{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Z5EME7DUF32QJNHNPKRFLWMFEN","short_pith_number":"pith:Z5EME7DU","canonical_record":{"source":{"id":"1607.01034","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-04T20:08:45Z","cross_cats_sorted":[],"title_canon_sha256":"d1e0fb68692025a209ce950ebd9b15dce4b4c5598121d897e2af54deab2911d9","abstract_canon_sha256":"9c97c92915932ede85bf903f25bc4c87bdb4941696bc46d1787e34d36cb77cb9"},"schema_version":"1.0"},"canonical_sha256":"cf48c27c742ef504b4ed7aa255d985236218ea8bb143aa392a15ae55d06f90d4","source":{"kind":"arxiv","id":"1607.01034","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01034","created_at":"2026-05-18T01:11:30Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01034v1","created_at":"2026-05-18T01:11:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01034","created_at":"2026-05-18T01:11:30Z"},{"alias_kind":"pith_short_12","alias_value":"Z5EME7DUF32Q","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z5EME7DUF32QJNHN","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z5EME7DU","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Z5EME7DUF32QJNHNPKRFLWMFEN","target":"record","payload":{"canonical_record":{"source":{"id":"1607.01034","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-04T20:08:45Z","cross_cats_sorted":[],"title_canon_sha256":"d1e0fb68692025a209ce950ebd9b15dce4b4c5598121d897e2af54deab2911d9","abstract_canon_sha256":"9c97c92915932ede85bf903f25bc4c87bdb4941696bc46d1787e34d36cb77cb9"},"schema_version":"1.0"},"canonical_sha256":"cf48c27c742ef504b4ed7aa255d985236218ea8bb143aa392a15ae55d06f90d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:30.252372Z","signature_b64":"J480DX20O4YsIZBR5/Dx2BmenPBLSQ+VVEmm7rR3/l1otqkU4pI3KaN3ZyroU1y2VANjP3VbMYhD0W+7AloXDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf48c27c742ef504b4ed7aa255d985236218ea8bb143aa392a15ae55d06f90d4","last_reissued_at":"2026-05-18T01:11:30.252030Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:30.252030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.01034","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":"2026-05-18T01:11:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TQndtyRem0zdcr8fVrCgpvFLHx/mUMUDpvDWu81LQPbzEWgrEKbRlx3gFKBscUIbMPGwVk9puy2XKQmeJ/+yAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T07:38:47.685603Z"},"content_sha256":"0241f3f35945c2aadd8cb48a904873a330c76f50252d41a9f36047e67df15b23","schema_version":"1.0","event_id":"sha256:0241f3f35945c2aadd8cb48a904873a330c76f50252d41a9f36047e67df15b23"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Z5EME7DUF32QJNHNPKRFLWMFEN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Blockers for simple Hamiltonian paths in convex geometric graphs of even order","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chaya Keller, Micha A. Perles","submitted_at":"2016-07-04T20:08:45Z","abstract_excerpt":"Let G be a complete convex geometric graph on 2m vertices, and let F be a family of subgraphs of G. A blocker for F is a set of edges, of smallest possible size, that meets every element of F. In [C. Keller and M. A. Perles, On the smallest sets blocking simple perfect matchings in a convex geometric graph, Israel J. Math. 187 (2012), pp. 465-484], we gave an explicit description of all blockers for the family of simple perfect matchings (SPMs) of G. In this paper we show that the family of simple Hamiltonian paths (SHPs) in G has exactly the same blockers as the family of SPMs. Our argument i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01034","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":"2026-05-18T01:11:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MCJys20Qs1pqs72h/hiAbHR0fd9T5fMPYZJGx8ymkcr01Eth5g5UsFyatq6VL2mtiI1ufamwwM2PJpQnh48HDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T07:38:47.685942Z"},"content_sha256":"fa0dfd623bdc1c25b738ac05d685445118e4f6156850cbbe83780e7e7126d7e7","schema_version":"1.0","event_id":"sha256:fa0dfd623bdc1c25b738ac05d685445118e4f6156850cbbe83780e7e7126d7e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5EME7DUF32QJNHNPKRFLWMFEN/bundle.json","state_url":"https://pith.science/pith/Z5EME7DUF32QJNHNPKRFLWMFEN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5EME7DUF32QJNHNPKRFLWMFEN/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":"2026-06-21T07:38:47Z","links":{"resolver":"https://pith.science/pith/Z5EME7DUF32QJNHNPKRFLWMFEN","bundle":"https://pith.science/pith/Z5EME7DUF32QJNHNPKRFLWMFEN/bundle.json","state":"https://pith.science/pith/Z5EME7DUF32QJNHNPKRFLWMFEN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5EME7DUF32QJNHNPKRFLWMFEN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Z5EME7DUF32QJNHNPKRFLWMFEN","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":"9c97c92915932ede85bf903f25bc4c87bdb4941696bc46d1787e34d36cb77cb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-04T20:08:45Z","title_canon_sha256":"d1e0fb68692025a209ce950ebd9b15dce4b4c5598121d897e2af54deab2911d9"},"schema_version":"1.0","source":{"id":"1607.01034","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.01034","created_at":"2026-05-18T01:11:30Z"},{"alias_kind":"arxiv_version","alias_value":"1607.01034v1","created_at":"2026-05-18T01:11:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01034","created_at":"2026-05-18T01:11:30Z"},{"alias_kind":"pith_short_12","alias_value":"Z5EME7DUF32Q","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z5EME7DUF32QJNHN","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z5EME7DU","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:fa0dfd623bdc1c25b738ac05d685445118e4f6156850cbbe83780e7e7126d7e7","target":"graph","created_at":"2026-05-18T01:11:30Z","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 G be a complete convex geometric graph on 2m vertices, and let F be a family of subgraphs of G. A blocker for F is a set of edges, of smallest possible size, that meets every element of F. In [C. Keller and M. A. Perles, On the smallest sets blocking simple perfect matchings in a convex geometric graph, Israel J. Math. 187 (2012), pp. 465-484], we gave an explicit description of all blockers for the family of simple perfect matchings (SPMs) of G. In this paper we show that the family of simple Hamiltonian paths (SHPs) in G has exactly the same blockers as the family of SPMs. Our argument i","authors_text":"Chaya Keller, Micha A. Perles","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-04T20:08:45Z","title":"Blockers for simple Hamiltonian paths in convex geometric graphs of even order"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01034","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":"sha256:0241f3f35945c2aadd8cb48a904873a330c76f50252d41a9f36047e67df15b23","target":"record","created_at":"2026-05-18T01:11:30Z","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":"9c97c92915932ede85bf903f25bc4c87bdb4941696bc46d1787e34d36cb77cb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-07-04T20:08:45Z","title_canon_sha256":"d1e0fb68692025a209ce950ebd9b15dce4b4c5598121d897e2af54deab2911d9"},"schema_version":"1.0","source":{"id":"1607.01034","kind":"arxiv","version":1}},"canonical_sha256":"cf48c27c742ef504b4ed7aa255d985236218ea8bb143aa392a15ae55d06f90d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf48c27c742ef504b4ed7aa255d985236218ea8bb143aa392a15ae55d06f90d4","first_computed_at":"2026-05-18T01:11:30.252030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:30.252030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J480DX20O4YsIZBR5/Dx2BmenPBLSQ+VVEmm7rR3/l1otqkU4pI3KaN3ZyroU1y2VANjP3VbMYhD0W+7AloXDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:30.252372Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.01034","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0241f3f35945c2aadd8cb48a904873a330c76f50252d41a9f36047e67df15b23","sha256:fa0dfd623bdc1c25b738ac05d685445118e4f6156850cbbe83780e7e7126d7e7"],"state_sha256":"40e1c5ce5727431e855b24bee593b8b62f8651b8c6815f47aa3b17e172c08448"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HcqpQAfsHIpMUw93TS92RPgDIv81e0njj2pf63Qg1rZatBancxg6vjX7WjcS24PuWKn4N05Emz2SPfnXSXG0BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T07:38:47.687765Z","bundle_sha256":"8fed9e31c39e045451db067771b26ff8d713079fce811a2c820c84312a7c5662"}}