{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:Z7WUAT2ULZBPHP2LRVSOXOSU3U","short_pith_number":"pith:Z7WUAT2U","schema_version":"1.0","canonical_sha256":"cfed404f545e42f3bf4b8d64ebba54dd23c1d77616c1ed8776e6c9b5952d192f","source":{"kind":"arxiv","id":"1012.2002","version":3},"attestation_state":"computed","paper":{"title":"A new periodicity concept for time scales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Murat Ad{\\i}var","submitted_at":"2010-12-09T13:46:39Z","abstract_excerpt":"By means of the shift operators we introduce a new periodicity concept on time scales. This new approach will enable researchers to investigate periodicity notion on a large class of time scales whose members may not satisfy the condition: \"there exists a $P>0$ such that $t\\pm P\\in\\mathbb{T}$ for all $t\\in\\mathbb{T}$\", unlike the existing literature. Therefore, the results of this paper open an avenue for the investigation of periodic solutions of $q$-difference equations."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.2002","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-12-09T13:46:39Z","cross_cats_sorted":[],"title_canon_sha256":"f8f228dfeb1e91d805cc927009b0aed87c26c85511e47623456b347eaff796aa","abstract_canon_sha256":"105c11d0c5536c4f16698efec7ba9bc14fb034c9d8e00eeda827456473ae27a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:16.542245Z","signature_b64":"ry55HSqDYU8oQSnME1C4so2dpLu1H4uEViBk/11IAzA+SRfekivRbnJKtCspL3dulRsNNazQWXcd63HqVgOBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfed404f545e42f3bf4b8d64ebba54dd23c1d77616c1ed8776e6c9b5952d192f","last_reissued_at":"2026-05-18T04:05:16.541698Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:16.541698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new periodicity concept for time scales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Murat Ad{\\i}var","submitted_at":"2010-12-09T13:46:39Z","abstract_excerpt":"By means of the shift operators we introduce a new periodicity concept on time scales. This new approach will enable researchers to investigate periodicity notion on a large class of time scales whose members may not satisfy the condition: \"there exists a $P>0$ such that $t\\pm P\\in\\mathbb{T}$ for all $t\\in\\mathbb{T}$\", unlike the existing literature. Therefore, the results of this paper open an avenue for the investigation of periodic solutions of $q$-difference equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2002","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1012.2002","created_at":"2026-05-18T04:05:16.541785+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.2002v3","created_at":"2026-05-18T04:05:16.541785+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2002","created_at":"2026-05-18T04:05:16.541785+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z7WUAT2ULZBP","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z7WUAT2ULZBPHP2L","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z7WUAT2U","created_at":"2026-05-18T12:26:17.028572+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z7WUAT2ULZBPHP2LRVSOXOSU3U","json":"https://pith.science/pith/Z7WUAT2ULZBPHP2LRVSOXOSU3U.json","graph_json":"https://pith.science/api/pith-number/Z7WUAT2ULZBPHP2LRVSOXOSU3U/graph.json","events_json":"https://pith.science/api/pith-number/Z7WUAT2ULZBPHP2LRVSOXOSU3U/events.json","paper":"https://pith.science/paper/Z7WUAT2U"},"agent_actions":{"view_html":"https://pith.science/pith/Z7WUAT2ULZBPHP2LRVSOXOSU3U","download_json":"https://pith.science/pith/Z7WUAT2ULZBPHP2LRVSOXOSU3U.json","view_paper":"https://pith.science/paper/Z7WUAT2U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.2002&json=true","fetch_graph":"https://pith.science/api/pith-number/Z7WUAT2ULZBPHP2LRVSOXOSU3U/graph.json","fetch_events":"https://pith.science/api/pith-number/Z7WUAT2ULZBPHP2LRVSOXOSU3U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z7WUAT2ULZBPHP2LRVSOXOSU3U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z7WUAT2ULZBPHP2LRVSOXOSU3U/action/storage_attestation","attest_author":"https://pith.science/pith/Z7WUAT2ULZBPHP2LRVSOXOSU3U/action/author_attestation","sign_citation":"https://pith.science/pith/Z7WUAT2ULZBPHP2LRVSOXOSU3U/action/citation_signature","submit_replication":"https://pith.science/pith/Z7WUAT2ULZBPHP2LRVSOXOSU3U/action/replication_record"}},"created_at":"2026-05-18T04:05:16.541785+00:00","updated_at":"2026-05-18T04:05:16.541785+00:00"}