Datasets:

cjc0013
/

ouroboros-pasterski-research-program

The discovery and bounded mathematical claim come first. Source, classification, checks, and payload identity follow so that the significance is legible without opening a machine-readable assertion.

1. Spectral no-radiation criterion

What Ouroboros established: 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.

Source paper: Radiation in Holography
Kernel: run_sabrina_ads_radiation_spectral_commutator
Public sources: arXiv:2404.02146
Classification: criterion theorem and spectral identity
Source-payload status: complete
Exact checks: 11
Scientific payload SHA-256: 241d637afce046d817e7a3107063956a87e7581ccc4ccb9230959c16a846ff1d

2. Exact two-interval scattering domain

What Ouroboros established: 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.

Source paper: Cryptographic tests of the python's lunch conjecture
Kernel: run_sabrina_ads_two_interval_scattering_feasibility
Public sources: arXiv:2411.10527
Classification: exact feasibility-domain theorem
Source-payload status: complete
Exact checks: 18
Scientific payload SHA-256: da08f86ea668e62889d14682aff488ad090f0b3c49d6ffc823e456f799cd580b

3. All-even-dimensional Ward normalization

What Ouroboros established: 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.

Source paper: Higher-Dimensional Supertranslations and Weinberg's Soft Graviton Theorem
Kernel: run_sabrina_all_even_d_ward_normalization
Public sources: arXiv:1502.07644
Classification: all-dimension theorem extension
Source-payload status: all_even_d_soft_hard_ward_normalization_exact_and_m_independent
Exact checks: 11
Scientific payload SHA-256: 36d368057821e69206d459c5b4f34e81d6d3b1df977de35db7a7bd523f3b529e

4. All-m transverse-nonlocality saturation theorem

What Ouroboros established: 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.

Source paper: All M Transverse Nonlocality Chain
Kernel: run_sabrina_all_m_transverse_nonlocality_chain
Public sources: arXiv:2211.14287, arXiv:2307.16801, arXiv:2607.28718
Classification: all-m theorem from finite ladder to exact closure
Source-payload status: all_m_transverse_nonlocality_depth_saturation_and_distribution_order_multiplicity_exact
Exact checks: 12
Scientific payload SHA-256: 6600de93b5e0dbb7dc6744cfc31499e4d84760267f62e18bc2a1c9a0e8470db5

5. Ambidextrous prefactor singularity lattice

What Ouroboros established: 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.

Source paper: Celestial amplitudes in an ambidextrous basis
Kernel: run_sabrina_ambidextrous_integer_prefactor_lattice
Public sources: arXiv:2212.00962
Classification: analytic zero-and-pole classification
Source-payload status: complete
Exact checks: 11
Scientific payload SHA-256: 77e01bb41ab0dd463176786be21185590dc2a06da27f2585d546e2a379c2ff4f

6. Boundary soft-scale cocycle

What Ouroboros established: 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.

Source paper: A Comment on Boundary Correlators: Soft Omissions and the Massless S-Matrix
Kernel: run_sabrina_boundary_soft_scale_cocycle
Public sources: arXiv:2410.20296
Classification: exact contact-term theorem
Source-payload status: complete
Exact checks: 12
Scientific payload SHA-256: a335d252d7be59f9c40e7abc990331da16b0b54eda70f70d4fa5172d95b2e084

7. All-orders Carrollian-Mellin intertwiner

What Ouroboros established: 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.

Source paper: Multiparticle States for the Flat Hologram
Kernel: run_sabrina_carrollian_celestial_weyl_intertwiner
Public sources: arXiv:2501.00462
Classification: all-orders representation theorem
Source-payload status: complete
Exact checks: 10
Scientific payload SHA-256: d0b52d420b0b0aae1fb470163344d5fb5916c44ba5527310e10482165c6132cd

8. Conglomerate-kernel rank stratification

What Ouroboros established: 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.

Source paper: Multiparticle States for the Flat Hologram
Kernel: run_sabrina_carrollian_conglomerate_kernel_stratification
Public sources: arXiv:2501.00462
Classification: hypothesis correction and boundary theorem
Source-payload status: complete
Exact checks: 12
Scientific payload SHA-256: 3bd160a7dfa798b30b4390d34d11f59d48bd1398ec53c50dcc434e3fe64a4737

9. Causal interior-inclusion lemma

What Ouroboros established: 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.

Source paper: On sufficient conditions for holographic scattering
Kernel: run_sabrina_causal_interior_inclusion_lemma
Public sources: arXiv:2509.26264
Classification: exact causal lemma
Source-payload status: complete
Exact checks: 10
Scientific payload SHA-256: d99b817c432380bbff4836ba0a169029b609c9519bb2ee813a581878f4ac7531

10. CDQS amplification parameter obstruction

What Ouroboros established: 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.

Source paper: Conditional disclosure of secrets with quantum resources
Kernel: run_sabrina_cdqs_amplification_singleton_obstruction
Public sources: arXiv:2404.14491
Classification: proof-parameter obstruction
Source-payload status: complete
Exact checks: 15
Scientific payload SHA-256: 030824c1879fcf5639d3fb849067dcd70eb43ab728bad7d3961c5fe44ac5f1b5

11. Strengthened CDQS fidelity envelope

What Ouroboros established: 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.

Source paper: Cryptographic tests of the python's lunch conjecture
Kernel: run_sabrina_cdqs_fidelity_envelope_strengthening
Public sources: arXiv:2411.10527
Classification: strict bound strengthening
Source-payload status: complete
Exact checks: 11
Scientific payload SHA-256: a74b4d88eeb5eac12a40fce9ce013f2e18f9e4a748ea1a973380efcbeadd519b

12. Celestial-circle convex-hull certificate

What Ouroboros established: 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.

Source paper: Celestial Geometry
Kernel: run_sabrina_celestial_circle_convex_hull_certificate
Public sources: arXiv:2204.02505
Classification: geometric equivalence and certificates
Source-payload status: complete
Exact checks: 11
Scientific payload SHA-256: e838335f66a4c68f81f7e6f5678fe10cea02f297400cd6d76dda8ab4d73e73eb

13. Eikonal logarithm gauge criterion

What Ouroboros established: 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.

Source paper: A Comment on Loop Corrections to the Celestial Stress Tensor
Kernel: run_sabrina_celestial_eikonal_logarithm_gauge
Public sources: arXiv:2205.10901
Classification: exact invariance criterion and converse
Source-payload status: complete
Exact checks: 11
Scientific payload SHA-256: 496aa27aa4e52fa3a6f9da412561aaa652cf21690744c98593d94d0ffbe1e6f8

14. Euclidean monodromy cancellation

What Ouroboros established: 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.

Source paper: Multicollinear Singularities in Celestial CFT
Kernel: run_sabrina_celestial_euclidean_monodromy_cancellation
Public sources: arXiv:2309.16602
Classification: monodromy theorem and boundary
Source-payload status: complete
Exact checks: 11
Scientific payload SHA-256: a1a2263b72c97030c657dcafd5ebb59be09b6c15290e6578fd342c0c83eba049

15. All-order celestial momentum prefactor

What Ouroboros established: 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.

Source paper: Shifting Spin on the Celestial Sphere
Kernel: run_sabrina_celestial_momentum_rising_factorial
Public sources: arXiv:2012.15694
Classification: all-orders operator identity
Source-payload status: complete
Exact checks: 11
Scientific payload SHA-256: 643a45bec4e1890d5a2fb13854b61ccd5e0eccb5cce7a7a293ce045edef79e9c

16. Closed celestial-recursion generating function

What Ouroboros established: 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.

Source paper: Celestial Recursion
Kernel: run_sabrina_celestial_recursion_pde_generating_function
Public sources: arXiv:2208.11635
Classification: generating-function resummation
Source-payload status: complete
Exact checks: 12
Scientific payload SHA-256: 94cf744ae42b66c5db61c4d853a7867562d928a7eb80e7cc3297657eb8fcf1cd

17. Universal Coulomb-branch complexity ratio

What Ouroboros established: 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.

Source paper: Flat Space Entanglement: A Coulomb Branch Perspective
Kernel: run_sabrina_coulomb_branch_complexity_ratio
Public sources: arXiv:2606.13889
Classification: exact universal ratio
Source-payload status: complete
Exact checks: 15
Scientific payload SHA-256: 0a48392a955f724766d46453ed8d209ae2f1cfca84d21c71d0807b479504eb06

18. Self-corrected detector sum identity

What Ouroboros established: 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.

Source paper: Detector Operators for Celestial Symmetries
Kernel: run_sabrina_detector_sum_identity_correction
Public sources: arXiv:2307.16801
Classification: self-correction and source confirmation
Source-payload status: v1_false_positive_superseded_source_local_falling_factorial_identity_exact
Exact checks: 15
Scientific payload SHA-256: a1b7a157ca0f6b33a4e558a471219f1c3b5c077bbca275918db542a467ec6aad

19. Memory-detector fluence tradeoff

What Ouroboros established: 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.

Source paper: Asymptotic Symmetries and Electromagnetic Memory
Kernel: run_sabrina_electromagnetic_memory_detector_tradeoff
Public sources: arXiv:1505.00716
Classification: sharp tradeoff bound
Source-payload status: complete
Exact checks: 21
Scientific payload SHA-256: 015631d9110b4b95c4a08337ca93d0143257d133d51159fe68736db9947d926e

20. Entanglement-scattering upper slack identity

What Ouroboros established: 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.

Source paper: Generalized Entanglement Wedges and the Connected Wedge Theorem
Kernel: run_sabrina_entanglement_scattering_slack_identity
Public sources: arXiv:2604.22612
Classification: exact slack decomposition
Source-payload status: complete
Exact checks: 11
Scientific payload SHA-256: 65ed4ac892b7bc06c0e00a75b8253eceebe84a4342dbbdfc165c226b7a62fdf3

21. Flat boundary-corner rank drop

What Ouroboros established: 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.

Source paper: Generalized Entanglement Wedges and the Connected Wedge Theorem
Kernel: run_sabrina_flat_boundary_corner_rank_drop
Public sources: arXiv:2604.22612
Classification: rank-drop theorem with exact kernel
Source-payload status: complete
Exact checks: 13
Scientific payload SHA-256: 0853ed3bb32e027bf8d6f6b380fcb29ace7776981e3c033036dac278b99443a6

22. Inverted Mellin normalization equivalence

What Ouroboros established: 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.

Source paper: Equating Extrapolate Dictionaries for Massless Scattering
Kernel: run_sabrina_inverted_mellin_equivalence
Public sources: arXiv:2310.02186
Classification: source-equivalence proof
Source-payload status: source_equation_consistent_normalization_rescaling_made_explicit
Exact checks: 14
Scientific payload SHA-256: 8238ba9f3410ddad34f4ba9d8b58fed3f8b73f2da4ac14bd651fe311098aed7e

23. Three-cut late-time null test

What Ouroboros established: 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.

Source paper: Implications of Superrotations
Kernel: run_sabrina_late_time_three_cut_null_test
Public sources: arXiv:1905.10052
Classification: exact null test and curvature extractor
Source-payload status: late_time_three_cut_affine_null_test_and_quadratic_curvature_extraction_exact
Exact checks: 12
Scientific payload SHA-256: fc350a6e78c22144f885c36d6387db83ad9717444e32af7a851e5a32136bcbe8

24. Two-cut late-time image reconstruction

What Ouroboros established: 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.

Source paper: Implications of Superrotations
Kernel: run_sabrina_late_time_two_cut_reconstruction
Public sources: arXiv:1905.10052
Classification: exact reconstruction theorem
Source-payload status: late_time_two_cut_image_reconstruction_exact_with_origin_covariance
Exact checks: 16
Scientific payload SHA-256: db1fd19b1f87b4ae81f8df3e51fb7af41553eddcc0138d1b499afb0ace0a7614

25. Goldilocks logarithmic pole-order correction

What Ouroboros established: 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.

Source paper: Goldilocks Modes and the Three Scattering Bases
Kernel: run_sabrina_logarithmic_mellin_pole_order_correction
Public sources: arXiv:2202.11127
Classification: pole-order theorem and correction
Source-payload status: complete
Exact checks: 11
Scientific payload SHA-256: 7e71ad1c811616ad2bae1d0eff9e16fe5a8aca3e975f7016352c215d2a8062a2

26. Low hard-generator nonclosure

What Ouroboros established: 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.

Source paper: Low's Subleading Soft Theorem as a Symmetry of QED
Kernel: run_sabrina_low_hard_generator_nonclosure
Public sources: arXiv:1407.3814
Classification: nonclosure theorem
Source-payload status: complete
Exact checks: 18
Scientific payload SHA-256: 923662d26ef1703e8e9b20da3584065e853328708a7abc6c4e522e16abb2d9b5

27. Exact finite stress-basis exclusion at m=3

What Ouroboros established: 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.

Source paper: M3 Unclassified Module Construction
Kernel: run_sabrina_m3_unclassified_module_construction
Public sources: source IDs recorded in the result payload
Classification: basis-exclusion theorem
Source-payload status: exact_full_stress_basis_exclusion
Exact checks: 11
Scientific payload SHA-256: 87a52883c1ab297c98ffbc371b709b01fb9e2a6054647a4be0487d54f0768bc7

28. Multiparticle beta-residue factor-two correction

What Ouroboros established: 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.

Source paper: Multiparticle States for the Flat Hologram
Kernel: run_sabrina_multiparticle_beta_residue_factor_two
Public sources: arXiv:2501.00462
Classification: source-equation correction
Source-payload status: complete
Exact checks: 11
Scientific payload SHA-256: 6485daa678a208dfd8860503be6c60a553e2d767188c34ec80b762520c23e455

29. Near-extremal radial pushforward

What Ouroboros established: 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).

Source paper: Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
Kernel: run_sabrina_near_extremal_radial_pushforward
Public sources: arXiv:1701.00049
Classification: exact change-of-variables theorem
Source-payload status: complete
Exact checks: 20
Scientific payload SHA-256: 2e51bc35b918b5683ba9f4c83c8ff6e0488713eb143c0d120e66640262410e4e

30. Omitted p=4 spherical entanglement extension

What Ouroboros established: 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).

Source paper: Flat Space Entanglement: A Coulomb Branch Perspective
Kernel: run_sabrina_p4_spherical_entanglement_expansion
Public sources: arXiv:2606.13889
Classification: theorem extension
Source-payload status: complete
Exact checks: 11
Scientific payload SHA-256: 15b684b9177c314bc5aeca308c80eae5ad95abfcd73c261eb7e7e51848f6b300

31. First nonzero p=4 refined-entropy term

What Ouroboros established: 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.

Source paper: Flat Space Entanglement: A Coulomb Branch Perspective
Kernel: run_sabrina_p4_spherical_refined_entropy
Public sources: arXiv:2606.13889
Classification: theorem extension and asymptotic result
Source-payload status: complete
Exact checks: 11
Scientific payload SHA-256: 391c082d381a39de409e09c5d5d1798607ab16101326c4103bafbd5f220a2345

32. Point-scattering lower slack identity

What Ouroboros established: 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.

Source paper: Generalized Entanglement Wedges and the Connected Wedge Theorem
Kernel: run_sabrina_points_scattering_lower_slack_identity
Public sources: arXiv:2604.22612
Classification: exact slack decomposition
Source-payload status: complete
Exact checks: 14
Scientific payload SHA-256: 7f9b013510e795182939e14d751abafa52301bf7e7cd140ff4fa5a32a2b8db69

33. All-integer-d Plancherel factorization

What Ouroboros established: 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.

Source paper: Implications of Superrotations
Kernel: run_sabrina_principal_series_plancherel_factorization
Public sources: arXiv:1905.10052
Classification: all-dimension factorization theorem
Source-payload status: principal_series_plancherel_measure_all_integer_d_factorization_exact
Exact checks: 14
Scientific payload SHA-256: 4047efe441ad0800b95a0d64b4354de371b4f6fdf6be4f1cbe59763680be8178

34. All-D, all-n projective Mellin scale cancellation

What Ouroboros established: 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.

Source paper: Gluon Amplitudes as 2d Conformal Correlators
Kernel: run_sabrina_projective_mellin_scale_theorem
Public sources: arXiv:1706.03917
Classification: all-D, all-n theorem
Source-payload status: all_D_all_n_projective_mellin_radial_scale_cancellation_exact_under_canonical_scaling
Exact checks: 12
Scientific payload SHA-256: bb866693a5cac8a1a30c7d4d3dec8feea3e6911173eca33cae0c27c503449354

35. Projective-simplex signed-minor theorem

What Ouroboros established: 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).

Source paper: Gluon Amplitudes as 2d Conformal Correlators
Kernel: run_sabrina_projective_simplex_positivity_theorem
Public sources: arXiv:1706.03917
Classification: support, positivity, and Jacobian theorem
Source-payload status: square_projective_simplex_signed_minor_support_and_jacobian_theorem_exact
Exact checks: 13
Scientific payload SHA-256: 04b196f77ef38f277dfbb7ebeccf2b1964f90157335f9a1dc268c6654d548af4

36. All-D projective-simplex rank theorem

What Ouroboros established: 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.

Source paper: Gluon Amplitudes as 2d Conformal Correlators
Kernel: run_sabrina_projective_simplex_rank_theorem
Public sources: arXiv:1706.03917
Classification: all-D rank and support theorem
Source-payload status: all_D_projective_simplex_localization_rank_theorem_exact_with_support_and_positivity_boundaries
Exact checks: 18
Scientific payload SHA-256: a4be65bfe6724693b679405e1985b33302d94ec8113edf75512620fcc58045f7

37. Quadrupole spin-memory cap duality

What Ouroboros established: 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.

Source paper: New Gravitational Memories
Kernel: run_sabrina_quadrupole_spin_memory_cap_duality
Public sources: arXiv:1502.06120
Classification: duality and factorization theorem
Source-payload status: complete
Exact checks: 16
Scientific payload SHA-256: ec237ce1930d800c155dbce44a6eb3a8c2c5c9d65bcf638d05a6583ce813ba9a

38. Radial Einstein operator is an exact square

What Ouroboros established: 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.

Source paper: Uplifting AdS3/CFT2 to Flat Space Holography
Kernel: run_sabrina_radial_einstein_square_factorization
Public sources: arXiv:1905.09809
Classification: operator factorization theorem
Source-payload status: complete
Exact checks: 10
Scientific payload SHA-256: 7ecf43b482eecb12234e230a243c73209adfdb80078a068221722a2dd1380e56

39. Analytic proof of the flat-space RT equality

What Ouroboros established: 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.

Source paper: Flat Space Entanglement: A Coulomb Branch Perspective
Kernel: run_sabrina_rt_area_boundary_identity
Public sources: arXiv:2606.13889
Classification: analytic proof of source equality
Source-payload status: complete
Exact checks: 14
Scientific payload SHA-256: ee27f366b07f19111f42a6487e69e75576daa09711cfb41f9012311047bff850

40. Full soft-charge cumulant hierarchy

What Ouroboros established: 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.

Source paper: Memory Correlators and Ward Identities in the 'in-in' Formalism
Kernel: run_sabrina_soft_charge_cumulant_hierarchy
Public sources: arXiv:2512.02825
Classification: all-orders hierarchy and obstruction
Source-payload status: complete
Exact checks: 13
Scientific payload SHA-256: 8ed6c8d8dcc8eabf62402d94d7fdfcc3c000f15edec4ba8c1f437a6040cb2731

41. Soft-charge reduced-state block theorem

What Ouroboros established: 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.

Source paper: HPS meets AMPS: How Soft Hair Dissolves the Firewall
Kernel: run_sabrina_soft_charge_reduced_state_theorem
Public sources: arXiv:2012.03850
Classification: reduced-state structure theorem
Source-payload status: complete
Exact checks: 15
Scientific payload SHA-256: 1934ba760699c1f3d024f8428611b3b7b3dde43b9a45a54fd868c65b4cc5a8f6

42. Soft-dressing factor-two no-go

What Ouroboros established: 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.

Source paper: Asymptotic charges as detectors and the memory effect in massive QED and perturbative quantum gravity
Kernel: run_sabrina_soft_dressing_factor_two_no_go
Public sources: arXiv:2604.19866
Classification: no-go theorem and repair boundary
Source-payload status: complete
Exact checks: 13
Scientific payload SHA-256: 694c94424ad44968ecc374bad8ce5fce735e410342d9142b79c566066a0ca029

43. Soft-Mellin factorial correction

What Ouroboros established: 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!.

Source paper: Revisiting the Conformally Soft Sector with Celestial Diamonds
Kernel: run_sabrina_soft_mellin_residue_identity
Public sources: arXiv:2105.09792
Classification: source-equation correction
Source-payload status: physical_n0_n1_exact_unqualified_all_n_extension_requires_factorial
Exact checks: 12
Scientific payload SHA-256: 2bac79f473b925a796d826a6c2d4fdd4003b5c269b8843d9f37dd83ed0e4d58f

44. Spin-1 shadow gauge obstruction

What Ouroboros established: 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.

Source paper: A Conformal Basis for Flat Space Amplitudes
Kernel: run_sabrina_spin1_shadow_gauge_obstruction
Public sources: arXiv:1705.01027
Classification: dimension-specific obstruction theorem
Source-payload status: complete
Exact checks: 19
Scientific payload SHA-256: 147d7f9336fd649e66d2d1995c6287514571d2ae8c83f798615712be5580eda5

45. Subleading-soft gauge-defect theorem

What Ouroboros established: 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.

Source paper: Semiclassical Virasoro Symmetry of the Quantum Gravity S-Matrix
Kernel: run_sabrina_subleading_soft_gauge_defect_theorem
Public sources: arXiv:1406.3312
Classification: if-and-only-if gauge theorem
Source-payload status: complete
Exact checks: 12
Scientific payload SHA-256: f7f1619f5cf9b96d1c0093c8a1f8c0aff35360814eeaa17ab81bc686a50a3b61

46. Infinite super-BMS commutator syzygy family

What Ouroboros established: 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.

Source paper: Conformally Soft Fermions
Kernel: run_sabrina_super_bms_commutator_syzygy_family
Public sources: arXiv:2108.11422
Classification: infinite algebraic identity family
Source-payload status: complete
Exact checks: 9
Scientific payload SHA-256: 0c0559f924de94f512ba19fd2d867bfef93412978ddcb2cfd055a85cdcf94086

47. Holomorphic superrotation charge cancellation

What Ouroboros established: 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.

Source paper: Asymptotic Symmetries and Celestial CFT
Kernel: run_sabrina_superrotation_charge_cancellation
Public sources: arXiv:2005.08990
Classification: exact source reduction
Source-payload status: source_consistent_holomorphic_superrotation_charge_exactly_reduced
Exact checks: 12
Scientific payload SHA-256: 9081bdaa476d9558567b5363b9a85389cdaf84998fd93684f74822acd8c1ad47

48. Two-particle kernel variance theorem

What Ouroboros established: 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.

Source paper: Multiparticle Contributions to the Celestial OPE
Kernel: run_sabrina_two_particle_kernel_variance
Public sources: arXiv:2402.18798
Classification: sharp bound and counterexample family
Source-payload status: complete
Exact checks: 14
Scientific payload SHA-256: 7b1aa48423c6010da14e5d02a47c618b324310dbf80b043db8546fbcc3ee59b6

49. Weyl-double-copy shadow involution

What Ouroboros established: 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.

Source paper: Shifting Spin on the Celestial Sphere
Kernel: run_sabrina_weyl_double_copy_shadow_involution
Public sources: arXiv:2012.15694
Classification: involution and equivariance theorem
Source-payload status: complete
Exact checks: 17
Scientific payload SHA-256: f6243bc6dfdd05769cab60b02d4e23c53ef9c0119f2ac7a10d54eda023956fee