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"two_point_seed_present": true }, "paper": { "arxiv_id": "2512.02825", "title": "Memory Correlators and Ward Identities in the 'in-in' Formalism" }, "result_version": "sabrina_soft_charge_cumulant_hierarchy_v1", "source_evidence": { "archive_sha256": "8d7eb8d846a8d632cea6032ceac8553720b36bde75a3ea45bb3d81dfb8882905", "block_hashes": { "one_point_charge_identity": "64662757ac621c2f661120727526498dd71bd4144be372e97e327c33c8879a04", "two_point_connected_identity": "893ef92e9828d79ab61085be97b53559b157a296a414f8a7d14e2b1d14ea72bc" }, "checks": { "archive_hash_matches": true, "connected_two_point_present": true, "member_hash_matches": true, "one_point_identity_present": true, "source_blocks_match": true, "two_point_seed_present": true }, "member_sha256": "62c649b64370d8f1dc4489188ef1a4765af5d8f4b6dc3d8bd06e83670de508b3" }, "status": "complete", "theorem": { "deterministic_shift": "incoming hard-charge eigenvalues do not affect connected cumulants of order n>=2", "factorized_reduction": "if every mixed hard-outgoing/soft-incoming cumulant vanishes, kappa_n(S^+)=(-1)^n kappa_n(H^+)+kappa_n(S^-)", "full_hierarchy": "for n>=2, kappa(S_1^+,...,S_n^+) is the sum over A subset [n] of (-1)^|A| kappa(H_A^+,S_[n]\\A^-)", "obstruction": "Ward conservation alone gives the full mixed expansion; it does not remove mixed cumulants" } }, "scientific_payload_sha256": "8ed6c8d8dcc8eabf62402d94d7fdfcc3c000f15edec4ba8c1f437a6040cb2731" }