{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:QKVEXSMP4GEDOUM7KPISSYZFJO","short_pith_number":"pith:QKVEXSMP","schema_version":"1.0","canonical_sha256":"82aa4bc98fe18837519f53d12963254b821b152fa650cc1d2f90c6a3727365e3","source":{"kind":"arxiv","id":"0905.4928","version":1},"attestation_state":"computed","paper":{"title":"The Shape of Compact Toroidal Dimensions $T^d_{\\theta}$ and the Casimir Effect on $M^D\\times T^d_{\\theta}$ spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"V.K.Oikonomou","submitted_at":"2009-05-29T17:50:45Z","abstract_excerpt":"We study the influence of the shape of compact dimensions to the Casimir energy and Casimir force of a scalar field. We examine both the massive and the massless scalar field. The total spacetime topology is $M^D\\times T^2_{\\theta}$, where $M^D$ is the $D$ dimensional Minkowski spacetime and $T^2_{\\theta}$ the twisted torus described by $R_1$, $R_2$ and $\\theta$. For the case $R_1=R_2$ we found that the massive bulk scalar field Casimir energy is singular for $D$=even and this singularity is $R$-dependent and remains even when the force is calculated. Also the massless Casimir energy and force"},"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":"0905.4928","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-05-29T17:50:45Z","cross_cats_sorted":[],"title_canon_sha256":"3e30de3a7fed868cbb066bbca6610493c3c2bac4a8f1f0ebb590d9884e04a0a4","abstract_canon_sha256":"825fb8a4376771b94c4eaede5073a985c8d19ecedb3e5f2747b329ecfe9b487d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:22.725296Z","signature_b64":"XSZmpoJ1FYndUdW/TovoOIIDQGm4aG5cL/tzOgTkF8Ginewm53YO3RO76pbQq/7mulRyRnAB3b2DNAWTHSR/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82aa4bc98fe18837519f53d12963254b821b152fa650cc1d2f90c6a3727365e3","last_reissued_at":"2026-05-18T04:31:22.724812Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:22.724812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Shape of Compact Toroidal Dimensions $T^d_{\\theta}$ and the Casimir Effect on $M^D\\times T^d_{\\theta}$ spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"V.K.Oikonomou","submitted_at":"2009-05-29T17:50:45Z","abstract_excerpt":"We study the influence of the shape of compact dimensions to the Casimir energy and Casimir force of a scalar field. We examine both the massive and the massless scalar field. The total spacetime topology is $M^D\\times T^2_{\\theta}$, where $M^D$ is the $D$ dimensional Minkowski spacetime and $T^2_{\\theta}$ the twisted torus described by $R_1$, $R_2$ and $\\theta$. For the case $R_1=R_2$ we found that the massive bulk scalar field Casimir energy is singular for $D$=even and this singularity is $R$-dependent and remains even when the force is calculated. Also the massless Casimir energy and force"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4928","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0905.4928","created_at":"2026-05-18T04:31:22.724884+00:00"},{"alias_kind":"arxiv_version","alias_value":"0905.4928v1","created_at":"2026-05-18T04:31:22.724884+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4928","created_at":"2026-05-18T04:31:22.724884+00:00"},{"alias_kind":"pith_short_12","alias_value":"QKVEXSMP4GED","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QKVEXSMP4GEDOUM7","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QKVEXSMP","created_at":"2026-05-18T12:26:01.383474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.17802","citing_title":"Instabilities in scale-separated Casimir vacua","ref_index":74,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QKVEXSMP4GEDOUM7KPISSYZFJO","json":"https://pith.science/pith/QKVEXSMP4GEDOUM7KPISSYZFJO.json","graph_json":"https://pith.science/api/pith-number/QKVEXSMP4GEDOUM7KPISSYZFJO/graph.json","events_json":"https://pith.science/api/pith-number/QKVEXSMP4GEDOUM7KPISSYZFJO/events.json","paper":"https://pith.science/paper/QKVEXSMP"},"agent_actions":{"view_html":"https://pith.science/pith/QKVEXSMP4GEDOUM7KPISSYZFJO","download_json":"https://pith.science/pith/QKVEXSMP4GEDOUM7KPISSYZFJO.json","view_paper":"https://pith.science/paper/QKVEXSMP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0905.4928&json=true","fetch_graph":"https://pith.science/api/pith-number/QKVEXSMP4GEDOUM7KPISSYZFJO/graph.json","fetch_events":"https://pith.science/api/pith-number/QKVEXSMP4GEDOUM7KPISSYZFJO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QKVEXSMP4GEDOUM7KPISSYZFJO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QKVEXSMP4GEDOUM7KPISSYZFJO/action/storage_attestation","attest_author":"https://pith.science/pith/QKVEXSMP4GEDOUM7KPISSYZFJO/action/author_attestation","sign_citation":"https://pith.science/pith/QKVEXSMP4GEDOUM7KPISSYZFJO/action/citation_signature","submit_replication":"https://pith.science/pith/QKVEXSMP4GEDOUM7KPISSYZFJO/action/replication_record"}},"created_at":"2026-05-18T04:31:22.724884+00:00","updated_at":"2026-05-18T04:31:22.724884+00:00"}