RESULT_ATLAS.md

# Verified Result Atlas

Status: **PAUSED research**. Each entry is independently recomputable by the included kernels.

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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/2211.14287), [arXiv:2307.16801](https://arxiv.org/abs/2307.16801), [arXiv:2607.28718](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/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](https://arxiv.org/abs/2012.15694)
- Classification: **involution and equivariance theorem**
- Source-payload status: `complete`
- Exact checks: 17
- Scientific payload SHA-256: `f6243bc6dfdd05769cab60b02d4e23c53ef9c0119f2ac7a10d54eda023956fee`