{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:L4RQBIBYDV2TXXHCDNL54AQX4F","short_pith_number":"pith:L4RQBIBY","canonical_record":{"source":{"id":"1409.4316","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-15T16:43:52Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"3511d576847a971fbc032951a8b1ca467c390ba9572f238694814af592f0a178","abstract_canon_sha256":"03a3b4135e641a40fcee99af98fb21658b513d044c6a6b2b63178a3ece4bc3fa"},"schema_version":"1.0"},"canonical_sha256":"5f2300a0381d753bdce21b57de0217e17c7934a0ce9cc4d7178955050ce30b55","source":{"kind":"arxiv","id":"1409.4316","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4316","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4316v2","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4316","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"L4RQBIBYDV2T","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L4RQBIBYDV2TXXHC","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L4RQBIBY","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:L4RQBIBYDV2TXXHCDNL54AQX4F","target":"record","payload":{"canonical_record":{"source":{"id":"1409.4316","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-15T16:43:52Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"3511d576847a971fbc032951a8b1ca467c390ba9572f238694814af592f0a178","abstract_canon_sha256":"03a3b4135e641a40fcee99af98fb21658b513d044c6a6b2b63178a3ece4bc3fa"},"schema_version":"1.0"},"canonical_sha256":"5f2300a0381d753bdce21b57de0217e17c7934a0ce9cc4d7178955050ce30b55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:45.627982Z","signature_b64":"3WPm8RvjjpaUXxXqL8w9/kTFQX/l1sgZRFVIjoTkQW4lLbrAJmK6xErZfUGv9dKFvu3ew5JIa3IK/ho8uIDYDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f2300a0381d753bdce21b57de0217e17c7934a0ce9cc4d7178955050ce30b55","last_reissued_at":"2026-05-18T02:42:45.627477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:45.627477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.4316","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":"2026-05-18T02:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VDQVspwBvZeWt0W5H0pOW6WKyNnsRmTln1UJGCtiu9w235D8TkkTRO0SoxnQAxE9UYnMHuJhHfvaqoe78VfYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:08:01.205205Z"},"content_sha256":"a69bd1a3fa37fe7fea548b9efe13e249c2f8379abf76cdaa506fffc0e98aed51","schema_version":"1.0","event_id":"sha256:a69bd1a3fa37fe7fea548b9efe13e249c2f8379abf76cdaa506fffc0e98aed51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:L4RQBIBYDV2TXXHCDNL54AQX4F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Open book structures on semi-algebraic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.AG","authors_text":"Antonio Andrade (ICMC), Nicolas Dutertre (I2M), Raimundo N. Ara\\'ujo Dos Santos (ICMC), Ying Chen (ICMC)","submitted_at":"2014-09-15T16:43:52Z","abstract_excerpt":"Given a $C^2$ semi-algebraic mapping $F: \\mathbb{R}^N \\rightarrow \\mathbb{R}^p,$ we consider its restriction to $W\\hookrightarrow \\mathbb{R^{N}}$ an embedded closed semi-algebraic manifold of dimension $n-1\\geq p\\geq 2$ and introduce sufficient conditions for the existence of a fibration structure (generalized open book structure) induced by the projection $\\frac{F}{\\Vert F \\Vert}:W\\setminus F^{-1}(0)\\to S^{p-1}$. Moreover, we show that the well known local and global Milnor fibrations, in the real and complex settings, follow as a byproduct by considering $W$ as spheres of small and big radii"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4316","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":"2026-05-18T02:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PRvkNOrm1tHYiWBYEVdcJ/0UDzt261LPZeOl/83HVyUjx7iylAZrc6qZkw+sxXX+sEk3Hn98rLrFMitsBM7pAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:08:01.205975Z"},"content_sha256":"22f63a9af9a248d4daeb23f0dd2687edec9028cc020a25f58554800527f4b6dc","schema_version":"1.0","event_id":"sha256:22f63a9af9a248d4daeb23f0dd2687edec9028cc020a25f58554800527f4b6dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L4RQBIBYDV2TXXHCDNL54AQX4F/bundle.json","state_url":"https://pith.science/pith/L4RQBIBYDV2TXXHCDNL54AQX4F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L4RQBIBYDV2TXXHCDNL54AQX4F/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":"2026-06-09T05:08:01Z","links":{"resolver":"https://pith.science/pith/L4RQBIBYDV2TXXHCDNL54AQX4F","bundle":"https://pith.science/pith/L4RQBIBYDV2TXXHCDNL54AQX4F/bundle.json","state":"https://pith.science/pith/L4RQBIBYDV2TXXHCDNL54AQX4F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L4RQBIBYDV2TXXHCDNL54AQX4F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:L4RQBIBYDV2TXXHCDNL54AQX4F","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":"03a3b4135e641a40fcee99af98fb21658b513d044c6a6b2b63178a3ece4bc3fa","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-15T16:43:52Z","title_canon_sha256":"3511d576847a971fbc032951a8b1ca467c390ba9572f238694814af592f0a178"},"schema_version":"1.0","source":{"id":"1409.4316","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4316","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4316v2","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4316","created_at":"2026-05-18T02:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"L4RQBIBYDV2T","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L4RQBIBYDV2TXXHC","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L4RQBIBY","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:22f63a9af9a248d4daeb23f0dd2687edec9028cc020a25f58554800527f4b6dc","target":"graph","created_at":"2026-05-18T02:42:45Z","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":"Given a $C^2$ semi-algebraic mapping $F: \\mathbb{R}^N \\rightarrow \\mathbb{R}^p,$ we consider its restriction to $W\\hookrightarrow \\mathbb{R^{N}}$ an embedded closed semi-algebraic manifold of dimension $n-1\\geq p\\geq 2$ and introduce sufficient conditions for the existence of a fibration structure (generalized open book structure) induced by the projection $\\frac{F}{\\Vert F \\Vert}:W\\setminus F^{-1}(0)\\to S^{p-1}$. Moreover, we show that the well known local and global Milnor fibrations, in the real and complex settings, follow as a byproduct by considering $W$ as spheres of small and big radii","authors_text":"Antonio Andrade (ICMC), Nicolas Dutertre (I2M), Raimundo N. Ara\\'ujo Dos Santos (ICMC), Ying Chen (ICMC)","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-15T16:43:52Z","title":"Open book structures on semi-algebraic manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4316","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:a69bd1a3fa37fe7fea548b9efe13e249c2f8379abf76cdaa506fffc0e98aed51","target":"record","created_at":"2026-05-18T02:42:45Z","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":"03a3b4135e641a40fcee99af98fb21658b513d044c6a6b2b63178a3ece4bc3fa","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-15T16:43:52Z","title_canon_sha256":"3511d576847a971fbc032951a8b1ca467c390ba9572f238694814af592f0a178"},"schema_version":"1.0","source":{"id":"1409.4316","kind":"arxiv","version":2}},"canonical_sha256":"5f2300a0381d753bdce21b57de0217e17c7934a0ce9cc4d7178955050ce30b55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f2300a0381d753bdce21b57de0217e17c7934a0ce9cc4d7178955050ce30b55","first_computed_at":"2026-05-18T02:42:45.627477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:45.627477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3WPm8RvjjpaUXxXqL8w9/kTFQX/l1sgZRFVIjoTkQW4lLbrAJmK6xErZfUGv9dKFvu3ew5JIa3IK/ho8uIDYDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:45.627982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4316","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a69bd1a3fa37fe7fea548b9efe13e249c2f8379abf76cdaa506fffc0e98aed51","sha256:22f63a9af9a248d4daeb23f0dd2687edec9028cc020a25f58554800527f4b6dc"],"state_sha256":"525332c91c8de282d03badae3abab99a32b0ef9ee9d986c929d6845dad80ce51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+TFfgCmvkHP5Kj93/tdWho1RiKLWiMnG/nHVDGwNB1YZ6pQ/TfxC8trsSR1OYUM6O8XLAFKQ0nwHqXE6LaGXCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:08:01.210163Z","bundle_sha256":"3af0e3d5e0b0b9f8ddf1f9c531cb494c017e6a94b2ebad524a059792e2507adc"}}