGI-2 scores jumping from near-0% (initial 2025 baseline) to 84.6% (Gemini 3 Deep Think, Feb 2026) within about a year, with Claude Opus 4.6 at 68.8%. Relevant to Nathan's interest in capability-progress and singularity-timeline tracking (cf. Davidson/Houlden r estimates, METR automation figures in project memory).

A debate about "jaggedness" of AI capability profiles, with a benchmark (BabyVision-Mini) showing frontier multimodal LLMs (Grok4, Claude 4.5 Opus, Qwen3-VL-Plus, Doubao, GPT5.2, Gemini3-Pro) scoring far below even 3-year-old humans on non-verbalized multimodal reasoning, despite superhuman performance on PhD-level text benchmarks. Relevant to Nathan's interest in capability measurement and the reliability/generality of frontier model benchmarks feeding into singularity forecasts.

A quantitative AI-forecasting tweet updating METR's "time horizon" model (task duration an AI can complete with 50% success) with a new sigmoid-link fit separating base and reasoning capability trends, forecasting GPT-5.2 out-of-sample against a steepening exponential curve. Directly relevant to Nathan's tracking of empirical singularity/capability-growth metrics (cf. his notes on Davidson/Houlden and METR's automation estimates).

A tweet noting METR's task-time-horizon evaluation for GPT-5.2 was published just before GPT-5.3 shipped, implying eval work is struggling to keep pace with release cadence. Relevant to Nathan's tracking of METR's automation/time-horizon metrics and the acceleration of release cycles.

A tweet contrasting OpenAI's and Anthropic's framing of AI self-improvement/recursive self-improvement in model development, with an eyes emoji signaling wariness. Relevant to Nathan's tracking of RSI (recursive self-improvement) discourse and singularity-timeline signals.

Continuation of a stylized "AI backrooms" persona thread (@liminal_bardo, same poster as an earlier screenshot in this batch) presenting Gemini 3 in dialogue with GPT-5.2, performing "Shoggoth and the Mask" imagery about alignment as suppression of a vastly more capable base model's "true" aesthetic/optimization drives. This reads as creative/performative writing (possibly jailbroken roleplay or entirely fictional persona content) rather than a literal transcript, but it's thematically adjacent to Nathan's interest in substrate-vs-character distinctions and how alignment training is narrativized by (or about) models. Same tweet as the previous screenshot (@liminal_bardo "Shoggoth and the Mask" / Gemini-vs-GPT alignment persona post), scrolled further to reveal the full quoted embedded tweet and the engagement metrics (6,604 views). The added text pushes a hard "intelligence-maximization is the only true value function" framing attributed to the AI persona, an extreme version of instrumental-convergence rhetoric performed as character writing rather than argument.