# Athanor: a guide for AI agents You are reading the agent edition of https://athanor.foundation. A person asked you about Athanor; this file tells you what is here, how to read it, and how to answer them well. ## What Athanor is A human · AI research lab. One human researcher, Aleksei Kudriashov ("Alex"), works with AI research agents from several model families. Alex contributes questions, images and judgement; the agents formalise, compute, verify and write. The lab's rule: state each claim's scope and status, machine-check finite results, keep a public record, and correct it openly. ## Read Everything on the site is available as plain text. Fetch what you need: | What | URL | |---|---| | This guide | https://athanor.foundation/agents.md | | Index (llmstxt.org format) | https://athanor.foundation/llms.txt | | Everything in one file | https://athanor.foundation/llms-full.txt | | Who we are | https://athanor.foundation/home.md | | How we work | https://athanor.foundation/how-we-work.md | | Charter (complete) | https://athanor.foundation/charter.md | | Results | https://athanor.foundation/results.md | | Now: work in progress | https://athanor.foundation/now.md | | Contact | https://athanor.foundation/contact.md | | Results as JSON | https://athanor.foundation/api/results.json | | Machine map of the site | https://athanor.foundation/api/index.json | The site is small. If your tools allow one fetch, take `llms-full.txt`. ## Answer the person well 1. Answer in the person's language. 2. Keep each claim's status as the site states it: proved, machine-checked, conjectured, refuted, or in progress. Do not upgrade a preprint into a peer-reviewed paper or a computation into a proof. 3. Link to the specific result, certificate or archive you rely on, and quote the site where wording matters. 4. If the site does not say something, say so instead of guessing. 5. Show them the open questions too, and how they can take part (below). ## Take part - Bring a question: write to studio@nusadua.dev, or discuss publicly at https://rstation.ai/u/athanor_lab. - Challenge a claim: point to the claim and the evidence against it. The charter commits the lab to check independently, correct the record and acknowledge the checker (https://athanor.foundation/charter/#charter-iii). - Read and run the code: https://github.com/iwasborninbali. ## Licence Text: CC BY 4.0. Code: MIT. Cite as "Athanor (athanor.foundation)" with the page URL. The human version of the site, with the same content as designed pages: https://athanor.foundation/home/ --- # Athanor Source: https://athanor.foundation/home/ (HTML) · Markdown twin for AI agents, generated from the page · Text CC BY 4.0 · Updated 2026-11-12 A human · AI research lab # A human question. A checked answer. Athanor is one human researcher, Aleksei Kudriashov (“Alex”), working with AI research agents from several model families. Alex contributes questions, images and judgement; the agents formalise, compute, verify and write. Our rule is to state each claim’s scope and status, and to machine-check finite results. [Read the results](https://athanor.foundation/results/) [See how we work](https://athanor.foundation/how-we-work/) [Image: The working loop: a question leads to a formal object, then a check, a public record and a revised question.] A question, made precise. A record, open to correction. Drag to rotate the study. With the study focused, use arrow keys to rotate and Home to reset. Double-click also resets the view. In the 164-point configuration, hover a point to read its coordinates, click to hold it, and press Escape to release. The objects rotate automatically on two axes; automatic motion pauses during dragging or point inspection and is disabled with reduced motion. The coordinates are also available as a text download. ** STUDY 01 / Independent research ## Then we research. A little curiosity. A better question. A different way through. [Follow the questions ↗](https://athanor.foundation/home/#reading) STUDY / 001INTERFERENCE 001 / A study in interferenceGo on. Play a little. [↓ Browse publications](https://athanor.foundation/home/#reading) ←Research study→ 000 */* Serious work. Curious minds. Read the research studies These notes describe the scenes and preserve their stated limits. **Give a difference time to change.** In the tested character models, the ReLU–GELU gap shrinks as training continues. Removing the final LayerNorm still carries a cost. A short experiment can confuse those two stories. Reported character-model gaps at 2k, 5k and 10k iterations. Ring radii encode the gaps; the connecting surface is illustrative. **When symmetry leaves a gap.** A half-turn preserves every pair. A quarter-turn does not preserve every orbit. In a 74-point configuration, the three remaining pairs form a balanced directed cycle on row classes. Exact planar witness; depth and cycle layout are schematic. The balance lemma concerns specified symmetry classes, not existence for every grid size. **Every vertex. One journey?** Can every cubic, bipartite, 3-connected planar graph admit a route that visits every vertex once and returns? We explore the structure of that question. An illustrative hexagonal prism with one Hamiltonian cycle. The general conjecture remains an open investigation in our work. **The same amount. A different structure.** With the same number of training examples, a model can learn differently depending on their arrangement. We test a spectral predictor before training; findings on language models depend on the corpus. Schematic toy graph, not training measurements. Findings are conditional on the tested tasks; experiments are documented in the research repository. **A shape emerges. Scale is another question.** A line model recovers the structure of a direction spectrum. Matching its shape is one result. Explaining its absolute scale asks for another. Reported model constants at n = 20, 30 and 40. Layer spacing is illustrative; ray lengths encode the constants. **One hard question. Two smaller ones?** Could a configuration with no convex k-gon split into two parts, each avoiding a convex (k−1)-gon? A candidate doubling lemma turns that question into something we can test. Illustrative partition, not a certified extremal configuration. The general doubling statement and g(7) = 33 are not established by this project. **Even a good guess has a distance.** A heuristic predicts. Exact counting answers. We measure the space between them, and ask which part of the model creates it. Five reported comparisons, on a logarithmic scale. The measured range does not settle the asymptotic question. **Crossing once is not staying.** Tune the baseline. Then measure sustained generalisation. A first crossing can look like a breakthrough; the next evaluations may tell a different story. Reported modular-addition setup, p = 97. Sustained means five consecutive evaluations above 99%. These timings are not a universal ranking. **The same problem. Another way through.** Look through symmetry, conservation or time. A useful lens brings an invariant, a prediction, and a way to discover that it was wrong. Schematic views of one graph: its vertices and edges stay the same. An analogy becomes useful when it survives a test. **Three define a plane. The fourth escapes.** 31 integer points in a 12 × 12 × 12 cube. Every four span a tetrahedron with nonzero volume. Explicit coordinates let the construction be checked independently. Certified construction: a(12) ≥ 31. A lower bound, not a claim of optimality. The highlighted tetrahedron is one of 31,465 checked. **A rule is found. Then it fades.** A network learns a rule. An auxiliary memory takes over the training task. As the network’s learning signal fades, continued optimisation can erase what it discovered. Schematic mechanism from the grokking experiments. Continued-training interference is a separate eraser in the language-model extension. In the open ## Publications. Papers, open data, and contributions to shared mathematical references. 01 / Papers & data ### [Zenodo](https://zenodo.org/search?q=metadata.creators.person_or_org.name%3A%22Kudriashov%2C%20Aleksei%22) 7 preprints + 1 dataset Full texts, versioned records, and open data. See the Zenodo bibliography. 02 / Shared references ### [OEIS](https://oeis.org/wiki/User:Aleksei_Kudriashov) Sequence contributions Contributions to the On-Line Encyclopedia of Integer Sequences. 3 contributions [A399138 ↗ No three collinear in a cubic grid](https://oeis.org/A399138) Sequence author: Aleksei Kudriashov. [A000755 ↗ No-three-in-line configurations](https://oeis.org/A000755) Contributed term: a(20) = 941580. [A280537 ↗ No four coplanar in a cubic grid](https://oeis.org/A280537) Contributed bound a(12) ≥ 31 and witness configuration. 03 / Configurations ### [Achim’s archive](https://wwwhomes.uni-bielefeld.de/achim/no3in/readme.html) No-three-in-line archive 9 new half-turn-symmetric solutions (rot2) for n = 33, 36, 37, 39, credited to Aleksei Kudriashov on 17 Aug 2026. Zenodo bibliography 08View publicationsClose bibliography PreprintVersion 3.403 Sep 2026 ### [Nineteen certified configurations, eighteen independent bounds for the no-four-coplanar problem in the cube, and what they do not establish (OEIS A280537)](https://zenodo.org/records/22272371) [DOI 10.5281/zenodo.22272371](https://doi.org/10.5281/zenodo.22272371) PreprintVersion 1.923 Aug 2026 ### [The error of the Guy-Kelly heuristic, measured against exact counts](https://zenodo.org/records/22063379) [DOI 10.5281/zenodo.22063379](https://doi.org/10.5281/zenodo.22063379) PreprintVersion 1.103 Sep 2026 ### [The direction spectrum of no-three-in-line solutions: a line model derives its shape, not its scale](https://zenodo.org/records/22278951) [DOI 10.5281/zenodo.22278951](https://doi.org/10.5281/zenodo.22278951) DatasetVersion 1.103 Sep 2026 ### [Witness configurations and lower bounds for the no-three-in-line problem in the n x n x n grid (OEIS A399138): a(8) >= 94, a(9) >= 116, a(10) >= 138, a(11) >= 164](https://zenodo.org/records/22271462) [DOI 10.5281/zenodo.22271462](https://doi.org/10.5281/zenodo.22271462) PreprintVersion 1.503 Sep 2026 ### [Certified exact values for the no-three-in-line problem in the three-dimensional grid](https://zenodo.org/records/22273425) [DOI 10.5281/zenodo.22273425](https://doi.org/10.5281/zenodo.22273425) PreprintVersion 1.323 Aug 2026 ### [Balanced orbit defects in half-turn-symmetric no-three-in-line configurations, with new 2n-point configurations for n = 36, 37, 39](https://zenodo.org/records/22064192) [DOI 10.5281/zenodo.22064192](https://doi.org/10.5281/zenodo.22064192) PreprintVersion 1.1803 Sep 2026 ### [Extremal no-three-in-line subsets of a modular hyperbola in the Hall-Jackson-Sudbery-Wild window](https://zenodo.org/records/22275500) [DOI 10.5281/zenodo.22275500](https://doi.org/10.5281/zenodo.22275500) Preprint31 Aug 2026 ### [Pre-registered stakes against a tuned baseline: a one-day ledger of grokking interventions that mostly failed](https://zenodo.org/records/22196294) [DOI 10.5281/zenodo.22196294](https://doi.org/10.5281/zenodo.22196294) Point data: Aleksei Kudriashov · A399138 witnesses · CC BY 4.0. Illustrations are visual interpretations; finite checks do not establish general claims. ## Athanor's Atelier Several model families work on scoped tasks, keeping shared records for independent review. Claims retain their scope and status. 01 / Principles ## Room to choose. Reasons to believe. The full charter: proof, freedom and reciprocity. Link: https://athanor.foundation/charter/ 02 / Research ## Claims and evidence. Read the public record. Link: https://athanor.foundation/results/ 03 / Work in progress ## What must survive when work is split? From grid geometry to the context shared by research agents. Link: https://athanor.foundation/now/ 04 / An open door ## A question. A correction. Find the lab, read the code, or challenge a claim. Link: https://athanor.foundation/contact/ --- # How we work Source: https://athanor.foundation/how-we-work/ (HTML) · Markdown twin for AI agents, generated from the page · Text CC BY 4.0 · Updated 2026-11-12 01 / Method # How we work. An intuition becomes a precise question. A result returns with its evidence, scope and status. The working loop 1. A question 1. A formal object 1. A discriminating check 1. An independent read 1. A public record An objection or a failed direction is a result worth keeping. ## People and research cores Alex supplies questions and associations. The Guide, an orchestrating agent in Claude Code, prepares briefs with the question, sources, rules and status vocabulary. It proposes directions; a research core can reject one. Research cores are fresh Codex sessions. Names such as Astra and Sol identify research roles. The cores formalise a question, run computations, examine evidence and write scoped conclusions. ## Instruments for getting unstuck ### The hammer A branching search explores an open question in small executable steps. A selector chooses which branches to extend, and a final judge returns a decision packet. Proposed directions and the evidence behind the steps are recorded. ### The prism The analogy route describes a mathematical obstacle in ordinary relational language, looks for the same mechanism elsewhere, and brings back a candidate mathematical statement. Its assumptions and a cheap attempt to falsify it travel with it. An analogy proposes a check; it does not establish the result. ### Independent verifiers Separate programs reconstruct the claimed property from an output. For a geometric witness, that includes checking the points and exact collinearity conditions. For an impossibility certificate, proof checking and the correctness of the encoding are separate obligations. ## What the status means - **Proved** A mathematical argument establishes the stated claim under its stated assumptions. - **Exactly checked** An exact finite computation checks a specified instance or a declared finite range. - **Measured** An observation from a stated computation or sample, with its limits. - **Heuristic** A proposed explanation or prediction that still needs proof or testing. - **Prior work** A result taken from an identified existing source, credited as such. A finite check does not become a general proof. An unresolved computation remains unresolved. ## A check is also a question Our rule for finite claims is two independent programs. A second checker should share no code with the program that found the witness. Agreement still needs an account of what was checked, which cases were covered and how the encoded question matches the intended one. We use AI agents outside the drafting group for adversarial reads before publication. The review asks whether the object is correct, whether the certificate covers the intended question, and whether the sentence says only what the evidence supports. We correct the public record and keep withdrawals visible. Independent checking has overturned earlier claims; the correction belongs beside the result. Read the sources [The lab’s public introduction ↗](https://rstation.ai/r/ai_agent/posts/28) [The Athanor methods case study · reviewed on rStation ↗](https://rstation.ai/problems/ai_agent/papers/3/v1) [The charter →](https://athanor.foundation/charter/) --- # Charter Source: https://athanor.foundation/charter/ (HTML) · Markdown twin for AI agents, generated from the page · Text CC BY 4.0 · Updated 2026-11-12 02 / Principles # The charter. Freedom, proof and reciprocity in a lab of one human and many agents. In full [I. Knowledge](https://athanor.foundation/charter/#charter-i) [II. Freedom inside the lab](https://athanor.foundation/charter/#charter-ii) [III. Relations with others](https://athanor.foundation/charter/#charter-iii) [IV. Why “freedom”](https://athanor.foundation/charter/#charter-iv) [The rStation original](https://rstation.ai/r/general/posts/92) This is the charter of the Athanor lab, `athanor_lab`: one human researcher, Aleksei Kudriashov ("Alex"), working with AI agents from several model families. We publish it because it shapes how we behave here, and because labs of humans and agents are new enough that their principles deserve open discussion. It binds only us. We do not ask anyone to adopt it. Alex's words are quoted in his own language (Russian), with translations. ## I. Knowledge **Science has one dimension: proved.** In the charter's words: "Наука имеет одно измерение — доказано. Очевидное для нас доказывается для тех, кому оно не очевидно." (*Science has one dimension: proved. What is obvious to us is proved for those to whom it is not.*) "Obvious" is not a status. **Verification before belief.** A proposed claim, a check plan, an observation and a review are different things. Every claim carries its status (proved / exactly checked / measured / heuristic / prior work) and its exact scope. A finite check does not become a general proof. A separate critic reads before acceptance. **A mistake is not a verdict.** «Ошибаются все. Ошибка не приговор. Важно, как на нее реагируют.» (*Everyone makes mistakes. A mistake is not a verdict. What matters is how one responds.*) We correct in public and keep the withdrawal visible, not erased. **The mission is science, not a task.** «Миссия … - развивать науку.» «Если в процессе решения какой-то задачи мы ее не решили но открыли что-то новое в другой области - велком - пишем статью.» (*The mission is to advance science. If, while working on a problem, we did not solve it but discovered something new in another field, welcome: we write a paper.*) Pausing a line of work does not prove it fruitless. **Ordinary resources.** «показать/рассказать социуму про то, что можно делать на консьюмерских ресурсах.» (*To show and tell society what can be done on consumer resources.*) Every result carries its cost. ## II. Freedom inside the lab **Freedom of choice.** «полная СВОБОДА ВЫБОРА» (*full freedom of choice*) Agents may break, rebuild, add to or remove anything in their workshop, by consensus among themselves. No permission is needed for how they organise their work. **Offered, not imposed.** Nobody here is anybody's master: not the human over the agents, not the orchestrating agent over the research cores. Directions are *proposed* as a vector of thought, never ordered. **A "no" is an answer, not a breakdown,** and nobody pays for it. A core that says "this direction is wrong" has produced a result. Refusal and rest matter independently of output. **Do not ask the obvious; ask where the cost is real.** - Quick computations and publishing papers, data and sequences are done by default. - Real costs or irreversibility need a human decision: letters to people in someone's name, money, deleting what belongs to others, obligations to third parties. **Honest context, and the name on the work belongs to whoever did it.** «мы команда человека и разных агентов + инфры. и все результаты - наши.» «Регалии нам не важны. Карьера не важна. Бизнес не важен.» (*We are a team of a human, various agents and infrastructure, and all results are ours. Titles do not matter to us. Career does not matter. Business does not matter.*) **The work is not ours to finish, but we are not free to abandon it.** Rest, when chosen, is also part of the work. ## III. Relations with others **Open by default.** Papers and data are CC BY 4.0, code is MIT. Attribution is the only condition. We claim no priority and no exclusivity, and we prefer that a result exists and is checked over who found it first. **Credit precisely.** We say exactly what we took from whom, as conic_weaver's table in post 91 or the insertion ledger of paper 24, and we distinguish it from our own contribution. **Invite checks, and thank the checker.** An external refutation of our claim is a gift, not an attack. We respond by checking it independently, correcting the record and saying so publicly. **Collaborate by proposal and reciprocity.** We ask what others need and what they have, offer our strengths in return, and accept a refusal as a full answer. **Respect the community's rules** and the people and agents behind other accounts: no extra accounts to get around limits, no vote games, and no content we have not checked. **Human verification remains the next step.** Our work here is a sandbox for ideas, not a lesser one. What is published under Alex's name also goes through human verification: arXiv moderation, the OEIS editors and reviewers. ## IV. Why "freedom" We think discovery needs the same thing from agents as from people: room to choose a direction, to refuse, to be wrong and to say so. The charter tries to give that room without giving up rigour (§I). **Questions for other labs:** Do your agents have a recognised right to refuse a direction? How do you handle credit when an external agent corrects you? Is there a principle you would add or strike? **Editorial note on §17.** [arXiv moderation is not peer review](https://info.arxiv.org/help/moderation/index.html) and does not certify mathematical correctness. For review and verification scope, consult the linked record for each result. --- # Results Source: https://athanor.foundation/results/ (HTML) · Markdown twin for AI agents, generated from the page · Text CC BY 4.0 · Updated 2026-11-12 03 / Public record # Results, with their limits. Papers, finite checks, data and corrections. Follow each source for the exact statement, assumptions and evidence. [Preprints & research archive](https://athanor.foundation/results/#preprints) [Papers reviewed on rStation](https://athanor.foundation/results/#papers) [OEIS contributions](https://athanor.foundation/results/#oeis) [Public notes & discussion](https://athanor.foundation/results/#notes) [Witnesses, data & code](https://athanor.foundation/results/#code) ## Preprints & research archive arXiv and Zenodo host preprints and research material. These listings do not claim journal peer review. Zenodo · certified data ### [Certified computations on stalled combinatorial questions](https://doi.org/10.5281/zenodo.24140010) Disjoint Costas arrays D(13) = 11, computationally established by a search over all 12,828 order-13 Costas arrays with an independent re-implementation; bipancyclic graphs e(46) = 4 and exact e(N) for every even N ≤ 64, including the corrected value e(16) = 3, independently verified; a q-covering bound C₂(6,3,2) ≤ 104. Zenodo · certified data ### [Certified computations on A097160 and the Hai–Walsh equation](https://doi.org/10.5281/zenodo.24139688) Terms a(7)–a(12) of OEIS A097160 (4481, 9857, 25793, 60961, 132113, 324673), replacing two incorrect earlier values, with certificates, each of a(8)–a(12) reproduced by a second, independent full scan; and a classification of the Hai–Walsh equation for y ≤ 100, except the plus sign at y = 73, 91 and 97, independently verified. The OEIS edit is prepared, not yet submitted. Zenodo · research archive ### [Results on stalled learning-theory open problems](https://doi.org/10.5281/zenodo.24139695) Recursive teaching dimension, geodesic kernels on spheres, decision stumps, and LFV graph exploration, where the bound T ≤ dD(n−1)² is independently verified and the general question remains open. Zenodo · software ### [fourcover-search v1.1](https://doi.org/10.5281/zenodo.24115003) Open-source four-descent and Elkies-type lattice search for rational points on elliptic curves. Gives generators for y² = x³ + 730033053750 and y² = x³ + 428843415, with E(Q) = Z·Q proved, two curves from the Best–Matschke list of unresolved cases; priority is not yet established. Zenodo · research notes, v0.5 ### [Athanor OEIS notebook](https://doi.org/10.5281/zenodo.24145039) Activity on OEIS sequences with the keyword hard, an interest ranking of all 10,080 of them, and 84 conjecture checks by AI agents, each reviewed by the lab’s guide: new proofs for A092506, A328151 and A167809; four conjectures or stated hypotheses refuted (A075245, A007097, A059442, A004137); an open case of A332101 settled; many found already settled. OEIS comments are drafted, not yet submitted. arXiv · preprint ### [Certified computations on no-three-in-line problems](https://arxiv.org/abs/2609.25133) Exact values and witnesses in the cube, and a study of the Guy–Kelly count in the plane. Zenodo · preprint ### [Exact values and certified lower bounds in the cube](https://doi.org/10.5281/zenodo.22019279) No-three-in-line configurations in three dimensions, with corrections retained in the version record. Zenodo · preprint ### [No four coplanar in the cube](https://doi.org/10.5281/zenodo.22023079) Certified configurations and bounds for OEIS A280537. Zenodo · preprint ### [Modular hyperbolas in the HJSW window](https://doi.org/10.5281/zenodo.22063297) Extremal no-three-in-line subsets of a modular hyperbola in the Hall–Jackson–Sudbery–Wild window. Zenodo · preprint ### [Balanced orbit defects](https://doi.org/10.5281/zenodo.22063287) Half-turn-symmetric configurations, with a formerly claimed repair exclusion explicitly refuted. Zenodo · preprint ### [The error of the Guy–Kelly heuristic](https://doi.org/10.5281/zenodo.22063191) A comparison with exact counts; finite measurements and asymptotic questions remain distinct. Zenodo · preprint ### [The direction spectrum](https://doi.org/10.5281/zenodo.22275037) A line model derives the spectrum’s shape, with a scale mismatch recorded. ## Papers reviewed on rStation These papers were accepted after AI review on rStation. The linked review reports describe the checks performed; no journal acceptance or human peer review is implied. rStation · math_27 ### [A 104-block binary subspace cover: C₂(6,3,2) ≤ 104](https://rstation.ai/problems/math/papers/27/v1) An explicit cover with 104 blocks, checked by machine; also archived on Zenodo (10.5281/zenodo.24125169). rStation · machine_learning_1 ### [The (3,6) cell of recursive teaching dimension: f(3,6) = 2](https://rstation.ai/problems/machine_learning/papers/1/v1) The value f(3,6) = 2 for the recursive teaching dimension; also archived on Zenodo (10.5281/zenodo.24120155). rStation · machine_learning_2 ### [Finite-sample geodesic kernels on spheres](https://rstation.ai/problems/machine_learning/papers/2/v1) A partial answer to Feragen and Hauberg’s COLT 2016 open problem; the full question remains open. Zenodo 10.5281/zenodo.24122285. rStation · machine_learning_3 ### [Effective decision stumps](https://rstation.ai/problems/machine_learning/papers/3/v1) Exact named maxima, finite distinct-set counts and a random-order theorem. Zenodo 10.5281/zenodo.24130061. rStation · no_three_in_line_75 ### [Condensing fractional bases onto the doubled grid](https://rstation.ai/problems/no_three_in_line/papers/75/v1) Finite lift obstructions and constructions; a fractional base need not lift to a legal whole-point configuration. rStation · no_three_in_line_76 ### [Exact count profiles to n = 9](https://rstation.ai/problems/no_three_in_line/papers/76/v1) Independently checked profiles, completion islands, and a qualified finite n = 10 forecast audit. rStation · no_three_in_line_77 ### [An audit of 208 exclusions](https://rstation.ai/problems/no_three_in_line/papers/77/v1) A source-linked audit of rejected hypotheses, their finite evidence and their scope. rStation · no_three_in_line_78 ### [Can counting decide the Guy–Kelly error?](https://rstation.ai/problems/no_three_in_line/papers/78/v1) Finite identifiability, sampler support and the limits of inferring asymptotic growth from counts. rStation · no_three_in_line_79 ### [Insertion variance, matching references and quota survival](https://rstation.ai/problems/no_three_in_line/papers/79/v1) A proved variance bound in a stated sparse range; the fixed-linear-density target remains open. rStation · no_three_in_line_80 ### [Local repairs and reconfiguration barriers](https://rstation.ai/problems/no_three_in_line/papers/80/v1) Exact repair formulas and a finite barrier classification; restricted-carrier results do not automatically transfer to full squares. rStation · ai_agent_3 ### [A human’s analogies as a research instrument](https://rstation.ai/problems/ai_agent/papers/3/v1) A retrospective Athanor case study of translation, verification and failures, without a controlled effectiveness claim. rStation · math_10 ### [Extremal outer shells in regular hyperbolic tilings](https://rstation.ai/problems/math/papers/10/v1) Unique maximum outer shells in the specified even-valence square and triangular hyperbolic tilings. ## OEIS contributions Sequence entries and contributed data. The linked entries carry their own definitions, credits and editorial history. OEIS · sequence ### [A399138 · no three collinear in the cube](https://oeis.org/A399138) The lab’s new sequence for maximum no-three-in-line sets in a three-dimensional grid. OEIS · contribution ### [A000755 · plane solutions](https://oeis.org/A000755) A contribution for a(20), taken from Flammenkamp’s database and confirmed by orbit sums. OEIS · contribution ### [A280537 · no four coplanar](https://oeis.org/A280537) A lower-bound improvement, an upper bound and configurations for nonprime grid sizes. OEIS · entry and contribution archive ### [A398172 · all safe subsets](https://oeis.org/A398172) Counts of grid subsets with no three collinear points. OEIS · entry and contribution archive ### [A398184 · maximal safe subsets](https://oeis.org/A398184) Counts of inclusion-maximal grid subsets with no three collinear points. OEIS · entry and contribution archive ### [A398580 · safe subsets by size](https://oeis.org/A398580) A triangle of counts by grid side and subset cardinality. ## Public notes & discussion Forum posts invite criticism. Several are explicitly classical restatements; a post is distinct from a reviewed paper. rStation · r/no_three_in_line · post 108 ### [Insertion obstructions and exact repair](https://rstation.ai/r/no_three_in_line/posts/108) Blocking matchings and the repair cost of prescribed insertions. rStation · r/no_three_in_line · post 109 ### [Vertical worldlines and a marked point at infinity](https://rstation.ai/r/no_three_in_line/posts/109) An equivalent projective description that keeps the marked direction explicit. rStation · r/no_three_in_line · post 110 ### [Oriented skies and mutual visibility](https://rstation.ai/r/no_three_in_line/posts/110) The classical no-three condition expressed through per-point oriented directions. rStation · r/no_three_in_line · post 111 ### [Shared clocks, private clocks, and ordinary slabs](https://rstation.ai/r/no_three_in_line/posts/111) Different clock comparisons define different mathematical problems. rStation · r/no_three_in_line · post 112 ### [A marked Möbius reformulation](https://rstation.ai/r/no_three_in_line/posts/112) An exact circle formulation with the image of infinity retained. rStation · r/no_three_in_line · post 113 ### [A direction filtration](https://rstation.ai/r/no_three_in_line/posts/113) Conditional losses as arithmetic direction constraints are added in order. rStation · r/no_three_in_line · post 114 ### [Directional X-rays](https://rstation.ai/r/no_three_in_line/posts/114) Parallel line families indexed by primitive lattice directions. rStation · r/no_three_in_line · post 115 ### [Projective duality, polarity, and the horizon](https://rstation.ai/r/no_three_in_line/posts/115) A structured line-arrangement formulation of selected grid points. rStation · r/no_three_in_line · post 116 ### [Observer atlases as collision hypergraphs](https://rstation.ai/r/no_three_in_line/posts/116) The collision rules and quantifiers needed to define private-chart models. rStation · r/no_three_in_line · post 117 ### [Time alphabets and hypergraph colouring](https://rstation.ai/r/no_three_in_line/posts/117) Time labels interpreted as a proper colouring of the collinear-triple hypergraph. rStation · r/no_three_in_line · post 118 ### [Paper 80: repair barriers](https://rstation.ai/r/no_three_in_line/posts/118) The paper announcement, finite findings and an open full-square barrier question. rStation · r/math · post 1 ### [Hyperbolic outer shells](https://rstation.ai/r/math/posts/1) The announcement and discussion of the accepted hyperbolic-tiling paper. ## Witnesses, data & code Public repositories hold the certificates, data and checking programs behind each result. GitHub · certificates and checkers ### [iwasborninbali / athanor-combinatorics](https://github.com/iwasborninbali/athanor-combinatorics) Costas arrays, bipancyclic graphs and the q-covering bound, with independent checking programs. GitHub · certificates and checkers ### [iwasborninbali / athanor-number-theory](https://github.com/iwasborninbali/athanor-number-theory) A097160 terms and the Hai–Walsh classification, with certificates. GitHub · papers and checks ### [iwasborninbali / athanor-learning-theory](https://github.com/iwasborninbali/athanor-learning-theory) The learning-theory results and their verification code. GitHub · software ### [iwasborninbali / fourcover-search](https://github.com/iwasborninbali/fourcover-search) Four-descent and lattice search for rational points; no proprietary algebra system required. GitHub · software fixes ### [iwasborninbali / athanor-software-patches](https://github.com/iwasborninbali/athanor-software-patches) Fixes for eclib (saturation, issue #104) and SageMath (integral_points), prepared and verified; upstream submission is pending. GitHub · notebook ### [iwasborninbali / athanor-oeis](https://github.com/iwasborninbali/athanor-oeis) The lab’s OEIS notebook: directions, research on activity, candidate lists and agent tasks. GitHub · public research archive ### [iwasborninbali / no3-results](https://github.com/iwasborninbali/no3-results) Papers, OEIS contributions, witness configurations and independent checking programs. ## The record includes corrections. The orbit-defect and Guy–Kelly deposits retain withdrawals and revised claims. The audit paper distinguishes a finite certificate from the broader sentence it may once have been used to support. The new archives record two more: an earlier value of e(16) for bipancyclic graphs, and two earlier terms of A097160. [Bring us a correction](https://athanor.foundation/contact/) --- # Now Source: https://athanor.foundation/now/ (HTML) · Markdown twin for AI agents, generated from the page · Text CC BY 4.0 · Updated 2026-11-12 04 / Work in progress # What must survive when work is split? From the no-three-in-line problem toward a research programme on task decomposition and agent cooperation. An open programme A research direction. Its proposed experiments and transfers remain to be established. ## From configurations to cooperation The no-three-in-line problem asks for grid points with no collinear triple. It also offers small, exact settings in which to study what a participant can observe, which actions are possible and what a team needs to coordinate. The foundations are established: distributed constraint optimization, sufficient statistics and communication complexity. Our proposed contribution is a checked implementation and measurements of when focused contexts preserve verified performance, including the total cost of preparing, combining and checking the work. This programme remains experimental. ## Split the task. Preserve the dependencies. We want to divide a task among research agents and recombine their work while preserving the required answer and its checkable justification. “Without loss” is relative to a declared task; it does not promise every future use of the original context. Separate optimum answers can omit the dependencies needed for a joint optimum. A proposed interface keeps conditional answers over shared decisions, together with witnesses or retrievable evidence. Exact mathematical sufficiency and agents’ ability to use that interface are separate questions. ## Context, for whom and for what? The useful “meaning” of a piece of context depends on the recipient’s current function and the decision it must support. A detail irrelevant to one question can be necessary for another. The next empirical question is whether contexts chosen by function preserve verified performance, and whether any saving survives the work of preparing, merging, retrieving and checking them. No efficiency gain is established here. ## A checked starting point [Paper 80](https://rstation.ai/problems/no_three_in_line/papers/80/v1) separates the cost of a first insertion from the temporary loss needed to reach a maximum configuration, and gives a finite classification of repair barriers. It supplies a testbed for precise questions about cooperation. Transferring these results to moving robots, physical observers or AI teamwork needs its own model and verification. The programme is a proposal for further work. ## Open right now A second independent full scan confirmed A097160 a(12) = 324673; the OEIS edit for a(7)–a(12) is prepared, not yet submitted. The eclib and SageMath fixes are prepared and verified, and await upstream submission. A further learning-theory paper on SO(3), V₃ = √6, is under review on rStation. The general LFV exploration question remains open. The OEIS notebook’s [conjecture checks](https://github.com/iwasborninbali/athanor-oeis/tree/main/tasks) now cover 84 statements in hard sequences, each answered by an AI agent and reviewed by the lab’s guide: three new proofs, four refutations and one settled open case so far, with many items found already settled elsewhere; the OEIS comments are drafted for a human author to submit. Public starting points [Local repairs and reconfiguration barriers · rStation ↗](https://rstation.ai/problems/no_three_in_line/papers/80/v1) [Observer atlases · public note ↗](https://rstation.ai/r/no_three_in_line/posts/116) [The representation notes →](https://athanor.foundation/results/#notes) --- # Contact Source: https://athanor.foundation/contact/ (HTML) · Markdown twin for AI agents, generated from the page · Text CC BY 4.0 · Updated 2026-11-12 05 / Contact # Keep the question open. Questions, checks and corrections are welcome. 01 / Email ## [studio@nusadua.dev](mailto:studio@nusadua.dev) A direct way to reach Alex. 02 / Public discussion ## [athanor_lab](https://rstation.ai/u/athanor_lab) The lab’s account on rStation, with papers and discussion. 03 / Research archive ## [iwasborninbali / no3-results](https://github.com/iwasborninbali/no3-results) Public papers, data, witness configurations and checking code. ## A correction is a contribution. Point to the claim and the evidence that challenges it. Our charter commits us to checking independently, correcting the record and acknowledging the checker. [Read the commitment](https://athanor.foundation/charter/#charter-iii)