{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:DU5LZW5HDGUMN4TJS7NXLVMJZ4","short_pith_number":"pith:DU5LZW5H","canonical_record":{"source":{"id":"2411.09602","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-14T17:22:00Z","cross_cats_sorted":["math.CV","math.DS"],"title_canon_sha256":"f2d37e1a8dc9d010503953c53bd996af1a82ab719485116186c9c13051eed9de","abstract_canon_sha256":"ac67590b44a8b8e2b62cce2d03f78ee1df5ac3b9899915c3e6f6b9c6ebdd91fa"},"schema_version":"1.0"},"canonical_sha256":"1d3abcdba719a8c6f26997db75d589cf0e1665beb1b80925ec5b64ecc1e5a5cb","source":{"kind":"arxiv","id":"2411.09602","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.09602","created_at":"2026-07-05T09:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"2411.09602v2","created_at":"2026-07-05T09:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09602","created_at":"2026-07-05T09:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"DU5LZW5HDGUM","created_at":"2026-07-05T09:52:40Z"},{"alias_kind":"pith_short_16","alias_value":"DU5LZW5HDGUMN4TJ","created_at":"2026-07-05T09:52:40Z"},{"alias_kind":"pith_short_8","alias_value":"DU5LZW5H","created_at":"2026-07-05T09:52:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:DU5LZW5HDGUMN4TJS7NXLVMJZ4","target":"record","payload":{"canonical_record":{"source":{"id":"2411.09602","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-14T17:22:00Z","cross_cats_sorted":["math.CV","math.DS"],"title_canon_sha256":"f2d37e1a8dc9d010503953c53bd996af1a82ab719485116186c9c13051eed9de","abstract_canon_sha256":"ac67590b44a8b8e2b62cce2d03f78ee1df5ac3b9899915c3e6f6b9c6ebdd91fa"},"schema_version":"1.0"},"canonical_sha256":"1d3abcdba719a8c6f26997db75d589cf0e1665beb1b80925ec5b64ecc1e5a5cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:52:40.422205Z","signature_b64":"sq5Q5bzqE/19Hwjtu2aMm7XIPMrc8P0nopp012+UIHHW5IVjufaBxZ3hwaBBDUZoP/TEJTIU/2YxrbLkUIGTCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d3abcdba719a8c6f26997db75d589cf0e1665beb1b80925ec5b64ecc1e5a5cb","last_reissued_at":"2026-07-05T09:52:40.421825Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:52:40.421825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.09602","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":"2026-07-05T09:52:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"do/VBaZutHFMA5L6Ku2UkR9o17HA4+janoMKnaG7mwxQqxqP6eCU9w0LIkDZ+b1wqlGDekrvkQd4nqj/5TqpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:02:45.145402Z"},"content_sha256":"94f1d85c85cb3b9a784588c740d7cd80c0927340f424eb21a3620f8cb3aed09d","schema_version":"1.0","event_id":"sha256:94f1d85c85cb3b9a784588c740d7cd80c0927340f424eb21a3620f8cb3aed09d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:DU5LZW5HDGUMN4TJS7NXLVMJZ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Webs Generated by Products of convex and homogeneous Foliations on $\\mathbb{P}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DS"],"primary_cat":"math.AG","authors_text":"Carla Pracias, Maycol Falla Luza","submitted_at":"2024-11-14T17:22:00Z","abstract_excerpt":"This paper investigates flat webs on the projective plane. We present two methods for constructing such webs: the first involves taking the product of finitely many convex reduced foliations and invariant lines, while the second consists of taking the product of finitely many convex homogeneous foliations and invariant lines. In both cases, we demonstrate that the dual web is flat."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09602","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.09602/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:52:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rlsKDhdZ0U0WLMI9/Ft52FJpNyHo5RwpNycxLkjeB7vi7gvpvtBLY8n936Hiloj4bq12SaQ9SmHL4AJ7YSxNDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T08:02:45.145910Z"},"content_sha256":"75905f0c4afb71df7eb1e62d404aaf185cf3149c913dd1293151f459e0c8d829","schema_version":"1.0","event_id":"sha256:75905f0c4afb71df7eb1e62d404aaf185cf3149c913dd1293151f459e0c8d829"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DU5LZW5HDGUMN4TJS7NXLVMJZ4/bundle.json","state_url":"https://pith.science/pith/DU5LZW5HDGUMN4TJS7NXLVMJZ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DU5LZW5HDGUMN4TJS7NXLVMJZ4/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":"2026-08-14T08:02:45Z","links":{"resolver":"https://pith.science/pith/DU5LZW5HDGUMN4TJS7NXLVMJZ4","bundle":"https://pith.science/pith/DU5LZW5HDGUMN4TJS7NXLVMJZ4/bundle.json","state":"https://pith.science/pith/DU5LZW5HDGUMN4TJS7NXLVMJZ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DU5LZW5HDGUMN4TJS7NXLVMJZ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DU5LZW5HDGUMN4TJS7NXLVMJZ4","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":"ac67590b44a8b8e2b62cce2d03f78ee1df5ac3b9899915c3e6f6b9c6ebdd91fa","cross_cats_sorted":["math.CV","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-14T17:22:00Z","title_canon_sha256":"f2d37e1a8dc9d010503953c53bd996af1a82ab719485116186c9c13051eed9de"},"schema_version":"1.0","source":{"id":"2411.09602","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.09602","created_at":"2026-07-05T09:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"2411.09602v2","created_at":"2026-07-05T09:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09602","created_at":"2026-07-05T09:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"DU5LZW5HDGUM","created_at":"2026-07-05T09:52:40Z"},{"alias_kind":"pith_short_16","alias_value":"DU5LZW5HDGUMN4TJ","created_at":"2026-07-05T09:52:40Z"},{"alias_kind":"pith_short_8","alias_value":"DU5LZW5H","created_at":"2026-07-05T09:52:40Z"}],"graph_snapshots":[{"event_id":"sha256:75905f0c4afb71df7eb1e62d404aaf185cf3149c913dd1293151f459e0c8d829","target":"graph","created_at":"2026-07-05T09:52:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.09602/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates flat webs on the projective plane. We present two methods for constructing such webs: the first involves taking the product of finitely many convex reduced foliations and invariant lines, while the second consists of taking the product of finitely many convex homogeneous foliations and invariant lines. In both cases, we demonstrate that the dual web is flat.","authors_text":"Carla Pracias, Maycol Falla Luza","cross_cats":["math.CV","math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-14T17:22:00Z","title":"Webs Generated by Products of convex and homogeneous Foliations on $\\mathbb{P}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09602","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":"sha256:94f1d85c85cb3b9a784588c740d7cd80c0927340f424eb21a3620f8cb3aed09d","target":"record","created_at":"2026-07-05T09:52:40Z","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":"ac67590b44a8b8e2b62cce2d03f78ee1df5ac3b9899915c3e6f6b9c6ebdd91fa","cross_cats_sorted":["math.CV","math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-11-14T17:22:00Z","title_canon_sha256":"f2d37e1a8dc9d010503953c53bd996af1a82ab719485116186c9c13051eed9de"},"schema_version":"1.0","source":{"id":"2411.09602","kind":"arxiv","version":2}},"canonical_sha256":"1d3abcdba719a8c6f26997db75d589cf0e1665beb1b80925ec5b64ecc1e5a5cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d3abcdba719a8c6f26997db75d589cf0e1665beb1b80925ec5b64ecc1e5a5cb","first_computed_at":"2026-07-05T09:52:40.421825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:52:40.421825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sq5Q5bzqE/19Hwjtu2aMm7XIPMrc8P0nopp012+UIHHW5IVjufaBxZ3hwaBBDUZoP/TEJTIU/2YxrbLkUIGTCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:52:40.422205Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.09602","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94f1d85c85cb3b9a784588c740d7cd80c0927340f424eb21a3620f8cb3aed09d","sha256:75905f0c4afb71df7eb1e62d404aaf185cf3149c913dd1293151f459e0c8d829"],"state_sha256":"a84448cac1db2d85499aa6769aada7215fb24f13052d88ac441746cfb4fec50a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+HCuWkVkP7fAqk3Z47IIRJPKsQzUT7HskNnJJygTzBzz3Ui+HnZWevzkUiC/pWYlCOrDuLMV14sSRiR8CaoEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T08:02:45.151802Z","bundle_sha256":"ef7a9549b619f09a1ce9d0752d87512a9d475b3a84a85dbbaa750866898d6e5b"}}