{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ZX5C7HHJMKXVI6OGGWWGIVMFZO","short_pith_number":"pith:ZX5C7HHJ","canonical_record":{"source":{"id":"1402.3850","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-16T22:26:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b07b3f4ed113d8144a037432ec106f0957e940bc273312f19e615311c813efb8","abstract_canon_sha256":"d3214505f08013b1630fd07129e9db9b49defa7abb58ce42cec81332b2187fb7"},"schema_version":"1.0"},"canonical_sha256":"cdfa2f9ce962af5479c635ac645585cb80ae384283932afa46f8b93de10c780e","source":{"kind":"arxiv","id":"1402.3850","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3850","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3850v2","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3850","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"pith_short_12","alias_value":"ZX5C7HHJMKXV","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZX5C7HHJMKXVI6OG","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZX5C7HHJ","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ZX5C7HHJMKXVI6OGGWWGIVMFZO","target":"record","payload":{"canonical_record":{"source":{"id":"1402.3850","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-16T22:26:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"b07b3f4ed113d8144a037432ec106f0957e940bc273312f19e615311c813efb8","abstract_canon_sha256":"d3214505f08013b1630fd07129e9db9b49defa7abb58ce42cec81332b2187fb7"},"schema_version":"1.0"},"canonical_sha256":"cdfa2f9ce962af5479c635ac645585cb80ae384283932afa46f8b93de10c780e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:01.217445Z","signature_b64":"t7SkrtmLx3Cygt5V1C0gAuHfv3qLptkfyWD+8kGcWVJ1hzExBelL36E9xCnnJdVnd9WC1hYJZHEKa9wTChXkAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdfa2f9ce962af5479c635ac645585cb80ae384283932afa46f8b93de10c780e","last_reissued_at":"2026-05-18T02:30:01.217058Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:01.217058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.3850","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":"2026-05-18T02:30:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uy96ji82g3vNNJzUO3Fp0VUkuhpYfwVnz08OYWQ4Wuy3egz4caNKQ6aV4KH6jHCAAYJix+kzwuyM1E1yuzsrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T08:48:15.786020Z"},"content_sha256":"36bcfc0233bf04431cfba588dba2ee7c4862f65b389e3c5900ec27897a0969e6","schema_version":"1.0","event_id":"sha256:36bcfc0233bf04431cfba588dba2ee7c4862f65b389e3c5900ec27897a0969e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ZX5C7HHJMKXVI6OGGWWGIVMFZO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modular symbols in Iwasawa theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Kazuya Kato, Romyar Sharifi, Takako Fukaya","submitted_at":"2014-02-16T22:26:49Z","abstract_excerpt":"This survey paper is focused on a connection between the geometry of $\\mathrm{GL}_d$ and the arithmetic of $\\mathrm{GL}_{d-1}$ over global fields, for integers $d \\ge 2$. For $d = 2$ over $\\mathbb{Q}$, there is an explicit conjecture of the third author relating the geometry of modular curves and the arithmetic of cyclotomic fields, and it is proven in many instances by the work of the first two authors. The paper is divided into three parts: in the first, we explain the conjecture of the third author and the main result of the first two authors on it. In the second, we explain an analogous co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3850","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":"2026-05-18T02:30:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IdNwkvWZqNEZ5SSg9AdxxM6Af957i0OHBtMpAQdQ3oS9ziomDmLabFqZj/YEz+tDWXQtx2uzSgu9lKGh7m2MDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T08:48:15.786713Z"},"content_sha256":"1ed34130da570c12d28637a71ceae0190ef8f0772bde530dfcd0025bacdd83f6","schema_version":"1.0","event_id":"sha256:1ed34130da570c12d28637a71ceae0190ef8f0772bde530dfcd0025bacdd83f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZX5C7HHJMKXVI6OGGWWGIVMFZO/bundle.json","state_url":"https://pith.science/pith/ZX5C7HHJMKXVI6OGGWWGIVMFZO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZX5C7HHJMKXVI6OGGWWGIVMFZO/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":"2026-07-01T08:48:15Z","links":{"resolver":"https://pith.science/pith/ZX5C7HHJMKXVI6OGGWWGIVMFZO","bundle":"https://pith.science/pith/ZX5C7HHJMKXVI6OGGWWGIVMFZO/bundle.json","state":"https://pith.science/pith/ZX5C7HHJMKXVI6OGGWWGIVMFZO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZX5C7HHJMKXVI6OGGWWGIVMFZO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ZX5C7HHJMKXVI6OGGWWGIVMFZO","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":"d3214505f08013b1630fd07129e9db9b49defa7abb58ce42cec81332b2187fb7","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-16T22:26:49Z","title_canon_sha256":"b07b3f4ed113d8144a037432ec106f0957e940bc273312f19e615311c813efb8"},"schema_version":"1.0","source":{"id":"1402.3850","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3850","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3850v2","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3850","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"pith_short_12","alias_value":"ZX5C7HHJMKXV","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZX5C7HHJMKXVI6OG","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZX5C7HHJ","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:1ed34130da570c12d28637a71ceae0190ef8f0772bde530dfcd0025bacdd83f6","target":"graph","created_at":"2026-05-18T02:30:01Z","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":"This survey paper is focused on a connection between the geometry of $\\mathrm{GL}_d$ and the arithmetic of $\\mathrm{GL}_{d-1}$ over global fields, for integers $d \\ge 2$. For $d = 2$ over $\\mathbb{Q}$, there is an explicit conjecture of the third author relating the geometry of modular curves and the arithmetic of cyclotomic fields, and it is proven in many instances by the work of the first two authors. The paper is divided into three parts: in the first, we explain the conjecture of the third author and the main result of the first two authors on it. In the second, we explain an analogous co","authors_text":"Kazuya Kato, Romyar Sharifi, Takako Fukaya","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-16T22:26:49Z","title":"Modular symbols in Iwasawa theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3850","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":"sha256:36bcfc0233bf04431cfba588dba2ee7c4862f65b389e3c5900ec27897a0969e6","target":"record","created_at":"2026-05-18T02:30:01Z","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":"d3214505f08013b1630fd07129e9db9b49defa7abb58ce42cec81332b2187fb7","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-16T22:26:49Z","title_canon_sha256":"b07b3f4ed113d8144a037432ec106f0957e940bc273312f19e615311c813efb8"},"schema_version":"1.0","source":{"id":"1402.3850","kind":"arxiv","version":2}},"canonical_sha256":"cdfa2f9ce962af5479c635ac645585cb80ae384283932afa46f8b93de10c780e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdfa2f9ce962af5479c635ac645585cb80ae384283932afa46f8b93de10c780e","first_computed_at":"2026-05-18T02:30:01.217058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:01.217058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t7SkrtmLx3Cygt5V1C0gAuHfv3qLptkfyWD+8kGcWVJ1hzExBelL36E9xCnnJdVnd9WC1hYJZHEKa9wTChXkAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:01.217445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.3850","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36bcfc0233bf04431cfba588dba2ee7c4862f65b389e3c5900ec27897a0969e6","sha256:1ed34130da570c12d28637a71ceae0190ef8f0772bde530dfcd0025bacdd83f6"],"state_sha256":"3e3e85f311443cbc3b2ca1773797b1988e2c4058e88a7117931e494991d64ae4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Klr8K45OJjpyjaGm+Y2gAn5LnwAd6TPCkfMPPILQOpc+pKScjBxnp9YzKJwX1ZU9FrhPsUvGQHQyhK1Mv7+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T08:48:15.790380Z","bundle_sha256":"6d6ee63126a5d857629edf6fe98f9fa209a59dbd070f632da42e851abf58b7d3"}}