{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7RQEHG3GZ6SSZ6Y47TCH3NSCLG","short_pith_number":"pith:7RQEHG3G","canonical_record":{"source":{"id":"1406.7312","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-27T20:43:18Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7a5ad08ceb8d24d0e602ee76c54fe68c16fd57ad6ab6452fb0aebc3529bf6d87","abstract_canon_sha256":"9b6458bf6ec2eb933983974a33279c2f9028e5273a9c2a00af420aaa2a211baa"},"schema_version":"1.0"},"canonical_sha256":"fc60439b66cfa52cfb1cfcc47db642599b81f39dae37d77ce6350f0e02a2c4f0","source":{"kind":"arxiv","id":"1406.7312","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7312","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7312v2","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7312","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"7RQEHG3GZ6SS","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7RQEHG3GZ6SSZ6Y4","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7RQEHG3G","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7RQEHG3GZ6SSZ6Y47TCH3NSCLG","target":"record","payload":{"canonical_record":{"source":{"id":"1406.7312","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-27T20:43:18Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"7a5ad08ceb8d24d0e602ee76c54fe68c16fd57ad6ab6452fb0aebc3529bf6d87","abstract_canon_sha256":"9b6458bf6ec2eb933983974a33279c2f9028e5273a9c2a00af420aaa2a211baa"},"schema_version":"1.0"},"canonical_sha256":"fc60439b66cfa52cfb1cfcc47db642599b81f39dae37d77ce6350f0e02a2c4f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:55.403685Z","signature_b64":"BYhzf3hr1tg8KCs8AJrSG4VBoEoM5mA4PunT0yKnfbPt9CK+NTXNA5YeEUn46O0B14e8Rgr5Xn3a9uEjhzD6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc60439b66cfa52cfb1cfcc47db642599b81f39dae37d77ce6350f0e02a2c4f0","last_reissued_at":"2026-05-18T01:11:55.403355Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:55.403355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.7312","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":"2026-05-18T01:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jni+Yy/xw391sfQQzrWQ+BnykNUZMaxY0Ac/Fk6P96EJaHd3FvlWtDazd+jTLFWYFr3y4LQzb1to7DWuEBOmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:40:15.664806Z"},"content_sha256":"98005b4b044c7e6e9205cb6615aaa8701b32499629e8a22a76707a1bbd984d1b","schema_version":"1.0","event_id":"sha256:98005b4b044c7e6e9205cb6615aaa8701b32499629e8a22a76707a1bbd984d1b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7RQEHG3GZ6SSZ6Y47TCH3NSCLG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational Connectivity and Analytic Contractibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Morgan Brown, Tyler Foster","submitted_at":"2014-06-27T20:43:18Z","abstract_excerpt":"Let k be an algebraically closed field of characteristic 0, and let f be a morphism of smooth projective varieties from X to Y over the ring k((t)) of formal Laurent series. We prove that if a general geometric fiber of f is rationally connected, then the Berkovich analytifications of X and Y are homotopy equivalent. Two important consequences of this result are that the homotopy type of the Berkovich analytification of any smooth projective variety X over k((t)) is a birational invariant of X, and that the Berkovich analytification of a rationally connected smooth projective variety over k((t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7312","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":"2026-05-18T01:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UmyRnJ7awW1XVDJXvzC500k35V/+J3hIjIUEssiQfySLDSO8VXZPDZn7GuGl883ZtPRVHB+Yxxuu3lFhqi0DBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:40:15.665148Z"},"content_sha256":"69389158b46f3301c2da99562afef9357257bdcaca7ac2975551d4a834fe1c98","schema_version":"1.0","event_id":"sha256:69389158b46f3301c2da99562afef9357257bdcaca7ac2975551d4a834fe1c98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RQEHG3GZ6SSZ6Y47TCH3NSCLG/bundle.json","state_url":"https://pith.science/pith/7RQEHG3GZ6SSZ6Y47TCH3NSCLG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RQEHG3GZ6SSZ6Y47TCH3NSCLG/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":"2026-06-02T14:40:15Z","links":{"resolver":"https://pith.science/pith/7RQEHG3GZ6SSZ6Y47TCH3NSCLG","bundle":"https://pith.science/pith/7RQEHG3GZ6SSZ6Y47TCH3NSCLG/bundle.json","state":"https://pith.science/pith/7RQEHG3GZ6SSZ6Y47TCH3NSCLG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RQEHG3GZ6SSZ6Y47TCH3NSCLG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7RQEHG3GZ6SSZ6Y47TCH3NSCLG","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":"9b6458bf6ec2eb933983974a33279c2f9028e5273a9c2a00af420aaa2a211baa","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-27T20:43:18Z","title_canon_sha256":"7a5ad08ceb8d24d0e602ee76c54fe68c16fd57ad6ab6452fb0aebc3529bf6d87"},"schema_version":"1.0","source":{"id":"1406.7312","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7312","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7312v2","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7312","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"7RQEHG3GZ6SS","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7RQEHG3GZ6SSZ6Y4","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7RQEHG3G","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:69389158b46f3301c2da99562afef9357257bdcaca7ac2975551d4a834fe1c98","target":"graph","created_at":"2026-05-18T01:11:55Z","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 k be an algebraically closed field of characteristic 0, and let f be a morphism of smooth projective varieties from X to Y over the ring k((t)) of formal Laurent series. We prove that if a general geometric fiber of f is rationally connected, then the Berkovich analytifications of X and Y are homotopy equivalent. Two important consequences of this result are that the homotopy type of the Berkovich analytification of any smooth projective variety X over k((t)) is a birational invariant of X, and that the Berkovich analytification of a rationally connected smooth projective variety over k((t","authors_text":"Morgan Brown, Tyler Foster","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-27T20:43:18Z","title":"Rational Connectivity and Analytic Contractibility"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7312","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":"sha256:98005b4b044c7e6e9205cb6615aaa8701b32499629e8a22a76707a1bbd984d1b","target":"record","created_at":"2026-05-18T01:11:55Z","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":"9b6458bf6ec2eb933983974a33279c2f9028e5273a9c2a00af420aaa2a211baa","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-06-27T20:43:18Z","title_canon_sha256":"7a5ad08ceb8d24d0e602ee76c54fe68c16fd57ad6ab6452fb0aebc3529bf6d87"},"schema_version":"1.0","source":{"id":"1406.7312","kind":"arxiv","version":2}},"canonical_sha256":"fc60439b66cfa52cfb1cfcc47db642599b81f39dae37d77ce6350f0e02a2c4f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc60439b66cfa52cfb1cfcc47db642599b81f39dae37d77ce6350f0e02a2c4f0","first_computed_at":"2026-05-18T01:11:55.403355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:55.403355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BYhzf3hr1tg8KCs8AJrSG4VBoEoM5mA4PunT0yKnfbPt9CK+NTXNA5YeEUn46O0B14e8Rgr5Xn3a9uEjhzD6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:55.403685Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7312","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98005b4b044c7e6e9205cb6615aaa8701b32499629e8a22a76707a1bbd984d1b","sha256:69389158b46f3301c2da99562afef9357257bdcaca7ac2975551d4a834fe1c98"],"state_sha256":"06e509e91dbd4f07a159e18aad81e1700d8c36482d028b96a1caa41932ee02f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gfr/vFWy+5ehq2lnOBhzxGd03PAW0WJK1NNYsK5vVvtzRLJGv8sEaf8n7PGkGF297JXJ+liLbtd66EDZD6iYDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:40:15.667409Z","bundle_sha256":"b11a6b4ef6b29c080be6f950b7b5388ea8497c44ac732f78f00b5b8923bceafd"}}