{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4JNJUNWSHPVLKZJFP2Y6RFBOO4","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":"965a9535c3843ce26ba4fff2df7c28383b9c7bb9e4bb5c05360e7eec112a4b8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-03-16T06:11:40Z","title_canon_sha256":"ddff8ce65d94f7f7387c2256c99a751f36274942343db759f8f33f5571a3de0a"},"schema_version":"1.0","source":{"id":"1103.3109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3109","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3109v1","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3109","created_at":"2026-05-18T04:26:44Z"},{"alias_kind":"pith_short_12","alias_value":"4JNJUNWSHPVL","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4JNJUNWSHPVLKZJF","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4JNJUNWS","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:97071f64bc85b261d9ef7aed27a48b2cb9ef7b1566db482c840482755d1ad9d4","target":"graph","created_at":"2026-05-18T04:26:44Z","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, we continue studying the properties of $\\gamma$-semi-continuous and $\\gamma$-semi-open functions introduced in [5].","authors_text":"Sabir Hussain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-03-16T06:11:40Z","title":"On $\\gamma$-Semi-Continuous Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3109","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":"sha256:7a2ebe10e2c018cf0bb95a10e5e3891767256e0ebf750c046c9a57b23061f6b1","target":"record","created_at":"2026-05-18T04:26:44Z","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":"965a9535c3843ce26ba4fff2df7c28383b9c7bb9e4bb5c05360e7eec112a4b8b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-03-16T06:11:40Z","title_canon_sha256":"ddff8ce65d94f7f7387c2256c99a751f36274942343db759f8f33f5571a3de0a"},"schema_version":"1.0","source":{"id":"1103.3109","kind":"arxiv","version":1}},"canonical_sha256":"e25a9a36d23beab565257eb1e8942e77297267170815602d041141ccfbaf5f19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e25a9a36d23beab565257eb1e8942e77297267170815602d041141ccfbaf5f19","first_computed_at":"2026-05-18T04:26:44.779764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:44.779764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IUiBrOkIjfCZApYr8f8jdtpdYtCCH4J5tX2XrC9Vp5jsL8YEzkdmQH6S9vCf0BC19x9LVRWL8TMEobw2vspmDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:44.780598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a2ebe10e2c018cf0bb95a10e5e3891767256e0ebf750c046c9a57b23061f6b1","sha256:97071f64bc85b261d9ef7aed27a48b2cb9ef7b1566db482c840482755d1ad9d4"],"state_sha256":"6a03ce6639f42966ec56b7d66e79ce3db32582135fdc8e580877b0ba7276279e"}