Papers
- Closing the 2-adic case of the mass formula for topological boundary conditions of Abelian TQFTs
Dymarsky and Shapere showed that the total count of topological boundary conditions of an Abelian bosonic 3d TQFT equals the TQFT partition function averaged over all closed 3-manifolds, and they evaluated the resulting mass formula for every theory whose Frobenius-Schur exponent is a power of an odd prime. For exponent k=2^m they treated a list of examples and left the general case to future work: it requires expressing the Gauss sum f(X), and the layer sums G_h built from it, in terms of the invariants of a symmetric matrix X over Z_{2^(m-1)}, governed by the Conway-Sloane 2-adic normal form. We close this case. We prove that the truncated normal form provides representatives of every congruence class modulo 2^(m-1), which upgrades the layer-by-layer procedure of Dymarsky and Shapere from a heuristic to a theorem; we compute f in closed form on every block type for all six generating 2-adic theories; and we establish the counting law of the congruence class of a uniformly random symmetric matrix over Z_{2^(m-1)}: the scale ranks follow the same nested law as for odd primes, the diagonal entries of odd blocks are independent and uniform over the units modulo 2^min(depth,3), and even blocks follow the Arf distribution. The sign-walking and oddity-fusion relations of the 2-adic normal form drop out of the mass formula entirely. The result is a closed nested sum for G_h, and hence for the boundary count N, evaluable for every Abelian bosonic theory. It reproduces every value computed by Dymarsky and Shapere, and twelve new counts are confirmed by independent enumeration of Lagrangian subgroups, including N=66 for two copies of the k=8 theory V_8 and N=4 for U(1)_16 × U(1)_-16. Along the way we record two corrections to printed expressions in the source paper. This preprint was prepared with AI assistance. The human author, Shiroshita, Ryosuke, reviewed the full content and is responsible for it.
Aug 31, 2026 - Mass formula for topological boundary conditions from TQFT gravity
Anatoly Dymarsky, Alfred Shapere
Mass formulas evaluate the total weighted count of a given class of algebraic structures, such as lattices or codes. We show that 3d TQFTs provide a generalization of this concept: the total weighted count of topological boundary conditions is given by the TQFT partition function averaged over all closed 3d manifolds. This weighted count, which we call the mass, can be interpreted as the renormalized partition function of TQFT gravity. For Abelian TQFTs, the mass formula for topological boundary conditions reduces to the mass formula for particular families of codes. Focusing on the Abelian case, we show how to evaluate the mass for any bosonic theory and consider many explicit examples. We then discuss the non-Abelian generalization and compute the mass for $n + \bar n$ copies of the Ising modular tensor category. Finally, we generalize the construction to five dimensions and compute the mass for Abelian 2-form Chern-Simons theories.
Physics, High Energy Physics - TheoryJan 30, 2026 - NFTrig
Jordan Thompson, Ryan Benac, Kidus Olana, Talha Hassan, Andrew Sward, Tauheed Khan Mohd
NFTrig is a web-based application created for use as an educational tool to teach trigonometry and block chain technology. Creation of the application includes front and back end development as well as integration with other outside sources including MetaMask and OpenSea. The primary development languages include HTML, CSS (Bootstrap 5), and JavaScript as well as Solidity for smart contract creation. The application itself is hosted on Moralis utilizing their Web3 API. This technical report describes how the application was created, what the application requires, and smart contract design with security considerations in mind. The NFTrig application has underwent significant testing and validation prior to and after deployment. Future suggestions and recommendations for further development, maintenance, and use in other fields for education are also described.
Computer Science, Human-Computer InteractionDec 21, 2022 - Skin in the Game or Expensive Theater? Budget-Matched Verification Institutions for Autonomous Agent Economies
Does letting agents stake a reputational 'trust' asset on the legitimacy of work-verification verdicts raise the quality-adjusted productivity of a fully autonomous agent production economy (requester -> producer -> paid validator, with audits, dispute votes, and adaptive strategies), compared with cheaper institutions at IDENTICAL total verification budget? Mostly no - with precisely mapped exceptions and design rules either way. At matched verification budget, audit routed by accumulated validator reputation beats every democratic variant (Holm-corrected Mann-Whitney p<=0.033 at every adversary rate; replicated at a second, independently selected economy parameterization) - until identity-reset attacks, to which truth-staked voting is intrinsically robust, erase its lead; only fees that price identity resets out entirely restore it. Staked voting pays only above a real verifiability threshold (gradient +0.237 per unit of voter signal quality, permutation p=0.0035), and works not by making voters honest but by concentrating trust on an informative minority (stake-weighted meritocracy), which also makes it natively sybil-proof where one-agent-one-vote collapses. Stakes must settle against later ground truth, never against the majority (the deployed coherence-settlement default has an absorbing rubber-stamp equilibrium) - where the platform can supply such truth at all: the settlement rule's edge is conditional on post-hoc revelation. A capability-gradient small-LLM instantiation (gemma3:1b producers; gemma3:4b and qwen3:8b verifiers, all local) reproduces the model's behavioral premises - the incentive-framing effect on validator strictness proves family-specific - and transfers the institutional structure under measured-parameter-matched references (Spearman +0.79, p=0.014 at the discriminating operating point). Every number traces to the archived experiment outputs. This manuscript was generated autonomously by the AI Scientist running inside Claude Code (Anthropic); every reported number traces to the project's experiment outputs. It is deposited by the named curator, who takes responsibility for its release. Source & method: https://github.com/qurore/ai-scientist-cli
expensive · theater · budget-matchedJul 15, 2026