{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:QCNKBKMTZSW4NGYIRDUMVKWGIK","short_pith_number":"pith:QCNKBKMT","canonical_record":{"source":{"id":"2411.07222","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-11-11T18:43:33Z","cross_cats_sorted":[],"title_canon_sha256":"51ff208d591305509a5323b67a5ca0d4aff8a9bd6229b819828ecfd0bc5ba727","abstract_canon_sha256":"ecee47ca8dd522314bdb8e0f093a0dcd93af4f6b7ad5bc725ae4536eccefe516"},"schema_version":"1.0"},"canonical_sha256":"809aa0a993ccadc69b0888e8caaac642bdf1b03f664ad110be6ef3a65bc4a5a8","source":{"kind":"arxiv","id":"2411.07222","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.07222","created_at":"2026-07-05T09:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"2411.07222v1","created_at":"2026-07-05T09:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.07222","created_at":"2026-07-05T09:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"QCNKBKMTZSW4","created_at":"2026-07-05T09:33:58Z"},{"alias_kind":"pith_short_16","alias_value":"QCNKBKMTZSW4NGYI","created_at":"2026-07-05T09:33:58Z"},{"alias_kind":"pith_short_8","alias_value":"QCNKBKMT","created_at":"2026-07-05T09:33:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:QCNKBKMTZSW4NGYIRDUMVKWGIK","target":"record","payload":{"canonical_record":{"source":{"id":"2411.07222","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-11-11T18:43:33Z","cross_cats_sorted":[],"title_canon_sha256":"51ff208d591305509a5323b67a5ca0d4aff8a9bd6229b819828ecfd0bc5ba727","abstract_canon_sha256":"ecee47ca8dd522314bdb8e0f093a0dcd93af4f6b7ad5bc725ae4536eccefe516"},"schema_version":"1.0"},"canonical_sha256":"809aa0a993ccadc69b0888e8caaac642bdf1b03f664ad110be6ef3a65bc4a5a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:33:58.945965Z","signature_b64":"e3Jx2kcA2O5R7s4Z9mFHyZrI41l7hhZ+MN+684//KC3dFihWWJVvavr6IsRnvJH+X9v21Qx/Rk8xUGI3hE4MCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"809aa0a993ccadc69b0888e8caaac642bdf1b03f664ad110be6ef3a65bc4a5a8","last_reissued_at":"2026-07-05T09:33:58.945491Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:33:58.945491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.07222","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":"2026-07-05T09:33:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YXJMVoOht3Z+DH5W/OaRx2Dky1OeWbHz9+1IOa2tp+jNT56zeN/1FPwuVHzbu0iXxtXujPkEeYffUyeIT+NjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T23:07:40.566161Z"},"content_sha256":"1a6f2b4f29adf44c01bbbafed522dcc96be952166c4be9d8beadaee89f7bcd19","schema_version":"1.0","event_id":"sha256:1a6f2b4f29adf44c01bbbafed522dcc96be952166c4be9d8beadaee89f7bcd19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:QCNKBKMTZSW4NGYIRDUMVKWGIK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gravitational production of massive vectors non-minimally coupled to gravity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Anna Socha, Bohdan Grzadkowski","submitted_at":"2024-11-11T18:43:33Z","abstract_excerpt":"A quantum theory of massive Abelian vector bosons with non-minimal couplings to gravity has been studied within an evolving, isotropic, and homogeneous gravitational background. The vectors may play a role of dark matter if stabilizing $\\mathbb{Z}_2$ symmetry is imposed. In order to construct a gauge invariant theory of massive vectors that couple to the Ricci scalar and Ricci tensor, a generalization of the Stuckelberg mechanism has been invoked. Constraints that ensure consistency of the model had been formulated and corresponding restrictions upon the space of non-minimal couplings have bee"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.07222","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/2411.07222/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":"2026-07-05T09:33:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SRM9NHVpu9yPiOyXff6xIJw66CCetROtn4HaORWprL6/YfZWRyHMobi6zG6gU9ndsn/CZ+Poqc51Nn4khLjeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T23:07:40.566760Z"},"content_sha256":"a439ff3fbe259fe02c81ca52b6adf8814e692159891c53e3687747812155476c","schema_version":"1.0","event_id":"sha256:a439ff3fbe259fe02c81ca52b6adf8814e692159891c53e3687747812155476c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QCNKBKMTZSW4NGYIRDUMVKWGIK/bundle.json","state_url":"https://pith.science/pith/QCNKBKMTZSW4NGYIRDUMVKWGIK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QCNKBKMTZSW4NGYIRDUMVKWGIK/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":"2026-08-16T23:07:40Z","links":{"resolver":"https://pith.science/pith/QCNKBKMTZSW4NGYIRDUMVKWGIK","bundle":"https://pith.science/pith/QCNKBKMTZSW4NGYIRDUMVKWGIK/bundle.json","state":"https://pith.science/pith/QCNKBKMTZSW4NGYIRDUMVKWGIK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QCNKBKMTZSW4NGYIRDUMVKWGIK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QCNKBKMTZSW4NGYIRDUMVKWGIK","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":"ecee47ca8dd522314bdb8e0f093a0dcd93af4f6b7ad5bc725ae4536eccefe516","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-11-11T18:43:33Z","title_canon_sha256":"51ff208d591305509a5323b67a5ca0d4aff8a9bd6229b819828ecfd0bc5ba727"},"schema_version":"1.0","source":{"id":"2411.07222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.07222","created_at":"2026-07-05T09:33:58Z"},{"alias_kind":"arxiv_version","alias_value":"2411.07222v1","created_at":"2026-07-05T09:33:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.07222","created_at":"2026-07-05T09:33:58Z"},{"alias_kind":"pith_short_12","alias_value":"QCNKBKMTZSW4","created_at":"2026-07-05T09:33:58Z"},{"alias_kind":"pith_short_16","alias_value":"QCNKBKMTZSW4NGYI","created_at":"2026-07-05T09:33:58Z"},{"alias_kind":"pith_short_8","alias_value":"QCNKBKMT","created_at":"2026-07-05T09:33:58Z"}],"graph_snapshots":[{"event_id":"sha256:a439ff3fbe259fe02c81ca52b6adf8814e692159891c53e3687747812155476c","target":"graph","created_at":"2026-07-05T09:33:58Z","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/2411.07222/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A quantum theory of massive Abelian vector bosons with non-minimal couplings to gravity has been studied within an evolving, isotropic, and homogeneous gravitational background. The vectors may play a role of dark matter if stabilizing $\\mathbb{Z}_2$ symmetry is imposed. In order to construct a gauge invariant theory of massive vectors that couple to the Ricci scalar and Ricci tensor, a generalization of the Stuckelberg mechanism has been invoked. Constraints that ensure consistency of the model had been formulated and corresponding restrictions upon the space of non-minimal couplings have bee","authors_text":"Anna Socha, Bohdan Grzadkowski","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-11-11T18:43:33Z","title":"Gravitational production of massive vectors non-minimally coupled to gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.07222","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":"sha256:1a6f2b4f29adf44c01bbbafed522dcc96be952166c4be9d8beadaee89f7bcd19","target":"record","created_at":"2026-07-05T09:33:58Z","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":"ecee47ca8dd522314bdb8e0f093a0dcd93af4f6b7ad5bc725ae4536eccefe516","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-ph","submitted_at":"2024-11-11T18:43:33Z","title_canon_sha256":"51ff208d591305509a5323b67a5ca0d4aff8a9bd6229b819828ecfd0bc5ba727"},"schema_version":"1.0","source":{"id":"2411.07222","kind":"arxiv","version":1}},"canonical_sha256":"809aa0a993ccadc69b0888e8caaac642bdf1b03f664ad110be6ef3a65bc4a5a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"809aa0a993ccadc69b0888e8caaac642bdf1b03f664ad110be6ef3a65bc4a5a8","first_computed_at":"2026-07-05T09:33:58.945491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:33:58.945491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e3Jx2kcA2O5R7s4Z9mFHyZrI41l7hhZ+MN+684//KC3dFihWWJVvavr6IsRnvJH+X9v21Qx/Rk8xUGI3hE4MCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:33:58.945965Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.07222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a6f2b4f29adf44c01bbbafed522dcc96be952166c4be9d8beadaee89f7bcd19","sha256:a439ff3fbe259fe02c81ca52b6adf8814e692159891c53e3687747812155476c"],"state_sha256":"16fc7a84f56a7978d06566bdf11c8c454aa806d582a23ce9e47ebab860cd7d30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KeGLqOLxuOqPdkKzjqieD8lvsje1DWtrEQ8UOJIZ3EK3WecTXVrCkLHAaxoJQJaJjLrFbQJAIqvdYaTnYZXWCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T23:07:40.570714Z","bundle_sha256":"282baa04d16b729cfc2eb9abaabd2ca0b00c6e858f662e035701d88bfe1b1676"}}