{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PU2KZP3NO7MLSJOI5463FTDR3F","short_pith_number":"pith:PU2KZP3N","canonical_record":{"source":{"id":"1209.3954","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-09-18T13:25:40Z","cross_cats_sorted":["cs.CG","math.CO"],"title_canon_sha256":"ba457c418448f8c2aac70bc13830a2bc6e48d86ef17103b0556084215b00b1c0","abstract_canon_sha256":"2b4b2b31f82dcd7e7bafd2b40a020c41e682aaeadacfc109ef6229c69a49c2cc"},"schema_version":"1.0"},"canonical_sha256":"7d34acbf6d77d8b925c8ef3db2cc71d95739ddf670cb28a673cb8ad3effd6214","source":{"kind":"arxiv","id":"1209.3954","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3954","created_at":"2026-05-18T03:45:22Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3954v1","created_at":"2026-05-18T03:45:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3954","created_at":"2026-05-18T03:45:22Z"},{"alias_kind":"pith_short_12","alias_value":"PU2KZP3NO7ML","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PU2KZP3NO7MLSJOI","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PU2KZP3N","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PU2KZP3NO7MLSJOI5463FTDR3F","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3954","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-09-18T13:25:40Z","cross_cats_sorted":["cs.CG","math.CO"],"title_canon_sha256":"ba457c418448f8c2aac70bc13830a2bc6e48d86ef17103b0556084215b00b1c0","abstract_canon_sha256":"2b4b2b31f82dcd7e7bafd2b40a020c41e682aaeadacfc109ef6229c69a49c2cc"},"schema_version":"1.0"},"canonical_sha256":"7d34acbf6d77d8b925c8ef3db2cc71d95739ddf670cb28a673cb8ad3effd6214","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:22.157330Z","signature_b64":"VeM3V0O9bLWFkJCLV+l1erR0Tokj8ThKBBrdkaicqz4UF2BEMBgb5UUWlI+bQyAUzxo/9d3c+I2439iMIO4PBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d34acbf6d77d8b925c8ef3db2cc71d95739ddf670cb28a673cb8ad3effd6214","last_reissued_at":"2026-05-18T03:45:22.156847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:22.156847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3954","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":"2026-05-18T03:45:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OCT0yHXte0l4uYaBcpegWmX4xKdO0Qh2ZB4HYlsIFYsUsICXyN5GNhzWjDM/Wh1QE0rHP0sXpk8SKd1Pb4P8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:43:01.484840Z"},"content_sha256":"7f5fe3236b95fb1425a36c90a62393a4147ce4f6859b40c953eabff45a69dc8d","schema_version":"1.0","event_id":"sha256:7f5fe3236b95fb1425a36c90a62393a4147ce4f6859b40c953eabff45a69dc8d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PU2KZP3NO7MLSJOI5463FTDR3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How Many Potatoes are in a Mesh?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.CO"],"primary_cat":"cs.DM","authors_text":"J\\'anos Pach, Maarten L\\\"offler, Marc van Kreveld","submitted_at":"2012-09-18T13:25:40Z","abstract_excerpt":"We consider the combinatorial question of how many convex polygons can be made by using the edges taken from a fixed triangulation of n vertices. For general triangulations, there can be exponentially many: we show a construction that has Omega(1.5028^n) convex polygons, and prove an O(1.62^n) upper bound in the worst case. If the triangulation is fat (every triangle has its angles lower-bounded by a constant delta>0), then there can be only polynomially many.\n  We also consider the problem of counting convex outerplanar polygons (i.e., they contain no vertices of the triangulation in their in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3954","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":"2026-05-18T03:45:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BVYE/XgA2CuR3lmZQLtrpTcSZ6H7iIr3C5n/HSX1JRixG6HzM/L8NKMu+VxqZaVvMz6wi+GDMzRgx5igTCZfDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:43:01.485448Z"},"content_sha256":"8461e74c79181eafaf6101970723cb87e299208eab5982c3a62e509136468712","schema_version":"1.0","event_id":"sha256:8461e74c79181eafaf6101970723cb87e299208eab5982c3a62e509136468712"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PU2KZP3NO7MLSJOI5463FTDR3F/bundle.json","state_url":"https://pith.science/pith/PU2KZP3NO7MLSJOI5463FTDR3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PU2KZP3NO7MLSJOI5463FTDR3F/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":"2026-06-07T20:43:01Z","links":{"resolver":"https://pith.science/pith/PU2KZP3NO7MLSJOI5463FTDR3F","bundle":"https://pith.science/pith/PU2KZP3NO7MLSJOI5463FTDR3F/bundle.json","state":"https://pith.science/pith/PU2KZP3NO7MLSJOI5463FTDR3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PU2KZP3NO7MLSJOI5463FTDR3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PU2KZP3NO7MLSJOI5463FTDR3F","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":"2b4b2b31f82dcd7e7bafd2b40a020c41e682aaeadacfc109ef6229c69a49c2cc","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-09-18T13:25:40Z","title_canon_sha256":"ba457c418448f8c2aac70bc13830a2bc6e48d86ef17103b0556084215b00b1c0"},"schema_version":"1.0","source":{"id":"1209.3954","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3954","created_at":"2026-05-18T03:45:22Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3954v1","created_at":"2026-05-18T03:45:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3954","created_at":"2026-05-18T03:45:22Z"},{"alias_kind":"pith_short_12","alias_value":"PU2KZP3NO7ML","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PU2KZP3NO7MLSJOI","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PU2KZP3N","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:8461e74c79181eafaf6101970723cb87e299208eab5982c3a62e509136468712","target":"graph","created_at":"2026-05-18T03:45:22Z","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 consider the combinatorial question of how many convex polygons can be made by using the edges taken from a fixed triangulation of n vertices. For general triangulations, there can be exponentially many: we show a construction that has Omega(1.5028^n) convex polygons, and prove an O(1.62^n) upper bound in the worst case. If the triangulation is fat (every triangle has its angles lower-bounded by a constant delta>0), then there can be only polynomially many.\n  We also consider the problem of counting convex outerplanar polygons (i.e., they contain no vertices of the triangulation in their in","authors_text":"J\\'anos Pach, Maarten L\\\"offler, Marc van Kreveld","cross_cats":["cs.CG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-09-18T13:25:40Z","title":"How Many Potatoes are in a Mesh?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3954","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":"sha256:7f5fe3236b95fb1425a36c90a62393a4147ce4f6859b40c953eabff45a69dc8d","target":"record","created_at":"2026-05-18T03:45:22Z","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":"2b4b2b31f82dcd7e7bafd2b40a020c41e682aaeadacfc109ef6229c69a49c2cc","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-09-18T13:25:40Z","title_canon_sha256":"ba457c418448f8c2aac70bc13830a2bc6e48d86ef17103b0556084215b00b1c0"},"schema_version":"1.0","source":{"id":"1209.3954","kind":"arxiv","version":1}},"canonical_sha256":"7d34acbf6d77d8b925c8ef3db2cc71d95739ddf670cb28a673cb8ad3effd6214","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d34acbf6d77d8b925c8ef3db2cc71d95739ddf670cb28a673cb8ad3effd6214","first_computed_at":"2026-05-18T03:45:22.156847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:22.156847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VeM3V0O9bLWFkJCLV+l1erR0Tokj8ThKBBrdkaicqz4UF2BEMBgb5UUWlI+bQyAUzxo/9d3c+I2439iMIO4PBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:22.157330Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3954","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f5fe3236b95fb1425a36c90a62393a4147ce4f6859b40c953eabff45a69dc8d","sha256:8461e74c79181eafaf6101970723cb87e299208eab5982c3a62e509136468712"],"state_sha256":"5880daf10baaeb8bdc2ac193319af20d35bd979843d0c83009a743879225180b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"47MoaxeE46DphSdDNmuRAl0r6WijSeIjkrvJTaxYwkvb+77ZbCM7n/KgUFDfk+/FAvWGkvi/wzTh5VLo4TOjAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:43:01.488663Z","bundle_sha256":"b05ecd14f1f6ee03caae2ed0b67c26072dbbfdcfeb31f1e86f54ad7d563ad9e0"}}