{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:M5CDPM7HWVSVSG2KJ6RAYAXNV5","short_pith_number":"pith:M5CDPM7H","canonical_record":{"source":{"id":"alg-geom/9703030","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1997-03-22T16:22:59Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"301e48458f3cf662cbbc38d48abf1983c9bd1fb4bbed3694d13860958423eefa","abstract_canon_sha256":"29f9991ffbbc82ab19f9e70dcea6cbe865a5177fe3281b6a307fa67cbbe0b773"},"schema_version":"1.0"},"canonical_sha256":"674437b3e7b565591b4a4fa20c02edaf7deb17b3e5608a0228bc39971a6f7507","source":{"kind":"arxiv","id":"alg-geom/9703030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9703030","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9703030v1","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9703030","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"pith_short_12","alias_value":"M5CDPM7HWVSV","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"M5CDPM7HWVSVSG2K","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"M5CDPM7H","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:M5CDPM7HWVSVSG2KJ6RAYAXNV5","target":"record","payload":{"canonical_record":{"source":{"id":"alg-geom/9703030","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1997-03-22T16:22:59Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"301e48458f3cf662cbbc38d48abf1983c9bd1fb4bbed3694d13860958423eefa","abstract_canon_sha256":"29f9991ffbbc82ab19f9e70dcea6cbe865a5177fe3281b6a307fa67cbbe0b773"},"schema_version":"1.0"},"canonical_sha256":"674437b3e7b565591b4a4fa20c02edaf7deb17b3e5608a0228bc39971a6f7507","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:49.121812Z","signature_b64":"pzN84jFy/EUmHrxKwQ8JZtr0J+Gb1dCTndrWeIP4o3B4Olct4xK8eee0AYJrhJbYBDC1kEpdPsA6SPGIIWRXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"674437b3e7b565591b4a4fa20c02edaf7deb17b3e5608a0228bc39971a6f7507","last_reissued_at":"2026-05-18T04:38:49.121387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:49.121387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"alg-geom/9703030","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":"2026-05-18T04:38:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EGbi4tk99FhImCMj2Kqq7qwqGeYMpBrq+ExS2A3wfruR2MeVt3HzWLUEtBsfvqes1VwNU6nfZM+TYJ/XayneAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:31:54.714405Z"},"content_sha256":"e4898b8167498670ce6bdd008bdd170e7448e1078aa5f65a91497dc4128ac7d9","schema_version":"1.0","event_id":"sha256:e4898b8167498670ce6bdd008bdd170e7448e1078aa5f65a91497dc4128ac7d9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:M5CDPM7HWVSVSG2KJ6RAYAXNV5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Alexander Invariants of Complex Hyperplane Arrangements","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Alexander I. Suciu, Daniel C. Cohen","submitted_at":"1997-03-22T16:22:59Z","abstract_excerpt":"Let A be an arrangement of complex hyperplanes. The fundamental group of the complement of A is determined by a braid monodromy homomorphism from a finitely generated free group to the pure braid group. Using the Gassner representation of the pure braid group, we find an explicit presentation for the Alexander invariant of A. From this presentation, we obtain combinatorial lower bounds for the ranks of the Chen groups of A. We also provide a combinatorial criterion for when these lower bounds are attained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9703030","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":"2026-05-18T04:38:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x4txzF/svC2XR6c2dSt/tfueXB6/fbfHcdgmSeZFdug2OvT4vBQ/MEb0LtTcp/BqQnvHSIRKocmllUkDeoo+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:31:54.715100Z"},"content_sha256":"65fd255de60fa3c9b86c507d78b9c171af8315ac410e1161a6b057d65f928a98","schema_version":"1.0","event_id":"sha256:65fd255de60fa3c9b86c507d78b9c171af8315ac410e1161a6b057d65f928a98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M5CDPM7HWVSVSG2KJ6RAYAXNV5/bundle.json","state_url":"https://pith.science/pith/M5CDPM7HWVSVSG2KJ6RAYAXNV5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M5CDPM7HWVSVSG2KJ6RAYAXNV5/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":"2026-06-04T23:31:54Z","links":{"resolver":"https://pith.science/pith/M5CDPM7HWVSVSG2KJ6RAYAXNV5","bundle":"https://pith.science/pith/M5CDPM7HWVSVSG2KJ6RAYAXNV5/bundle.json","state":"https://pith.science/pith/M5CDPM7HWVSVSG2KJ6RAYAXNV5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M5CDPM7HWVSVSG2KJ6RAYAXNV5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:M5CDPM7HWVSVSG2KJ6RAYAXNV5","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":"29f9991ffbbc82ab19f9e70dcea6cbe865a5177fe3281b6a307fa67cbbe0b773","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1997-03-22T16:22:59Z","title_canon_sha256":"301e48458f3cf662cbbc38d48abf1983c9bd1fb4bbed3694d13860958423eefa"},"schema_version":"1.0","source":{"id":"alg-geom/9703030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9703030","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9703030v1","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9703030","created_at":"2026-05-18T04:38:49Z"},{"alias_kind":"pith_short_12","alias_value":"M5CDPM7HWVSV","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"M5CDPM7HWVSVSG2K","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"M5CDPM7H","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:65fd255de60fa3c9b86c507d78b9c171af8315ac410e1161a6b057d65f928a98","target":"graph","created_at":"2026-05-18T04:38:49Z","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 A be an arrangement of complex hyperplanes. The fundamental group of the complement of A is determined by a braid monodromy homomorphism from a finitely generated free group to the pure braid group. Using the Gassner representation of the pure braid group, we find an explicit presentation for the Alexander invariant of A. From this presentation, we obtain combinatorial lower bounds for the ranks of the Chen groups of A. We also provide a combinatorial criterion for when these lower bounds are attained.","authors_text":"Alexander I. Suciu, Daniel C. Cohen","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1997-03-22T16:22:59Z","title":"Alexander Invariants of Complex Hyperplane Arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9703030","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:e4898b8167498670ce6bdd008bdd170e7448e1078aa5f65a91497dc4128ac7d9","target":"record","created_at":"2026-05-18T04:38:49Z","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":"29f9991ffbbc82ab19f9e70dcea6cbe865a5177fe3281b6a307fa67cbbe0b773","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1997-03-22T16:22:59Z","title_canon_sha256":"301e48458f3cf662cbbc38d48abf1983c9bd1fb4bbed3694d13860958423eefa"},"schema_version":"1.0","source":{"id":"alg-geom/9703030","kind":"arxiv","version":1}},"canonical_sha256":"674437b3e7b565591b4a4fa20c02edaf7deb17b3e5608a0228bc39971a6f7507","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"674437b3e7b565591b4a4fa20c02edaf7deb17b3e5608a0228bc39971a6f7507","first_computed_at":"2026-05-18T04:38:49.121387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:49.121387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pzN84jFy/EUmHrxKwQ8JZtr0J+Gb1dCTndrWeIP4o3B4Olct4xK8eee0AYJrhJbYBDC1kEpdPsA6SPGIIWRXBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:49.121812Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9703030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4898b8167498670ce6bdd008bdd170e7448e1078aa5f65a91497dc4128ac7d9","sha256:65fd255de60fa3c9b86c507d78b9c171af8315ac410e1161a6b057d65f928a98"],"state_sha256":"1c56ae63c0096ada5130da43507f7d733cb66721f31285ec3b1222c17c324d4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jrBSJRk+11ELmJNaAsGJ1VRRUYsJHKYHanHL34bipeaycp7LBzviNQfb8efvp9B+NmRNo7iXhvfB0rHRSrXHBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:31:54.718815Z","bundle_sha256":"40fb84de9d2bbc5163d13c9258c03a674602343176229207ea2ce7b28ce58a50"}}