{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:EJVNWFWT65RXIF6ZDWQ5NJXWAC","short_pith_number":"pith:EJVNWFWT","canonical_record":{"source":{"id":"2408.05137","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-08-09T15:47:44Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"794366e88892abc6bac1ebdc0e21f18a84d4b7a0a65ecd5382a6e59d6542d00b","abstract_canon_sha256":"fcb23796cbd60a392017aed6d97b96719d19ec037a0bb771c24d26e6376f37c2"},"schema_version":"1.0"},"canonical_sha256":"226adb16d3f7637417d91da1d6a6f600acac869650bbed48f0f3890f38ed7c36","source":{"kind":"arxiv","id":"2408.05137","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.05137","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"arxiv_version","alias_value":"2408.05137v2","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.05137","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"pith_short_12","alias_value":"EJVNWFWT65RX","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"pith_short_16","alias_value":"EJVNWFWT65RXIF6Z","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"pith_short_8","alias_value":"EJVNWFWT","created_at":"2026-07-05T10:54:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:EJVNWFWT65RXIF6ZDWQ5NJXWAC","target":"record","payload":{"canonical_record":{"source":{"id":"2408.05137","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-08-09T15:47:44Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"794366e88892abc6bac1ebdc0e21f18a84d4b7a0a65ecd5382a6e59d6542d00b","abstract_canon_sha256":"fcb23796cbd60a392017aed6d97b96719d19ec037a0bb771c24d26e6376f37c2"},"schema_version":"1.0"},"canonical_sha256":"226adb16d3f7637417d91da1d6a6f600acac869650bbed48f0f3890f38ed7c36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:54:35.299860Z","signature_b64":"rJeMhQYwJccDUBmQhwJKqvMxNgVcNdBngbLHTiB8PWGjCqNTNHAfX3YR9DJjrix8EPArrOYv6zitV4bjdgWrDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"226adb16d3f7637417d91da1d6a6f600acac869650bbed48f0f3890f38ed7c36","last_reissued_at":"2026-07-05T10:54:35.299455Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:54:35.299455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.05137","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:54:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pHs2VdkwU4vdHF6zd0G8G5H7dQMcDWoIRhGbrlZOMl5sImcSlSH4ZEQsK/OeA/X1Jf6Ej+OPw47aghgiBsb5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T20:03:59.863613Z"},"content_sha256":"f884b7632ef597fe994fa7394cd697088c246db28d3e961edba649a12ebfae7e","schema_version":"1.0","event_id":"sha256:f884b7632ef597fe994fa7394cd697088c246db28d3e961edba649a12ebfae7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:EJVNWFWT65RXIF6ZDWQ5NJXWAC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tensor Reduction for Feynman Integrals with Lorentz and Spinor Indices","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Anthony Kennedy, Franz Herzog, Jae Goode, Jos Vermaseren, Sam Teale","submitted_at":"2024-08-09T15:47:44Z","abstract_excerpt":"We present an efficient graphical approach to construct projectors for the tensor reduction of multi-loop Feynman integrals with both Lorentz and spinor indices in $D$ dimensions. An ansatz for the projectors is constructed making use of its symmetry properties via an orbit partition formula. The graphical approach allows to identify and enumerate the orbits in each case. For the case without spinor indices we find a 1 to 1 correspondence between orbits and integer partitions describing the cycle structure of certain bi-chord graphs. This leads to compact combinatorial formulae for the project"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.05137","kind":"arxiv","version":2},"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/2408.05137/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":"2026-07-05T10:54:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xu5xOGf9pvPyIp4aN9CCv1Dp2IrLnNMhv9pKuAulCSH4ulC59lU6n2s7uB0TJTFNodozOdri/Qrif4nL1BrsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T20:03:59.864098Z"},"content_sha256":"2dd9e301cd13a462f22c22c2aa2a88f101885fdf6c3be355172fbd915caf0361","schema_version":"1.0","event_id":"sha256:2dd9e301cd13a462f22c22c2aa2a88f101885fdf6c3be355172fbd915caf0361"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EJVNWFWT65RXIF6ZDWQ5NJXWAC/bundle.json","state_url":"https://pith.science/pith/EJVNWFWT65RXIF6ZDWQ5NJXWAC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EJVNWFWT65RXIF6ZDWQ5NJXWAC/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":"2026-08-06T20:03:59Z","links":{"resolver":"https://pith.science/pith/EJVNWFWT65RXIF6ZDWQ5NJXWAC","bundle":"https://pith.science/pith/EJVNWFWT65RXIF6ZDWQ5NJXWAC/bundle.json","state":"https://pith.science/pith/EJVNWFWT65RXIF6ZDWQ5NJXWAC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EJVNWFWT65RXIF6ZDWQ5NJXWAC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:EJVNWFWT65RXIF6ZDWQ5NJXWAC","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":"fcb23796cbd60a392017aed6d97b96719d19ec037a0bb771c24d26e6376f37c2","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-08-09T15:47:44Z","title_canon_sha256":"794366e88892abc6bac1ebdc0e21f18a84d4b7a0a65ecd5382a6e59d6542d00b"},"schema_version":"1.0","source":{"id":"2408.05137","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.05137","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"arxiv_version","alias_value":"2408.05137v2","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.05137","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"pith_short_12","alias_value":"EJVNWFWT65RX","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"pith_short_16","alias_value":"EJVNWFWT65RXIF6Z","created_at":"2026-07-05T10:54:35Z"},{"alias_kind":"pith_short_8","alias_value":"EJVNWFWT","created_at":"2026-07-05T10:54:35Z"}],"graph_snapshots":[{"event_id":"sha256:2dd9e301cd13a462f22c22c2aa2a88f101885fdf6c3be355172fbd915caf0361","target":"graph","created_at":"2026-07-05T10:54:35Z","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/2408.05137/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present an efficient graphical approach to construct projectors for the tensor reduction of multi-loop Feynman integrals with both Lorentz and spinor indices in $D$ dimensions. An ansatz for the projectors is constructed making use of its symmetry properties via an orbit partition formula. The graphical approach allows to identify and enumerate the orbits in each case. For the case without spinor indices we find a 1 to 1 correspondence between orbits and integer partitions describing the cycle structure of certain bi-chord graphs. This leads to compact combinatorial formulae for the project","authors_text":"Anthony Kennedy, Franz Herzog, Jae Goode, Jos Vermaseren, Sam Teale","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-08-09T15:47:44Z","title":"Tensor Reduction for Feynman Integrals with Lorentz and Spinor Indices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.05137","kind":"arxiv","version":2},"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:f884b7632ef597fe994fa7394cd697088c246db28d3e961edba649a12ebfae7e","target":"record","created_at":"2026-07-05T10:54:35Z","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":"fcb23796cbd60a392017aed6d97b96719d19ec037a0bb771c24d26e6376f37c2","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-08-09T15:47:44Z","title_canon_sha256":"794366e88892abc6bac1ebdc0e21f18a84d4b7a0a65ecd5382a6e59d6542d00b"},"schema_version":"1.0","source":{"id":"2408.05137","kind":"arxiv","version":2}},"canonical_sha256":"226adb16d3f7637417d91da1d6a6f600acac869650bbed48f0f3890f38ed7c36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"226adb16d3f7637417d91da1d6a6f600acac869650bbed48f0f3890f38ed7c36","first_computed_at":"2026-07-05T10:54:35.299455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:54:35.299455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rJeMhQYwJccDUBmQhwJKqvMxNgVcNdBngbLHTiB8PWGjCqNTNHAfX3YR9DJjrix8EPArrOYv6zitV4bjdgWrDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:54:35.299860Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.05137","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f884b7632ef597fe994fa7394cd697088c246db28d3e961edba649a12ebfae7e","sha256:2dd9e301cd13a462f22c22c2aa2a88f101885fdf6c3be355172fbd915caf0361"],"state_sha256":"d85251e16428c3f58b19fb5a371376ac8a88c715641f60d38451cac2a7d20414"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0iOQ2SxoW68Jrz3vhA5oW3VIc/13eJaoV850wgMfZrCv//vC+mqW2oWKVv73q7NKYES6sdGZJFVfmj9GQ77VCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T20:03:59.868565Z","bundle_sha256":"543ef748c86a7e013a98209309c45fdf593818e25b4e984e4f42a679b2f3191f"}}