{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SYLCOEO5WIFP2S4DUY4K3JEJE2","short_pith_number":"pith:SYLCOEO5","canonical_record":{"source":{"id":"1301.5299","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T20:13:14Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"3e6e9bcc1381159ebf9db580c0f1249f544c9152f0dd0d25a7eac369c97aa2c4","abstract_canon_sha256":"58ec600b2ee5644739bed280adddb68954e90a6c62903876b75d598c23a17587"},"schema_version":"1.0"},"canonical_sha256":"96162711ddb20afd4b83a638ada489269352d6faf71d35930a5ad78bb1ceb1ab","source":{"kind":"arxiv","id":"1301.5299","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5299","created_at":"2026-05-18T00:06:56Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5299v3","created_at":"2026-05-18T00:06:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5299","created_at":"2026-05-18T00:06:56Z"},{"alias_kind":"pith_short_12","alias_value":"SYLCOEO5WIFP","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SYLCOEO5WIFP2S4D","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SYLCOEO5","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SYLCOEO5WIFP2S4DUY4K3JEJE2","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5299","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T20:13:14Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"3e6e9bcc1381159ebf9db580c0f1249f544c9152f0dd0d25a7eac369c97aa2c4","abstract_canon_sha256":"58ec600b2ee5644739bed280adddb68954e90a6c62903876b75d598c23a17587"},"schema_version":"1.0"},"canonical_sha256":"96162711ddb20afd4b83a638ada489269352d6faf71d35930a5ad78bb1ceb1ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:56.900345Z","signature_b64":"x7XVS4J1rRH3BDBa/KvyMcdt62yZ4Q6PmQQqqXBxObrhUyC69KnhqqePicFu4GoxDHZ8+ZE0j8wQQCUcTQjTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96162711ddb20afd4b83a638ada489269352d6faf71d35930a5ad78bb1ceb1ab","last_reissued_at":"2026-05-18T00:06:56.899756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:56.899756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5299","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fMUqsETt7wUwxIUzMN3yn/soYJrpxB1Iajy1h8e4/P72K0c/C3VTV49nQES2Sn7ye7l8vPji0kJI46vpZvnCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:46:09.990616Z"},"content_sha256":"cb2292c013652fb2deb545c9dd82fee17bd77607e3a142e9e4958a9d67ed1c60","schema_version":"1.0","event_id":"sha256:cb2292c013652fb2deb545c9dd82fee17bd77607e3a142e9e4958a9d67ed1c60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SYLCOEO5WIFP2S4DUY4K3JEJE2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Left regular bands and real Conic-Line arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"David Garber, Michael Friedman (IF)","submitted_at":"2013-01-22T20:13:14Z","abstract_excerpt":"An arrangement of curves in the real plane divides it into a collection of faces. In the case of line arrangements, there exists an associative product which gives this collection a structure of a left regular band. A natural question is whether the same is possible for other arrangements. In this paper, we try to answer this question for the simplest generalization of line arrangements, that is, conic--line arrangements.\n  Investigating the different algebraic structures induced by the face poset of a conic--line arrangement, we present two different generalizations for the product and its as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5299","kind":"arxiv","version":3},"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":"2026-05-18T00:06:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4HW2ttxPfBmVs+ie7Ghd6IKPdnH/aitSRl0+Yr1kAq6wg85INZez/mNziMpadVl3D2nu1lb5Fe6jSD8Jt1TABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:46:09.990971Z"},"content_sha256":"1af41a0c606d9f104715be9bfba354cd4267a9d3bc1521c45a44c334035635a2","schema_version":"1.0","event_id":"sha256:1af41a0c606d9f104715be9bfba354cd4267a9d3bc1521c45a44c334035635a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SYLCOEO5WIFP2S4DUY4K3JEJE2/bundle.json","state_url":"https://pith.science/pith/SYLCOEO5WIFP2S4DUY4K3JEJE2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SYLCOEO5WIFP2S4DUY4K3JEJE2/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":"2026-05-28T11:46:09Z","links":{"resolver":"https://pith.science/pith/SYLCOEO5WIFP2S4DUY4K3JEJE2","bundle":"https://pith.science/pith/SYLCOEO5WIFP2S4DUY4K3JEJE2/bundle.json","state":"https://pith.science/pith/SYLCOEO5WIFP2S4DUY4K3JEJE2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SYLCOEO5WIFP2S4DUY4K3JEJE2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SYLCOEO5WIFP2S4DUY4K3JEJE2","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":"58ec600b2ee5644739bed280adddb68954e90a6c62903876b75d598c23a17587","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T20:13:14Z","title_canon_sha256":"3e6e9bcc1381159ebf9db580c0f1249f544c9152f0dd0d25a7eac369c97aa2c4"},"schema_version":"1.0","source":{"id":"1301.5299","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5299","created_at":"2026-05-18T00:06:56Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5299v3","created_at":"2026-05-18T00:06:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5299","created_at":"2026-05-18T00:06:56Z"},{"alias_kind":"pith_short_12","alias_value":"SYLCOEO5WIFP","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SYLCOEO5WIFP2S4D","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SYLCOEO5","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:1af41a0c606d9f104715be9bfba354cd4267a9d3bc1521c45a44c334035635a2","target":"graph","created_at":"2026-05-18T00:06:56Z","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":"An arrangement of curves in the real plane divides it into a collection of faces. In the case of line arrangements, there exists an associative product which gives this collection a structure of a left regular band. A natural question is whether the same is possible for other arrangements. In this paper, we try to answer this question for the simplest generalization of line arrangements, that is, conic--line arrangements.\n  Investigating the different algebraic structures induced by the face poset of a conic--line arrangement, we present two different generalizations for the product and its as","authors_text":"David Garber, Michael Friedman (IF)","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T20:13:14Z","title":"On Left regular bands and real Conic-Line arrangements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5299","kind":"arxiv","version":3},"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:cb2292c013652fb2deb545c9dd82fee17bd77607e3a142e9e4958a9d67ed1c60","target":"record","created_at":"2026-05-18T00:06:56Z","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":"58ec600b2ee5644739bed280adddb68954e90a6c62903876b75d598c23a17587","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-01-22T20:13:14Z","title_canon_sha256":"3e6e9bcc1381159ebf9db580c0f1249f544c9152f0dd0d25a7eac369c97aa2c4"},"schema_version":"1.0","source":{"id":"1301.5299","kind":"arxiv","version":3}},"canonical_sha256":"96162711ddb20afd4b83a638ada489269352d6faf71d35930a5ad78bb1ceb1ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96162711ddb20afd4b83a638ada489269352d6faf71d35930a5ad78bb1ceb1ab","first_computed_at":"2026-05-18T00:06:56.899756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:56.899756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x7XVS4J1rRH3BDBa/KvyMcdt62yZ4Q6PmQQqqXBxObrhUyC69KnhqqePicFu4GoxDHZ8+ZE0j8wQQCUcTQjTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:56.900345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5299","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb2292c013652fb2deb545c9dd82fee17bd77607e3a142e9e4958a9d67ed1c60","sha256:1af41a0c606d9f104715be9bfba354cd4267a9d3bc1521c45a44c334035635a2"],"state_sha256":"6a3ad8ad51c0b0a1167d511d7a59bcd1e298eada0e1616139248f6ba7cc6989a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FwOyCo9HdHw2kiaPnptZk82Iuwk771JuOZT0psUve4p6Z0sddiU+Exb825QOybyIbVoFifpko6eq8NH24L9iCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:46:09.992914Z","bundle_sha256":"b1d393ad50587094db24bf368c0435dc7e3d1c1d55a15e863c339c3b7dd3be06"}}