{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7S2ZDYFHTE4DZKFPOWN2HGCFWV","short_pith_number":"pith:7S2ZDYFH","canonical_record":{"source":{"id":"1111.5103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-11-22T05:43:49Z","cross_cats_sorted":[],"title_canon_sha256":"1997ef05630b10cf68e5b724f78c02548fe19fc91aee819a0092cae9938dc4fb","abstract_canon_sha256":"f576b93b63cf9626e7da533fd2538cc52492da4e3c37aaa2be4602266742d7f7"},"schema_version":"1.0"},"canonical_sha256":"fcb591e0a799383ca8af759ba39845b5776cda55d059c457a4b47eb787ad4464","source":{"kind":"arxiv","id":"1111.5103","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5103","created_at":"2026-05-18T04:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5103v1","created_at":"2026-05-18T04:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5103","created_at":"2026-05-18T04:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"7S2ZDYFHTE4D","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7S2ZDYFHTE4DZKFP","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7S2ZDYFH","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7S2ZDYFHTE4DZKFPOWN2HGCFWV","target":"record","payload":{"canonical_record":{"source":{"id":"1111.5103","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-11-22T05:43:49Z","cross_cats_sorted":[],"title_canon_sha256":"1997ef05630b10cf68e5b724f78c02548fe19fc91aee819a0092cae9938dc4fb","abstract_canon_sha256":"f576b93b63cf9626e7da533fd2538cc52492da4e3c37aaa2be4602266742d7f7"},"schema_version":"1.0"},"canonical_sha256":"fcb591e0a799383ca8af759ba39845b5776cda55d059c457a4b47eb787ad4464","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:53.436789Z","signature_b64":"8iCNZMcgM5c3XXBK1TgebUSEaicyIfx8IWADkulRfvjg1eDKRGCTrV7aURtgBWuNuQ4FTOE8y5gJPzfTz0vyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fcb591e0a799383ca8af759ba39845b5776cda55d059c457a4b47eb787ad4464","last_reissued_at":"2026-05-18T04:07:53.436294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:53.436294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.5103","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":"2026-05-18T04:07:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0+ck0WiTjel+LbGH2uIqT7X8b6nN1lrCVpUG6mbBsqM63Z6BkZuwFp0izhIZ/woBau8ne8s96WlsqjymuWlICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:06:56.202575Z"},"content_sha256":"4a9ce5f982d5be594ab60cd145f1c6d55b5e3e9975c88e48119722b32f323ec3","schema_version":"1.0","event_id":"sha256:4a9ce5f982d5be594ab60cd145f1c6d55b5e3e9975c88e48119722b32f323ec3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7S2ZDYFHTE4DZKFPOWN2HGCFWV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wijsman Hyperspaces: Subspaces and Embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Heikki J. K. Junnila, Jiling Cao, Warren B. Moors","submitted_at":"2011-11-22T05:43:49Z","abstract_excerpt":"In this paper, topological properties of Wijsman hyperspaces are investigated. We study the existence of isolated points in Wijsman hyperspaces. We show that every Tychonoff space can be embedded as a closed subspace in the Wijsman hyperspace of a complete metric space which is locally R."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5103","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":"2026-05-18T04:07:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E1zNlH5ReTIwW0hdr820eMPssC+0drkE7281T47aswwOp87gSCl5lWqtMU2Mt0NhpWOXzLQHX5NGKW1oVzBPBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:06:56.202918Z"},"content_sha256":"7093b195ded7c536853038c42d3b6309962bf8878f59e985b09daa4e62ee9ec7","schema_version":"1.0","event_id":"sha256:7093b195ded7c536853038c42d3b6309962bf8878f59e985b09daa4e62ee9ec7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7S2ZDYFHTE4DZKFPOWN2HGCFWV/bundle.json","state_url":"https://pith.science/pith/7S2ZDYFHTE4DZKFPOWN2HGCFWV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7S2ZDYFHTE4DZKFPOWN2HGCFWV/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":"2026-06-25T17:06:56Z","links":{"resolver":"https://pith.science/pith/7S2ZDYFHTE4DZKFPOWN2HGCFWV","bundle":"https://pith.science/pith/7S2ZDYFHTE4DZKFPOWN2HGCFWV/bundle.json","state":"https://pith.science/pith/7S2ZDYFHTE4DZKFPOWN2HGCFWV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7S2ZDYFHTE4DZKFPOWN2HGCFWV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7S2ZDYFHTE4DZKFPOWN2HGCFWV","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":"f576b93b63cf9626e7da533fd2538cc52492da4e3c37aaa2be4602266742d7f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-11-22T05:43:49Z","title_canon_sha256":"1997ef05630b10cf68e5b724f78c02548fe19fc91aee819a0092cae9938dc4fb"},"schema_version":"1.0","source":{"id":"1111.5103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5103","created_at":"2026-05-18T04:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5103v1","created_at":"2026-05-18T04:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5103","created_at":"2026-05-18T04:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"7S2ZDYFHTE4D","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7S2ZDYFHTE4DZKFP","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7S2ZDYFH","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:7093b195ded7c536853038c42d3b6309962bf8878f59e985b09daa4e62ee9ec7","target":"graph","created_at":"2026-05-18T04:07:53Z","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":"In this paper, topological properties of Wijsman hyperspaces are investigated. We study the existence of isolated points in Wijsman hyperspaces. We show that every Tychonoff space can be embedded as a closed subspace in the Wijsman hyperspace of a complete metric space which is locally R.","authors_text":"Heikki J. K. Junnila, Jiling Cao, Warren B. Moors","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-11-22T05:43:49Z","title":"Wijsman Hyperspaces: Subspaces and Embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5103","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":"sha256:4a9ce5f982d5be594ab60cd145f1c6d55b5e3e9975c88e48119722b32f323ec3","target":"record","created_at":"2026-05-18T04:07:53Z","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":"f576b93b63cf9626e7da533fd2538cc52492da4e3c37aaa2be4602266742d7f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-11-22T05:43:49Z","title_canon_sha256":"1997ef05630b10cf68e5b724f78c02548fe19fc91aee819a0092cae9938dc4fb"},"schema_version":"1.0","source":{"id":"1111.5103","kind":"arxiv","version":1}},"canonical_sha256":"fcb591e0a799383ca8af759ba39845b5776cda55d059c457a4b47eb787ad4464","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcb591e0a799383ca8af759ba39845b5776cda55d059c457a4b47eb787ad4464","first_computed_at":"2026-05-18T04:07:53.436294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:53.436294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8iCNZMcgM5c3XXBK1TgebUSEaicyIfx8IWADkulRfvjg1eDKRGCTrV7aURtgBWuNuQ4FTOE8y5gJPzfTz0vyDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:53.436789Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a9ce5f982d5be594ab60cd145f1c6d55b5e3e9975c88e48119722b32f323ec3","sha256:7093b195ded7c536853038c42d3b6309962bf8878f59e985b09daa4e62ee9ec7"],"state_sha256":"595668a4ef1056ec5f43b6cecefa8375b2119ebe1850c985b394aa0368abe2fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DFYRNQGuEEBuum5njNN9Yr965FfkxMSWhbeuKU/YRnnSEEpw3zHEg4HaI/dUsDFSIya9Z4Yl8iYB2L9975x1Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T17:06:56.204851Z","bundle_sha256":"cdf8573c7d1a25ad963ffeae3018c9c56bdb1ae0dcaf8a644a6ff0346a2e5f78"}}