{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:F2JHG5PWI6ECW4PXSUT52YS5PK","short_pith_number":"pith:F2JHG5PW","canonical_record":{"source":{"id":"0805.0829","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2008-05-07T14:35:33Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"a92c27baa98170b0d014c9e68f2812cba236763dab74eb4aa1083168a9d57e6c","abstract_canon_sha256":"71226245fd2b5906e47a96264d01f25c8169087c965959ba06461e4ac7b14318"},"schema_version":"1.0"},"canonical_sha256":"2e927375f647882b71f79527dd625d7a9059371d8849db6f8f18d0c1a921d72c","source":{"kind":"arxiv","id":"0805.0829","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.0829","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"arxiv_version","alias_value":"0805.0829v4","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.0829","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"pith_short_12","alias_value":"F2JHG5PWI6EC","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"F2JHG5PWI6ECW4PX","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"F2JHG5PW","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:F2JHG5PWI6ECW4PXSUT52YS5PK","target":"record","payload":{"canonical_record":{"source":{"id":"0805.0829","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2008-05-07T14:35:33Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"a92c27baa98170b0d014c9e68f2812cba236763dab74eb4aa1083168a9d57e6c","abstract_canon_sha256":"71226245fd2b5906e47a96264d01f25c8169087c965959ba06461e4ac7b14318"},"schema_version":"1.0"},"canonical_sha256":"2e927375f647882b71f79527dd625d7a9059371d8849db6f8f18d0c1a921d72c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:22.315182Z","signature_b64":"/hVFhNqiOk1U3NSSBlDB+z/ns/fzt14ChLfPmQNkL2BqGt0LBJBCINGfeCSy6YyzCcAUvcd+tAfcMkG/AM23Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e927375f647882b71f79527dd625d7a9059371d8849db6f8f18d0c1a921d72c","last_reissued_at":"2026-05-18T04:32:22.314444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:22.314444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0805.0829","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:32:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aegkyi4D49sXHv1LC9DsauOIJwNnOamTIuDFyxgZ0pd63LMCbZz0pUYeNIfPVqjfH56Go+oXZCxtGWn57ETqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:35:48.422516Z"},"content_sha256":"ce65e972979103af9c30df27263240f97685d6361bf8a2991bdee4609448e944","schema_version":"1.0","event_id":"sha256:ce65e972979103af9c30df27263240f97685d6361bf8a2991bdee4609448e944"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:F2JHG5PWI6ECW4PXSUT52YS5PK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global Fractional Analytic Perturbation Theory in QCD with Selected Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Alexander P. Bakulev","submitted_at":"2008-05-07T14:35:33Z","abstract_excerpt":"We give the generalization of Fractional Analytic Perturbation Theory (FAPT) for QCD observables, recently developed both for the Euclidean and Minkowski regions of squared momentum transfer q^2, which takes into account heavy-quark thresholds. The original analytic approach to QCD, initiated by Jones, Solovtsov and Shirkov, is shortly summarized. We also shortly consider the basic aspects of FAPT and then concentrate on the accounting for the heavy-quark thresholds problem and the construction of global version of FAPT. We discuss what one should use as an analytic coupling in the timelike re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.0829","kind":"arxiv","version":4},"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":"2026-05-18T04:32:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rVAqWgOIjgc7fS1jxkA9qksIxBaEvGcw3KTXw6DX9vt1FL64n3zKKifaorc1Fpsg6F14J80z/euv3tobhUEpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:35:48.423230Z"},"content_sha256":"2d813f58f560115068d5447d6997f8fc0b934ca10de010265f8296c0684c9aa6","schema_version":"1.0","event_id":"sha256:2d813f58f560115068d5447d6997f8fc0b934ca10de010265f8296c0684c9aa6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F2JHG5PWI6ECW4PXSUT52YS5PK/bundle.json","state_url":"https://pith.science/pith/F2JHG5PWI6ECW4PXSUT52YS5PK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F2JHG5PWI6ECW4PXSUT52YS5PK/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":"2026-06-10T13:35:48Z","links":{"resolver":"https://pith.science/pith/F2JHG5PWI6ECW4PXSUT52YS5PK","bundle":"https://pith.science/pith/F2JHG5PWI6ECW4PXSUT52YS5PK/bundle.json","state":"https://pith.science/pith/F2JHG5PWI6ECW4PXSUT52YS5PK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F2JHG5PWI6ECW4PXSUT52YS5PK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:F2JHG5PWI6ECW4PXSUT52YS5PK","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":"71226245fd2b5906e47a96264d01f25c8169087c965959ba06461e4ac7b14318","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2008-05-07T14:35:33Z","title_canon_sha256":"a92c27baa98170b0d014c9e68f2812cba236763dab74eb4aa1083168a9d57e6c"},"schema_version":"1.0","source":{"id":"0805.0829","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.0829","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"arxiv_version","alias_value":"0805.0829v4","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.0829","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"pith_short_12","alias_value":"F2JHG5PWI6EC","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"F2JHG5PWI6ECW4PX","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"F2JHG5PW","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:2d813f58f560115068d5447d6997f8fc0b934ca10de010265f8296c0684c9aa6","target":"graph","created_at":"2026-05-18T04:32:22Z","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 give the generalization of Fractional Analytic Perturbation Theory (FAPT) for QCD observables, recently developed both for the Euclidean and Minkowski regions of squared momentum transfer q^2, which takes into account heavy-quark thresholds. The original analytic approach to QCD, initiated by Jones, Solovtsov and Shirkov, is shortly summarized. We also shortly consider the basic aspects of FAPT and then concentrate on the accounting for the heavy-quark thresholds problem and the construction of global version of FAPT. We discuss what one should use as an analytic coupling in the timelike re","authors_text":"Alexander P. Bakulev","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2008-05-07T14:35:33Z","title":"Global Fractional Analytic Perturbation Theory in QCD with Selected Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.0829","kind":"arxiv","version":4},"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:ce65e972979103af9c30df27263240f97685d6361bf8a2991bdee4609448e944","target":"record","created_at":"2026-05-18T04:32:22Z","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":"71226245fd2b5906e47a96264d01f25c8169087c965959ba06461e4ac7b14318","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2008-05-07T14:35:33Z","title_canon_sha256":"a92c27baa98170b0d014c9e68f2812cba236763dab74eb4aa1083168a9d57e6c"},"schema_version":"1.0","source":{"id":"0805.0829","kind":"arxiv","version":4}},"canonical_sha256":"2e927375f647882b71f79527dd625d7a9059371d8849db6f8f18d0c1a921d72c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e927375f647882b71f79527dd625d7a9059371d8849db6f8f18d0c1a921d72c","first_computed_at":"2026-05-18T04:32:22.314444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:22.314444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/hVFhNqiOk1U3NSSBlDB+z/ns/fzt14ChLfPmQNkL2BqGt0LBJBCINGfeCSy6YyzCcAUvcd+tAfcMkG/AM23Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:22.315182Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.0829","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce65e972979103af9c30df27263240f97685d6361bf8a2991bdee4609448e944","sha256:2d813f58f560115068d5447d6997f8fc0b934ca10de010265f8296c0684c9aa6"],"state_sha256":"48f681a8d9b564042dc4e2c69a98a15b7b64e90412b0ff55ce2a26c042ada7c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"drSRVvubWSvvBZkD+84XW8mwtgGScjAggCnFTnCR2EH6lqOL26tiXTyeZOx/tOxUfP8zqM9vNJdQ6OVkeXA4BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T13:35:48.427438Z","bundle_sha256":"ec0ce7a368a3d2485ab3ff68d7d871f2e7d8a2f2590b39f3a419f0eab0bc65b4"}}