{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HSZAP3RRJBHF6K4B5WF2CXE2DM","short_pith_number":"pith:HSZAP3RR","canonical_record":{"source":{"id":"1503.02489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-09T14:41:20Z","cross_cats_sorted":[],"title_canon_sha256":"38db89e2ccc8fc6ee9845344e3c854eda3cacfb8f3885f25a32f77a29b565db5","abstract_canon_sha256":"cd56eeda3a7d5d542560cf69a29a0a72d81d043c4f992132469feef4e139c69f"},"schema_version":"1.0"},"canonical_sha256":"3cb207ee31484e5f2b81ed8ba15c9a1b09d3027c937058dc7cf10de5e35cad3f","source":{"kind":"arxiv","id":"1503.02489","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02489","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02489v1","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02489","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"pith_short_12","alias_value":"HSZAP3RRJBHF","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HSZAP3RRJBHF6K4B","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HSZAP3RR","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HSZAP3RRJBHF6K4B5WF2CXE2DM","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-09T14:41:20Z","cross_cats_sorted":[],"title_canon_sha256":"38db89e2ccc8fc6ee9845344e3c854eda3cacfb8f3885f25a32f77a29b565db5","abstract_canon_sha256":"cd56eeda3a7d5d542560cf69a29a0a72d81d043c4f992132469feef4e139c69f"},"schema_version":"1.0"},"canonical_sha256":"3cb207ee31484e5f2b81ed8ba15c9a1b09d3027c937058dc7cf10de5e35cad3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:19.510702Z","signature_b64":"PfJY4/pQBZAN85RGNO4GnLDaKNiyDKDExEUIYg89ROtZhKnetNJKRM/cCERVvcZ0ShKO0Wly0Lv38jrW9DIIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cb207ee31484e5f2b81ed8ba15c9a1b09d3027c937058dc7cf10de5e35cad3f","last_reissued_at":"2026-05-18T02:25:19.510364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:19.510364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02489","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":"2026-05-18T02:25:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3vc29Ig7Wjukli0xoIJC6s8pFn6Yuhyl9o7iMUYsIs8TfIxOi8N3//WzUZHrAu4SNsw1E7TuSsW3/l+oCDDBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:26:54.331033Z"},"content_sha256":"f1e689267e99edaf1dabad4dd3548bf7cb13d01a648f0b81a30f168ddba94850","schema_version":"1.0","event_id":"sha256:f1e689267e99edaf1dabad4dd3548bf7cb13d01a648f0b81a30f168ddba94850"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HSZAP3RRJBHF6K4B5WF2CXE2DM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arithmetic analogues of some basic concepts from Riemannian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alexandru Buium","submitted_at":"2015-03-09T14:41:20Z","abstract_excerpt":"Following recent work of the author, partly in collaboration with T. Dupuy and M. Barrett, we describe arithmetic analogues of some key concepts from Riemannian geometry such as: metrics, Chern connections, curvature, etc. Theorems are stated to the effect that the spectrum of the integers has a non-vanishing curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02489","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":"2026-05-18T02:25:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OOQ1uthTNJ/j6HgOqRbDd1R0rt+OGLpRHU3HBjjz6Chxp3Ny6rZByBVVe2IfsmX9e1MmBKSs5auMAGwqiyx7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:26:54.331377Z"},"content_sha256":"4159c591b02588a2ba4322ec9d5d04f5e569ac16b7ccc92c7b27341cb5c53cf9","schema_version":"1.0","event_id":"sha256:4159c591b02588a2ba4322ec9d5d04f5e569ac16b7ccc92c7b27341cb5c53cf9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HSZAP3RRJBHF6K4B5WF2CXE2DM/bundle.json","state_url":"https://pith.science/pith/HSZAP3RRJBHF6K4B5WF2CXE2DM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HSZAP3RRJBHF6K4B5WF2CXE2DM/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":"2026-06-03T01:26:54Z","links":{"resolver":"https://pith.science/pith/HSZAP3RRJBHF6K4B5WF2CXE2DM","bundle":"https://pith.science/pith/HSZAP3RRJBHF6K4B5WF2CXE2DM/bundle.json","state":"https://pith.science/pith/HSZAP3RRJBHF6K4B5WF2CXE2DM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HSZAP3RRJBHF6K4B5WF2CXE2DM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HSZAP3RRJBHF6K4B5WF2CXE2DM","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":"cd56eeda3a7d5d542560cf69a29a0a72d81d043c4f992132469feef4e139c69f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-09T14:41:20Z","title_canon_sha256":"38db89e2ccc8fc6ee9845344e3c854eda3cacfb8f3885f25a32f77a29b565db5"},"schema_version":"1.0","source":{"id":"1503.02489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02489","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02489v1","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02489","created_at":"2026-05-18T02:25:19Z"},{"alias_kind":"pith_short_12","alias_value":"HSZAP3RRJBHF","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HSZAP3RRJBHF6K4B","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HSZAP3RR","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:4159c591b02588a2ba4322ec9d5d04f5e569ac16b7ccc92c7b27341cb5c53cf9","target":"graph","created_at":"2026-05-18T02:25:19Z","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":"Following recent work of the author, partly in collaboration with T. Dupuy and M. Barrett, we describe arithmetic analogues of some key concepts from Riemannian geometry such as: metrics, Chern connections, curvature, etc. Theorems are stated to the effect that the spectrum of the integers has a non-vanishing curvature.","authors_text":"Alexandru Buium","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-09T14:41:20Z","title":"Arithmetic analogues of some basic concepts from Riemannian geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02489","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:f1e689267e99edaf1dabad4dd3548bf7cb13d01a648f0b81a30f168ddba94850","target":"record","created_at":"2026-05-18T02:25:19Z","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":"cd56eeda3a7d5d542560cf69a29a0a72d81d043c4f992132469feef4e139c69f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-03-09T14:41:20Z","title_canon_sha256":"38db89e2ccc8fc6ee9845344e3c854eda3cacfb8f3885f25a32f77a29b565db5"},"schema_version":"1.0","source":{"id":"1503.02489","kind":"arxiv","version":1}},"canonical_sha256":"3cb207ee31484e5f2b81ed8ba15c9a1b09d3027c937058dc7cf10de5e35cad3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cb207ee31484e5f2b81ed8ba15c9a1b09d3027c937058dc7cf10de5e35cad3f","first_computed_at":"2026-05-18T02:25:19.510364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:19.510364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PfJY4/pQBZAN85RGNO4GnLDaKNiyDKDExEUIYg89ROtZhKnetNJKRM/cCERVvcZ0ShKO0Wly0Lv38jrW9DIIDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:19.510702Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1e689267e99edaf1dabad4dd3548bf7cb13d01a648f0b81a30f168ddba94850","sha256:4159c591b02588a2ba4322ec9d5d04f5e569ac16b7ccc92c7b27341cb5c53cf9"],"state_sha256":"6e3c9f647f07955afd3f3c594baa9909f73fba51a536275060bc2d015db787fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2B9aGZHf40wuk5q4JtW2MHouiY2dRsNFt1my1X7F8wQ70Qpwu7jZ4ugXhQdfJLtfUMkDETX4qtE8WStU8y4nCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:26:54.333264Z","bundle_sha256":"85936b73c517a647945518897553b3f479c20f3b87ad33bcecc7a1e8adbeb8bc"}}