{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WIWH6JNNAW7BLRBIS5Q5O44Z7U","short_pith_number":"pith:WIWH6JNN","canonical_record":{"source":{"id":"1604.02381","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-08T15:41:31Z","cross_cats_sorted":[],"title_canon_sha256":"3a63a6ccc9a294059c725972d1aa96d112897aa2fca47ac05e0eaa1c71ca5d9b","abstract_canon_sha256":"0b204dcf6c76d9f02d922e2f723bf961bc938a75857cd64235993bcc13c97136"},"schema_version":"1.0"},"canonical_sha256":"b22c7f25ad05be15c4289761d77399fd01ce60c45deaf65c37fe356c30ca7907","source":{"kind":"arxiv","id":"1604.02381","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02381","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02381v2","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02381","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"WIWH6JNNAW7B","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WIWH6JNNAW7BLRBI","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WIWH6JNN","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WIWH6JNNAW7BLRBIS5Q5O44Z7U","target":"record","payload":{"canonical_record":{"source":{"id":"1604.02381","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-08T15:41:31Z","cross_cats_sorted":[],"title_canon_sha256":"3a63a6ccc9a294059c725972d1aa96d112897aa2fca47ac05e0eaa1c71ca5d9b","abstract_canon_sha256":"0b204dcf6c76d9f02d922e2f723bf961bc938a75857cd64235993bcc13c97136"},"schema_version":"1.0"},"canonical_sha256":"b22c7f25ad05be15c4289761d77399fd01ce60c45deaf65c37fe356c30ca7907","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:12.617024Z","signature_b64":"mgLXZLlcbuypdWC22Lex1oqJmJy9Zu9AaBaT3xzPFr2FZx61JXIcdKEix3sW6fxdwa6l3XPD8JfgnEHQTEaRCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b22c7f25ad05be15c4289761d77399fd01ce60c45deaf65c37fe356c30ca7907","last_reissued_at":"2026-05-18T00:07:12.616502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:12.616502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.02381","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":"2026-05-18T00:07:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h5SVJVDxiNxOsvDBH59u0H4s6OYvitzaMFWKBeRyTr2CEA5ZgDSyBRt4YrMQlmGm6nHNy8LfeqsI78t3wZ9pBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:06:47.137946Z"},"content_sha256":"befc09eae760bed367269724bf57f90960d15c76f9e81f703d384605c76a6d38","schema_version":"1.0","event_id":"sha256:befc09eae760bed367269724bf57f90960d15c76f9e81f703d384605c76a6d38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WIWH6JNNAW7BLRBIS5Q5O44Z7U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Morphisms of 1-motives defined by line bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cristiana Bertolin, Sylvain Brochard","submitted_at":"2016-04-08T15:41:31Z","abstract_excerpt":"Let $S$ be a normal base scheme. The aim of this paper is to study the line bundles on 1-motives defined over $S$. We first compute a d\\'evissage of the Picard group of a 1-motive $M$ according to the weight filtration of $M$. This d\\'evissage allows us to associate, to each line bundle $L$ on $M$, a linear morphism $\\varphi_{L}: M \\rightarrow M^*$ from $M$ to its Cartier dual. This yields a group homomorphism $\\Phi : Pic(M) / Pic(S) \\to Hom(M,M^*)$. We also prove the Theorem of the Cube for 1-motives, which furnishes another construction of the group homomorphism $\\Phi : Pic(M) / Pic(S) \\to H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02381","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":"2026-05-18T00:07:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gCqHfSMHJCYSNHAJkRq/21wYx7j8+xBfEZQa09y12mUOECwljSjbaIy93o1scrQqsOwV0oVTwyMRFMFU3qorBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:06:47.138730Z"},"content_sha256":"3f8f610e5f22ed5ce751e2f68d8babad1b2059b95c1d72e6ac4fcdd4103c40d6","schema_version":"1.0","event_id":"sha256:3f8f610e5f22ed5ce751e2f68d8babad1b2059b95c1d72e6ac4fcdd4103c40d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WIWH6JNNAW7BLRBIS5Q5O44Z7U/bundle.json","state_url":"https://pith.science/pith/WIWH6JNNAW7BLRBIS5Q5O44Z7U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WIWH6JNNAW7BLRBIS5Q5O44Z7U/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":"2026-06-11T01:06:47Z","links":{"resolver":"https://pith.science/pith/WIWH6JNNAW7BLRBIS5Q5O44Z7U","bundle":"https://pith.science/pith/WIWH6JNNAW7BLRBIS5Q5O44Z7U/bundle.json","state":"https://pith.science/pith/WIWH6JNNAW7BLRBIS5Q5O44Z7U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WIWH6JNNAW7BLRBIS5Q5O44Z7U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WIWH6JNNAW7BLRBIS5Q5O44Z7U","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":"0b204dcf6c76d9f02d922e2f723bf961bc938a75857cd64235993bcc13c97136","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-08T15:41:31Z","title_canon_sha256":"3a63a6ccc9a294059c725972d1aa96d112897aa2fca47ac05e0eaa1c71ca5d9b"},"schema_version":"1.0","source":{"id":"1604.02381","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02381","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02381v2","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02381","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"WIWH6JNNAW7B","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"WIWH6JNNAW7BLRBI","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"WIWH6JNN","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:3f8f610e5f22ed5ce751e2f68d8babad1b2059b95c1d72e6ac4fcdd4103c40d6","target":"graph","created_at":"2026-05-18T00:07:12Z","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 $S$ be a normal base scheme. The aim of this paper is to study the line bundles on 1-motives defined over $S$. We first compute a d\\'evissage of the Picard group of a 1-motive $M$ according to the weight filtration of $M$. This d\\'evissage allows us to associate, to each line bundle $L$ on $M$, a linear morphism $\\varphi_{L}: M \\rightarrow M^*$ from $M$ to its Cartier dual. This yields a group homomorphism $\\Phi : Pic(M) / Pic(S) \\to Hom(M,M^*)$. We also prove the Theorem of the Cube for 1-motives, which furnishes another construction of the group homomorphism $\\Phi : Pic(M) / Pic(S) \\to H","authors_text":"Cristiana Bertolin, Sylvain Brochard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-08T15:41:31Z","title":"Morphisms of 1-motives defined by line bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02381","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:befc09eae760bed367269724bf57f90960d15c76f9e81f703d384605c76a6d38","target":"record","created_at":"2026-05-18T00:07:12Z","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":"0b204dcf6c76d9f02d922e2f723bf961bc938a75857cd64235993bcc13c97136","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-04-08T15:41:31Z","title_canon_sha256":"3a63a6ccc9a294059c725972d1aa96d112897aa2fca47ac05e0eaa1c71ca5d9b"},"schema_version":"1.0","source":{"id":"1604.02381","kind":"arxiv","version":2}},"canonical_sha256":"b22c7f25ad05be15c4289761d77399fd01ce60c45deaf65c37fe356c30ca7907","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b22c7f25ad05be15c4289761d77399fd01ce60c45deaf65c37fe356c30ca7907","first_computed_at":"2026-05-18T00:07:12.616502Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:12.616502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mgLXZLlcbuypdWC22Lex1oqJmJy9Zu9AaBaT3xzPFr2FZx61JXIcdKEix3sW6fxdwa6l3XPD8JfgnEHQTEaRCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:12.617024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02381","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:befc09eae760bed367269724bf57f90960d15c76f9e81f703d384605c76a6d38","sha256:3f8f610e5f22ed5ce751e2f68d8babad1b2059b95c1d72e6ac4fcdd4103c40d6"],"state_sha256":"01853a755ae7ce232687a76384810d78da12604ff9fcfeda00d0ea76015896f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vs6nyIHFGPcCyEZBX2r83kcs3TgOnfWeFNyHeyXVsBYMbplOjbz4vCFIGWy2GWZzpNIYyIZMiUUqBUP22UlDCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T01:06:47.142463Z","bundle_sha256":"642cba7b7100d9924af84a3a53242fdd52462665dde9ccf5caf32f9606e9bcf9"}}