{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JPNCQ5HQ7AIS5M2I3OSNAHO53A","short_pith_number":"pith:JPNCQ5HQ","canonical_record":{"source":{"id":"1111.5298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-14T16:35:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"35c0dff0345ffba523865ab520543ba82c532733717a36dcdb6b5fb2e51a5a6d","abstract_canon_sha256":"817057a78a99ebc4b0bbc10226fc4e7dd69d077bac429dbab08176be12e3578e"},"schema_version":"1.0"},"canonical_sha256":"4bda2874f0f8112eb348dba4d01dddd83de01a8ea8d6e3081032ce41bf0caba2","source":{"kind":"arxiv","id":"1111.5298","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5298","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5298v1","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5298","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"pith_short_12","alias_value":"JPNCQ5HQ7AIS","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JPNCQ5HQ7AIS5M2I","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JPNCQ5HQ","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JPNCQ5HQ7AIS5M2I3OSNAHO53A","target":"record","payload":{"canonical_record":{"source":{"id":"1111.5298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-14T16:35:16Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"35c0dff0345ffba523865ab520543ba82c532733717a36dcdb6b5fb2e51a5a6d","abstract_canon_sha256":"817057a78a99ebc4b0bbc10226fc4e7dd69d077bac429dbab08176be12e3578e"},"schema_version":"1.0"},"canonical_sha256":"4bda2874f0f8112eb348dba4d01dddd83de01a8ea8d6e3081032ce41bf0caba2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:52.966595Z","signature_b64":"NK0pWF/s8sFXlOF/NTXwTVg8Fvm+TirQWtNnWVWcCUC36RaElxE43+NDdW756kkVT1txTG6zoXuzjEVUb8VsBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bda2874f0f8112eb348dba4d01dddd83de01a8ea8d6e3081032ce41bf0caba2","last_reissued_at":"2026-05-18T04:07:52.966199Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:52.966199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.5298","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":"2026-05-18T04:07:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FT2Mvlekx61An7msd0redDAu10YHEoHDmC8TY8PVdYtMKoUQ9ut7VqW/3HPPdf2yGNHUucVlMTFi4hiyiDqWAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:02:34.832495Z"},"content_sha256":"9ce5553f95f2a140682b8b0c8951d898c1952553ecccc77de4fe598ce49a303c","schema_version":"1.0","event_id":"sha256:9ce5553f95f2a140682b8b0c8951d898c1952553ecccc77de4fe598ce49a303c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JPNCQ5HQ7AIS5M2I3OSNAHO53A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Twist of fractional oscillations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Aleksander Stanislavsky","submitted_at":"2011-11-14T16:35:16Z","abstract_excerpt":"Using the method of the Laplace transform, we consider fractional oscillations. They are obtained by the time-clock randomization of ordinary harmonic vibrations. In contrast to sine and cosine, the functions describing the fractional oscillations exhibit a finite number of damped oscillations with an algebraic decay. Their fractional differential equation is derived."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5298","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":"2026-05-18T04:07:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ThDbEXkpQNTBEKizGcMkLTiPgcU/2vhzj+VWnBcCxsQbBWsHYNFy5WN0dnkW0ZqRe3UJMMbX6he8bcorwJ4ACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:02:34.833171Z"},"content_sha256":"185583f26dcf2bc3dddac0555ffc0c61238fa809ec108a7d8011c4920b5411c1","schema_version":"1.0","event_id":"sha256:185583f26dcf2bc3dddac0555ffc0c61238fa809ec108a7d8011c4920b5411c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPNCQ5HQ7AIS5M2I3OSNAHO53A/bundle.json","state_url":"https://pith.science/pith/JPNCQ5HQ7AIS5M2I3OSNAHO53A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPNCQ5HQ7AIS5M2I3OSNAHO53A/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":"2026-06-11T05:02:34Z","links":{"resolver":"https://pith.science/pith/JPNCQ5HQ7AIS5M2I3OSNAHO53A","bundle":"https://pith.science/pith/JPNCQ5HQ7AIS5M2I3OSNAHO53A/bundle.json","state":"https://pith.science/pith/JPNCQ5HQ7AIS5M2I3OSNAHO53A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPNCQ5HQ7AIS5M2I3OSNAHO53A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JPNCQ5HQ7AIS5M2I3OSNAHO53A","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":"817057a78a99ebc4b0bbc10226fc4e7dd69d077bac429dbab08176be12e3578e","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-14T16:35:16Z","title_canon_sha256":"35c0dff0345ffba523865ab520543ba82c532733717a36dcdb6b5fb2e51a5a6d"},"schema_version":"1.0","source":{"id":"1111.5298","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5298","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5298v1","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5298","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"pith_short_12","alias_value":"JPNCQ5HQ7AIS","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JPNCQ5HQ7AIS5M2I","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JPNCQ5HQ","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:185583f26dcf2bc3dddac0555ffc0c61238fa809ec108a7d8011c4920b5411c1","target":"graph","created_at":"2026-05-18T04:07:52Z","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":"Using the method of the Laplace transform, we consider fractional oscillations. They are obtained by the time-clock randomization of ordinary harmonic vibrations. In contrast to sine and cosine, the functions describing the fractional oscillations exhibit a finite number of damped oscillations with an algebraic decay. Their fractional differential equation is derived.","authors_text":"Aleksander Stanislavsky","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-14T16:35:16Z","title":"Twist of fractional oscillations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5298","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":"sha256:9ce5553f95f2a140682b8b0c8951d898c1952553ecccc77de4fe598ce49a303c","target":"record","created_at":"2026-05-18T04:07:52Z","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":"817057a78a99ebc4b0bbc10226fc4e7dd69d077bac429dbab08176be12e3578e","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-11-14T16:35:16Z","title_canon_sha256":"35c0dff0345ffba523865ab520543ba82c532733717a36dcdb6b5fb2e51a5a6d"},"schema_version":"1.0","source":{"id":"1111.5298","kind":"arxiv","version":1}},"canonical_sha256":"4bda2874f0f8112eb348dba4d01dddd83de01a8ea8d6e3081032ce41bf0caba2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bda2874f0f8112eb348dba4d01dddd83de01a8ea8d6e3081032ce41bf0caba2","first_computed_at":"2026-05-18T04:07:52.966199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:52.966199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NK0pWF/s8sFXlOF/NTXwTVg8Fvm+TirQWtNnWVWcCUC36RaElxE43+NDdW756kkVT1txTG6zoXuzjEVUb8VsBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:52.966595Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5298","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ce5553f95f2a140682b8b0c8951d898c1952553ecccc77de4fe598ce49a303c","sha256:185583f26dcf2bc3dddac0555ffc0c61238fa809ec108a7d8011c4920b5411c1"],"state_sha256":"ee4860d05663a4080140ce665c22cb13da35fa4ae3a9f2d67661ed67fcd7163b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y5a8YslB/HB7Qys4OqVKp1BEfE0ZOaQp4S1mIHUGHKWUggkYzOiXv7xvdJGOzwP8heckOA7xEHmhn6lrsg7OAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T05:02:34.837035Z","bundle_sha256":"2cba3311ef9cc38e61ca1e36211c28ba4651e5e661cd0959893954186f9ee78d"}}