{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1992:ESCFURAAJGKJHAPIWXRR7FYBO5","short_pith_number":"pith:ESCFURAA","canonical_record":{"source":{"id":"hep-th/9210013","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1992-10-02T09:35:00Z","cross_cats_sorted":[],"title_canon_sha256":"eb90a3982b2e09697f41cec5f69fe70eba4742758a5381a74ddff3885bb4c404","abstract_canon_sha256":"1d8d4588ffff0a85d73abe001e62802c4248dabb2aa93ae47afda00a5b5a0c22"},"schema_version":"1.0"},"canonical_sha256":"24845a440049949381e8b5e31f9701776136b0524c0d8607b143802586a4d87f","source":{"kind":"arxiv","id":"hep-th/9210013","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9210013","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9210013v1","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9210013","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"ESCFURAAJGKJ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"ESCFURAAJGKJHAPI","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"ESCFURAA","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1992:ESCFURAAJGKJHAPIWXRR7FYBO5","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/9210013","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"1992-10-02T09:35:00Z","cross_cats_sorted":[],"title_canon_sha256":"eb90a3982b2e09697f41cec5f69fe70eba4742758a5381a74ddff3885bb4c404","abstract_canon_sha256":"1d8d4588ffff0a85d73abe001e62802c4248dabb2aa93ae47afda00a5b5a0c22"},"schema_version":"1.0"},"canonical_sha256":"24845a440049949381e8b5e31f9701776136b0524c0d8607b143802586a4d87f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:43.877062Z","signature_b64":"sAtgG+1ofE8rigCt0UsDae+l6JNAPkUpL0GNngTW+Cvf0BTJFjqx5YD7DEBueT+pb4iooOECg/vkHBwznFpHAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24845a440049949381e8b5e31f9701776136b0524c0d8607b143802586a4d87f","last_reissued_at":"2026-05-18T04:37:43.876480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:43.876480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/9210013","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":"2026-05-18T04:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pvdC30Bof3VmdX+GA9VmyasgLTeYmL+BHahYqK9bLUNjBzmk5GJR4duyAlPZRxOGtlRbectUbVTpYhHHsmpRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:17:32.671163Z"},"content_sha256":"d524302a4fed657241e10f515bb996b67d6f7383b7179885c15225106fbe02d8","schema_version":"1.0","event_id":"sha256:d524302a4fed657241e10f515bb996b67d6f7383b7179885c15225106fbe02d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1992:ESCFURAAJGKJHAPIWXRR7FYBO5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vacuum energy on orbifold factors of spheres","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"J.S.Dowker, Peter Chang","submitted_at":"1992-10-02T09:35:00Z","abstract_excerpt":"The vacuum energy is calculated for a free, conformally-coupled scalar field on the orbifold space-time \\R$\\times \\S^2/\\Gamma$ where $\\Gamma$ is a finite subgroup of O(3) acting with fixed points. The energy vanishes when $\\Gamma$ is composed of pure rotations but not otherwise. It is shown on general grounds that the same conclusion holds for all even-dimensional factored spheres and the vacuum energies are given as generalised Bernoulli functions (i.e. Todd polynomials). The relevant $\\zeta$- functions are analysed in some detail and several identities are incidentally derived. The general d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9210013","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:37:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2vmOOqVBg0hxKygoQhmbmZeOqHcn0E3PAMlGkE832ETwEh6SfE9UAQImxO6z2ngZBKNl334HZdwq4HgpzvhmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:17:32.671809Z"},"content_sha256":"f4872de64060e5ab9708dd885bc4206ea9405f9c05e0595970f822e2e401b013","schema_version":"1.0","event_id":"sha256:f4872de64060e5ab9708dd885bc4206ea9405f9c05e0595970f822e2e401b013"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ESCFURAAJGKJHAPIWXRR7FYBO5/bundle.json","state_url":"https://pith.science/pith/ESCFURAAJGKJHAPIWXRR7FYBO5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ESCFURAAJGKJHAPIWXRR7FYBO5/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":"2026-05-28T17:17:32Z","links":{"resolver":"https://pith.science/pith/ESCFURAAJGKJHAPIWXRR7FYBO5","bundle":"https://pith.science/pith/ESCFURAAJGKJHAPIWXRR7FYBO5/bundle.json","state":"https://pith.science/pith/ESCFURAAJGKJHAPIWXRR7FYBO5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ESCFURAAJGKJHAPIWXRR7FYBO5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1992:ESCFURAAJGKJHAPIWXRR7FYBO5","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":"1d8d4588ffff0a85d73abe001e62802c4248dabb2aa93ae47afda00a5b5a0c22","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1992-10-02T09:35:00Z","title_canon_sha256":"eb90a3982b2e09697f41cec5f69fe70eba4742758a5381a74ddff3885bb4c404"},"schema_version":"1.0","source":{"id":"hep-th/9210013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9210013","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9210013v1","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9210013","created_at":"2026-05-18T04:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"ESCFURAAJGKJ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"ESCFURAAJGKJHAPI","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"ESCFURAA","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:f4872de64060e5ab9708dd885bc4206ea9405f9c05e0595970f822e2e401b013","target":"graph","created_at":"2026-05-18T04:37:43Z","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":"The vacuum energy is calculated for a free, conformally-coupled scalar field on the orbifold space-time \\R$\\times \\S^2/\\Gamma$ where $\\Gamma$ is a finite subgroup of O(3) acting with fixed points. The energy vanishes when $\\Gamma$ is composed of pure rotations but not otherwise. It is shown on general grounds that the same conclusion holds for all even-dimensional factored spheres and the vacuum energies are given as generalised Bernoulli functions (i.e. Todd polynomials). The relevant $\\zeta$- functions are analysed in some detail and several identities are incidentally derived. The general d","authors_text":"J.S.Dowker, Peter Chang","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1992-10-02T09:35:00Z","title":"Vacuum energy on orbifold factors of spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9210013","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:d524302a4fed657241e10f515bb996b67d6f7383b7179885c15225106fbe02d8","target":"record","created_at":"2026-05-18T04:37:43Z","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":"1d8d4588ffff0a85d73abe001e62802c4248dabb2aa93ae47afda00a5b5a0c22","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"1992-10-02T09:35:00Z","title_canon_sha256":"eb90a3982b2e09697f41cec5f69fe70eba4742758a5381a74ddff3885bb4c404"},"schema_version":"1.0","source":{"id":"hep-th/9210013","kind":"arxiv","version":1}},"canonical_sha256":"24845a440049949381e8b5e31f9701776136b0524c0d8607b143802586a4d87f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24845a440049949381e8b5e31f9701776136b0524c0d8607b143802586a4d87f","first_computed_at":"2026-05-18T04:37:43.876480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:43.876480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sAtgG+1ofE8rigCt0UsDae+l6JNAPkUpL0GNngTW+Cvf0BTJFjqx5YD7DEBueT+pb4iooOECg/vkHBwznFpHAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:43.877062Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9210013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d524302a4fed657241e10f515bb996b67d6f7383b7179885c15225106fbe02d8","sha256:f4872de64060e5ab9708dd885bc4206ea9405f9c05e0595970f822e2e401b013"],"state_sha256":"f5c5b5256d3ea38829aa9936c473ea35b961bd19059b448dd8c41c7ac3d188ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vJ6vckwq/+PVFgv+20A41CyAGfHy2Vvz21vyqJ1qA/JfmYGZ8Ys6tEfbahB1HxUUZxSLgGudd5TWFd8VcRjNDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:17:32.675629Z","bundle_sha256":"545f24a5f4a5ed82a300261f17786b23428b513538cc36b2eeea673bacdd481b"}}