{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:GPUHEAICPGYQKHSP6OQHLX66VR","short_pith_number":"pith:GPUHEAIC","canonical_record":{"source":{"id":"hep-th/0406113","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-06-13T21:05:21Z","cross_cats_sorted":["gr-qc","math.NT"],"title_canon_sha256":"b6c7d537ae21790ea745cebf1567855d122009f98e247f1f0afc4b40765ba5c3","abstract_canon_sha256":"fada9413b0339d6619c816a5c5e8f726837a75cfb9fe0683c010c335ed01dca4"},"schema_version":"1.0"},"canonical_sha256":"33e872010279b1051e4ff3a075dfdeac57611b79fd8cd3386a1faf6f6f7de5ca","source":{"kind":"arxiv","id":"hep-th/0406113","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0406113","created_at":"2026-05-18T04:35:23Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0406113v4","created_at":"2026-05-18T04:35:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0406113","created_at":"2026-05-18T04:35:23Z"},{"alias_kind":"pith_short_12","alias_value":"GPUHEAICPGYQ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"GPUHEAICPGYQKHSP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"GPUHEAIC","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:GPUHEAICPGYQKHSP6OQHLX66VR","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0406113","kind":"arxiv","version":4},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-06-13T21:05:21Z","cross_cats_sorted":["gr-qc","math.NT"],"title_canon_sha256":"b6c7d537ae21790ea745cebf1567855d122009f98e247f1f0afc4b40765ba5c3","abstract_canon_sha256":"fada9413b0339d6619c816a5c5e8f726837a75cfb9fe0683c010c335ed01dca4"},"schema_version":"1.0"},"canonical_sha256":"33e872010279b1051e4ff3a075dfdeac57611b79fd8cd3386a1faf6f6f7de5ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:23.078005Z","signature_b64":"lELuBVQiGow0yMZsDkucU2maFA9ubTEcbmgdhrWOvNZ06XTZGjCe3Kxt0AvV5e4HC3OzwbrjLDqxqTGxvf+gAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33e872010279b1051e4ff3a075dfdeac57611b79fd8cd3386a1faf6f6f7de5ca","last_reissued_at":"2026-05-18T04:35:23.077462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:23.077462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0406113","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hla8fAQ7Ml4FRToWBXcaM+f7KbVqtDWgb8DSPYwJVkaOlKoj00YTO1YCrXHer318upgqcij10ZUl7RiufzeCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:02:18.379790Z"},"content_sha256":"eedf1b1afab91ecb82710b54b3a281cb6a971f43dfe37a38d2d4011dbbfc4167","schema_version":"1.0","event_id":"sha256:eedf1b1afab91ecb82710b54b3a281cb6a971f43dfe37a38d2d4011dbbfc4167"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:GPUHEAICPGYQKHSP6OQHLX66VR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical Casimir energies and Dedekind sums","license":"","headline":"","cross_cats":["gr-qc","math.NT"],"primary_cat":"hep-th","authors_text":"J.S.Dowker","submitted_at":"2004-06-13T21:05:21Z","abstract_excerpt":"Casimir energies on space-times having general lens spaces as their spatial sections are shown to be given in terms of generalised Dedekind sums related to Zagier's. These are evaluated explicitly in certain cases as functions of the order of the lens space. An easily implemented recursion approach is used."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0406113","kind":"arxiv","version":4},"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":"2026-05-18T04:35:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sUwKa27iCERMs+sFxZ2lSivFeXX0ItMFDWT+vQGmbUGSoD2btUsg2onDgiHKdivqLdB02yamr0uW8c1Zla/gAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T10:02:18.380466Z"},"content_sha256":"9fad63b13e3fb1e3dc4f057c6133c60d5ce217dc1abdeddbf0f73423abd7e4ff","schema_version":"1.0","event_id":"sha256:9fad63b13e3fb1e3dc4f057c6133c60d5ce217dc1abdeddbf0f73423abd7e4ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GPUHEAICPGYQKHSP6OQHLX66VR/bundle.json","state_url":"https://pith.science/pith/GPUHEAICPGYQKHSP6OQHLX66VR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GPUHEAICPGYQKHSP6OQHLX66VR/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":"2026-06-07T10:02:18Z","links":{"resolver":"https://pith.science/pith/GPUHEAICPGYQKHSP6OQHLX66VR","bundle":"https://pith.science/pith/GPUHEAICPGYQKHSP6OQHLX66VR/bundle.json","state":"https://pith.science/pith/GPUHEAICPGYQKHSP6OQHLX66VR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GPUHEAICPGYQKHSP6OQHLX66VR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:GPUHEAICPGYQKHSP6OQHLX66VR","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":"fada9413b0339d6619c816a5c5e8f726837a75cfb9fe0683c010c335ed01dca4","cross_cats_sorted":["gr-qc","math.NT"],"license":"","primary_cat":"hep-th","submitted_at":"2004-06-13T21:05:21Z","title_canon_sha256":"b6c7d537ae21790ea745cebf1567855d122009f98e247f1f0afc4b40765ba5c3"},"schema_version":"1.0","source":{"id":"hep-th/0406113","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0406113","created_at":"2026-05-18T04:35:23Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0406113v4","created_at":"2026-05-18T04:35:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0406113","created_at":"2026-05-18T04:35:23Z"},{"alias_kind":"pith_short_12","alias_value":"GPUHEAICPGYQ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"GPUHEAICPGYQKHSP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"GPUHEAIC","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:9fad63b13e3fb1e3dc4f057c6133c60d5ce217dc1abdeddbf0f73423abd7e4ff","target":"graph","created_at":"2026-05-18T04:35:23Z","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":"Casimir energies on space-times having general lens spaces as their spatial sections are shown to be given in terms of generalised Dedekind sums related to Zagier's. These are evaluated explicitly in certain cases as functions of the order of the lens space. An easily implemented recursion approach is used.","authors_text":"J.S.Dowker","cross_cats":["gr-qc","math.NT"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2004-06-13T21:05:21Z","title":"Spherical Casimir energies and Dedekind sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0406113","kind":"arxiv","version":4},"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:eedf1b1afab91ecb82710b54b3a281cb6a971f43dfe37a38d2d4011dbbfc4167","target":"record","created_at":"2026-05-18T04:35:23Z","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":"fada9413b0339d6619c816a5c5e8f726837a75cfb9fe0683c010c335ed01dca4","cross_cats_sorted":["gr-qc","math.NT"],"license":"","primary_cat":"hep-th","submitted_at":"2004-06-13T21:05:21Z","title_canon_sha256":"b6c7d537ae21790ea745cebf1567855d122009f98e247f1f0afc4b40765ba5c3"},"schema_version":"1.0","source":{"id":"hep-th/0406113","kind":"arxiv","version":4}},"canonical_sha256":"33e872010279b1051e4ff3a075dfdeac57611b79fd8cd3386a1faf6f6f7de5ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33e872010279b1051e4ff3a075dfdeac57611b79fd8cd3386a1faf6f6f7de5ca","first_computed_at":"2026-05-18T04:35:23.077462Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:23.077462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lELuBVQiGow0yMZsDkucU2maFA9ubTEcbmgdhrWOvNZ06XTZGjCe3Kxt0AvV5e4HC3OzwbrjLDqxqTGxvf+gAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:23.078005Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0406113","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eedf1b1afab91ecb82710b54b3a281cb6a971f43dfe37a38d2d4011dbbfc4167","sha256:9fad63b13e3fb1e3dc4f057c6133c60d5ce217dc1abdeddbf0f73423abd7e4ff"],"state_sha256":"15b097ae172bceb72f06f9c86eb250858e04605f6123f08cdb975a5a8b8cabb9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wt933lPp9SfMkP9+PPbmVfUM7UblP84qUaAPx+EKqxkJWgT8EOCVQZrY9aMPIcwBvvpXuinHs+uBfkrotPXUDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T10:02:18.384030Z","bundle_sha256":"c50e5e11907e95f5c8cd3882ebfcfdfb4463ec0dc992e05954f20840e3a99c52"}}