data/result_catalog.json

{
  "count": 49,
  "results": [
    {
      "arxiv_ids": [
        "2404.02146"
      ],
      "claim": "The proposed super-Poynting criterion vanishes exactly when the Cotton-York and stress tensors commute; the commutator norm is a Cotton-eigenvalue-gap-weighted sum of stress-frame misalignments.",
      "classification": "criterion theorem and spectral identity",
      "discovery": "Spectral no-radiation criterion",
      "exact_check_count": 11,
      "index": 1,
      "kernel": "run_sabrina_ads_radiation_spectral_commutator",
      "scientific_payload_sha256": "241d637afce046d817e7a3107063956a87e7581ccc4ccb9230959c16a846ff1d",
      "source_classification": "complete",
      "summary": "The proposed super-Poynting criterion vanishes exactly when the Cotton-York and stress tensors commute; the commutator norm is a Cotton-eigenvalue-gap-weighted sum of stress-frame misalignments.",
      "title": "Radiation in Holography"
    },
    {
      "arxiv_ids": [
        "2411.10527"
      ],
      "claim": "The nonempty scattering region is exactly pi/2 <= mu <= arccos(-1/3) with tau_*(mu) <= tau <= pi-mu, including the collapsed endpoint and linear and quadratic onset laws.",
      "classification": "exact feasibility-domain theorem",
      "discovery": "Exact two-interval scattering domain",
      "exact_check_count": 18,
      "index": 2,
      "kernel": "run_sabrina_ads_two_interval_scattering_feasibility",
      "scientific_payload_sha256": "da08f86ea668e62889d14682aff488ad090f0b3c49d6ffc823e456f799cd580b",
      "source_classification": "complete",
      "summary": "The nonempty scattering region is exactly pi/2 <= mu <= arccos(-1/3) with tau_*(mu) <= tau <= pi-mu, including the collapsed endpoint and linear and quadratic onset laws.",
      "title": "Cryptographic tests of the python's lunch conjecture"
    },
    {
      "arxiv_ids": [
        "1502.07644"
      ],
      "claim": "For every d=2m+2 with integer m>=2, every m-dependent factor cancels between the soft charge, Green function, and hard action, leaving the same normalized Ward identity.",
      "classification": "all-dimension theorem extension",
      "discovery": "All-even-dimensional Ward normalization",
      "exact_check_count": 11,
      "index": 3,
      "kernel": "run_sabrina_all_even_d_ward_normalization",
      "scientific_payload_sha256": "36d368057821e69206d459c5b4f34e81d6d3b1df977de35db7a7bd523f3b529e",
      "source_classification": "all_even_d_soft_hard_ward_normalization_exact_and_m_independent",
      "summary": "For every d=2m+2 with integer m>=2, every m-dependent factor cancels between the soft charge, Green function, and hard action, leaving the same normalized Ward identity.",
      "title": "Higher-Dimensional Supertranslations and Weinberg's Soft Graviton Theorem"
    },
    {
      "arxiv_ids": [
        "2211.14287",
        "2307.16801",
        "2607.28718"
      ],
      "claim": "For every integer m>=3, the minimal inverse-total-Z depth is exactly d_min(m)=m-3; distribution order r has exact total-Z multiplicity r+2 through r=m-1, and all orders r>=m vanish.",
      "classification": "all-m theorem from finite ladder to exact closure",
      "discovery": "All-m transverse-nonlocality saturation theorem",
      "exact_check_count": 12,
      "index": 4,
      "kernel": "run_sabrina_all_m_transverse_nonlocality_chain",
      "scientific_payload_sha256": "6600de93b5e0dbb7dc6744cfc31499e4d84760267f62e18bc2a1c9a0e8470db5",
      "source_classification": "all_m_transverse_nonlocality_depth_saturation_and_distribution_order_multiplicity_exact",
      "summary": "For every integer m>=3, the minimal inverse-total-Z depth is exactly d_min(m)=m-3; distribution order r has exact total-Z multiplicity r+2 through r=m-1, and all orders r>=m vanish.",
      "title": "All M Transverse Nonlocality Chain"
    },
    {
      "arxiv_ids": [
        "2212.00962"
      ],
      "claim": "The symmetric and antisymmetric celestial prefactors alternate zeros and finite values at positive integers, while complementary simple poles and zeros occur at nonpositive integers, with exact residues at Delta=0 and 1.",
      "classification": "analytic zero-and-pole classification",
      "discovery": "Ambidextrous prefactor singularity lattice",
      "exact_check_count": 11,
      "index": 5,
      "kernel": "run_sabrina_ambidextrous_integer_prefactor_lattice",
      "scientific_payload_sha256": "77e01bb41ab0dd463176786be21185590dc2a06da27f2585d546e2a379c2ff4f",
      "source_classification": "complete",
      "summary": "The symmetric and antisymmetric celestial prefactors alternate zeros and finite values at positive integers, while complementary simple poles and zeros occur at nonpositive integers, with exact residues at Delta=0 and 1.",
      "title": "Celestial amplitudes in an ambidextrous basis"
    },
    {
      "arxiv_ids": [
        "2410.20296"
      ],
      "claim": "Changing the infrared scale shifts the correlator only by -(log lambda)/(4 pi) times the angular contact delta; separated-point correlators and logarithmic-time derivatives are invariant.",
      "classification": "exact contact-term theorem",
      "discovery": "Boundary soft-scale cocycle",
      "exact_check_count": 12,
      "index": 6,
      "kernel": "run_sabrina_boundary_soft_scale_cocycle",
      "scientific_payload_sha256": "a335d252d7be59f9c40e7abc990331da16b0b54eda70f70d4fa5172d95b2e084",
      "source_classification": "complete",
      "summary": "Changing the infrared scale shifts the correlator only by -(log lambda)/(4 pi) times the angular contact delta; separated-point correlators and logarithmic-time derivatives are invariant.",
      "title": "A Comment on Boundary Correlators: Soft Omissions and the Massless S-Matrix"
    },
    {
      "arxiv_ids": [
        "2501.00462"
      ],
      "claim": "The transform of u^m partial_u^r Phi is fixed at every order by Gamma(nu)/Gamma(nu-m), and the induced raising and lowering operations obey the Weyl relation [D,U]=1.",
      "classification": "all-orders representation theorem",
      "discovery": "All-orders Carrollian-Mellin intertwiner",
      "exact_check_count": 10,
      "index": 7,
      "kernel": "run_sabrina_carrollian_celestial_weyl_intertwiner",
      "scientific_payload_sha256": "d0b52d420b0b0aae1fb470163344d5fb5916c44ba5527310e10482165c6132cd",
      "source_classification": "complete",
      "summary": "The transform of u^m partial_u^r Phi is fixed at every order by Gamma(nu)/Gamma(nu-m), and the induced raising and lowering operations obey the Weyl relation [D,U]=1.",
      "title": "Multiparticle States for the Flat Hologram"
    },
    {
      "arxiv_ids": [
        "2501.00462"
      ],
      "claim": "The published coefficient vector is unique only when both chiral weight pairs are nonzero; the kernel jumps to dimension two or four on the corresponding boundary loci.",
      "classification": "hypothesis correction and boundary theorem",
      "discovery": "Conglomerate-kernel rank stratification",
      "exact_check_count": 12,
      "index": 8,
      "kernel": "run_sabrina_carrollian_conglomerate_kernel_stratification",
      "scientific_payload_sha256": "3bd160a7dfa798b30b4390d34d11f59d48bd1398ec53c50dcc434e3fe64a4737",
      "source_classification": "complete",
      "summary": "The published coefficient vector is unique only when both chiral weight pairs are nonzero; the kernel jumps to dimension two or four on the corresponding boundary loci.",
      "title": "Multiparticle States for the Flat Hologram"
    },
    {
      "arxiv_ids": [
        "2509.26264"
      ],
      "claim": "If A lies in the manifold interior of B, then J+(A) lies in I+(B) and J-(A) lies in I-(B), with the closed-set boundary corollary stated explicitly.",
      "classification": "exact causal lemma",
      "discovery": "Causal interior-inclusion lemma",
      "exact_check_count": 10,
      "index": 9,
      "kernel": "run_sabrina_causal_interior_inclusion_lemma",
      "scientific_payload_sha256": "d99b817c432380bbff4836ba0a169029b609c9519bb2ee813a581878f4ac7531",
      "source_classification": "complete",
      "summary": "If A lies in the manifold interior of B, then J+(A) lies in I+(B) and J-(A) lies in I-(B), with the closed-set boundary corollary stated explicitly.",
      "title": "On sufficient conditions for holographic scattering"
    },
    {
      "arxiv_ids": [
        "2404.14491"
      ],
      "claim": "The cited alpha=0.495 code cannot correct arbitrary t-qubit errors, and after enforcing alpha<=1/4 the stated i.i.d. exponent is positive at base error 0.09; the package isolates repair classes without claiming the amplification theorem false.",
      "classification": "proof-parameter obstruction",
      "discovery": "CDQS amplification parameter obstruction",
      "exact_check_count": 15,
      "index": 10,
      "kernel": "run_sabrina_cdqs_amplification_singleton_obstruction",
      "scientific_payload_sha256": "030824c1879fcf5639d3fb849067dcd70eb43ab728bad7d3961c5fe44ac5f1b5",
      "source_classification": "complete",
      "summary": "The cited alpha=0.495 code cannot correct arbitrary t-qubit errors, and after enforcing alpha<=1/4 the stated i.i.d. exponent is positive at base error 0.09; the package isolates repair classes without claiming the amplification theorem false.",
      "title": "Conditional disclosure of secrets with quantum resources"
    },
    {
      "arxiv_ids": [
        "2411.10527"
      ],
      "claim": "Combining F<=min(1,2a) with I>=-2 log F yields I>=max(0,-2 log(2a)), strictly strengthening the displayed -log(a)-1 bound for every a>0.",
      "classification": "strict bound strengthening",
      "discovery": "Strengthened CDQS fidelity envelope",
      "exact_check_count": 11,
      "index": 11,
      "kernel": "run_sabrina_cdqs_fidelity_envelope_strengthening",
      "scientific_payload_sha256": "a74b4d88eeb5eac12a40fce9ce013f2e18f9e4a748ea1a973380efcbeadd519b",
      "source_classification": "complete",
      "summary": "Combining F<=min(1,2a) with I>=-2 log F yields I>=max(0,-2 log(2a)), strictly strengthening the displayed -log(a)-1 bound for every a>0.",
      "title": "Cryptographic tests of the python's lunch conjecture"
    },
    {
      "arxiv_ids": [
        "2204.02505"
      ],
      "claim": "A strict celestial circle separates finite incoming and outgoing point sets exactly when their embedded convex hulls are disjoint; either a separating plane or a finite Caratheodory obstruction certifies the answer.",
      "classification": "geometric equivalence and certificates",
      "discovery": "Celestial-circle convex-hull certificate",
      "exact_check_count": 11,
      "index": 12,
      "kernel": "run_sabrina_celestial_circle_convex_hull_certificate",
      "scientific_payload_sha256": "e838335f66a4c68f81f7e6f5678fe10cea02f297400cd6d76dda8ab4d73e73eb",
      "source_classification": "complete",
      "summary": "A strict celestial circle separates finite incoming and outgoing point sets exactly when their embedded convex hulls are disjoint; either a separating plane or a finite Caratheodory obstruction certifies the answer.",
      "title": "Celestial Geometry"
    },
    {
      "arxiv_ids": [
        "2205.10901"
      ],
      "claim": "Signed momentum conservation removes every leg-separable logarithm shift, and under the spanning hypothesis cancellation for all independent shifts conversely forces each participating p_i dot P to vanish.",
      "classification": "exact invariance criterion and converse",
      "discovery": "Eikonal logarithm gauge criterion",
      "exact_check_count": 11,
      "index": 13,
      "kernel": "run_sabrina_celestial_eikonal_logarithm_gauge",
      "scientific_payload_sha256": "496aa27aa4e52fa3a6f9da412561aaa652cf21690744c98593d94d0ffbe1e6f8",
      "source_classification": "complete",
      "summary": "Signed momentum conservation removes every leg-separable logarithm shift, and under the spanning hypothesis cancellation for all independent shifts conversely forces each participating p_i dot P to vanish.",
      "title": "A Comment on Loop Corrections to the Celestial Stress Tensor"
    },
    {
      "arxiv_ids": [
        "2309.16602"
      ],
      "claim": "Opposite Euclidean winding gives monodromy exp(2 pi i(alpha-beta)); paired factors are single-valued exactly for integer alpha-beta, while a one-variable complexified continuation remains obstructed generically.",
      "classification": "monodromy theorem and boundary",
      "discovery": "Euclidean monodromy cancellation",
      "exact_check_count": 11,
      "index": 14,
      "kernel": "run_sabrina_celestial_euclidean_monodromy_cancellation",
      "scientific_payload_sha256": "a1a2263b72c97030c657dcafd5ebb59be09b6c15290e6578fd342c0c83eba049",
      "source_classification": "complete",
      "summary": "Opposite Euclidean winding gives monodromy exp(2 pi i(alpha-beta)); paired factors are single-valued exactly for integer alpha-beta, while a one-variable complexified continuation remains obstructed generically.",
      "title": "Multicollinear Singularities in Celestial CFT"
    },
    {
      "arxiv_ids": [
        "2012.15694"
      ],
      "claim": "Repeated momentum insertions generate the exact rising-factorial ratio (Delta)_r/Delta^r, including its recurrence, zeros at negative integers, and pole of order r-1 at Delta=0.",
      "classification": "all-orders operator identity",
      "discovery": "All-order celestial momentum prefactor",
      "exact_check_count": 11,
      "index": 15,
      "kernel": "run_sabrina_celestial_momentum_rising_factorial",
      "scientific_payload_sha256": "643a45bec4e1890d5a2fb13854b61ccd5e0eccb5cce7a7a293ce045edef79e9c",
      "source_classification": "complete",
      "summary": "Repeated momentum insertions generate the exact rising-factorial ratio (Delta)_r/Delta^r, including its recurrence, zeros at negative integers, and pole of order r-1 at Delta=0.",
      "title": "Shifting Spin on the Celestial Sphere"
    },
    {
      "arxiv_ids": [
        "2208.11635"
      ],
      "claim": "The complete symmetric polynomial recursion resums to 1/((1-ax)(1-bx)) and exponentiates the amplitude PDE into an exact two-factor rational translation law.",
      "classification": "generating-function resummation",
      "discovery": "Closed celestial-recursion generating function",
      "exact_check_count": 12,
      "index": 16,
      "kernel": "run_sabrina_celestial_recursion_pde_generating_function",
      "scientific_payload_sha256": "94cf744ae42b66c5db61c4d853a7867562d928a7eb80e7cc3297657eb8fcf1cd",
      "source_classification": "complete",
      "summary": "The complete symmetric polynomial recursion resums to 1/((1-ax)(1-bx)) and exponentiates the amplitude PDE into an exact two-factor rational translation law.",
      "title": "Celestial Recursion"
    },
    {
      "arxiv_ids": [
        "2606.13889"
      ],
      "claim": "All geometric and gravitational scales cancel from C_flat/C_throat=[32+(7-p)^2]/[16(9-p)]; p=3 uniquely gives the maximal one-half reduction.",
      "classification": "exact universal ratio",
      "discovery": "Universal Coulomb-branch complexity ratio",
      "exact_check_count": 15,
      "index": 17,
      "kernel": "run_sabrina_coulomb_branch_complexity_ratio",
      "scientific_payload_sha256": "0a48392a955f724766d46453ed8d209ae2f1cfca84d21c71d0807b479504eb06",
      "source_classification": "complete",
      "summary": "All geometric and gravitational scales cancel from C_flat/C_throat=[32+(7-p)^2]/[16(9-p)]; p=3 uniquely gives the maximal one-half reduction.",
      "title": "Flat Space Entanglement: A Coulomb Branch Perspective"
    },
    {
      "arxiv_ids": [
        "2307.16801"
      ],
      "claim": "A prior Ouroboros correction was a false positive caused by reading source-local falling-factorial notation as a rising Pochhammer symbol; the source identity is exact under its stated convention, and the earlier claim is superseded.",
      "classification": "self-correction and source confirmation",
      "discovery": "Self-corrected detector sum identity",
      "exact_check_count": 15,
      "index": 18,
      "kernel": "run_sabrina_detector_sum_identity_correction",
      "scientific_payload_sha256": "a1b7a157ca0f6b33a4e558a471219f1c3b5c077bbca275918db542a467ec6aad",
      "source_classification": "v1_false_positive_superseded_source_local_falling_factorial_identity_exact",
      "summary": "A prior Ouroboros correction was a false positive caused by reading source-local falling-factorial notation as a rising Pochhammer symbol; the source identity is exact under its stated convention, and the earlier claim is superseded.",
      "title": "Detector Operators for Celestial Symmetries"
    },
    {
      "arxiv_ids": [
        "1505.00716"
      ],
      "claim": "For a fixed memory impulse M delivered over duration T, the driving fluence obeys Phi>=M^2/T, with equality for a constant ramp and an exact signal-to-noise relation for the detector.",
      "classification": "sharp tradeoff bound",
      "discovery": "Memory-detector fluence tradeoff",
      "exact_check_count": 21,
      "index": 19,
      "kernel": "run_sabrina_electromagnetic_memory_detector_tradeoff",
      "scientific_payload_sha256": "015631d9110b4b95c4a08337ca93d0143257d133d51159fe68736db9947d926e",
      "source_classification": "complete",
      "summary": "For a fixed memory impulse M delivered over duration T, the driving fluence obeys Phi>=M^2/T, with equality for a constant ramp and an exact signal-to-noise relation for the detector.",
      "title": "Asymptotic Symmetries and Electromagnetic Memory"
    },
    {
      "arxiv_ids": [
        "2604.22612"
      ],
      "claim": "The gap S_gen(s_ent)-I(V1;V2) is exactly the sum of four nonnegative geometric slacks divided by 4G_N, so saturation occurs if and only if all four source inequalities saturate.",
      "classification": "exact slack decomposition",
      "discovery": "Entanglement-scattering upper slack identity",
      "exact_check_count": 11,
      "index": 20,
      "kernel": "run_sabrina_entanglement_scattering_slack_identity",
      "scientific_payload_sha256": "65ed4ac892b7bc06c0e00a75b8253eceebe84a4342dbbdfc165c226b7a62fdf3",
      "source_classification": "complete",
      "summary": "The gap S_gen(s_ent)-I(V1;V2) is exactly the sum of four nonnegative geometric slacks divided by 4G_N, so saturation occurs if and only if all four source inequalities saturate.",
      "title": "Generalized Entanglement Wedges and the Connected Wedge Theorem"
    },
    {
      "arxiv_ids": [
        "2604.22612"
      ],
      "claim": "The finite-scale endpoint map is an eight-dimensional bijection with determinant -ell^-4, but its strict flat limit has rank four and loses exactly the four endpoint-time directions.",
      "classification": "rank-drop theorem with exact kernel",
      "discovery": "Flat boundary-corner rank drop",
      "exact_check_count": 13,
      "index": 21,
      "kernel": "run_sabrina_flat_boundary_corner_rank_drop",
      "scientific_payload_sha256": "0853ed3bb32e027bf8d6f6b380fcb29ace7776981e3c033036dac278b99443a6",
      "source_classification": "complete",
      "summary": "The finite-scale endpoint map is an eight-dimensional bijection with determinant -ell^-4, but its strict flat limit has rank four and loses exactly the four endpoint-time directions.",
      "title": "Generalized Entanglement Wedges and the Connected Wedge Theorem"
    },
    {
      "arxiv_ids": [
        "2310.02186"
      ],
      "claim": "The displayed extrapolate-dictionary equivalence is exact: the apparently missing factor is supplied by the positive rescaling t=(2u)^-1 together with the regulator rename, with no branch or normalization error.",
      "classification": "source-equivalence proof",
      "discovery": "Inverted Mellin normalization equivalence",
      "exact_check_count": 14,
      "index": 22,
      "kernel": "run_sabrina_inverted_mellin_equivalence",
      "scientific_payload_sha256": "8238ba9f3410ddad34f4ba9d8b58fed3f8b73f2da4ac14bd651fe311098aed7e",
      "source_classification": "source_equation_consistent_normalization_rescaling_made_explicit",
      "summary": "The displayed extrapolate-dictionary equivalence is exact: the apparently missing factor is supplied by the positive rescaling t=(2u)^-1 together with the regulator rename, with no branch or normalization error.",
      "title": "Equating Extrapolate Dictionaries for Massless Scattering"
    },
    {
      "arxiv_ids": [
        "1905.10052"
      ],
      "claim": "A permutation-invariant three-cut residual vanishes for every affine late-time signal and factorizes into a Vandermonde product times the quadratic curvature coefficient for the first nonlinear correction.",
      "classification": "exact null test and curvature extractor",
      "discovery": "Three-cut late-time null test",
      "exact_check_count": 12,
      "index": 23,
      "kernel": "run_sabrina_late_time_three_cut_null_test",
      "scientific_payload_sha256": "fc350a6e78c22144f885c36d6387db83ad9717444e32af7a851e5a32136bcbe8",
      "source_classification": "late_time_three_cut_affine_null_test_and_quadratic_curvature_extraction_exact",
      "summary": "A permutation-invariant three-cut residual vanishes for every affine late-time signal and factorizes into a Vandermonde product times the quadratic curvature coefficient for the first nonlinear correction.",
      "title": "Implications of Superrotations"
    },
    {
      "arxiv_ids": [
        "1905.10052"
      ],
      "claim": "Two cuts reconstruct the four late-time image components exactly, with an explicit origin-shift law and the additional condition required for origin-independent cross-order matching.",
      "classification": "exact reconstruction theorem",
      "discovery": "Two-cut late-time image reconstruction",
      "exact_check_count": 16,
      "index": 24,
      "kernel": "run_sabrina_late_time_two_cut_reconstruction",
      "scientific_payload_sha256": "db1fd19b1f87b4ae81f8df3e51fb7af41553eddcc0138d1b499afb0ace0a7614",
      "source_classification": "late_time_two_cut_image_reconstruction_exact_with_origin_covariance",
      "summary": "Two cuts reconstruct the four late-time image components exactly, with an explicit origin-shift law and the additional condition required for origin-independent cross-order matching.",
      "title": "Implications of Superrotations"
    },
    {
      "arxiv_ids": [
        "2202.11127"
      ],
      "claim": "A nonzero omega^m log^r(omega/mu) term produces a pole of exact order r+1 at Delta=-m with leading coefficient (-1)^r r!; changing scale mixes only lower poles.",
      "classification": "pole-order theorem and correction",
      "discovery": "Goldilocks logarithmic pole-order correction",
      "exact_check_count": 11,
      "index": 25,
      "kernel": "run_sabrina_logarithmic_mellin_pole_order_correction",
      "scientific_payload_sha256": "7e71ad1c811616ad2bae1d0eff9e16fe5a8aca3e975f7016352c215d2a8062a2",
      "source_classification": "complete",
      "summary": "A nonzero omega^m log^r(omega/mu) term produces a pole of exact order r+1 at Delta=-m with leading coefficient (-1)^r r!; changing scale mixes only lower poles.",
      "title": "Goldilocks Modes and the Three Scattering Bases"
    },
    {
      "arxiv_ids": [
        "1407.3814"
      ],
      "claim": "The commutator of two Low hard generators has no angular component and closes in the original family only when a specific covariant derivative vanishes; generic monomial modes provide explicit obstructions.",
      "classification": "nonclosure theorem",
      "discovery": "Low hard-generator nonclosure",
      "exact_check_count": 18,
      "index": 26,
      "kernel": "run_sabrina_low_hard_generator_nonclosure",
      "scientific_payload_sha256": "923662d26ef1703e8e9b20da3584065e853328708a7abc6c4e522e16abb2d9b5",
      "source_classification": "complete",
      "summary": "The commutator of two Low hard generators has no angular component and closes in the original family only when a specific covariant derivative vanishes; generic monomial modes provide explicit obstructions.",
      "title": "Low's Subleading Soft Theorem as a Symmetry of QED"
    },
    {
      "arxiv_ids": [],
      "claim": "For the ordered complex conformal-scalar witness, the complete finite weight-(2,0) stress-tensor light-ray basis has rank three while the augmented system has rank four; an explicit left-null witness evaluates to 105/16.",
      "classification": "basis-exclusion theorem",
      "discovery": "Exact finite stress-basis exclusion at m=3",
      "exact_check_count": 11,
      "index": 27,
      "kernel": "run_sabrina_m3_unclassified_module_construction",
      "scientific_payload_sha256": "87a52883c1ab297c98ffbc371b709b01fb9e2a6054647a4be0487d54f0768bc7",
      "source_classification": "exact_full_stress_basis_exclusion",
      "summary": "For the ordered complex conformal-scalar witness, the complete finite weight-(2,0) stress-tensor light-ray basis has rank three while the augmented system has rank four; an explicit left-null witness evaluates to 105/16.",
      "title": "M3 Unclassified Module Construction"
    },
    {
      "arxiv_ids": [
        "2501.00462"
      ],
      "claim": "Each displayed beta-function pole has twice the printed residue because its pole-bearing Gamma argument has slope -1/2 in Delta; when branches collide, the corrected residues sum exactly to the coalesced tower.",
      "classification": "source-equation correction",
      "discovery": "Multiparticle beta-residue factor-two correction",
      "exact_check_count": 11,
      "index": 28,
      "kernel": "run_sabrina_multiparticle_beta_residue_factor_two",
      "scientific_payload_sha256": "6485daa678a208dfd8860503be6c60a553e2d767188c34ec80b762520c23e455",
      "source_classification": "complete",
      "summary": "Each displayed beta-function pole has twice the printed residue because its pole-bearing Gamma argument has slope -1/2 in Delta; when branches collide, the corrected residues sum exactly to the coalesced tower.",
      "title": "Multiparticle States for the Flat Hologram"
    },
    {
      "arxiv_ids": [
        "1701.00049"
      ],
      "claim": "The angular variable pushes forward exactly to a bounded radial interval with dc=(rho^2+2 epsilon)/(2 epsilon rho^2)drho, width and endpoint product 2 epsilon, and median sqrt(2 epsilon).",
      "classification": "exact change-of-variables theorem",
      "discovery": "Near-extremal radial pushforward",
      "exact_check_count": 20,
      "index": 29,
      "kernel": "run_sabrina_near_extremal_radial_pushforward",
      "scientific_payload_sha256": "2e51bc35b918b5683ba9f4c83c8ff6e0488713eb143c0d120e66640262410e4e",
      "source_classification": "complete",
      "summary": "The angular variable pushes forward exactly to a bounded radial interval with dc=(rho^2+2 epsilon)/(2 epsilon rho^2)drho, width and endpoint product 2 epsilon, and median sqrt(2 epsilon).",
      "title": "Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere"
    },
    {
      "arxiv_ids": [
        "2606.13889"
      ],
      "claim": "The p=4 spherical extremal surface admits an explicit matched large-P expansion through the first two nontrivial orders, including the renormalized area -3gR^2P^3/10+81g^2RP/35+O(P^-1).",
      "classification": "theorem extension",
      "discovery": "Omitted p=4 spherical entanglement extension",
      "exact_check_count": 11,
      "index": 30,
      "kernel": "run_sabrina_p4_spherical_entanglement_expansion",
      "scientific_payload_sha256": "15b684b9177c314bc5aeca308c80eae5ad95abfcd73c261eb7e7e51848f6b300",
      "source_classification": "complete",
      "summary": "The p=4 spherical extremal surface admits an explicit matched large-P expansion through the first two nontrivial orders, including the renormalized area -3gR^2P^3/10+81g^2RP/35+O(P^-1).",
      "title": "Flat Space Entanglement: A Coulomb Branch Perspective"
    },
    {
      "arxiv_ids": [
        "2606.13889"
      ],
      "claim": "Applying the refined-entropy operator to the p=4 spherical expansion gives g^3/P[45 log(P/R)/16+82933/560000]+O(P^-3), positive in the stated infrared regime and decaying to zero.",
      "classification": "theorem extension and asymptotic result",
      "discovery": "First nonzero p=4 refined-entropy term",
      "exact_check_count": 11,
      "index": 31,
      "kernel": "run_sabrina_p4_spherical_refined_entropy",
      "scientific_payload_sha256": "391c082d381a39de409e09c5d5d1798607ab16101326c4103bafbd5f220a2345",
      "source_classification": "complete",
      "summary": "Applying the refined-entropy operator to the p=4 spherical expansion gives g^3/P[45 log(P/R)/16+82933/560000]+O(P^-3), positive in the stated infrared regime and decaying to zero.",
      "title": "Flat Space Entanglement: A Coulomb Branch Perspective"
    },
    {
      "arxiv_ids": [
        "2604.22612"
      ],
      "claim": "The lower gap I(V1;V2)-S_gen(e_max(s_pts'')) is exactly the sum of four nonnegative CWT, ridge, focusing, and maximization slacks, with an if-and-only-if saturation criterion.",
      "classification": "exact slack decomposition",
      "discovery": "Point-scattering lower slack identity",
      "exact_check_count": 14,
      "index": 32,
      "kernel": "run_sabrina_points_scattering_lower_slack_identity",
      "scientific_payload_sha256": "7f9b013510e795182939e14d751abafa52301bf7e7cd140ff4fa5a32a2b8db69",
      "source_classification": "complete",
      "summary": "The lower gap I(V1;V2)-S_gen(e_max(s_pts'')) is exactly the sum of four nonnegative CWT, ridge, focusing, and maximization slacks, with an if-and-only-if saturation criterion.",
      "title": "Generalized Entanglement Wedges and the Connected Wedge Theorem"
    },
    {
      "arxiv_ids": [
        "1905.10052"
      ],
      "claim": "The principal-series measure factorizes into explicit positive polynomials for every even and odd integer dimension, obeys a two-dimension recurrence, and has the correct quadratic zero at the origin.",
      "classification": "all-dimension factorization theorem",
      "discovery": "All-integer-d Plancherel factorization",
      "exact_check_count": 14,
      "index": 33,
      "kernel": "run_sabrina_principal_series_plancherel_factorization",
      "scientific_payload_sha256": "4047efe441ad0800b95a0d64b4354de371b4f6fdf6be4f1cbe59763680be8178",
      "source_classification": "principal_series_plancherel_measure_all_integer_d_factorization_exact",
      "summary": "The principal-series measure factorizes into explicit positive polynomials for every even and odd integer dimension, obeys a two-dimension recurrence, and has the correct quadratic zero at the origin.",
      "title": "Implications of Superrotations"
    },
    {
      "arxiv_ids": [
        "1706.03917"
      ],
      "claim": "Under canonical massless scaling, stripped-amplitude, Mellin-weight, momentum-delta, and projective-Jacobian degrees cancel exactly for arbitrary spacetime dimension D and particle count n.",
      "classification": "all-D, all-n theorem",
      "discovery": "All-D, all-n projective Mellin scale cancellation",
      "exact_check_count": 12,
      "index": 34,
      "kernel": "run_sabrina_projective_mellin_scale_theorem",
      "scientific_payload_sha256": "bb866693a5cac8a1a30c7d4d3dec8feea3e6911173eca33cae0c27c503449354",
      "source_classification": "all_D_all_n_projective_mellin_radial_scale_cancellation_exact_under_canonical_scaling",
      "summary": "Under canonical massless scaling, stripped-amplitude, Mellin-weight, momentum-delta, and projective-Jacobian degrees cancel exactly for arbitrary spacetime dimension D and particle count n.",
      "title": "Gluon Amplitudes as 2d Conformal Correlators"
    },
    {
      "arxiv_ids": [
        "1706.03917"
      ],
      "claim": "For a square localization system, Cramer signed-minor ratios give the unique simplex coordinates; strict positivity characterizes interior support, nonnegativity with a zero characterizes the boundary, and the Jacobian is 1/abs(det M).",
      "classification": "support, positivity, and Jacobian theorem",
      "discovery": "Projective-simplex signed-minor theorem",
      "exact_check_count": 13,
      "index": 35,
      "kernel": "run_sabrina_projective_simplex_positivity_theorem",
      "scientific_payload_sha256": "04b196f77ef38f277dfbb7ebeccf2b1964f90157335f9a1dc268c6654d548af4",
      "source_classification": "square_projective_simplex_signed_minor_support_and_jacobian_theorem_exact",
      "summary": "For a square localization system, Cramer signed-minor ratios give the unique simplex coordinates; strict positivity characterizes interior support, nonnegativity with a zero characterizes the boundary, and the Jacobian is 1/abs(det M).",
      "title": "Gluon Amplitudes as 2d Conformal Correlators"
    },
    {
      "arxiv_ids": [
        "1706.03917"
      ],
      "claim": "For a (D+1)-by-n constraint matrix of generic rank min(D+1,n), the theorem gives the exact number of residual external constraints or unfixed simplex moduli and separates unique, boundary, incompatible, and continuous-support regimes.",
      "classification": "all-D rank and support theorem",
      "discovery": "All-D projective-simplex rank theorem",
      "exact_check_count": 18,
      "index": 36,
      "kernel": "run_sabrina_projective_simplex_rank_theorem",
      "scientific_payload_sha256": "a4be65bfe6724693b679405e1985b33302d94ec8113edf75512620fcc58045f7",
      "source_classification": "all_D_projective_simplex_localization_rank_theorem_exact_with_support_and_positivity_boundaries",
      "summary": "For a (D+1)-by-n constraint matrix of generic rank min(D+1,n), the theorem gives the exact number of residual external constraints or unfixed simplex moduli and separates unique, boundary, incompatible, and continuous-support regimes.",
      "title": "Gluon Amplitudes as 2d Conformal Correlators"
    },
    {
      "arxiv_ids": [
        "1502.06120"
      ],
      "claim": "The cap response is an explicit quintic with antipodal-complement antisymmetry F(1-x)=-F(x), complete physical zero set {0,1/2,1}, and an exact factorization exposing every sign change.",
      "classification": "duality and factorization theorem",
      "discovery": "Quadrupole spin-memory cap duality",
      "exact_check_count": 16,
      "index": 37,
      "kernel": "run_sabrina_quadrupole_spin_memory_cap_duality",
      "scientific_payload_sha256": "ec237ce1930d800c155dbce44a6eb3a8c2c5c9d65bcf638d05a6583ce813ba9a",
      "source_classification": "complete",
      "summary": "The cap response is an explicit quintic with antipodal-complement antisymmetry F(1-x)=-F(x), complete physical zero set {0,1/2,1}, and an exact factorization exposing every sign change.",
      "title": "New Gravitational Memories"
    },
    {
      "arxiv_ids": [
        "1905.09809"
      ],
      "claim": "The published fourth-order radial equation factorizes exactly as [rho^2(D^2-4)+4L]^2, revealing generalized-kernel modes killed by the square but not by the second-order factor.",
      "classification": "operator factorization theorem",
      "discovery": "Radial Einstein operator is an exact square",
      "exact_check_count": 10,
      "index": 38,
      "kernel": "run_sabrina_radial_einstein_square_factorization",
      "scientific_payload_sha256": "7ecf43b482eecb12234e230a243c73209adfdb80078a068221722a2dd1380e56",
      "source_classification": "complete",
      "summary": "The published fourth-order radial equation factorizes exactly as [rho^2(D^2-4)+4L]^2, revealing generalized-kernel modes killed by the square but not by the second-order factor.",
      "title": "Uplifting AdS3/CFT2 to Flat Space Holography"
    },
    {
      "arxiv_ids": [
        "2606.13889"
      ],
      "claim": "An exact boundary identity proves the coefficient equality previously supported numerically: C3^(p)=(7-p)/(9-p)[(C1^(p))^2+(C2^(p))^2], with the mechanism traced to alpha^2+beta^2=7-p.",
      "classification": "analytic proof of source equality",
      "discovery": "Analytic proof of the flat-space RT equality",
      "exact_check_count": 14,
      "index": 39,
      "kernel": "run_sabrina_rt_area_boundary_identity",
      "scientific_payload_sha256": "ee27f366b07f19111f42a6487e69e75576daa09711cfb41f9012311047bff850",
      "source_classification": "complete",
      "summary": "An exact boundary identity proves the coefficient equality previously supported numerically: C3^(p)=(7-p)/(9-p)[(C1^(p))^2+(C2^(p))^2], with the mechanism traced to alpha^2+beta^2=7-p.",
      "title": "Flat Space Entanglement: A Coulomb Branch Perspective"
    },
    {
      "arxiv_ids": [
        "2512.02825"
      ],
      "claim": "Ward conservation gives an exact subset-sum formula for every connected soft cumulant of order n>=2; deterministic incoming charge drops out, while mixed cumulants are the precise obstruction to a factorized hard-only reduction.",
      "classification": "all-orders hierarchy and obstruction",
      "discovery": "Full soft-charge cumulant hierarchy",
      "exact_check_count": 13,
      "index": 40,
      "kernel": "run_sabrina_soft_charge_cumulant_hierarchy",
      "scientific_payload_sha256": "8ed6c8d8dcc8eabf62402d94d7fdfcc3c000f15edec4ba8c1f437a6040cb2731",
      "source_classification": "complete",
      "summary": "Ward conservation gives an exact subset-sum formula for every connected soft cumulant of order n>=2; deterministic incoming charge drops out, while mixed cumulants are the precise obstruction to a factorized hard-only reduction.",
      "title": "Memory Correlators and Ward Identities in the 'in-in' Formalism"
    },
    {
      "arxiv_ids": [
        "2012.03850"
      ],
      "claim": "Fixed total-charge support forces the reduced radiation state to commute with its charge, permits arbitrary degeneracy inside each charge block, and yields the exact entropy decomposition into sector entropy plus within-sector entropy.",
      "classification": "reduced-state structure theorem",
      "discovery": "Soft-charge reduced-state block theorem",
      "exact_check_count": 15,
      "index": 41,
      "kernel": "run_sabrina_soft_charge_reduced_state_theorem",
      "scientific_payload_sha256": "1934ba760699c1f3d024f8428611b3b7b3dde43b9a45a54fd868c65b4cc5a8f6",
      "source_classification": "complete",
      "summary": "Fixed total-charge support forces the reduced radiation state to commute with its charge, permits arbitrary degeneracy inside each charge block, and yields the exact entropy decomposition into sector entropy plus within-sector entropy.",
      "title": "HPS meets AMPS: How Soft Hair Dissolves the Firewall"
    },
    {
      "arxiv_ids": [
        "2604.19866"
      ],
      "claim": "Under linear mode action and the derivation rule, multiplying every elementary charge commutator by lambda multiplies the whole dressing commutator by lambda; lambda=2 cannot preserve a nonzero target without compensating repair.",
      "classification": "no-go theorem and repair boundary",
      "discovery": "Soft-dressing factor-two no-go",
      "exact_check_count": 13,
      "index": 42,
      "kernel": "run_sabrina_soft_dressing_factor_two_no_go",
      "scientific_payload_sha256": "694c94424ad44968ecc374bad8ce5fce735e410342d9142b79c566066a0ca029",
      "source_classification": "complete",
      "summary": "Under linear mode action and the derivation rule, multiplying every elementary charge commutator by lambda multiplies the whole dressing commutator by lambda; lambda=2 cannot preserve a nonzero target without compensating repair.",
      "title": "Asymptotic charges as detectors and the memory effect in massive QED and perturbative quantum gravity"
    },
    {
      "arxiv_ids": [
        "2105.09792"
      ],
      "claim": "The unqualified all-n identity requires an n! factor: the Mellin residue is g^(n)(0)/n!, so the source formula is exact at n=0,1 and is restored for all n by multiplying the residue side by n! or dividing u^n by n!.",
      "classification": "source-equation correction",
      "discovery": "Soft-Mellin factorial correction",
      "exact_check_count": 12,
      "index": 43,
      "kernel": "run_sabrina_soft_mellin_residue_identity",
      "scientific_payload_sha256": "2bac79f473b925a796d826a6c2d4fdd4003b5c269b8843d9f37dd83ed0e4d58f",
      "source_classification": "physical_n0_n1_exact_unqualified_all_n_extension_requires_factorial",
      "summary": "The unqualified all-n identity requires an n! factor: the Mellin residue is g^(n)(0)/n!, so the source formula is exact at n=0,1 and is restored for all n by multiplying the residue side by n! or dividing u^n by n!.",
      "title": "Revisiting the Conformally Soft Sector with Celestial Diamonds"
    },
    {
      "arxiv_ids": [
        "1705.01027"
      ],
      "claim": "The formal Delta=1 shadow field strength carries an unavoidable factor d-2 and has an explicit nonzero component for d!=2; only d=2 is self-shadow and pure gauge in the tested sense.",
      "classification": "dimension-specific obstruction theorem",
      "discovery": "Spin-1 shadow gauge obstruction",
      "exact_check_count": 19,
      "index": 44,
      "kernel": "run_sabrina_spin1_shadow_gauge_obstruction",
      "scientific_payload_sha256": "147d7f9336fd649e66d2d1995c6287514571d2ae8c83f798615712be5580eda5",
      "source_classification": "complete",
      "summary": "The formal Delta=1 shadow field strength carries an unavoidable factor d-2 and has an explicit nonzero component for d!=2; only d=2 is self-shadow and pure gauge in the tested sense.",
      "title": "A Conformal Basis for Flat Space Amplitudes"
    },
    {
      "arxiv_ids": [
        "1406.3312"
      ],
      "claim": "Pure-gauge variation of the subleading soft factor vanishes for every reference pair exactly when the summed angular-momentum defect Delta J is zero; basis polarizations recover every defect component.",
      "classification": "if-and-only-if gauge theorem",
      "discovery": "Subleading-soft gauge-defect theorem",
      "exact_check_count": 12,
      "index": 45,
      "kernel": "run_sabrina_subleading_soft_gauge_defect_theorem",
      "scientific_payload_sha256": "f7f1619f5cf9b96d1c0093c8a1f8c0aff35360814eeaa17ab81bc686a50a3b61",
      "source_classification": "complete",
      "summary": "Pure-gauge variation of the subleading soft factor vanishes for every reference pair exactly when the summed angular-momentum defect Delta J is zero; basis polarizations recover every defect component.",
      "title": "Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix"
    },
    {
      "arxiv_ids": [
        "2108.11422"
      ],
      "claim": "All routes to a fixed fermionic mode span a rank-one commutator image and obey an exact pairwise syzygy, with a classified exceptional route whenever m=2t/3 is integral.",
      "classification": "infinite algebraic identity family",
      "discovery": "Infinite super-BMS commutator syzygy family",
      "exact_check_count": 9,
      "index": 46,
      "kernel": "run_sabrina_super_bms_commutator_syzygy_family",
      "scientific_payload_sha256": "0c0559f924de94f512ba19fd2d867bfef93412978ddcb2cfd055a85cdcf94086",
      "source_classification": "complete",
      "summary": "All routes to a fixed fermionic mode span a rank-one commutator image and obey an exact pairwise syzygy, with a classified exceptional route whenever m=2t/3 is integral.",
      "title": "Conformally Soft Fermions"
    },
    {
      "arxiv_ids": [
        "2005.08990"
      ],
      "claim": "Under the source's explicit holomorphic restriction, the boundary term cancels both shear terms and the antiholomorphic news term, doubles only the holomorphic news term, and reproduces the exact 1/(16 pi G) charge.",
      "classification": "exact source reduction",
      "discovery": "Holomorphic superrotation charge cancellation",
      "exact_check_count": 12,
      "index": 47,
      "kernel": "run_sabrina_superrotation_charge_cancellation",
      "scientific_payload_sha256": "9081bdaa476d9558567b5363b9a85389cdaf84998fd93684f74822acd8c1ad47",
      "source_classification": "source_consistent_holomorphic_superrotation_charge_exactly_reduced",
      "summary": "Under the source's explicit holomorphic restriction, the boundary term cancels both shear terms and the antiholomorphic news term, doubles only the holomorphic news term, and reproduces the exact 1/(16 pi G) charge.",
      "title": "Asymptotic Symmetries and Celestial CFT"
    },
    {
      "arxiv_ids": [
        "2402.18798"
      ],
      "claim": "The OPE ambiguity depends on the normalized kernel only through M[f]=1/4-integral f(t)(t-1/2)^2dt; positivity gives the sharp interval [0,1/4], while normalization alone admits an explicit unbounded signed family.",
      "classification": "sharp bound and counterexample family",
      "discovery": "Two-particle kernel variance theorem",
      "exact_check_count": 14,
      "index": 48,
      "kernel": "run_sabrina_two_particle_kernel_variance",
      "scientific_payload_sha256": "7b1aa48423c6010da14e5d02a47c618b324310dbf80b043db8546fbcc3ee59b6",
      "source_classification": "complete",
      "summary": "The OPE ambiguity depends on the normalized kernel only through M[f]=1/4-integral f(t)(t-1/2)^2dt; positivity gives the sharp interval [0,1/4], while normalization alone admits an explicit unbounded signed family.",
      "title": "Multiparticle Contributions to the Celestial OPE"
    },
    {
      "arxiv_ids": [
        "2012.15694"
      ],
      "claim": "Delta maps to 2-Delta as an exact involution exchanging primary and shadow gauge, scalar, and Weyl data while preserving the reduced double-copy quotient and exchanging its Delta=0 and 2 divisors.",
      "classification": "involution and equivariance theorem",
      "discovery": "Weyl-double-copy shadow involution",
      "exact_check_count": 17,
      "index": 49,
      "kernel": "run_sabrina_weyl_double_copy_shadow_involution",
      "scientific_payload_sha256": "f6243bc6dfdd05769cab60b02d4e23c53ef9c0119f2ac7a10d54eda023956fee",
      "source_classification": "complete",
      "summary": "Delta maps to 2-Delta as an exact involution exchanging primary and shadow gauge, scalar, and Weyl data while preserving the reduced double-copy quotient and exchanging its Delta=0 and 2 divisors.",
      "title": "Shifting Spin on the Celestial Sphere"
    }
  ],
  "schema": "ouroboros_result_catalog_v1"
}