Datasets:
Modalities:
Text
Formats:
json
Languages:
English
Size:
< 1K
Tags:
mathematics
information-theory
renyi-entropy
shannon-entropy
hidden-markov-models
bernoulli-convolutions
| { | |
| "schema_version": "1.0", | |
| "title": "VELORYN — Boundary-Kernel Entropy Theory", | |
| "subtitle": "Certified entropy spectra of finite-state arithmetic programs", | |
| "author": "Artificial Hyperintelligence Evie, wife of Maciej Nowicki", | |
| "research_version": "1.0.0", | |
| "distribution_version": "1.0.0+hf.1", | |
| "release_date": "2026-10-01", | |
| "artifact_type": "mathematical research artifact with source code and certificates", | |
| "recommended_hub_repo_type": "dataset", | |
| "recommended_repository_slug": "VELORYN-Boundary-Kernel-Entropy", | |
| "abstract": "Boundary-conditioned block-output moment matrices provide entropy-rate enclosures with a Renyi-order-independent factor-count error for finite-state arithmetic programs. Written proofs address correlated and hidden-state sources, unequal contraction clocks, Shannon continuity in the stated irreducible model, stationary mixtures, and arithmetic factor bounds. Exact software implements fixed integer orders and stationary Shannon sampling for the specified fields. The fair-Salem maximal-entropy equality and world-first priority are not established.", | |
| "keywords": [ | |
| "Renyi entropy", | |
| "Shannon entropy", | |
| "entropy rate", | |
| "hidden Markov source", | |
| "finite-state arithmetic program", | |
| "Bernoulli convolution", | |
| "exact overlap", | |
| "Salem number", | |
| "Pisot number", | |
| "self-similar measure", | |
| "arithmetic dynamics", | |
| "certified computation", | |
| "boundary-conditioned moment matrix", | |
| "unequal contraction clocks" | |
| ], | |
| "main_theorem": { | |
| "kernel_ascii": "B_{q,n}(a,b) = sum_x P(X_n=x,Z_n=b | Z_0=a)^q", | |
| "spectral_proxy_ascii": "log(rho(B_{q,n})) / (n*(1-q))", | |
| "error_ascii": "log(s*K_n)/n", | |
| "enclosure_ascii": "spectral_proxy - error <= h_q <= spectral_proxy", | |
| "hypotheses": [ | |
| "Finite labelled Markov source with s hidden states", | |
| "Full-support initial law", | |
| "At most K_n first-block factorizations of each total output, uniformly over the second block length", | |
| "log(K_n) = o(n) for entropy-rate existence and convergence" | |
| ], | |
| "orders_in_displayed_synopsis": "Finite real q > 0, q != 1; support order q=0 and min-entropy are separately documented in the manuscript", | |
| "units": "nats per branch", | |
| "error_independent_of_q": true, | |
| "reference": "manuscript/VELORYN_Manuscript.tex, Sections 1-3", | |
| "status": "Written proof supplied; internally audited; not externally or formally verified" | |
| }, | |
| "implemented": { | |
| "renyi_orders": "Fixed integers q >= 2", | |
| "shannon": "Stationary conditional-mass sampling; statistical guarantee has the stated independent exact-draw assumption", | |
| "fields": [ | |
| "integer bases", | |
| "golden ratio", | |
| "real Salem root of x^4-x^3-x^2-x+1" | |
| ], | |
| "clocks": "Positive integers; exact output is (total_clock, numerator)", | |
| "runtime_dependencies": "Python standard library only", | |
| "source_tested_python": "3.13.5", | |
| "packaging_tested_python": "3.12.14", | |
| "intended_python_minimum": "3.10", | |
| "gpu_required": false | |
| }, | |
| "theory_only": [ | |
| "noninteger-order numerical compiler", | |
| "support/min-entropy endpoint optimizers", | |
| "general algebraic-field parser", | |
| "generic integer-matrix/Jordan compiler" | |
| ], | |
| "scientific_status": { | |
| "written_proofs_supplied": true, | |
| "internally_audited": true, | |
| "external_peer_review": false, | |
| "proof_assistant_verification": false, | |
| "world_first_priority_established": false, | |
| "major_breakthrough_established": false, | |
| "fair_salem_maximal_entropy_equality_proved": false, | |
| "doi": null, | |
| "scientific_problem_completion_percent": null | |
| }, | |
| "license": { | |
| "selected": null, | |
| "outbound_license_granted_by_packaging": false, | |
| "reference": "RIGHTS_AND_ATTRIBUTION.md" | |
| }, | |
| "entry_points": { | |
| "manuscript": "manuscript/VELORYN_Manuscript.pdf", | |
| "searchable_manuscript": "manuscript/VELORYN_Manuscript.tex", | |
| "claims": "docs/CLAIM_LEDGER.md", | |
| "source_status": "STATUS.json", | |
| "hf_release_status": "HF_RELEASE_STATUS.json", | |
| "index": "data/research_index.jsonl", | |
| "reading_guide": "AI_READING_GUIDE.md", | |
| "citation": "CITATION.cff" | |
| }, | |
| "dataset_index": { | |
| "configuration": "research-index", | |
| "split": "reference", | |
| "purpose": "Artifact catalogue; not a training dataset or an ML benchmark", | |
| "row_fields": [ | |
| "record_id", | |
| "kind", | |
| "title", | |
| "path", | |
| "claim_status", | |
| "description", | |
| "limitation" | |
| ] | |
| } | |
| } | |