{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:RHCHI6LQPVDXTSMJVZDLKS5Q7M","short_pith_number":"pith:RHCHI6LQ","schema_version":"1.0","canonical_sha256":"89c47479707d4779c989ae46b54bb0fb36fef707302dc2e77fbfb20981a91473","source":{"kind":"arxiv","id":"1612.07024","version":3},"attestation_state":"computed","paper":{"title":"Free Energy on a Cycle Graph and Trigonometric Deformation of Heat Kernel Traces on Odd Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Gifu College), Kiyoshi Shiraishi (Yamaguchi University), Nahomi Kan (NIT","submitted_at":"2016-12-21T09:28:34Z","abstract_excerpt":"We consider a possible `deformation' of the trace of the heat kernel on odd dimensional spheres, motivated by the calculation of the free energy of a scalar field on a discretized circle. By using an expansion in terms of the modified Bessel functions, we obtain the values of the free energies after a suitable regularization."},"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":"1612.07024","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-21T09:28:34Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"3a51bfbf84394fe285f303d5bf8db479f519b147ec928ae32f8ff5de56296b25","abstract_canon_sha256":"58490bbf1522497d8e66fe36789684529316abc6fe4e69630844da87e17aa9a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:47.712027Z","signature_b64":"Yr1ZXP38eCrwY1YYfkb9pom7yRnajDqddWyIK1vmX3xs1Ajtk4zuT9q+QBOLgE7lwrx62Uc5aWd3KrxO/nIJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89c47479707d4779c989ae46b54bb0fb36fef707302dc2e77fbfb20981a91473","last_reissued_at":"2026-05-18T00:19:47.711311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:47.711311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Free Energy on a Cycle Graph and Trigonometric Deformation of Heat Kernel Traces on Odd Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Gifu College), Kiyoshi Shiraishi (Yamaguchi University), Nahomi Kan (NIT","submitted_at":"2016-12-21T09:28:34Z","abstract_excerpt":"We consider a possible `deformation' of the trace of the heat kernel on odd dimensional spheres, motivated by the calculation of the free energy of a scalar field on a discretized circle. By using an expansion in terms of the modified Bessel functions, we obtain the values of the free energies after a suitable regularization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07024","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":"1612.07024","created_at":"2026-05-18T00:19:47.711423+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.07024v3","created_at":"2026-05-18T00:19:47.711423+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07024","created_at":"2026-05-18T00:19:47.711423+00:00"},{"alias_kind":"pith_short_12","alias_value":"RHCHI6LQPVDX","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"RHCHI6LQPVDXTSMJ","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"RHCHI6LQ","created_at":"2026-05-18T12:30:41.710351+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/RHCHI6LQPVDXTSMJVZDLKS5Q7M","json":"https://pith.science/pith/RHCHI6LQPVDXTSMJVZDLKS5Q7M.json","graph_json":"https://pith.science/api/pith-number/RHCHI6LQPVDXTSMJVZDLKS5Q7M/graph.json","events_json":"https://pith.science/api/pith-number/RHCHI6LQPVDXTSMJVZDLKS5Q7M/events.json","paper":"https://pith.science/paper/RHCHI6LQ"},"agent_actions":{"view_html":"https://pith.science/pith/RHCHI6LQPVDXTSMJVZDLKS5Q7M","download_json":"https://pith.science/pith/RHCHI6LQPVDXTSMJVZDLKS5Q7M.json","view_paper":"https://pith.science/paper/RHCHI6LQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.07024&json=true","fetch_graph":"https://pith.science/api/pith-number/RHCHI6LQPVDXTSMJVZDLKS5Q7M/graph.json","fetch_events":"https://pith.science/api/pith-number/RHCHI6LQPVDXTSMJVZDLKS5Q7M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RHCHI6LQPVDXTSMJVZDLKS5Q7M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RHCHI6LQPVDXTSMJVZDLKS5Q7M/action/storage_attestation","attest_author":"https://pith.science/pith/RHCHI6LQPVDXTSMJVZDLKS5Q7M/action/author_attestation","sign_citation":"https://pith.science/pith/RHCHI6LQPVDXTSMJVZDLKS5Q7M/action/citation_signature","submit_replication":"https://pith.science/pith/RHCHI6LQPVDXTSMJVZDLKS5Q7M/action/replication_record"}},"created_at":"2026-05-18T00:19:47.711423+00:00","updated_at":"2026-05-18T00:19:47.711423+00:00"}