{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DEECJ4AOJ5KCNTQKA5745FTARO","short_pith_number":"pith:DEECJ4AO","canonical_record":{"source":{"id":"1509.06353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-09-21T19:24:54Z","cross_cats_sorted":[],"title_canon_sha256":"6aa7c033c497f85a3af754ebd98738237dd339199bc4a6ea797c098a981ecc8d","abstract_canon_sha256":"51f204a5c966034ad8e04201d5ee08042da91fcaa56c51b3ce187ce8f4256feb"},"schema_version":"1.0"},"canonical_sha256":"190824f00e4f5426ce0a077fce96608b9eac0117528ac6b1d17466815e43c43c","source":{"kind":"arxiv","id":"1509.06353","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06353","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06353v1","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06353","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"DEECJ4AOJ5KC","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DEECJ4AOJ5KCNTQK","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DEECJ4AO","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DEECJ4AOJ5KCNTQKA5745FTARO","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-09-21T19:24:54Z","cross_cats_sorted":[],"title_canon_sha256":"6aa7c033c497f85a3af754ebd98738237dd339199bc4a6ea797c098a981ecc8d","abstract_canon_sha256":"51f204a5c966034ad8e04201d5ee08042da91fcaa56c51b3ce187ce8f4256feb"},"schema_version":"1.0"},"canonical_sha256":"190824f00e4f5426ce0a077fce96608b9eac0117528ac6b1d17466815e43c43c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:35.285149Z","signature_b64":"ShfxbX90c8e7CrkCyyeajOuDqUuyXphjqBypM94poBQptOrAS8At0YKlk55Zyj8Wd29o/L94EzwvzAWcpbNvBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"190824f00e4f5426ce0a077fce96608b9eac0117528ac6b1d17466815e43c43c","last_reissued_at":"2026-05-18T01:32:35.284724Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:35.284724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06353","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":"2026-05-18T01:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7TmZlUZdRqivG318kecH6rOo77Ds2sxyfgusM6uRk4DCFVFgWFbE7fYZtKwmBGtZ0r9gcnzNfr45GaNLZjJNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:01:45.295159Z"},"content_sha256":"45db4edd2c428e3eaddd91e13f4d44c8ce8d6a884c0e4136a2e8a6f9c1eeb3d3","schema_version":"1.0","event_id":"sha256:45db4edd2c428e3eaddd91e13f4d44c8ce8d6a884c0e4136a2e8a6f9c1eeb3d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DEECJ4AOJ5KCNTQKA5745FTARO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Scott topology of a rooted non-metric tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Josnei Novacoski","submitted_at":"2015-09-21T19:24:54Z","abstract_excerpt":"In this paper we prove that the Scott topology $\\mathfrak S$ on a rooted non-metric tree $\\mathcal T$ is strictly coarser than the weak tree topology. Moreover, for each $t\\in \\mathcal T$, we consider a natural order $\\preceq_t$ on $\\mathcal T$ under which $t$ is the root of $\\mathcal T$. Then the weak tree topology is generated by the union of the Scott topologies $\\mathfrak S_t$ associated to $\\preceq_t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06353","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":"2026-05-18T01:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ii3fF9bV2fMnAs0QlXirrchPS5nbbyqI661TaCLWMIolJioq2P+S3ls8jqyHXeC7nqnf3QwEBNbGHQTZj9qICw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:01:45.295540Z"},"content_sha256":"986df5f0e0eb01bb24758d1213effb7fd734803dae35b8e16524947a16ed5f9d","schema_version":"1.0","event_id":"sha256:986df5f0e0eb01bb24758d1213effb7fd734803dae35b8e16524947a16ed5f9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DEECJ4AOJ5KCNTQKA5745FTARO/bundle.json","state_url":"https://pith.science/pith/DEECJ4AOJ5KCNTQKA5745FTARO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DEECJ4AOJ5KCNTQKA5745FTARO/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":"2026-05-30T09:01:45Z","links":{"resolver":"https://pith.science/pith/DEECJ4AOJ5KCNTQKA5745FTARO","bundle":"https://pith.science/pith/DEECJ4AOJ5KCNTQKA5745FTARO/bundle.json","state":"https://pith.science/pith/DEECJ4AOJ5KCNTQKA5745FTARO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DEECJ4AOJ5KCNTQKA5745FTARO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DEECJ4AOJ5KCNTQKA5745FTARO","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":"51f204a5c966034ad8e04201d5ee08042da91fcaa56c51b3ce187ce8f4256feb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-09-21T19:24:54Z","title_canon_sha256":"6aa7c033c497f85a3af754ebd98738237dd339199bc4a6ea797c098a981ecc8d"},"schema_version":"1.0","source":{"id":"1509.06353","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06353","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06353v1","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06353","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"DEECJ4AOJ5KC","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DEECJ4AOJ5KCNTQK","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DEECJ4AO","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:986df5f0e0eb01bb24758d1213effb7fd734803dae35b8e16524947a16ed5f9d","target":"graph","created_at":"2026-05-18T01:32:35Z","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 prove that the Scott topology $\\mathfrak S$ on a rooted non-metric tree $\\mathcal T$ is strictly coarser than the weak tree topology. Moreover, for each $t\\in \\mathcal T$, we consider a natural order $\\preceq_t$ on $\\mathcal T$ under which $t$ is the root of $\\mathcal T$. Then the weak tree topology is generated by the union of the Scott topologies $\\mathfrak S_t$ associated to $\\preceq_t$.","authors_text":"Josnei Novacoski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-09-21T19:24:54Z","title":"The Scott topology of a rooted non-metric tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06353","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":"sha256:45db4edd2c428e3eaddd91e13f4d44c8ce8d6a884c0e4136a2e8a6f9c1eeb3d3","target":"record","created_at":"2026-05-18T01:32:35Z","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":"51f204a5c966034ad8e04201d5ee08042da91fcaa56c51b3ce187ce8f4256feb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-09-21T19:24:54Z","title_canon_sha256":"6aa7c033c497f85a3af754ebd98738237dd339199bc4a6ea797c098a981ecc8d"},"schema_version":"1.0","source":{"id":"1509.06353","kind":"arxiv","version":1}},"canonical_sha256":"190824f00e4f5426ce0a077fce96608b9eac0117528ac6b1d17466815e43c43c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"190824f00e4f5426ce0a077fce96608b9eac0117528ac6b1d17466815e43c43c","first_computed_at":"2026-05-18T01:32:35.284724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:35.284724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ShfxbX90c8e7CrkCyyeajOuDqUuyXphjqBypM94poBQptOrAS8At0YKlk55Zyj8Wd29o/L94EzwvzAWcpbNvBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:35.285149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06353","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45db4edd2c428e3eaddd91e13f4d44c8ce8d6a884c0e4136a2e8a6f9c1eeb3d3","sha256:986df5f0e0eb01bb24758d1213effb7fd734803dae35b8e16524947a16ed5f9d"],"state_sha256":"c3dc7725ea703b9bbe212eece0041a2c7403808883ed9040bf651d4ec72799c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O8+Pe+w5OUDHeV6WgSiHhjvl4sU3NVi4BHYkBlmv0IXc6hyOw6UOu3YniN0Hi1kPSHfAeH13EeV9z1fQQkVnCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:01:45.297691Z","bundle_sha256":"41f58ac931620c71b3a57562360b9e7539ab3c410b5b97a28df9b444bf8b1724"}}