{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:4T23C4UKEJWLQU3BCN3DW7QB27","short_pith_number":"pith:4T23C4UK","schema_version":"1.0","canonical_sha256":"e4f5b1728a226cb8536113763b7e01d7f75f861922639d047d7693511e07a323","source":{"kind":"arxiv","id":"2606.31509","version":1},"attestation_state":"computed","paper":{"title":"Temporal-Plane Carroll--Schr\\\"odinger Dynamics and Vortex Sectors in (2,2) Klein Space","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jos\\'e Rojas, Melvin Arias","submitted_at":"2026-06-30T11:24:54Z","abstract_excerpt":"Motivated by the temporal dynamics identified in the $(1+1)$ Carroll-Schr\\\"odinger theory, we derive a post-Carrollian Schr\\\"odinger dynamics in flat Klein space with signature $(2,2)$. Starting from the tachyonic Klein-Gordon equation in double-polar coordinates and removing a spacelike carrier, the spatial radius behaves as an effective evolution parameter, whereas the temporal two-plane $(t_1,t_2)$ serves as the equal-radius configuration space. The additional time direction supplies an $SO(2)$ temporal angular momentum $J$, produces temporal vortex sectors, and gives the centrifugal contri"},"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":"2606.31509","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"quant-ph","submitted_at":"2026-06-30T11:24:54Z","cross_cats_sorted":[],"title_canon_sha256":"b852677140cd52b5359a7e29ca4ae8147d1de57ecc8da3f633fea3c05252fe86","abstract_canon_sha256":"9209f7dc7328df10b9b5fb46fa99f54eb9aeda473549aa4a1f07ffd45d1fad98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:18:05.434372Z","signature_b64":"WJbq3hLJZDDjJ/4SePruFiKf0E9Tt4jJprq4urEkj0dimANeG73D56vg9KZ7ZG9XdsHcJD47QSxkv9DyXQYZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4f5b1728a226cb8536113763b7e01d7f75f861922639d047d7693511e07a323","last_reissued_at":"2026-07-01T01:18:05.433908Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:18:05.433908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Temporal-Plane Carroll--Schr\\\"odinger Dynamics and Vortex Sectors in (2,2) Klein Space","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jos\\'e Rojas, Melvin Arias","submitted_at":"2026-06-30T11:24:54Z","abstract_excerpt":"Motivated by the temporal dynamics identified in the $(1+1)$ Carroll-Schr\\\"odinger theory, we derive a post-Carrollian Schr\\\"odinger dynamics in flat Klein space with signature $(2,2)$. Starting from the tachyonic Klein-Gordon equation in double-polar coordinates and removing a spacelike carrier, the spatial radius behaves as an effective evolution parameter, whereas the temporal two-plane $(t_1,t_2)$ serves as the equal-radius configuration space. The additional time direction supplies an $SO(2)$ temporal angular momentum $J$, produces temporal vortex sectors, and gives the centrifugal contri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31509","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/2606.31509/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.31509","created_at":"2026-07-01T01:18:05.433981+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.31509v1","created_at":"2026-07-01T01:18:05.433981+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31509","created_at":"2026-07-01T01:18:05.433981+00:00"},{"alias_kind":"pith_short_12","alias_value":"4T23C4UKEJWL","created_at":"2026-07-01T01:18:05.433981+00:00"},{"alias_kind":"pith_short_16","alias_value":"4T23C4UKEJWLQU3B","created_at":"2026-07-01T01:18:05.433981+00:00"},{"alias_kind":"pith_short_8","alias_value":"4T23C4UK","created_at":"2026-07-01T01:18:05.433981+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/4T23C4UKEJWLQU3BCN3DW7QB27","json":"https://pith.science/pith/4T23C4UKEJWLQU3BCN3DW7QB27.json","graph_json":"https://pith.science/api/pith-number/4T23C4UKEJWLQU3BCN3DW7QB27/graph.json","events_json":"https://pith.science/api/pith-number/4T23C4UKEJWLQU3BCN3DW7QB27/events.json","paper":"https://pith.science/paper/4T23C4UK"},"agent_actions":{"view_html":"https://pith.science/pith/4T23C4UKEJWLQU3BCN3DW7QB27","download_json":"https://pith.science/pith/4T23C4UKEJWLQU3BCN3DW7QB27.json","view_paper":"https://pith.science/paper/4T23C4UK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.31509&json=true","fetch_graph":"https://pith.science/api/pith-number/4T23C4UKEJWLQU3BCN3DW7QB27/graph.json","fetch_events":"https://pith.science/api/pith-number/4T23C4UKEJWLQU3BCN3DW7QB27/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4T23C4UKEJWLQU3BCN3DW7QB27/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4T23C4UKEJWLQU3BCN3DW7QB27/action/storage_attestation","attest_author":"https://pith.science/pith/4T23C4UKEJWLQU3BCN3DW7QB27/action/author_attestation","sign_citation":"https://pith.science/pith/4T23C4UKEJWLQU3BCN3DW7QB27/action/citation_signature","submit_replication":"https://pith.science/pith/4T23C4UKEJWLQU3BCN3DW7QB27/action/replication_record"}},"created_at":"2026-07-01T01:18:05.433981+00:00","updated_at":"2026-07-01T01:18:05.433981+00:00"}