{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:O326DSJR43BS37PCWYKERNGXJ3","short_pith_number":"pith:O326DSJR","canonical_record":{"source":{"id":"1805.10501","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-26T15:53:59Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"a81b56fba5d46f5acc2e6a4bd904975e42d8a17c68b44d495c5d3b49ad949365","abstract_canon_sha256":"0c686a95b477fc63a3be57e3b9259d64a57220fc7aa966c8e162069fdacaa2f0"},"schema_version":"1.0"},"canonical_sha256":"76f5e1c931e6c32dfde2b61448b4d74edfce57fb23f7304c4367e20813f367be","source":{"kind":"arxiv","id":"1805.10501","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10501","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10501v1","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10501","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"O326DSJR43BS","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"O326DSJR43BS37PC","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"O326DSJR","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:O326DSJR43BS37PCWYKERNGXJ3","target":"record","payload":{"canonical_record":{"source":{"id":"1805.10501","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-26T15:53:59Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"a81b56fba5d46f5acc2e6a4bd904975e42d8a17c68b44d495c5d3b49ad949365","abstract_canon_sha256":"0c686a95b477fc63a3be57e3b9259d64a57220fc7aa966c8e162069fdacaa2f0"},"schema_version":"1.0"},"canonical_sha256":"76f5e1c931e6c32dfde2b61448b4d74edfce57fb23f7304c4367e20813f367be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:52.332714Z","signature_b64":"VQjwZqla/J7LWmrU6rRDWi+32QM1ECMWya1uI2iKClkPrqm/Nb2Itm5HlxYg0hqM3b5DRmy23XLLUJ8AiIq4Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76f5e1c931e6c32dfde2b61448b4d74edfce57fb23f7304c4367e20813f367be","last_reissued_at":"2026-05-18T00:14:52.332164Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:52.332164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.10501","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":"2026-05-18T00:14:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d9/9ifT9kTtT32qjmaxWtst2uIFuZysHnqdHJPvzu4QpSThI9TuGFyVlo1tECru7RuTSR+fzJvj1fWvXyRLvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:50:41.441228Z"},"content_sha256":"e3428d765104ccc161a7e3235e44d46f449138f94d085f317ce4b482b94812e5","schema_version":"1.0","event_id":"sha256:e3428d765104ccc161a7e3235e44d46f449138f94d085f317ce4b482b94812e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:O326DSJR43BS37PCWYKERNGXJ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Riemann-Roch strategy, Complex lift of the Scaling Site","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.NT","authors_text":"Alain Connes, Caterina Consani","submitted_at":"2018-05-26T15:53:59Z","abstract_excerpt":"We describe the Riemann-Roch strategy which consists of adapting in characteristic zero Weil's proof, of RH in positive characteristic, following the ideas of Mattuck, Tate and Grothendieck. As a new step in this strategy we implement the technique of tropical descent that allows one to deduce existence results in characteristic one from the Riemann-Roch result over the complex numbers. In order to deal with arbitrary distribution functions this technique involves the results of Bohr, Jessen and Tornehave on almost periodic functions. Our main result is the construction, at the adelic level, o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10501","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":"2026-05-18T00:14:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r1+n7eewH3SxEqzrfmcYF1Dcn4Q+mA9B2V8q0Lv2uxt7CxLDigS4Z4Hy9jUm+UlzyYWsJmPch1vfVPBrsiO6Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T14:50:41.441583Z"},"content_sha256":"caa7fa4c324911c576f23ff6412b67a3460c2a31469a089a78c471cb2f7810f8","schema_version":"1.0","event_id":"sha256:caa7fa4c324911c576f23ff6412b67a3460c2a31469a089a78c471cb2f7810f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O326DSJR43BS37PCWYKERNGXJ3/bundle.json","state_url":"https://pith.science/pith/O326DSJR43BS37PCWYKERNGXJ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O326DSJR43BS37PCWYKERNGXJ3/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":"2026-06-03T14:50:41Z","links":{"resolver":"https://pith.science/pith/O326DSJR43BS37PCWYKERNGXJ3","bundle":"https://pith.science/pith/O326DSJR43BS37PCWYKERNGXJ3/bundle.json","state":"https://pith.science/pith/O326DSJR43BS37PCWYKERNGXJ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O326DSJR43BS37PCWYKERNGXJ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O326DSJR43BS37PCWYKERNGXJ3","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":"0c686a95b477fc63a3be57e3b9259d64a57220fc7aa966c8e162069fdacaa2f0","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-26T15:53:59Z","title_canon_sha256":"a81b56fba5d46f5acc2e6a4bd904975e42d8a17c68b44d495c5d3b49ad949365"},"schema_version":"1.0","source":{"id":"1805.10501","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10501","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10501v1","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10501","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"O326DSJR43BS","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"O326DSJR43BS37PC","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"O326DSJR","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:caa7fa4c324911c576f23ff6412b67a3460c2a31469a089a78c471cb2f7810f8","target":"graph","created_at":"2026-05-18T00:14:52Z","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":"We describe the Riemann-Roch strategy which consists of adapting in characteristic zero Weil's proof, of RH in positive characteristic, following the ideas of Mattuck, Tate and Grothendieck. As a new step in this strategy we implement the technique of tropical descent that allows one to deduce existence results in characteristic one from the Riemann-Roch result over the complex numbers. In order to deal with arbitrary distribution functions this technique involves the results of Bohr, Jessen and Tornehave on almost periodic functions. Our main result is the construction, at the adelic level, o","authors_text":"Alain Connes, Caterina Consani","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-26T15:53:59Z","title":"The Riemann-Roch strategy, Complex lift of the Scaling Site"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10501","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:e3428d765104ccc161a7e3235e44d46f449138f94d085f317ce4b482b94812e5","target":"record","created_at":"2026-05-18T00:14:52Z","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":"0c686a95b477fc63a3be57e3b9259d64a57220fc7aa966c8e162069fdacaa2f0","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-05-26T15:53:59Z","title_canon_sha256":"a81b56fba5d46f5acc2e6a4bd904975e42d8a17c68b44d495c5d3b49ad949365"},"schema_version":"1.0","source":{"id":"1805.10501","kind":"arxiv","version":1}},"canonical_sha256":"76f5e1c931e6c32dfde2b61448b4d74edfce57fb23f7304c4367e20813f367be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76f5e1c931e6c32dfde2b61448b4d74edfce57fb23f7304c4367e20813f367be","first_computed_at":"2026-05-18T00:14:52.332164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:52.332164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VQjwZqla/J7LWmrU6rRDWi+32QM1ECMWya1uI2iKClkPrqm/Nb2Itm5HlxYg0hqM3b5DRmy23XLLUJ8AiIq4Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:52.332714Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10501","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3428d765104ccc161a7e3235e44d46f449138f94d085f317ce4b482b94812e5","sha256:caa7fa4c324911c576f23ff6412b67a3460c2a31469a089a78c471cb2f7810f8"],"state_sha256":"c5924b3657197b697c00f2713befcaef75a9523c043753088954b528853ae225"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PxwOMlo4wR1QpdnSCKX6NOIViQzhT+vJqjJ2QqmKqTA61xWx6c2nkb8+I+PiR+o5HBEMqr0vBtHasT3sfBdEBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T14:50:41.443523Z","bundle_sha256":"86280dcac64d371a44c8d08f38868ea50c238b1ce23e59c8e80429fa4ed9ab57"}}