{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:6BQWJHDWHZPJBVEEIQCMGGQI5N","short_pith_number":"pith:6BQWJHDW","canonical_record":{"source":{"id":"gr-qc/0106082","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2001-06-26T12:45:28Z","cross_cats_sorted":[],"title_canon_sha256":"a77e996598121ac7aa84dfbda4ba39b275999337739dfa47c2b1fb64f1bd0921","abstract_canon_sha256":"8133ef36172f1b1b59a97d79d9d7f885bb29ccc378471b6fc2ad896112c3b567"},"schema_version":"1.0"},"canonical_sha256":"f061649c763e5e90d4844404c31a08eb525dd924a818c02a882166f7f6bcba51","source":{"kind":"arxiv","id":"gr-qc/0106082","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0106082","created_at":"2026-07-04T15:51:20Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0106082v1","created_at":"2026-07-04T15:51:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0106082","created_at":"2026-07-04T15:51:20Z"},{"alias_kind":"pith_short_12","alias_value":"6BQWJHDWHZPJ","created_at":"2026-07-04T15:51:20Z"},{"alias_kind":"pith_short_16","alias_value":"6BQWJHDWHZPJBVEE","created_at":"2026-07-04T15:51:20Z"},{"alias_kind":"pith_short_8","alias_value":"6BQWJHDW","created_at":"2026-07-04T15:51:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:6BQWJHDWHZPJBVEEIQCMGGQI5N","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0106082","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2001-06-26T12:45:28Z","cross_cats_sorted":[],"title_canon_sha256":"a77e996598121ac7aa84dfbda4ba39b275999337739dfa47c2b1fb64f1bd0921","abstract_canon_sha256":"8133ef36172f1b1b59a97d79d9d7f885bb29ccc378471b6fc2ad896112c3b567"},"schema_version":"1.0"},"canonical_sha256":"f061649c763e5e90d4844404c31a08eb525dd924a818c02a882166f7f6bcba51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:51:20.293033Z","signature_b64":"8grjCjVWUa4wdAsHy2LnzKiaGgbY3X0lZnkLE9HRDTCGcosvo2SbbmcAjLQYTtC0kD//HFTFGOq4Yo8IbelECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f061649c763e5e90d4844404c31a08eb525dd924a818c02a882166f7f6bcba51","last_reissued_at":"2026-07-04T15:51:20.292688Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:51:20.292688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0106082","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:51:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TzLZ+XO1oGRwEES0CPeJ0y/psJiYppCf7rcZImvpI9+lHqXMvUmPnsAu1V8UfKXCsnecQWn3yoiT4xvZXjfNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T18:18:40.669980Z"},"content_sha256":"5be394621e3d8c8188eb275b7a8704c35b712bc1cc97d420a37809a2eac34a47","schema_version":"1.0","event_id":"sha256:5be394621e3d8c8188eb275b7a8704c35b712bc1cc97d420a37809a2eac34a47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:6BQWJHDWHZPJBVEEIQCMGGQI5N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Green's function for a n-dimensional closed, static universe and with a spherical boundary","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Mustafa Ozcan","submitted_at":"2001-06-26T12:45:28Z","abstract_excerpt":"We construct the Hadamard Green's function by using the eigenfunction, which are obtained by solving the wave equation for the massless conformal scalar field on the S^n-1 of a n-dimensional closed, static universe. We also consider the half space case with both the Dirichlet and the Neumann boundary conditions. Solving of eigenfunction and eigenvalues of the corresponding field equation is interesting since the Casimir energy could be calculated analytically by various methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0106082","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/gr-qc/0106082/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:51:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KBOT5V2gjyUkD8/9JWGTSteXTWWxUKmaTHsfvZkpt9ipcLLwAaUYcJ54diJAyObQEqzxNZuhbj6leg+hVgalBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T18:18:40.670872Z"},"content_sha256":"46b378976f4b56fcffb91f1649d8caa2405bc5004711c241cc33bc60e8432345","schema_version":"1.0","event_id":"sha256:46b378976f4b56fcffb91f1649d8caa2405bc5004711c241cc33bc60e8432345"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6BQWJHDWHZPJBVEEIQCMGGQI5N/bundle.json","state_url":"https://pith.science/pith/6BQWJHDWHZPJBVEEIQCMGGQI5N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6BQWJHDWHZPJBVEEIQCMGGQI5N/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":"2026-08-15T18:18:40Z","links":{"resolver":"https://pith.science/pith/6BQWJHDWHZPJBVEEIQCMGGQI5N","bundle":"https://pith.science/pith/6BQWJHDWHZPJBVEEIQCMGGQI5N/bundle.json","state":"https://pith.science/pith/6BQWJHDWHZPJBVEEIQCMGGQI5N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6BQWJHDWHZPJBVEEIQCMGGQI5N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:6BQWJHDWHZPJBVEEIQCMGGQI5N","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":"8133ef36172f1b1b59a97d79d9d7f885bb29ccc378471b6fc2ad896112c3b567","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2001-06-26T12:45:28Z","title_canon_sha256":"a77e996598121ac7aa84dfbda4ba39b275999337739dfa47c2b1fb64f1bd0921"},"schema_version":"1.0","source":{"id":"gr-qc/0106082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0106082","created_at":"2026-07-04T15:51:20Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0106082v1","created_at":"2026-07-04T15:51:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0106082","created_at":"2026-07-04T15:51:20Z"},{"alias_kind":"pith_short_12","alias_value":"6BQWJHDWHZPJ","created_at":"2026-07-04T15:51:20Z"},{"alias_kind":"pith_short_16","alias_value":"6BQWJHDWHZPJBVEE","created_at":"2026-07-04T15:51:20Z"},{"alias_kind":"pith_short_8","alias_value":"6BQWJHDW","created_at":"2026-07-04T15:51:20Z"}],"graph_snapshots":[{"event_id":"sha256:46b378976f4b56fcffb91f1649d8caa2405bc5004711c241cc33bc60e8432345","target":"graph","created_at":"2026-07-04T15:51:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/gr-qc/0106082/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct the Hadamard Green's function by using the eigenfunction, which are obtained by solving the wave equation for the massless conformal scalar field on the S^n-1 of a n-dimensional closed, static universe. We also consider the half space case with both the Dirichlet and the Neumann boundary conditions. Solving of eigenfunction and eigenvalues of the corresponding field equation is interesting since the Casimir energy could be calculated analytically by various methods.","authors_text":"Mustafa Ozcan","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2001-06-26T12:45:28Z","title":"Green's function for a n-dimensional closed, static universe and with a spherical boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0106082","kind":"arxiv","version":1},"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":"sha256:5be394621e3d8c8188eb275b7a8704c35b712bc1cc97d420a37809a2eac34a47","target":"record","created_at":"2026-07-04T15:51:20Z","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":"8133ef36172f1b1b59a97d79d9d7f885bb29ccc378471b6fc2ad896112c3b567","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2001-06-26T12:45:28Z","title_canon_sha256":"a77e996598121ac7aa84dfbda4ba39b275999337739dfa47c2b1fb64f1bd0921"},"schema_version":"1.0","source":{"id":"gr-qc/0106082","kind":"arxiv","version":1}},"canonical_sha256":"f061649c763e5e90d4844404c31a08eb525dd924a818c02a882166f7f6bcba51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f061649c763e5e90d4844404c31a08eb525dd924a818c02a882166f7f6bcba51","first_computed_at":"2026-07-04T15:51:20.292688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:51:20.292688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8grjCjVWUa4wdAsHy2LnzKiaGgbY3X0lZnkLE9HRDTCGcosvo2SbbmcAjLQYTtC0kD//HFTFGOq4Yo8IbelECA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:51:20.293033Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0106082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5be394621e3d8c8188eb275b7a8704c35b712bc1cc97d420a37809a2eac34a47","sha256:46b378976f4b56fcffb91f1649d8caa2405bc5004711c241cc33bc60e8432345"],"state_sha256":"45cade2af801cbf8d5e02ec30772efaee2568a07685de1408529f31619b3c62b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VOA3MNb9jUqIww+3aKCGbUTehsZxENrmQousELaws5uU1hoZd+bJCi/TkcnBY7tN6oQsoQ5AZqC3MpVPopjZCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T18:18:40.680073Z","bundle_sha256":"e1895a9fbbedc6bdb372efe2446a4bfb3258820e7f398e9c64cb4bd6560fcd3d"}}