{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:OMRFJDTAC7FTLJYEZZFI72ML3I","short_pith_number":"pith:OMRFJDTA","canonical_record":{"source":{"id":"1607.03157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-11T20:37:03Z","cross_cats_sorted":[],"title_canon_sha256":"2859be0b1e7e032ca474cf70364d5658d01d2c46ea65f35584bb0c7458c10d30","abstract_canon_sha256":"b995728eeba49ed4b4068d73945da58618437c750a44f6c4f325d641be770d63"},"schema_version":"1.0"},"canonical_sha256":"7322548e6017cb35a704ce4a8fe98bda23b78950bb0c748b62aaf5848d6cff06","source":{"kind":"arxiv","id":"1607.03157","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03157","created_at":"2026-05-18T00:26:21Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03157v1","created_at":"2026-05-18T00:26:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03157","created_at":"2026-05-18T00:26:21Z"},{"alias_kind":"pith_short_12","alias_value":"OMRFJDTAC7FT","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OMRFJDTAC7FTLJYE","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OMRFJDTA","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:OMRFJDTAC7FTLJYEZZFI72ML3I","target":"record","payload":{"canonical_record":{"source":{"id":"1607.03157","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-11T20:37:03Z","cross_cats_sorted":[],"title_canon_sha256":"2859be0b1e7e032ca474cf70364d5658d01d2c46ea65f35584bb0c7458c10d30","abstract_canon_sha256":"b995728eeba49ed4b4068d73945da58618437c750a44f6c4f325d641be770d63"},"schema_version":"1.0"},"canonical_sha256":"7322548e6017cb35a704ce4a8fe98bda23b78950bb0c748b62aaf5848d6cff06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:21.491689Z","signature_b64":"NkbQCbNYF14uZdxuqeuNFtKWjdwz8iXOHvFfsutkeUdyN6dS89kwdaL0fHmwf/muq8k4Hq3ZIlYXUawdlcWnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7322548e6017cb35a704ce4a8fe98bda23b78950bb0c748b62aaf5848d6cff06","last_reissued_at":"2026-05-18T00:26:21.491047Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:21.491047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.03157","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":"2026-05-18T00:26:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hiaQoi/pwxUsw9IoHnlqXZGvOy9rMyGBpnmfhej9D+QbM/4kWElIiigumfcEmI1Ajcj31k/8BtqKrGj1jjqlDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:46:28.479544Z"},"content_sha256":"285424d1ce2763f9bb393db46ed4ef6646e492817abf3efcb05fcaa98e854f2f","schema_version":"1.0","event_id":"sha256:285424d1ce2763f9bb393db46ed4ef6646e492817abf3efcb05fcaa98e854f2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:OMRFJDTAC7FTLJYEZZFI72ML3I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characteristic cycle of the exterior product of constructible sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Takeshi Saito","submitted_at":"2016-07-11T20:37:03Z","abstract_excerpt":"We show that the characteristic cycle of the exterior product of constructible complexes is the exterior product of the characteristic cycles of factors. This implies the compatibility of characteristic cycles with smooth pull-back which is a first step in the proof of the index formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03157","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":"2026-05-18T00:26:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ft2Z1QYIUIdTGm0bBxFDzXFmPV1XRtTndhx+lLl5x06DdOopLchiM0n5WVUCfM8cXGlAlxk/Akhq+uBXeN+jBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:46:28.480273Z"},"content_sha256":"03822489942e8773116f192ca66f712feb5062a57a1471561ca32f64c067e908","schema_version":"1.0","event_id":"sha256:03822489942e8773116f192ca66f712feb5062a57a1471561ca32f64c067e908"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OMRFJDTAC7FTLJYEZZFI72ML3I/bundle.json","state_url":"https://pith.science/pith/OMRFJDTAC7FTLJYEZZFI72ML3I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OMRFJDTAC7FTLJYEZZFI72ML3I/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":"2026-06-05T19:46:28Z","links":{"resolver":"https://pith.science/pith/OMRFJDTAC7FTLJYEZZFI72ML3I","bundle":"https://pith.science/pith/OMRFJDTAC7FTLJYEZZFI72ML3I/bundle.json","state":"https://pith.science/pith/OMRFJDTAC7FTLJYEZZFI72ML3I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OMRFJDTAC7FTLJYEZZFI72ML3I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OMRFJDTAC7FTLJYEZZFI72ML3I","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":"b995728eeba49ed4b4068d73945da58618437c750a44f6c4f325d641be770d63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-11T20:37:03Z","title_canon_sha256":"2859be0b1e7e032ca474cf70364d5658d01d2c46ea65f35584bb0c7458c10d30"},"schema_version":"1.0","source":{"id":"1607.03157","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03157","created_at":"2026-05-18T00:26:21Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03157v1","created_at":"2026-05-18T00:26:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03157","created_at":"2026-05-18T00:26:21Z"},{"alias_kind":"pith_short_12","alias_value":"OMRFJDTAC7FT","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OMRFJDTAC7FTLJYE","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OMRFJDTA","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:03822489942e8773116f192ca66f712feb5062a57a1471561ca32f64c067e908","target":"graph","created_at":"2026-05-18T00:26:21Z","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 show that the characteristic cycle of the exterior product of constructible complexes is the exterior product of the characteristic cycles of factors. This implies the compatibility of characteristic cycles with smooth pull-back which is a first step in the proof of the index formula.","authors_text":"Takeshi Saito","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-11T20:37:03Z","title":"Characteristic cycle of the exterior product of constructible sheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03157","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":"sha256:285424d1ce2763f9bb393db46ed4ef6646e492817abf3efcb05fcaa98e854f2f","target":"record","created_at":"2026-05-18T00:26:21Z","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":"b995728eeba49ed4b4068d73945da58618437c750a44f6c4f325d641be770d63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-07-11T20:37:03Z","title_canon_sha256":"2859be0b1e7e032ca474cf70364d5658d01d2c46ea65f35584bb0c7458c10d30"},"schema_version":"1.0","source":{"id":"1607.03157","kind":"arxiv","version":1}},"canonical_sha256":"7322548e6017cb35a704ce4a8fe98bda23b78950bb0c748b62aaf5848d6cff06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7322548e6017cb35a704ce4a8fe98bda23b78950bb0c748b62aaf5848d6cff06","first_computed_at":"2026-05-18T00:26:21.491047Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:21.491047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NkbQCbNYF14uZdxuqeuNFtKWjdwz8iXOHvFfsutkeUdyN6dS89kwdaL0fHmwf/muq8k4Hq3ZIlYXUawdlcWnAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:21.491689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.03157","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:285424d1ce2763f9bb393db46ed4ef6646e492817abf3efcb05fcaa98e854f2f","sha256:03822489942e8773116f192ca66f712feb5062a57a1471561ca32f64c067e908"],"state_sha256":"fd377279f1153435022ca0883d68f90962a2043c377045511df77f328ff9461f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ViNYYf5Qk5JBiGtp1fGiboyt7+B2ZyaZsLzSepvYkLkYTe1jhwCn1dtvFm95hvjmaoljLQDX9muuhF/cxE2UBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:46:28.485425Z","bundle_sha256":"791797a71bfe602c4dd6935bbf45e0a39a8b71bd1618eb5ca74393e7d1bb5f77"}}