{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EYB6C47TLGWZUC3KLUDKQIVVCO","short_pith_number":"pith:EYB6C47T","canonical_record":{"source":{"id":"2507.12537","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2025-07-16T18:00:09Z","cross_cats_sorted":[],"title_canon_sha256":"f781b379e8055c57eaa9c568b64ce9c785baf9ffbe952dee0108d87384dc3194","abstract_canon_sha256":"95e2fe8853e73f997d82141f66afb63a5c04df236679aa305a00df2ef15b7c57"},"schema_version":"1.0"},"canonical_sha256":"2603e173f359ad9a0b6a5d06a822b513b02b92bdc47379a598b1d40e0838fa80","source":{"kind":"arxiv","id":"2507.12537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.12537","created_at":"2026-07-05T11:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"2507.12537v1","created_at":"2026-07-05T11:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12537","created_at":"2026-07-05T11:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"EYB6C47TLGWZ","created_at":"2026-07-05T11:38:34Z"},{"alias_kind":"pith_short_16","alias_value":"EYB6C47TLGWZUC3K","created_at":"2026-07-05T11:38:34Z"},{"alias_kind":"pith_short_8","alias_value":"EYB6C47T","created_at":"2026-07-05T11:38:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EYB6C47TLGWZUC3KLUDKQIVVCO","target":"record","payload":{"canonical_record":{"source":{"id":"2507.12537","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2025-07-16T18:00:09Z","cross_cats_sorted":[],"title_canon_sha256":"f781b379e8055c57eaa9c568b64ce9c785baf9ffbe952dee0108d87384dc3194","abstract_canon_sha256":"95e2fe8853e73f997d82141f66afb63a5c04df236679aa305a00df2ef15b7c57"},"schema_version":"1.0"},"canonical_sha256":"2603e173f359ad9a0b6a5d06a822b513b02b92bdc47379a598b1d40e0838fa80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:34.145645Z","signature_b64":"YXWgIA+EZNemYNNh+Gy9O97N1FFVEIfg52Sgv/hNQ6tH4wOoTVikueUwOLbdkidHTmn77Ed+4EMa7TAwR4jhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2603e173f359ad9a0b6a5d06a822b513b02b92bdc47379a598b1d40e0838fa80","last_reissued_at":"2026-07-05T11:38:34.145145Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:34.145145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.12537","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LMkStVdrYk5/HWjpG52zqu+bZXbgdA7fKLccBxrN+I4dAoWK2OjEMbUJwjxojhDJ21F6h9km0s/JPKkqIud6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T09:31:53.756593Z"},"content_sha256":"a105a82b381c9d45ac39cc074d859d4791888d6490cda7fd19999c0afc8ba97b","schema_version":"1.0","event_id":"sha256:a105a82b381c9d45ac39cc074d859d4791888d6490cda7fd19999c0afc8ba97b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EYB6C47TLGWZUC3KLUDKQIVVCO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase-space sectors for ordered momentum mappings in local subtraction up to N$^3$LO","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Matteo Marcoli, Xuan Chen","submitted_at":"2025-07-16T18:00:09Z","abstract_excerpt":"Ordered momentum mappings present optimal convergence in soft and collinear configurations and are particularly suitable for the numerical implementation of local subtraction schemes. However, ordered mappings cannot be directly applied in the presence of multiple unordered emissions, which typically appear beyond the leading-colour approximation. A possible solution consists in separating individual singularities at the level of local counterterms by means of partial fractioning, which can become cumbersome at higher orders and introduce large cancellations in intermediate steps of the calcul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12537","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.12537/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:38:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ygAiqss4V8WfNFj9GsQQkoARu+Q4b/50m4shWHDQduQr8GJyXQHhKKHG4cbIpNY9/z34NWxNJ2UfF+7QnkL/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T09:31:53.757390Z"},"content_sha256":"f97589fbab8646a5dde81d5178f02145129caab5b5fd787d5f4906631ca4bb9d","schema_version":"1.0","event_id":"sha256:f97589fbab8646a5dde81d5178f02145129caab5b5fd787d5f4906631ca4bb9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EYB6C47TLGWZUC3KLUDKQIVVCO/bundle.json","state_url":"https://pith.science/pith/EYB6C47TLGWZUC3KLUDKQIVVCO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EYB6C47TLGWZUC3KLUDKQIVVCO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-07T09:31:53Z","links":{"resolver":"https://pith.science/pith/EYB6C47TLGWZUC3KLUDKQIVVCO","bundle":"https://pith.science/pith/EYB6C47TLGWZUC3KLUDKQIVVCO/bundle.json","state":"https://pith.science/pith/EYB6C47TLGWZUC3KLUDKQIVVCO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EYB6C47TLGWZUC3KLUDKQIVVCO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EYB6C47TLGWZUC3KLUDKQIVVCO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"95e2fe8853e73f997d82141f66afb63a5c04df236679aa305a00df2ef15b7c57","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2025-07-16T18:00:09Z","title_canon_sha256":"f781b379e8055c57eaa9c568b64ce9c785baf9ffbe952dee0108d87384dc3194"},"schema_version":"1.0","source":{"id":"2507.12537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.12537","created_at":"2026-07-05T11:38:34Z"},{"alias_kind":"arxiv_version","alias_value":"2507.12537v1","created_at":"2026-07-05T11:38:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12537","created_at":"2026-07-05T11:38:34Z"},{"alias_kind":"pith_short_12","alias_value":"EYB6C47TLGWZ","created_at":"2026-07-05T11:38:34Z"},{"alias_kind":"pith_short_16","alias_value":"EYB6C47TLGWZUC3K","created_at":"2026-07-05T11:38:34Z"},{"alias_kind":"pith_short_8","alias_value":"EYB6C47T","created_at":"2026-07-05T11:38:34Z"}],"graph_snapshots":[{"event_id":"sha256:f97589fbab8646a5dde81d5178f02145129caab5b5fd787d5f4906631ca4bb9d","target":"graph","created_at":"2026-07-05T11:38:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.12537/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ordered momentum mappings present optimal convergence in soft and collinear configurations and are particularly suitable for the numerical implementation of local subtraction schemes. However, ordered mappings cannot be directly applied in the presence of multiple unordered emissions, which typically appear beyond the leading-colour approximation. A possible solution consists in separating individual singularities at the level of local counterterms by means of partial fractioning, which can become cumbersome at higher orders and introduce large cancellations in intermediate steps of the calcul","authors_text":"Matteo Marcoli, Xuan Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2025-07-16T18:00:09Z","title":"Phase-space sectors for ordered momentum mappings in local subtraction up to N$^3$LO"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12537","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a105a82b381c9d45ac39cc074d859d4791888d6490cda7fd19999c0afc8ba97b","target":"record","created_at":"2026-07-05T11:38:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"95e2fe8853e73f997d82141f66afb63a5c04df236679aa305a00df2ef15b7c57","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2025-07-16T18:00:09Z","title_canon_sha256":"f781b379e8055c57eaa9c568b64ce9c785baf9ffbe952dee0108d87384dc3194"},"schema_version":"1.0","source":{"id":"2507.12537","kind":"arxiv","version":1}},"canonical_sha256":"2603e173f359ad9a0b6a5d06a822b513b02b92bdc47379a598b1d40e0838fa80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2603e173f359ad9a0b6a5d06a822b513b02b92bdc47379a598b1d40e0838fa80","first_computed_at":"2026-07-05T11:38:34.145145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:34.145145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YXWgIA+EZNemYNNh+Gy9O97N1FFVEIfg52Sgv/hNQ6tH4wOoTVikueUwOLbdkidHTmn77Ed+4EMa7TAwR4jhBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:34.145645Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.12537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a105a82b381c9d45ac39cc074d859d4791888d6490cda7fd19999c0afc8ba97b","sha256:f97589fbab8646a5dde81d5178f02145129caab5b5fd787d5f4906631ca4bb9d"],"state_sha256":"4e35e4fa5b3214ab315f00e33c561bb9d7367c89120ac9cfcbc822a5699ff588"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xC+NJsb1+1blKBRqHImPUK9VawEb8/RuVMnyxmfd3PrEf/P8+0UHITIOyyuHXtZKnNKbjlTrbMRBqC6XO9iAAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T09:31:53.764223Z","bundle_sha256":"6f2c5a65b949a2f6c5733ab1d9fbef659d7b354b7e6b1f1b6011623b451b74fd"}}