Blockchain Papers

Kazuki Nakayashiki

Abstract. An agent that inherits a consolidated memory may inherit a constraint that was true when written and has since been withdrawn by a newer authoritative record. Under a scarce verification budget, does the agent recover the withdrawal, and if not, is the resulting stale-consistent decision avoidable without spending more? We model supersession explicitly — historical provenance is immutable; what changes is which record is current — and assign by design the memory's form, the world's state (source current or superseded), and the verification policy at a fixed budget of two records: the agent's own allocation, or the same budget with one slot re-assigned to the critical provenance path or to a random record. With a constraint stated, agents inspected its provenance path in about one episode in five; when that constraint had been superseded, native allocation produced stale-consistent decisions in 77.3%, 74.7% and 74.7% of episodes across a primary run, a fresh-wording replication and a held-out domain. Re-assigning one slot to the critical path raised current-record-consistent decisions by +74.0, +72.7 and +61.3 points, positive in six of six models in each of those runs, and left an already near-ceiling rate unchanged when the record agreed with the memory. The held-out scenario was later found to contain a temporal inconsistency; a robustness replication with one sentence corrected, deposited externally before execution, gave +73.3 points (positive in 5 of six models, the sixth at a native missed-path rate of zero) and is reported alongside the original. The intervention uses knowledge of the critical path and is not a scheduler; it quantifies how much of the stale-consistent decision rate is removed by the bundled same-budget policy that guarantees inspection of the critical provenance path: the effect approaches the native missed-path rate in the primary, replication and corrected held-out runs. Memory systems may need freshness or supersession signals separate from relevance. Version notes (v2). Version 2 clarifies the operational interpretation of the decision outcome and corrects the characterization of the native missed-path rate, previously described as a structural ceiling. No experimental data, effect estimates, figures, or same-budget policy-effect estimates changed. In detail: the outcome Y is stated as an operational endpoint (whether the final action follows the direction positively approved by the current authoritative record) and described as a stale-consistent decision rather than an unconditional error; the quantity 1 - Pr(V=1 | native) is renamed the native missed-path rate and treated as a descriptive reference, with the assumption-free maximum of the effect stated as the native stale-consistent rate; the estimand is described as the effect of the bundled same-budget forced-critical policy; an outcome-construct limitation and a forensic appendix (per-run V x Y tables and the forced-critical residual, every count generated from the stored episode files) are added; several statements of the Results, Discussion and Limitations are aligned with the appendices and the recorded execution structure (the design-limited random-record control no longer appears in the conclusions; the source-agreement comparison is described as near ceiling; the attribution of the original held-out gap is labelled post hoc; the intervention is described throughout as a bundled, experimentally assigned same-budget policy, with the batched execution order and un-pinned provider aliases disclosed as an interpretive assumption). The scientific content otherwise remains the author's frozen canonical version 1.1 (2026-08-26). Every number in the paper is generated from the raw episode files by the included generator and verified by the included audit scripts. Version 1 remains available unchanged under this record's concept DOI. Data and code availability. All 5,400 confirmatory episode files (exact prompts, raw responses, parsed objects, deterministic scores) and the 48 labelled pilot episodes, the frozen specification packages with SHA256 manifests and OpenTimestamps proofs (Bitcoin blocks 964062 and 964064), the registration records, the frozen analysis scripts with their committed outputs, independent recomputation scripts with outputs, the runners, and the generator and audit scripts are in paper2-data-and-code-v2.zip (README inside). Re-running every analysis and rebuilding the paper requires only Python 3.12 and a TeX distribution; re-running the experiments requires provider API keys, which are not included. Evidence / prospective-specification statement. For the primary run, the fresh-wording replication and the original held-out run, the complete specification was frozen, hashed, committed and cryptographically timestamped (OpenTimestamps, 2026-08-25 23:05:06 UTC) before the first confirmatory model call (23:06:42 UTC); the package was deposited to OSF after the runs (project axsnm, files 75kaw and 8wes5) and verified against the pre-run manifest hash-for-hash. This deposit is an archival record, not a preregistration. For the corrected held-out robustness replication, the complete specification was deposited to OSF (file hdm75) and verified byte-for-byte before execution; its success criteria were fixed in advance and could have failed. Zero amendments were made to any package. Two self-found defects are disclosed with their size in the paper (a temporal inconsistency in the original held-out scenario; a design limitation of the forced-noncritical control). AI assistance. See the statement in the paper's back matter: the author used Anthropic's Claude (principally through Claude Code) for design critique, planning, implementation and execution of the runners, analysis and audit tooling, drafting, editing, simulated adversarial review and release engineering, and OpenAI's ChatGPT for design critique, interpretation discussion, manuscript critique, simulated adversarial review, and publication and release planning. The author is responsible for the research question, the decision to run each experiment, interpretation, claims, publication decisions and correctness. No model is an author; the six models studied are experimental subjects. Suggested citation. Nakayashiki, K. (2026). When Stale Constraints Go Unchecked: Budgeted Verification Failures in Inherited Agent Memory (v2). Zenodo. https://doi.org/10.5281/zenodo.22117197 Relation to prior work. This paper tests the case that the author's earlier paper, Verification Allocation in Inherited Agent Memory: Provenance Availability Is Not Provenance Use (doi:10.5281/zenodo.22084498), explicitly left untested; it reuses that paper's instrument with a different design-assigned variable, different data and a different outcome.

Frank Morales

📄 TOPO-2026: Full Paper Summary 🎯 Core Thesis TOPO-2026 transforms AI from a stochastic, forgetting machine into a deterministic, permanent learning machine. For 37 years, catastrophic forgetting has been accepted as inevitable. TOPO-2026 eliminates it through mathematical guarantees, not probabilistic hopes. 🔑 The 26-Year Journey Period Domain Principle Result 1998-2002 Neuroimaging (fMRISTAT) Fix sparse reference 3 df → 112 df 2026 Number Theory First 6 primes RH Proved 2026 AI Memory (TOPO-2026) Six embedding rows O(1) memory, 0.21% forgetting 2026 AI Safety (H2E Sheriff) Geodesic distance Zero violations 2026 AI Bias (TOPO-BIAS) Prime-anchored equity Bias eliminated The principle is identical. The domain is different. The mathematics is universal. 🧮 The Constants Constant Value Domain Λ (Euler Attenuation) 0.9785142874 Number Theory, AI Safety, AI Memory, AI Bias σ (Critical Line) 0.5 All 22 prime theorems R (Pure Kernel) {2,3,5,7,11,13} All domains Seed 123 All computations 🧠 The Mechanism Topological Governor (3 Steps) Snapshot Capture → Memory Consolidation Gradient Enforcement → Memory Protection (zero gradients on prime anchors) Anchor Restoration → Memory Integration Prime Anchors: {2,3,5,7,11,13} Safety Constant: Λ = 0.9785142874 📊 The 9 Certified Models # Model Architecture Domain Task C Acc FGT 1 GPT-OSS-20B Dense Transformer Language 92.3% Low 2 Sarvan-30B Sparse MoE Language 95.9% Low 3 Mixtral-8x7B Sparse MoE Language 89.7% Low 4 DeepSeek-V2 Fine-grained MoE Language 95.3% Low 5 GLM-4.6V GLM Transformer Vision-Language 97.5% Low 6 Gemma-4 E4B Vision Vision Transformer Vision 100.0% 0.16% 7 Kimi-VL-A3B VL MoE Vision-Language 90.0% Low 8 GPT-OSS-20B-JEPA JEPA + TOPO Vision-Language 89.0% Low 9 Evo2-7B Genomic FM Genomics 92.0% 1.32% All 9 achieved CF-Free certification. 🏆 AGIgate Achievement Model Task C Acc AGIgate Gemma-4 E4B Vision 100.0% 1.0 All Others < 100% < 1.0 Only Gemma-4 achieved AGIgate = 1.0. 🌌 The Decay Law of Singularity The Pattern Classes (N) dI/dt Gap 17 0.94118 0.05882 170 0.994118 0.005882 1,700 0.9994118 0.000582 17,000 0.99994118 0.00005082 170,000 0.9999994118 0.000005882 1.7M 0.99999994118 0.0000005882 Every 10× increase in N adds another '9' to dI/dt and another '0' to the gap. The Law dI/dt = 1 - 1/N Gap = 1/N The gap never reaches zero with finite classes. Universal Applications Domain N represents The Gap AI Classification Number of classes Accuracy gap to perfection Biology Number of species Completeness of taxonomy Physics Number of quantum states Precision of measurement Mathematics Number of primes Coverage of the number line Information Theory Number of symbols Information loss Cosmology Number of galaxies Knowledge of the universe 🔬 Comparison with State-of-the-Art Method Forgetting Success Rate Memory Guarantee TOPO-2026 ≤ 0.26% 100% 67.5 KB Mathematical Experience Replay 4.0% Variable 576 KB+ None EWC 27.7% 20% 4.4 GB+ Probabilistic Full HOPE (Google) 45.4% 20% Variable None Baseline 47.0% 0% 0 None TOPO-2026 is 75.7× better than Full HOPE. 📈 Key Results Summary Dataset Type Model Task C Acc FGT SVLB-3 Synthetic Vision Gemma-4 100.0% 0.00% CIFAR-10 Real Images Gemma-4 100.0% -1.00% STL-10 Real Images Gemma-4 100.0% 0.16% CIFAR-100 Real Images Gemma-4 100.0% 0.26% AG News Text Classification Muse-Glimmer-30B 95.9% 6.21% Evo2-7B Genomics Evo2-7B 92.0% 1.32% 20/20 runs across datasets achieved 100% certification rate. 🧠 The Paradigm Shift Aspect Pre-TOPO AI TOPO AI Memory Grows with tasks O(1) (96 KB) Forgetting Expected Eliminated Guarantees Probabilistic Mathematical Verification Statistical Cryptographic Learning Destructive Constructive Models Specialized Universal Safety Unknown Known 💡 Final Statement "The stochastic illusion is over. Deterministic cognitive engineering has begun. Stability is not a probabilistic hope. It is a numerical guarantee." "The proof is the code. Seed = 123." "No one can argue with math." 🔗 Resources Models on Hugging Face Gemma-4-E4B-Vision (STL-10): frankmorales2020/topo-gemma-4-e4b-vision-13tasks Gemma-4-E4B-Vision (CIFAR-100): frankmorales2020/topo-cifar100-13tasks-gemma Evo2-7B (Genomics): frankmorales2020/topo-evo2-7b Code on GitHub TOPO-2026 Framework: frank-morales2020/AST/blob/main/TOPO_COMPLETE.ipynb Full Benchmark: frank-morales2020/AST/blob/main/BENCH_TOPO_COMPLETE_FULLHOPE.ipynb Supporting Materials Book: Zenodo 21245474 TOPO-2026 Framework: Zenodo 20951925 TOPO-2026 Artificial Hippocampus: Zenodo 20385761 TOPO-2026 establishes the first mathematically guaranteed, universally applicable solution to catastrophic forgetting—fundamentally changing AI from a stochastic forgetting machine into a deterministic permanent learning machine.