{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AU4ZRVPDKG5W6ETVNYMLYX6HYH","short_pith_number":"pith:AU4ZRVPD","canonical_record":{"source":{"id":"1410.1948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-08T00:07:53Z","cross_cats_sorted":[],"title_canon_sha256":"acfb1227cbed878b6a9fd04302000c62059601ad184a20ed246f6322d11df1de","abstract_canon_sha256":"a553d5da6854a75981242e9c79f6cf070b09a7375ddec8eabb694189695bed62"},"schema_version":"1.0"},"canonical_sha256":"053998d5e351bb6f12756e18bc5fc7c1cd0a525e0e6a6a0c0300de14a01cfb31","source":{"kind":"arxiv","id":"1410.1948","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1948","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1948v2","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1948","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"pith_short_12","alias_value":"AU4ZRVPDKG5W","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AU4ZRVPDKG5W6ETV","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AU4ZRVPD","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AU4ZRVPDKG5W6ETVNYMLYX6HYH","target":"record","payload":{"canonical_record":{"source":{"id":"1410.1948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-08T00:07:53Z","cross_cats_sorted":[],"title_canon_sha256":"acfb1227cbed878b6a9fd04302000c62059601ad184a20ed246f6322d11df1de","abstract_canon_sha256":"a553d5da6854a75981242e9c79f6cf070b09a7375ddec8eabb694189695bed62"},"schema_version":"1.0"},"canonical_sha256":"053998d5e351bb6f12756e18bc5fc7c1cd0a525e0e6a6a0c0300de14a01cfb31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:13.325967Z","signature_b64":"B2RAGjkDOP/ayuBVrIkN+a9Ka0LKpnTbF+1AMmq1iuY7l7FX+PjA8jELw6WF5TVMOtb8Nml3LNWcJP1V7Xb5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"053998d5e351bb6f12756e18bc5fc7c1cd0a525e0e6a6a0c0300de14a01cfb31","last_reissued_at":"2026-05-18T01:34:13.325214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:13.325214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.1948","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DGnxm6hbRdgn3BDvMh4YdTaZy4gOnTyvYF3O5sb5jpjnmLaYhaqiF/T/2mo4h8YQ/bZuQp8wA3m4lOPkT6zNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:25:35.971233Z"},"content_sha256":"0c0013a42ff0a6dee6b20ee4db5aaeac2f2f488e2c6e9ab86907f5e19cb07f3b","schema_version":"1.0","event_id":"sha256:0c0013a42ff0a6dee6b20ee4db5aaeac2f2f488e2c6e9ab86907f5e19cb07f3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AU4ZRVPDKG5W6ETVNYMLYX6HYH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schemes as functors on topological rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cec\\'ilia Salgado, Oliver Lorscheid","submitted_at":"2014-10-08T00:07:53Z","abstract_excerpt":"Let $X$ be a scheme. In this text, we extend the known definitions of a topology on the set $X(R)$ of $R$-rational points from topological fields, local rings and ad\\`ele rings to any ring $R$ with a topology. This definition is functorial in both $X$ and $R$, and it does not rely on any restriction on $X$ like separability or finiteness conditions. We characterize properties of $R$, such as being a topological Hausdorff ring, a local ring or having $R^\\times$ as an open subset for which inversion is continuous, in terms of functorial properties of the topology of $X(R)$. Particular instances "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1948","kind":"arxiv","version":2},"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":"2026-05-18T01:34:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ttdEnxjMY0m+EFcM3rH5Xtn8wzO7gP4mUgE0woIGIWBsWSxeEldJS1XE4F9G1HSvnkTWUA8H2YZLUIlfXVHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:25:35.971576Z"},"content_sha256":"f87b9e42a3e886145f1a904e44ca1463cc639b3b708dfb42f21f98eeb11fba92","schema_version":"1.0","event_id":"sha256:f87b9e42a3e886145f1a904e44ca1463cc639b3b708dfb42f21f98eeb11fba92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AU4ZRVPDKG5W6ETVNYMLYX6HYH/bundle.json","state_url":"https://pith.science/pith/AU4ZRVPDKG5W6ETVNYMLYX6HYH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AU4ZRVPDKG5W6ETVNYMLYX6HYH/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":"2026-07-04T23:25:35Z","links":{"resolver":"https://pith.science/pith/AU4ZRVPDKG5W6ETVNYMLYX6HYH","bundle":"https://pith.science/pith/AU4ZRVPDKG5W6ETVNYMLYX6HYH/bundle.json","state":"https://pith.science/pith/AU4ZRVPDKG5W6ETVNYMLYX6HYH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AU4ZRVPDKG5W6ETVNYMLYX6HYH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AU4ZRVPDKG5W6ETVNYMLYX6HYH","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":"a553d5da6854a75981242e9c79f6cf070b09a7375ddec8eabb694189695bed62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-08T00:07:53Z","title_canon_sha256":"acfb1227cbed878b6a9fd04302000c62059601ad184a20ed246f6322d11df1de"},"schema_version":"1.0","source":{"id":"1410.1948","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.1948","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"arxiv_version","alias_value":"1410.1948v2","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1948","created_at":"2026-05-18T01:34:13Z"},{"alias_kind":"pith_short_12","alias_value":"AU4ZRVPDKG5W","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AU4ZRVPDKG5W6ETV","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AU4ZRVPD","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:f87b9e42a3e886145f1a904e44ca1463cc639b3b708dfb42f21f98eeb11fba92","target":"graph","created_at":"2026-05-18T01:34:13Z","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":"Let $X$ be a scheme. In this text, we extend the known definitions of a topology on the set $X(R)$ of $R$-rational points from topological fields, local rings and ad\\`ele rings to any ring $R$ with a topology. This definition is functorial in both $X$ and $R$, and it does not rely on any restriction on $X$ like separability or finiteness conditions. We characterize properties of $R$, such as being a topological Hausdorff ring, a local ring or having $R^\\times$ as an open subset for which inversion is continuous, in terms of functorial properties of the topology of $X(R)$. Particular instances ","authors_text":"Cec\\'ilia Salgado, Oliver Lorscheid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-08T00:07:53Z","title":"Schemes as functors on topological rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1948","kind":"arxiv","version":2},"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":"sha256:0c0013a42ff0a6dee6b20ee4db5aaeac2f2f488e2c6e9ab86907f5e19cb07f3b","target":"record","created_at":"2026-05-18T01:34:13Z","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":"a553d5da6854a75981242e9c79f6cf070b09a7375ddec8eabb694189695bed62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-10-08T00:07:53Z","title_canon_sha256":"acfb1227cbed878b6a9fd04302000c62059601ad184a20ed246f6322d11df1de"},"schema_version":"1.0","source":{"id":"1410.1948","kind":"arxiv","version":2}},"canonical_sha256":"053998d5e351bb6f12756e18bc5fc7c1cd0a525e0e6a6a0c0300de14a01cfb31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"053998d5e351bb6f12756e18bc5fc7c1cd0a525e0e6a6a0c0300de14a01cfb31","first_computed_at":"2026-05-18T01:34:13.325214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:13.325214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B2RAGjkDOP/ayuBVrIkN+a9Ka0LKpnTbF+1AMmq1iuY7l7FX+PjA8jELw6WF5TVMOtb8Nml3LNWcJP1V7Xb5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:13.325967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.1948","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c0013a42ff0a6dee6b20ee4db5aaeac2f2f488e2c6e9ab86907f5e19cb07f3b","sha256:f87b9e42a3e886145f1a904e44ca1463cc639b3b708dfb42f21f98eeb11fba92"],"state_sha256":"a6379bc94b8c38360d6cb39025462c53ded735f1c990355e337421154fec09f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dgRvqo4jNGOw0DJODYNRAUlV0XI3NG7ykWOVVY+B5SgB5qQlpQKyWrBzPKJedA55KSWt6QwFC8QVadNXqoy/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T23:25:35.973528Z","bundle_sha256":"0051680a49e775ed585b3324207d545638a5452cc52bdb63e381f4c2ee00b6e0"}}