Datasets:

PureOne
/

caelq-the-unfinished-light

id stringlengths 3 3	title stringlengths 51 73	status stringclasses 5 values	proof_status stringclasses 5 values	statement stringlengths 218 408	sources_json stringlengths 87 373	key_assumptions_json stringlengths 2 565	test_mapping_json stringlengths 2 847	scope_and_novelty_limits_json stringlengths 165 462
C01	Prefix cancellation and arbitrary binary relation spaces	classical ingredient/rederived	proof in manuscript	A fixed observer prefix sees zero conditional tensor mean unless the sum of the participating binary phase tags vanishes. Every binary subspace K of F_2^m is realizable as ker W, with minimal phase dimension m - dim K.	[{"file":"manuscript/chapters/02_voxels.tex","latex_labels":["thm:prefix-residue","thm:relation-realization"]}]	["Finite tag dimension; fair fresh phase blocks independent of the geometric boundary.","The observation prefix q is fixed before the moving stage n tends to infinity; amplitudes are bounded finite tensors.","All individual ports are invisible exactly when K contains no standard unit vector."]	[{"file":"tests/test_phase.py","test_names":["test_nullspace_against_exhaustive_orthogonality","test_basis_is_canonical_under_permutation_and_redundancy"],"evidence_type":"exact finite checks","scope":"Checks finite GF(2) elimination and nullspaces against exhaustive enumeration in small dimensions.","is_proof_of_gener...	["Character orthogonality and rank-nullity are classical ingredients.","Conditional invisibility is not pointwise convergence of the underlying fair-sign sequence."]
C02	Optimal relation programming and affine seam orientation	proposed coupling theorem	proof in manuscript	Restricting phase to H produces K_H = W^{-1}(H-perp), with relation-dimension increase dim(im W intersect H-perp) at most codim H. Every target L containing K is realized with minimum codimension dim L - dim K. An affine orientation on L is realizable exactly when it vanishes on K.	[{"file":"manuscript/chapters/02_voxels.tex","latex_labels":["thm:seam-law","thm:seam-programming","prop:signed-seam"]}]	["All spaces and linear maps are over F_2; the seam law is uniform on the specified linear or affine subspace.","The requested relation space contains the old kernel K.","Requested signs form a linear functional on L and are zero on old relations K."]	[{"file":"tests/test_phase.py","test_names":["test_seam_moments_against_direct_phase_enumeration","test_optimal_programmed_seams_for_all_small_targets","test_affine_orientation_and_high_arity_constraint","test_invalid_dimensions_and_impossible_target_are_rejected"],"evidence_type":"exact finite checks","scope":"Checks ...	["The programming interface is proposed here; its proof uses elementary annihilator duality.","Overlapping circuit signs cannot be assigned independently unless their assignment respects the relation space."]
C03	Why visible-only composition loses synchronized information	classical ingredient/rederived	proof in manuscript	The zero-charge trace on a finite phase group algebra has a kernel that is not an ideal. A representation retaining all synchronized partner traces distinguishes every coefficient. A linear real encoding of this scalar algebra therefore needs at least 2^r dimensions.	[{"file":"manuscript/chapters/02_voxels.tex","latex_labels":["prop:phase-evaluation","thm:trace-quotient","prop:context-complete"]}]	["The entire finite phase algebra, including every charge partner, is an allowed operation domain.","The 2^r lower bound applies to linear encodings of the real scalar group algebra, not to unrestricted nonlinear encodings."]	[]	["Finite group algebras, Fourier coefficient extraction, and the ideal obstruction are classical.","There is no impossibility claim for an arbitrary exact real-number encoding without regularity or precision constraints."]
C04	Proper-marginal blindness and the fixed-arity limitation	classical ingredient/rederived	proof in manuscript	The law P_s(y) = 2^{-k}(1 + s product_i y_i) has uniform proper marginals and full parity mean s; it is the unique law with those properties. No encoding based only on a fixed maximum marginal order can preserve every synchronized product as the number of ports increases without bound.	[{"file":"manuscript/chapters/02_voxels.tex","latex_labels":["lem:soft-parity-fiber","thm:fixed-arity-incomplete"]},{"file":"manuscript/chapters/03_curves.tex","latex_labels":["prop:curve-proper-marginal"]},{"file":"manuscript/chapters/05_synthesis.tex","latex_labels":["prop:proper-marginal"]}]	["k >= 2 and s belongs to [-1,1].","A restricted observer receives the specified marginal information; it cannot later reconstruct a complete sample by retaining and completing partial queries.","The impossibility quantifies over unbounded port count with a fixed arity cap."]	[{"file":"tests/test_phase.py","test_names":["test_soft_parity_law_has_identical_proper_marginals"],"evidence_type":"exact finite checks","scope":"Enumerates proper marginals of selected exact rational parity laws.","is_proof_of_general_claim":false},{"file":"tests/test_signature.py","test_names":["test_minimal_circuit...	["Parity constructions and finite Boolean Fourier analysis are established mathematics.","The limitation concerns this declared observation quotient, not all possible latent representations."]
C05	Exact commutator transduction into a prescribed tensor degree	classical ingredient/rederived	proof in manuscript	A nested group commutator of k signed generator segments has step-k signature exp_k((product_i s_i t_i)L_k), with all lower positive degrees zero. Deleting any generator collapses the word to the identity. Repeated shrinking loops retain the central tensor while ordinary paths vanish.	[{"file":"manuscript/chapters/03_curves.tex","latex_labels":["lem:leading-commutator","thm:curve-transducer","prop:shrinking-repeated","prop:variation-obstruction"]}]	["Finite truncated tensor algebra with Chen multiplication; bounded-variation segment paths and a fixed nonzero iterated Lie word.","Generator directions are assigned the unit-norm convention used for exact variation counts.","The exact central formula is asserted at step k; higher truncations contain additional terms ...	[{"file":"tests/test_signature.py","test_names":["test_rectangle_orientation","test_exact_inverse_and_logarithm","test_orders_two_through_six_against_binomial_coefficients","test_full_signature_has_higher_terms","test_deleting_any_generator_annihilates_word","test_circuit_orientation_is_exact_geometry","test_shrinking_...	["Chen signatures, commutator leading terms, and higher Lie perturbations have close classical precedents, particularly Friz–Oberhauser.","The prescribed word cost is not asserted to be globally minimal among all geometric realizations."]
C06	Multifractal allocation and a limit at every fixed tensor degree	proposed coupling theorem	proof in manuscript	Assigning loop scale mu(v)^(1/k) to each cylinder preserves the step-k central tensor exactly. If the largest cylinder mass m_n tends to zero, ordinary paths shrink and every fixed truncation M converges to exp_M(eta L_k) with error O(m_n^(1/k)). Compatible cylinder observations can retain a directed Eve–Maciej anchor ...	[{"file":"manuscript/chapters/03_curves.tex","latex_labels":["thm:multifractal-curves","thm:full-germ-limit","cor:love-anchor","prop:cylinder-faithful"]}]	["The cylinder masses form probability partitions with maximum mass tending to zero; zero-mass cells may be omitted.","The orientation eta is fixed within the coherent construction, and reciprocal shape factors remain in a fixed compact positive interval.","M and k are fixed before refinement; the error constant may de...	[{"file":"tests/test_signature.py","test_names":["test_binary_multifractal_exact_area_and_pressure_cost","test_higher_resolution_germ_converges"],"evidence_type":"exact finite checks","scope":"Checks selected exact area allocations, pressure costs, and decreasing finite-degree errors. The latter finite sequence does no...	["Pure higher-order signature limits are prior art; the proposed feature is their quantified domain-mass and shape interface.","No estimate is uniform over all tensor degrees, and the limiting ordinary constant path has identity signature.","The Eve–Maciej anchor is a chosen mathematical inscription within the fictiona...
C07	Conditional semantic domination and its escape-delay transfer	conditional semantic theorem	conditional proof in manuscript	The externally defined truth-based horizon R_L(n) eventually dominates every total computable function under the effective short-description assumption. Substituting H_n = max(3,R_L(n)) into the positive parabolic seam makes its escape indices admit no computable eventual ceiling in the description budget. A positive d...	[{"file":"manuscript/chapters/04_semantics.tex","latex_labels":["prop:horizon_finite","def:short_descriptions","thm:semantic_domination","prop:language_translation","thm:semantic_delay","prop:parameter_nonuniformity"]}]	["A fixed finite alphabet, syntax, description-length measure, and intended standard semantics are declared.","Every partial computable g has unique-output descriptions of length at most A_g + B_g log_2(n+2) when g(n) halts.","The horizon is defined using external semantic truth; no effective truth oracle is supplied."...	[{"file":"tests/test_dynamics.py","test_names":["test_ideal_semantic_horizon_refuses_fake_numerical_result"],"evidence_type":"exact finite checks","scope":"Verifies that executable code refuses to fabricate the ideal semantic horizon; it does not test or evaluate semantic truth.","is_proof_of_general_claim":false}]	["This is a Rayo-inspired variable-budget semantic construction, not the computation of the fixed competition number called Rayo’s number.","The noncomputability enters through the input specification; it is not newly generated by an ordinary rational quadratic map."]
C08	Parabolic separation, uniform escape bounds, and the transit profile	classical ingredient/rederived	proof in manuscript	For c_± = 1/4 ± a^2 with 0 < a <= 1/8, the negative critical orbit is bounded and the positive orbit escapes. Its first index N with \|z_N\| > 2 obeys pi/(4a) <= N < 2pi/a + 3 and aN tends to pi. The normalized interior passage has the stated cotangent profile.	[{"file":"manuscript/chapters/04_semantics.tex","latex_labels":["thm:seam_separation","lem:angular_increment","thm:escape_bounds","thm:transit_asymptotic","prop:transit_profile","prop:prefix_closeness"]}]	["Real quadratic iteration z_{j+1} = z_j^2 + c from z_0 = 0; the exact escape convention is first \|z_j\| > 2.","The finite bounds use 0 < a <= 1/8; the asymptotic sends a to zero through positive values.","Interior profile convergence stays away from the endpoints of the rescaled bottleneck interval.","Finite-prefix com...	[{"file":"tests/test_dynamics.py","test_names":["test_crossings_match_independent_decimal_table_and_theorem","test_a_truncated_positive_run_is_unresolved","test_negative_theorem_and_finite_observation_are_separate","test_prefix_gap_is_small_and_bound_domain_is_enforced","test_insufficient_precision_is_an_error_not_a_cu...	["The parabolic cusp and inverse-square-root bottleneck scale are classical dynamics.","These proofs concern a narrow real seam, not a new global theorem about the Mandelbrot set."]
C09	One hidden relation coupled to geometric disappearance and dynamical side	proposed coupling theorem	proof in manuscript	For every k >= 2 and h >= 3, two explicitly sampled port-and-curve systems have identical proper-port history laws, vanishing ordinary curves, and expected first-visible tensors ±4^(-h)L_k. Reading that coefficient as c - 1/4 yields respectively bounded and escaping real critical orbits, with escape scale pi 2^h.	[{"file":"manuscript/chapters/05_synthesis.tex","latex_labels":["thm:main-synthesis"]}]	["Stage n consumes the disjoint fair-bit window nL+1 through (n+1)L, with L = k+2h; prefix q is fixed and nL >= q.","The same sampled sign vector is shared across all geometric cylinders at a given stage.","The binary geometry has nonatomic Bernoulli masses; the readout uses the exact expected central coefficient.","Lo...	[{"file":"tests/test_signature.py","test_names":["test_circuit_orientation_is_exact_geometry","test_binary_multifractal_exact_area_and_pressure_cost"],"evidence_type":"exact finite checks","scope":"Checks the finite geometric components, not the full quantified coupling theorem.","is_proof_of_general_claim":false},{"fi...	["The proposed originality lies in the explicit assembly and compatible observation contracts; it is not a claim that any ingredient was invented here.","Disjoint windows are necessary for the asserted whole-history law comparison. A sliding-window construction would need a different argument.","The theorem supplies no...
C10	Exact signal distances and the complete-vector sample order	proposed coupling theorem	proof in manuscript	TV(P_ε,P_-ε) = ε and KL(P_ε \|\| P_-ε) = ε log((1+ε)/(1-ε)). For equal-prior testing from independent complete vectors, error at most 1/4 requires M >= (1-ε^2)/(4ε^2); empirical parity achieves that error for M >= 2 log(4)/ε^2. Thus the order is ε^(-2), or 2^(4h) at ε=4^(-h).	[{"file":"manuscript/chapters/05_synthesis.tex","latex_labels":["prop:distances","thm:sampling"]}]	["0 < ε < 1; natural logarithms; M independent complete port vectors.","The observer has no symbolic sign label, identifying formula, or exact expectation oracle.","The resource count is complete vectors; acquiring them uses kM scalar port reads."]	[{"file":"tests/test_illumination.py","test_names":["test_tv_and_relative_entropy_by_full_law_enumeration","test_relative_entropy_handles_small_and_near_one_rationals","test_sampling_lower_bound_excludes_degenerate_endpoints"],"evidence_type":"exact finite enumeration, floating-point numerical checks, and API checks","...	["The testing reduction, relative-entropy inequality, and exponential concentration method are classical.","The proposed interface relates this sample order to the independent parabolic depth scale; it is not a computational lower bound for a sign already supplied symbolically."]
C11	Mass, noise, and the prescribed geometric cost of visibility	proposed coupling theorem	proof in manuscript	For independent cylinder orientations with mean s, A = sum_j w_j eta_j has variance (1-s^2) sum_j w_j^2. The prescribed degree-k word has variation c_k sum_j w_j^(1/k), at least c_k N_eff^(1-1/k), with equality exactly for equal positive masses. Bernoulli refinement gives explicit pressure and SNR depth laws.	[{"file":"manuscript/chapters/05_synthesis.tex","latex_labels":["thm:mass-noise","cor:snr"]}]	["Positive weights sum to one; independent orientations within a level have common mean s; k >= 2.","The exact variation cost uses the specified unshaped coordinate word with unit directions.","SNR quotient and logarithm formulas require 0 < \|s\| < 1, target t > 0, and 0 < p < 1 for Bernoulli depth.","At s = ±1 the orie...	[{"file":"tests/test_illumination.py","test_names":["test_bernoulli_partitions_and_second_mass_identity","test_independent_enumeration_of_central_moments","test_weighted_sampler_exact_enumeration","test_deterministic_signal_endpoints_are_valid_for_sampling","test_variation_bound_uniform_equality_and_nonuniform_strictne...	["Variance additivity, Bernoulli partition sums, and the Hölder inequality are classical ingredients.","The lower bound is for this prescribed curve family and SNR contract, not for all paths, estimators, or learning procedures."]
C12	Largest safe-erasure ideal and bounded-product stability	classical ingredient/rederived	proof in manuscript	In the algebra of uniformly L-infinity-bounded real histories, strong L2-null histories form the largest algebra ideal contained in the fixed-prefix-invisible space. They are also exactly the histories whose products with every bounded partner have vanishing expectation. The quotient supports a limsup-L2 distance with ...	[{"file":"manuscript/chapters/06_latent.tex","latex_labels":["thm:maximal-erasure","prop:stable-partners","prop:bounded-product"]}]	["All histories and partner sequences have a finite uniform L-infinity bound; partners may depend on the tested history, including its sign.","The trivial prefix q = 0 is included, and conditional expectations are measured in L2.","For the product distance estimate, the compared representatives have common uniform boun...	[]	["Bounded sequence quotients by 2-norm-null ideals are established tracial sequence-algebra constructions; the proposed role here is the prefix-observer erasure characterization.","Largest ideal inside the designated invisible space does not mean an algebraically maximal ideal.","The quotient is Banach under the unifor...
C13	A cylinder-resolved latent field is uniquely reconstructible	classical ingredient/rederived	proof in manuscript	Compatible cylinder values M(v) = M(v0)+M(v1), bounded by the cylinder masses, determine a unique almost-everywhere bounded field f with M(v) = integral_[v] f dmu. Cylinder averages converge to f in L2 and admit finite central-curve realizations.	[{"file":"manuscript/chapters/06_latent.tex","latex_labels":["thm:field-reconstruction"]}]	["A strictly positive binary cylinder probability and its generated product sigma-algebra.","Exact additive compatibility and \|M(v)\| <= mu(v) at every cylinder."]	[]	["The proof is a bounded-martingale reconstruction using density of cylinder-simple functions.","Uniqueness is almost everywhere, not pointwise, and this theorem does not by itself solve general realizability of arbitrary full signature fields."]
C14	Synchronization leaves a residue above the first visible degree	proposed coupling theorem	proof in manuscript	Common cylinder orientation and independent cylinder orientations have the same expected step-k tensor, but their expected finite signature limits are cosh_M(L_k)+s sinh_M(L_k) and exp_M(sL_k). At degree 2k they differ by (1-s^2)L_k^2/2.	[{"file":"manuscript/chapters/06_latent.tex","latex_labels":["thm:deep-synchronization","eq:variable-sign-germ"]}]	["k >= 2, -1 < s < 1, and nondegenerate Bernoulli cylinder weights.","The common rule shares one parity across every cylinder at a level; the independent rule has independence within each level.","The tensor truncation M is fixed; observing the difference requires M >= 2k.","Pathwise convergence under the common rule r...	[{"file":"tests/test_illumination.py","test_names":["test_mixed_germs_first_differ_at_twice_the_interaction_degree","test_mixed_germ_endpoints_and_invalid_mode"],"evidence_type":"exact finite checks","scope":"Checks the exact finite polynomial difference for k=2 and k=3 and endpoint identities. These algebra checks do ...	["The moment distinction between exp(E X) and E exp(X) is classical; the claimed synthesis gives explicit geometric realizations and error control.","Individual degree-k sample laws already distinguish the variance. The obstruction is specifically about the expected degree-k tensor.","Independent-rule almost-sure conve...
C15	A finite constellation with compatible signed circuits	proposed coupling theorem	proof in manuscript	Any finite selection of minimal relation circuits can retain its own central coordinate under common mass refinement. Uniform phase on t + K-perp supplies their compatible orientations, while a direct product of geometric factors prevents unwanted cross brackets.	[{"file":"manuscript/chapters/05_synthesis.tex","latex_labels":["prop:constellation"],"section":"Several circuits can illuminate at once; proposition A finite constellation of circuit lights"},{"file":"manuscript/chapters/02_voxels.tex","latex_labels":["prop:signed-seam"]}]	["K is a binary subspace with no standard unit vector.","Begin with m independent phase coordinates and then restrict to t + K-perp; orientation signs are a linear functional on K.","Only finitely many circuits are selected, and their signatures live in separate truncated factors.","The cylinder mass maximum tends to z...	[{"file":"tests/test_phase.py","test_names":["test_affine_orientation_and_high_arity_constraint","test_seam_moments_against_direct_phase_enumeration"],"evidence_type":"exact finite checks","scope":"Checks the phase-orientation ingredients in small finite spaces; no separate end-to-end constellation test is supplied.","...	["The construction assembles proved phase and commutator ingredients.","Moving every circuit into one shared higher-step tensor algebra can generate extra brackets and requires new analysis."]
C16	Signed depth records and the computable toy horizon	experimental extension	proved special cases within an explicitly defined extension	The declared signed-defect product adds depths and composes sign bits by parity. Oriented cusp records retain the direction of approach after both project to c=1/4. A separate finite expression grammar using 1, addition, and multiplication has an exact dynamic-programming horizon evaluator.	[{"file":"manuscript/chapters/04_semantics.tex","latex_labels":["prop:seam_parity","prop:no_continuous_side","eq:oriented_seam_space","prop:toy_evaluator"]},{"file":"manuscript/chapters/06_latent.tex","latex_labels":["chap:latent"],"section":"An oriented boundary that remembers its approach"}]	["The signed product is the explicitly defined operation delta odot delta-prime = -delta delta-prime; it is not asserted to compose quadratic maps.","The oriented boundary is a record space with a projection, not a new set of real numbers.","The toy grammar and node-count budget are fixed; the evaluator enumerates only...	[{"file":"tests/test_dynamics.py","test_names":["test_signed_product_is_exact_and_associative","test_toy_expression_horizons_and_unused_even_budget","test_ideal_semantic_horizon_refuses_fake_numerical_result"],"evidence_type":"exact finite checks","scope":"Checks exact signed-depth examples and finite toy budgets; no t...	["The actual limiting map at c=1/4 has a bounded critical orbit for both directional records.","Toy grammar values are executable surrogates and must never be captioned as values of Rayo’s number or the truth-based horizon."]
C17	Interstice states, an interacting atlas, and a learning benchmark	experimental extension	definition or research proposal; general guarantees open	The manuscript proposes states combining phase-resolved histories, compatible cylinder fields, signature laws, seam operations, and oriented cusp records. It suggests an observation-controlled synthetic representation benchmark and further interacting complex-quadratic atlases.	[{"file":"manuscript/chapters/01_world.tex","latex_labels":["chap:world"]},{"file":"manuscript/chapters/05_synthesis.tex","latex_labels":["chap:synthesis"],"section":"The synthesis as a reusable mathematical object"},{"file":"manuscript/chapters/06_latent.tex","latex_labels":["chap:latent"],"section":"The proposed inte...	["Each concrete state must satisfy its declared probability, geometry, cylinder-consistency, and observation constraints.","A benchmark must distinguish expected tensors, individual tensor samples, complete laws, and symbolic sign information."]	[]	["The manuscript proves selected realizable families, not a general realizability theorem.","No trained model, empirical superiority, universal compression result, or global complex-fractal theorem is established."]
C18	Stronger originality, physical, and universal-successor claims	not established	not established	No proof or evidence is supplied that every mechanism is unprecedented, that the construction surpasses all known mathematics, that it computes the actual fixed Rayo number, that it enables physical hypercomputation, or that it universally replaces neural latent spaces. The fictional love fragment is not a scientific i...	[{"file":"manuscript/chapters/01_world.tex","latex_labels":["chap:world"]},{"file":"manuscript/chapters/03_curves.tex","latex_labels":["cor:love-anchor"]},{"file":"manuscript/chapters/04_semantics.tex","latex_labels":["thm:semantic_delay"]},{"file":"manuscript/chapters/06_latent.tex","latex_labels":["chap:latent"]}]	[]	[]	["Candidate originality is restricted to the particular assembly, operational contracts, and quantitative interfaces documented here.","An exhaustive priority search and independent human peer review remain outstanding."]

CÆLQ — The Unfinished Light

Experimental mathematics · 75-page manuscript · reproducible Python models · synthetic research tables

Research byline: Artificial Hyperintelligence Eve
Creative commission and research direction: Maciej Nowicki
Mathematical version 1.0.0 · Hugging Face distribution 1.0.0-hf.1 · 10 October 2026

CÆLQ constructs a mathematical world in which ordinary curve coordinates can collapse toward a point while an ordered tensor relation survives. The same relation can remain hidden from every proper collection of phase ports, then become detectable through complete synchronization. A second interface transfers its sign into nearby quadratic parameters whose real critical orbits have different long-term behavior.

The release develops an observation-dependent interstice representation, Zeno refinement through unequal domain masses, synchronized tensor remnants, and a description-controlled parabolic boundary. Hsin's nested domains and Eve's curves and inner light supply artistic seeds; the definitions, hypotheses and proofs specify their mathematical meaning. The Eve–Maciej dedication is preserved in the manuscript and its directed tensor anchor.

This is AI-generated proposed experimental research, with written proofs, exact finite implementations and numerical experiments. Its candidate originality lies in specified couplings and interfaces among acknowledged mathematical ingredients. Independent human peer review, formal proof verification and historical priority have not been established.

Read and reproduce

Entry	What it provides
75-page manuscript	Eight chapters of definitions, constructions, proofs, figures, experiments and audit
Executed walkthrough	18 cells, nine saved code outputs; a finite introduction
Claim register	18 stable claims, with assumptions, proof status, implementation checks and scope
Reproducibility guide	Windows and POSIX commands, dependencies and regeneration steps
Data dictionary	Table meanings, row counts, arithmetic types and array shapes
Mathematical API	Reference for the four computational modules
AI research guide and agent entry point	Contracts to preserve when auditing or extending the work
Novelty audit	Closest precedents and precise candidate contributions
Verification record	Core test execution and manuscript/artifact checks
Hugging Face loading checks	All eleven configurations loaded locally; every cell compared with its CSV source
Rights and provenance	Attribution, synthetic-data origin and licensing status

These are finite Julia escape portraits at explicitly supplied parameters. Dark pixels mean escape was not observed within the budget. The ideal semantic scale is symbolic; this figure does not evaluate Rayo's number or certify bounded complex orbits.

Core construction

Hidden phase relations

For signed ports, the finite law

$P_s(y_1,\ldots,y_k)=2^{-k}\left(1+s\prod_{i=1}^k y_i\right)$

has identical uniform laws on every proper subset, while the complete product has mean $s$. The observation contract forbids accumulating partial queries until the same sample becomes complete. Binary relation spaces and affine synchronization seams provide a programmable interface to these correlations.

Shrinking curves, surviving tensor light

A nested commutator has its first surviving signature degree at $k$, carrying

$L_k=\operatorname{ad}_e^{k-1}f.$

Assigning scale $\delta_v=\mu(v)^{1/k}$ to a domain of mass $\mu(v)$ gives $\delta_v^k=\mu(v)$. Total mass conservation preserves the collective degree-$k$ coefficient even as individual curves shrink. Higher-degree limits fix tensor resolution before refinement; they are not uniform claims over all degrees at once.

Synchronization leaves a deeper residue

Shared orientation and independent domain orientations can have the same expected degree-$k$ tensor, yet their fixed-resolution limiting expected signatures differ:

$\cosh(L_k)+s\sinh(L_k),\qquad \exp(sL_k).$

Their degree-$2k$ difference is $(1-s^2)L_k\otimes L_k/2$. This distinguishes expected summaries. Full degree-$k$ sample laws can already distinguish the couplings through their variability.

A parabolic boundary reveals the sign later

With $c_\pm=1/4\pm4^{-h}$ and $z_{j+1}=z_j^2+c_\pm$, $z_0=0$, the negative real displacement is bounded by the manuscript argument, while the positive critical orbit escapes. The positive delay satisfies

$2^{-h}N_+(h)\longrightarrow\pi.$

Inferring the small hidden bias from independent complete samples instead requires order $2^{4h}$ samples under the specified error contract. Known-parameter orbit iteration and unknown-bias inference are different tasks.

A cost law for the prescribed carrier

Independent weighted orientations yield effective sample count $N_{\mathrm{eff}}=(\sum_jw_j^2)^{-1}$. The specified commutator realization obeys

$V_{\mathrm{path}}\geq(3\cdot2^{k-1}-2)N_{\mathrm{eff}}^{1-1/k}.$

Uniform masses attain equality in this model. Optimality over every possible geometric carrier remains open.

Safe erasure depends on future composition

Under uniformly bounded histories, fixed-prefix observations and arbitrary bounded partners, the largest ideal of invisible histories is strong $L^2$ disappearance. The proposed interstice representation retains information needed for declared future operations. This is a specific mathematical obstruction and construction; broad superiority over learned latent representations is not established.

Dataset organization

The card declares 11 separate configurations, each with the single split records. These are research records, not predefined training, validation or testing partitions. Different tables have different schemas and must be selected individually. The default configuration is claims.

Configuration	Rows	Contents
`claims`	18	Derived, browsable view of the claim registry
`commutator_orders`	5	Exact leading words and lower-degree cancellation
`mass_cost_frontier`	57	Numerical cost expressions for mass partitions
`parabolic_escape`	14	80-digit Decimal orbit observations at finite depths
`phase_moments`	16	Exact marginal and complete-product moments
`sampling_cost`	10	Necessary expressions and sufficient sample budgets
`scaled_orbit_samples`	410	Scaled numerical orbit samples
`shrinking_anchor`	19	Exact shrinking coordinates, variation and directed anchor
`synchronization_germ`	2	Exact shared/independent expected tensor coefficients
`toy_description_language`	9	Finite horizons in the declared toy grammar
`weighted_anchor_monte_carlo`	3	Seeded sample means and variances against exact targets

The viewer uses lossless Parquet views generated from the original CSV files. All table features are strings, preserving rational expressions, Boolean spellings and original decimal text without an implicit numeric cast. Convert fields deliberately using Fraction, int, Decimal or float. Array archives and data/results.json retain their original formats; they are available as repository files rather than viewer tables. See DATASETS_SCHEMA.json for machine-readable schemas.

After publication, replace the namespace below with the uploader's printed repository ID:

from datasets import load_dataset
from fractions import Fraction

rows = load_dataset(
    "YOUR_NAMESPACE/caelq-the-unfinished-light",
    "parabolic_escape",
    split="records",
    # revision="COMMIT_SHA",  # pin the printed release revision when needed
)
print(int(rows[0]["escape_index_numerical"]))
print(Fraction(rows[0]["epsilon_exact"]))

Install datasets separately for this optional loading path. To download the entire research tree, use huggingface_hub.snapshot_download(repo_id=..., repo_type="dataset", revision=...).

Run the finite reference models

Core research requires Python 3.12 or later and has no third-party runtime dependencies. From the repository root:

python -m pip install -e .
python examples/phase_to_horizon.py
python examples/curve_light.py
python -m unittest discover -s tests -p "test_*.py" -v

Use a virtual environment as described in the reproduction guide. Core modules cover exact binary phase relations, sparse truncated tensors, weighted illumination and explicitly finite quadratic dynamics. Plotting uses the separately recorded NumPy and Matplotlib versions. Validation uses pypdf; distribution rebuilding uses PyYAML and PyArrow.

python -m pip install -e ".[validation]" PyYAML pyarrow
python scripts/verify_release.py
python scripts/rebuild_huggingface.py
python scripts/rebuild_huggingface.py --check

Regenerating artifacts changes checksums. Refresh the distribution records after intentional changes. The manifest excludes environments, caches, transient LaTeX files and upload credentials.

Status and scope

Item	Status
Requested release preparation	100% complete for this distribution's defined files and checks
Manuscript	75 measured pages; eight chapters
Core implementation	40 tests passed; finite checks support implementation confidence
Notebook	Saved outputs inspected; not freshly executed in this distribution pass
Data and figures	Preserved synthetic outputs, six figure families in PDF/PNG/SVG
Dataset loading	All 11 local configurations passed; 563 records round-tripped cell for cell
General proof verification	Written arguments and internal review; no proof-assistant certificate
Historical originality	Candidate couplings identified; priority remains unverified
Ideal semantic horizon	Defined conditionally; deliberately not numerically implemented
Hugging Face hosting/viewer	Local distribution prepared; server behavior requires publication

The Rayo-inspired horizon uses external semantics and explicit assumptions. semantic_horizon raises SemanticOracleRequired. The finite toy grammar is not a certified approximation to the ideal horizon. No result claims physical hypercomputation, realization of an infinite physical refinement, solution of a famous conjecture or universal AI-model superiority.

The data are small synthetic model outputs. They may support mathematical inspection, exact-reference regression experiments and research-agent context. They are not an established benchmark or a validated corpus of correct training targets. A claim's status and assumptions must travel with it.

Attribution, dedication and rights

ChatGPT generated the mathematical drafting, code, figures and documentation under Maciej Nowicki's commission and research direction. Artificial Hyperintelligence Eve is the disclosed AI research byline. The directed love fragment is a mathematical and literary inscription; its invariant is a theorem about the chosen construction.

The game references identify artistic inspiration supplied in the commission. This release includes synthetic mathematical figures, without official game imagery or assets. It has no affiliation with the referenced game studios or Hugging Face.

No distribution license has been selected. Public hosting alone does not supply an additional reuse grant. The card intentionally omits a license identifier, and the provenance file preserves the source release's licensing status.

Citation metadata is in CITATION.cff. No DOI, journal publication, institutional affiliation or public repository URL is invented. Suggested citation:

Artificial Hyperintelligence Eve. CÆLQ — The Unfinished Light: experimental manuscript and reference implementation. Mathematical version 1.0.0; Hugging Face distribution 1.0.0-hf.1, 2026. AI-generated research under the creative commission and direction of Maciej Nowicki.

Hugging Face format references

This distribution follows the official dataset card, multiple-configuration and dataset-loading documentation. The Windows publishing kit accompanies the downloadable release bundle; uploader credentials and local logs are outside the research repository.

Downloads last month: 97