{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CLUXZ5LIAE3PEM3THHOKXIC6DT","short_pith_number":"pith:CLUXZ5LI","canonical_record":{"source":{"id":"1504.01949","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-04-08T13:16:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a6d98bafd155af40871660720ca29a0ef08de1abf5d2a7435a9f90bfe76f8ff2","abstract_canon_sha256":"385b118dfdc7487dee0599276e82e2771da2d756a399bd195a59508dd5fa5ac1"},"schema_version":"1.0"},"canonical_sha256":"12e97cf5680136f2337339dcaba05e1cc5b68db25cbf0b8f4cbe3b2063d96d87","source":{"kind":"arxiv","id":"1504.01949","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01949","created_at":"2026-05-18T02:19:17Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01949v1","created_at":"2026-05-18T02:19:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01949","created_at":"2026-05-18T02:19:17Z"},{"alias_kind":"pith_short_12","alias_value":"CLUXZ5LIAE3P","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CLUXZ5LIAE3PEM3T","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CLUXZ5LI","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CLUXZ5LIAE3PEM3THHOKXIC6DT","target":"record","payload":{"canonical_record":{"source":{"id":"1504.01949","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-04-08T13:16:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a6d98bafd155af40871660720ca29a0ef08de1abf5d2a7435a9f90bfe76f8ff2","abstract_canon_sha256":"385b118dfdc7487dee0599276e82e2771da2d756a399bd195a59508dd5fa5ac1"},"schema_version":"1.0"},"canonical_sha256":"12e97cf5680136f2337339dcaba05e1cc5b68db25cbf0b8f4cbe3b2063d96d87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:17.728351Z","signature_b64":"bQVUVoFt7hH6QhsUdBYBs+Xs3raPrUcMH02Ma8Dgn43Y2bSZRn3xu0H/OCs5hif+yURpv/QRrILVhXIagRQeDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12e97cf5680136f2337339dcaba05e1cc5b68db25cbf0b8f4cbe3b2063d96d87","last_reissued_at":"2026-05-18T02:19:17.727672Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:17.727672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.01949","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":"2026-05-18T02:19:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IpxGFsV38F1MgSinGY4CJP1AHVp+zElDby/scwKjjCZuyTz26i8FN4jjZsFBP8/XUyz6BliKukSyKWFiH8ptDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:05:25.235807Z"},"content_sha256":"e4d5f3324dfe6ee93895ae8ed60b223b45f4cb8830e6f0e20260e28b1b5af195","schema_version":"1.0","event_id":"sha256:e4d5f3324dfe6ee93895ae8ed60b223b45f4cb8830e6f0e20260e28b1b5af195"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CLUXZ5LIAE3PEM3THHOKXIC6DT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A lower bound on the order of the largest induced forest in planar graphs with high girth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Alexandre Pinlou, Fran\\c{c}ois Dross, Mickael Montassier","submitted_at":"2015-04-08T13:16:17Z","abstract_excerpt":"We give here new upper bounds on the size of a smallest feedback vertex set in planar graphs with high girth. In particular, we prove that a planar graph with girth $g$ and size $m$ has a feedback vertex set of size at most $\\frac{4m}{3g}$, improving the trivial bound of $\\frac{2m}{g}$. We also prove that every $2$-connected graph with maximum degree $3$ and order $n$ has a feedback vertex set of size at most $\\frac{n+2}{3}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01949","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":"2026-05-18T02:19:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HbqTmo6qgvf58RlcSompf8jC7neJb5uS4kVt6vfu6TOnXL2ptL8kzUuoH1WNjMsojhv1rliAnALkGWd4Q+XXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:05:25.236135Z"},"content_sha256":"5b089710cf424b73c8fa6173f20aaddef3af6032991f32a84f3a3206ee7725cf","schema_version":"1.0","event_id":"sha256:5b089710cf424b73c8fa6173f20aaddef3af6032991f32a84f3a3206ee7725cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CLUXZ5LIAE3PEM3THHOKXIC6DT/bundle.json","state_url":"https://pith.science/pith/CLUXZ5LIAE3PEM3THHOKXIC6DT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CLUXZ5LIAE3PEM3THHOKXIC6DT/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":"2026-06-20T04:05:25Z","links":{"resolver":"https://pith.science/pith/CLUXZ5LIAE3PEM3THHOKXIC6DT","bundle":"https://pith.science/pith/CLUXZ5LIAE3PEM3THHOKXIC6DT/bundle.json","state":"https://pith.science/pith/CLUXZ5LIAE3PEM3THHOKXIC6DT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CLUXZ5LIAE3PEM3THHOKXIC6DT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CLUXZ5LIAE3PEM3THHOKXIC6DT","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":"385b118dfdc7487dee0599276e82e2771da2d756a399bd195a59508dd5fa5ac1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-04-08T13:16:17Z","title_canon_sha256":"a6d98bafd155af40871660720ca29a0ef08de1abf5d2a7435a9f90bfe76f8ff2"},"schema_version":"1.0","source":{"id":"1504.01949","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01949","created_at":"2026-05-18T02:19:17Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01949v1","created_at":"2026-05-18T02:19:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01949","created_at":"2026-05-18T02:19:17Z"},{"alias_kind":"pith_short_12","alias_value":"CLUXZ5LIAE3P","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CLUXZ5LIAE3PEM3T","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CLUXZ5LI","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:5b089710cf424b73c8fa6173f20aaddef3af6032991f32a84f3a3206ee7725cf","target":"graph","created_at":"2026-05-18T02:19:17Z","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":"We give here new upper bounds on the size of a smallest feedback vertex set in planar graphs with high girth. In particular, we prove that a planar graph with girth $g$ and size $m$ has a feedback vertex set of size at most $\\frac{4m}{3g}$, improving the trivial bound of $\\frac{2m}{g}$. We also prove that every $2$-connected graph with maximum degree $3$ and order $n$ has a feedback vertex set of size at most $\\frac{n+2}{3}$.","authors_text":"Alexandre Pinlou, Fran\\c{c}ois Dross, Mickael Montassier","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-04-08T13:16:17Z","title":"A lower bound on the order of the largest induced forest in planar graphs with high girth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01949","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:e4d5f3324dfe6ee93895ae8ed60b223b45f4cb8830e6f0e20260e28b1b5af195","target":"record","created_at":"2026-05-18T02:19:17Z","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":"385b118dfdc7487dee0599276e82e2771da2d756a399bd195a59508dd5fa5ac1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-04-08T13:16:17Z","title_canon_sha256":"a6d98bafd155af40871660720ca29a0ef08de1abf5d2a7435a9f90bfe76f8ff2"},"schema_version":"1.0","source":{"id":"1504.01949","kind":"arxiv","version":1}},"canonical_sha256":"12e97cf5680136f2337339dcaba05e1cc5b68db25cbf0b8f4cbe3b2063d96d87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12e97cf5680136f2337339dcaba05e1cc5b68db25cbf0b8f4cbe3b2063d96d87","first_computed_at":"2026-05-18T02:19:17.727672Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:17.727672Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bQVUVoFt7hH6QhsUdBYBs+Xs3raPrUcMH02Ma8Dgn43Y2bSZRn3xu0H/OCs5hif+yURpv/QRrILVhXIagRQeDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:17.728351Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01949","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4d5f3324dfe6ee93895ae8ed60b223b45f4cb8830e6f0e20260e28b1b5af195","sha256:5b089710cf424b73c8fa6173f20aaddef3af6032991f32a84f3a3206ee7725cf"],"state_sha256":"dca745bf972a2025d35338bac7d05188c97b5d4c830e5d985ba29469924e05bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tcgd/hddLo4Sfmsr9j7UxiBHKpbdf38gQiaouaz30D5KSMrIJrnsml2Dgg2c8fGkfRGLVxgxbT4NYlyjBHDjCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T04:05:25.237942Z","bundle_sha256":"9bafe7d85d3a36fff433393213f36b3b10cac26b14249eac001ed8efaf419d70"}}