{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FLH6XTNDS6KXCITRQQS3LVHRNC","short_pith_number":"pith:FLH6XTND","canonical_record":{"source":{"id":"1204.5782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-04-25T21:54:15Z","cross_cats_sorted":["astro-ph.HE","hep-th"],"title_canon_sha256":"d7a338381a3313af0b9e6be4935b8e03d38fcb08a4cacd3d144addd8a29895d9","abstract_canon_sha256":"3ac4926782ced55a1f87b133b2c470c03628635a44dba1f6631d4488d029f964"},"schema_version":"1.0"},"canonical_sha256":"2acfebcda397957122718425b5d4f168859f0817c2eb1a2a903c6541d2eeefad","source":{"kind":"arxiv","id":"1204.5782","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5782","created_at":"2026-05-18T01:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5782v1","created_at":"2026-05-18T01:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5782","created_at":"2026-05-18T01:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"FLH6XTNDS6KX","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FLH6XTNDS6KXCITR","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FLH6XTND","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FLH6XTNDS6KXCITRQQS3LVHRNC","target":"record","payload":{"canonical_record":{"source":{"id":"1204.5782","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-04-25T21:54:15Z","cross_cats_sorted":["astro-ph.HE","hep-th"],"title_canon_sha256":"d7a338381a3313af0b9e6be4935b8e03d38fcb08a4cacd3d144addd8a29895d9","abstract_canon_sha256":"3ac4926782ced55a1f87b133b2c470c03628635a44dba1f6631d4488d029f964"},"schema_version":"1.0"},"canonical_sha256":"2acfebcda397957122718425b5d4f168859f0817c2eb1a2a903c6541d2eeefad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:44.130828Z","signature_b64":"RvsEEhZaP2TkWQuL2GSLazIrOjVOORaX+bBFyhFaB6jEfBD38eUGoVG1fF6wdZ9VyKfJ7+YnaKROxhMcQx/PBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2acfebcda397957122718425b5d4f168859f0817c2eb1a2a903c6541d2eeefad","last_reissued_at":"2026-05-18T01:57:44.130304Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:44.130304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.5782","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":"2026-05-18T01:57:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pgxe5HsTG/oj8Gs9EnBMKgHDIuNrnhEzAOu3w/8fdto0sJmMCKLr4at/5LxBO3iDQEas7yJz9zEjz1LBqbEfDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T04:44:49.610244Z"},"content_sha256":"e918d25541e8f6b8bb977815394bba1e56691f59275fb4746e61e9d0e66a204c","schema_version":"1.0","event_id":"sha256:e918d25541e8f6b8bb977815394bba1e56691f59275fb4746e61e9d0e66a204c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FLH6XTNDS6KXCITRQQS3LVHRNC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On calculation of cross sections in Lorentz violating theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.HE","hep-th"],"primary_cat":"hep-ph","authors_text":"Grigory Rubtsov, Petr Satunin, Sergey Sibiryakov","submitted_at":"2012-04-25T21:54:15Z","abstract_excerpt":"We develop a systematic approach to the calculation of scattering cross sections in theories with violation of the Lorentz invariance taking into account the whole information about the theory Lagrangian. As an illustration we derive the Feynman rules and formulas for sums over polarizations in spinor electrodynamics with Lorentz violating operators of dimensions four and six. These rules are applied to compute the probabilities of several astrophysically relevant processes. We calculate the rates of photon decay and vacuum Cherenkov radiation along with the cross sections of electron-positron"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5782","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":""},"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":"2026-05-18T01:57:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ve1xDFbb/NOo1ntCI8M2jYJYJcimeH3J9FdiUYDNcyfzVXclo1y1Vwv+sEh25OUoVMZZ6NGrMj7i0upHMZLrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T04:44:49.610943Z"},"content_sha256":"1b635224257ff715d8192d9d560c5d2ddfbc630993dbb4c6f5f187e6d56f9158","schema_version":"1.0","event_id":"sha256:1b635224257ff715d8192d9d560c5d2ddfbc630993dbb4c6f5f187e6d56f9158"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FLH6XTNDS6KXCITRQQS3LVHRNC/bundle.json","state_url":"https://pith.science/pith/FLH6XTNDS6KXCITRQQS3LVHRNC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FLH6XTNDS6KXCITRQQS3LVHRNC/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":"2026-05-25T04:44:49Z","links":{"resolver":"https://pith.science/pith/FLH6XTNDS6KXCITRQQS3LVHRNC","bundle":"https://pith.science/pith/FLH6XTNDS6KXCITRQQS3LVHRNC/bundle.json","state":"https://pith.science/pith/FLH6XTNDS6KXCITRQQS3LVHRNC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FLH6XTNDS6KXCITRQQS3LVHRNC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FLH6XTNDS6KXCITRQQS3LVHRNC","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":"3ac4926782ced55a1f87b133b2c470c03628635a44dba1f6631d4488d029f964","cross_cats_sorted":["astro-ph.HE","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-04-25T21:54:15Z","title_canon_sha256":"d7a338381a3313af0b9e6be4935b8e03d38fcb08a4cacd3d144addd8a29895d9"},"schema_version":"1.0","source":{"id":"1204.5782","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5782","created_at":"2026-05-18T01:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5782v1","created_at":"2026-05-18T01:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5782","created_at":"2026-05-18T01:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"FLH6XTNDS6KX","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FLH6XTNDS6KXCITR","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FLH6XTND","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:1b635224257ff715d8192d9d560c5d2ddfbc630993dbb4c6f5f187e6d56f9158","target":"graph","created_at":"2026-05-18T01:57:44Z","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"},"paper":{"abstract_excerpt":"We develop a systematic approach to the calculation of scattering cross sections in theories with violation of the Lorentz invariance taking into account the whole information about the theory Lagrangian. As an illustration we derive the Feynman rules and formulas for sums over polarizations in spinor electrodynamics with Lorentz violating operators of dimensions four and six. These rules are applied to compute the probabilities of several astrophysically relevant processes. We calculate the rates of photon decay and vacuum Cherenkov radiation along with the cross sections of electron-positron","authors_text":"Grigory Rubtsov, Petr Satunin, Sergey Sibiryakov","cross_cats":["astro-ph.HE","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-04-25T21:54:15Z","title":"On calculation of cross sections in Lorentz violating theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5782","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:e918d25541e8f6b8bb977815394bba1e56691f59275fb4746e61e9d0e66a204c","target":"record","created_at":"2026-05-18T01:57:44Z","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":"3ac4926782ced55a1f87b133b2c470c03628635a44dba1f6631d4488d029f964","cross_cats_sorted":["astro-ph.HE","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2012-04-25T21:54:15Z","title_canon_sha256":"d7a338381a3313af0b9e6be4935b8e03d38fcb08a4cacd3d144addd8a29895d9"},"schema_version":"1.0","source":{"id":"1204.5782","kind":"arxiv","version":1}},"canonical_sha256":"2acfebcda397957122718425b5d4f168859f0817c2eb1a2a903c6541d2eeefad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2acfebcda397957122718425b5d4f168859f0817c2eb1a2a903c6541d2eeefad","first_computed_at":"2026-05-18T01:57:44.130304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:44.130304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RvsEEhZaP2TkWQuL2GSLazIrOjVOORaX+bBFyhFaB6jEfBD38eUGoVG1fF6wdZ9VyKfJ7+YnaKROxhMcQx/PBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:44.130828Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5782","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e918d25541e8f6b8bb977815394bba1e56691f59275fb4746e61e9d0e66a204c","sha256:1b635224257ff715d8192d9d560c5d2ddfbc630993dbb4c6f5f187e6d56f9158"],"state_sha256":"58815c14ba0622d356685c57657fe38b3b227cdd6318835a26fd940d6cf2f373"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CbIi/EfVZoprmTXjgS6XYCYJ8QMi6clErp87o/uIWYvTXF4DvOGBKx2BKhwx334PKAmWVf0oKjxDjwInri+XDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T04:44:49.614579Z","bundle_sha256":"36beb06e121a8715892a90fbe70d0aad5a3f80597b9a35acdc4c8373144b018e"}}