{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:FZ6FSLQJNUXNANX2FMERS5AF3P","short_pith_number":"pith:FZ6FSLQJ","canonical_record":{"source":{"id":"1010.1599","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-08T06:01:16Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"54c5638e581e608e188240c788edec43e326bbabc25b6c7d405a997aac97f09e","abstract_canon_sha256":"b81092a028b0183267add5ec93406957ebcb25ce060bed70d59a6419492f2c04"},"schema_version":"1.0"},"canonical_sha256":"2e7c592e096d2ed036fa2b09197405dbc3aedbeebf401a6215c58437a1aae5d7","source":{"kind":"arxiv","id":"1010.1599","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1599","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1599v4","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1599","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"pith_short_12","alias_value":"FZ6FSLQJNUXN","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FZ6FSLQJNUXNANX2","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FZ6FSLQJ","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:FZ6FSLQJNUXNANX2FMERS5AF3P","target":"record","payload":{"canonical_record":{"source":{"id":"1010.1599","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-08T06:01:16Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"54c5638e581e608e188240c788edec43e326bbabc25b6c7d405a997aac97f09e","abstract_canon_sha256":"b81092a028b0183267add5ec93406957ebcb25ce060bed70d59a6419492f2c04"},"schema_version":"1.0"},"canonical_sha256":"2e7c592e096d2ed036fa2b09197405dbc3aedbeebf401a6215c58437a1aae5d7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:30.257859Z","signature_b64":"a5tZ+tF7FA0514v4s/4jR+2kOXqo3q7MdVO+uwP48doyfHK4mJ203qwiBw23PmcXnwCArmK05Qvxr5PTpWqlDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e7c592e096d2ed036fa2b09197405dbc3aedbeebf401a6215c58437a1aae5d7","last_reissued_at":"2026-05-18T02:29:30.257409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:30.257409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.1599","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:29:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"86zbumDrdhiZE/bczC92Ef2vaCwYT5GoIDwWs4PesMd9AgKapIZL3jn6P3Ss5dN5l0OR59R9c1RsxJszcaeVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:32:18.186365Z"},"content_sha256":"47a07eba2d0f6075cc10aee93c8ee069dc6446eddc571a39fff5f632550e3b38","schema_version":"1.0","event_id":"sha256:47a07eba2d0f6075cc10aee93c8ee069dc6446eddc571a39fff5f632550e3b38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:FZ6FSLQJNUXNANX2FMERS5AF3P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toward Dirichlet's unit theorem on arithmetic varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Atsushi Moriwaki","submitted_at":"2010-10-08T06:01:16Z","abstract_excerpt":"In this paper, we would like to propose a fundamental question about a higher dimensional analogue of Dirichlet's unit theorem. We also give a partial answer to the question as an application of the arithmetic Hodge index theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1599","kind":"arxiv","version":4},"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":"2026-05-18T02:29:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xk1jnVQtlRXYGo/efBi82JRSi9WibJZ5co0SxVYXoSdXDoLt1H1G56XAMNTXsHlTK4d4gXepBEymYNe3Ly2WAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T08:32:18.186729Z"},"content_sha256":"7a7c550d4bddd8210cd071ee043cd4616ed9c8fbe8071e4144c1979ed3a76a16","schema_version":"1.0","event_id":"sha256:7a7c550d4bddd8210cd071ee043cd4616ed9c8fbe8071e4144c1979ed3a76a16"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZ6FSLQJNUXNANX2FMERS5AF3P/bundle.json","state_url":"https://pith.science/pith/FZ6FSLQJNUXNANX2FMERS5AF3P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZ6FSLQJNUXNANX2FMERS5AF3P/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":"2026-05-28T08:32:18Z","links":{"resolver":"https://pith.science/pith/FZ6FSLQJNUXNANX2FMERS5AF3P","bundle":"https://pith.science/pith/FZ6FSLQJNUXNANX2FMERS5AF3P/bundle.json","state":"https://pith.science/pith/FZ6FSLQJNUXNANX2FMERS5AF3P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZ6FSLQJNUXNANX2FMERS5AF3P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:FZ6FSLQJNUXNANX2FMERS5AF3P","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":"b81092a028b0183267add5ec93406957ebcb25ce060bed70d59a6419492f2c04","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-08T06:01:16Z","title_canon_sha256":"54c5638e581e608e188240c788edec43e326bbabc25b6c7d405a997aac97f09e"},"schema_version":"1.0","source":{"id":"1010.1599","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.1599","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"arxiv_version","alias_value":"1010.1599v4","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.1599","created_at":"2026-05-18T02:29:30Z"},{"alias_kind":"pith_short_12","alias_value":"FZ6FSLQJNUXN","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"FZ6FSLQJNUXNANX2","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"FZ6FSLQJ","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:7a7c550d4bddd8210cd071ee043cd4616ed9c8fbe8071e4144c1979ed3a76a16","target":"graph","created_at":"2026-05-18T02:29:30Z","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 would like to propose a fundamental question about a higher dimensional analogue of Dirichlet's unit theorem. We also give a partial answer to the question as an application of the arithmetic Hodge index theorem.","authors_text":"Atsushi Moriwaki","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-08T06:01:16Z","title":"Toward Dirichlet's unit theorem on arithmetic varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1599","kind":"arxiv","version":4},"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":"sha256:47a07eba2d0f6075cc10aee93c8ee069dc6446eddc571a39fff5f632550e3b38","target":"record","created_at":"2026-05-18T02:29:30Z","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":"b81092a028b0183267add5ec93406957ebcb25ce060bed70d59a6419492f2c04","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-08T06:01:16Z","title_canon_sha256":"54c5638e581e608e188240c788edec43e326bbabc25b6c7d405a997aac97f09e"},"schema_version":"1.0","source":{"id":"1010.1599","kind":"arxiv","version":4}},"canonical_sha256":"2e7c592e096d2ed036fa2b09197405dbc3aedbeebf401a6215c58437a1aae5d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e7c592e096d2ed036fa2b09197405dbc3aedbeebf401a6215c58437a1aae5d7","first_computed_at":"2026-05-18T02:29:30.257409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:30.257409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a5tZ+tF7FA0514v4s/4jR+2kOXqo3q7MdVO+uwP48doyfHK4mJ203qwiBw23PmcXnwCArmK05Qvxr5PTpWqlDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:30.257859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.1599","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47a07eba2d0f6075cc10aee93c8ee069dc6446eddc571a39fff5f632550e3b38","sha256:7a7c550d4bddd8210cd071ee043cd4616ed9c8fbe8071e4144c1979ed3a76a16"],"state_sha256":"02294a8d826be997004460670ea59f44c0cac10ee840915d15f9405cdb4f9e3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R2LJEWjhXhvnjNB/LPUFXfP0lLNGUhHPET1llCNX+Q5Wv7OCVa+HxMS0B0Hq5L+HOXp2dG8H8/SCkqhfoXFdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T08:32:18.188880Z","bundle_sha256":"44c6cd72f196f54c81a9489cd83eabca0d7012938bb00dd90de92069d8422220"}}