{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DHWLP4F46LRPAO755EHRCKEU6C","short_pith_number":"pith:DHWLP4F4","canonical_record":{"source":{"id":"1901.10683","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-30T06:13:41Z","cross_cats_sorted":[],"title_canon_sha256":"79703c63f427b4edc966b6f32b80fde19f90baa3a59d95d98c57fc432ea6964d","abstract_canon_sha256":"3c4363c785056f906603db30633e4fc564bac72bcd4e34ba91887975b811a489"},"schema_version":"1.0"},"canonical_sha256":"19ecb7f0bcf2e2f03bfde90f112894f0951f384b900d129432e18b5a6e6f2525","source":{"kind":"arxiv","id":"1901.10683","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.10683","created_at":"2026-05-17T23:54:02Z"},{"alias_kind":"arxiv_version","alias_value":"1901.10683v2","created_at":"2026-05-17T23:54:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10683","created_at":"2026-05-17T23:54:02Z"},{"alias_kind":"pith_short_12","alias_value":"DHWLP4F46LRP","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DHWLP4F46LRPAO75","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DHWLP4F4","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DHWLP4F46LRPAO755EHRCKEU6C","target":"record","payload":{"canonical_record":{"source":{"id":"1901.10683","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-30T06:13:41Z","cross_cats_sorted":[],"title_canon_sha256":"79703c63f427b4edc966b6f32b80fde19f90baa3a59d95d98c57fc432ea6964d","abstract_canon_sha256":"3c4363c785056f906603db30633e4fc564bac72bcd4e34ba91887975b811a489"},"schema_version":"1.0"},"canonical_sha256":"19ecb7f0bcf2e2f03bfde90f112894f0951f384b900d129432e18b5a6e6f2525","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:02.136438Z","signature_b64":"JRzKXAoToj+7DyBIKG4x09uLE0s540v4fRaYtA/xJn+XD8vhyC0jQnJUro/LaRiS8+/YBwTO0pYmr6al3S1XDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19ecb7f0bcf2e2f03bfde90f112894f0951f384b900d129432e18b5a6e6f2525","last_reissued_at":"2026-05-17T23:54:02.135821Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:02.135821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.10683","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":"2026-05-17T23:54:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kU5FWin2dvSprmByfnuMiwwaqqPp5Cdel9TMsFt0goTsIILz02WK7OaoGV9Hl29dTbAQCrwbamXqXMHQ0bS7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:05:48.585172Z"},"content_sha256":"f8577077655ead60b1e15f1981e628c78a6c3315f037cbfb1b5f42343c985f90","schema_version":"1.0","event_id":"sha256:f8577077655ead60b1e15f1981e628c78a6c3315f037cbfb1b5f42343c985f90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DHWLP4F46LRPAO755EHRCKEU6C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Highly-connected planar cubic graphs with few or many Hamilton cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gordon Royle, Irene Pivotto","submitted_at":"2019-01-30T06:13:41Z","abstract_excerpt":"In this paper we consider the number of Hamilton cycles in planar cubic graphs of high cyclic edge-connectivity, answering two questions raised by Chia and Thomassen (\"On the number of longest and almost longest cycles in cubic graphs\", Ars Combin., 104, 307--320, 2012) about extremal graphs in these families. In particular, we find families of cyclically $5$-edge connected planar cubic graphs with more Hamilton cycles than the generalized Petersen graphs $P(2n,2)$. The graphs themselves are fullerene graphs that correspond to certain carbon molecules known as nanotubes --- more precisely, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10683","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":""},"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":"2026-05-17T23:54:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y2KtND4AmUvnDNkx5m0UEyFS1hxbpbuQo7NZUQAd8n2VtiUsyDHUNaesyq9hrAqRW3Dq3zNJylDfaTPen3+PDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T00:05:48.585911Z"},"content_sha256":"1f6896cfe077596a531067f5c4c668b76ebc405a2c152ad43cb8a9ac0cbc0866","schema_version":"1.0","event_id":"sha256:1f6896cfe077596a531067f5c4c668b76ebc405a2c152ad43cb8a9ac0cbc0866"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C/bundle.json","state_url":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DHWLP4F46LRPAO755EHRCKEU6C/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":"2026-06-12T00:05:48Z","links":{"resolver":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C","bundle":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C/bundle.json","state":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DHWLP4F46LRPAO755EHRCKEU6C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DHWLP4F46LRPAO755EHRCKEU6C","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":"3c4363c785056f906603db30633e4fc564bac72bcd4e34ba91887975b811a489","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-30T06:13:41Z","title_canon_sha256":"79703c63f427b4edc966b6f32b80fde19f90baa3a59d95d98c57fc432ea6964d"},"schema_version":"1.0","source":{"id":"1901.10683","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.10683","created_at":"2026-05-17T23:54:02Z"},{"alias_kind":"arxiv_version","alias_value":"1901.10683v2","created_at":"2026-05-17T23:54:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10683","created_at":"2026-05-17T23:54:02Z"},{"alias_kind":"pith_short_12","alias_value":"DHWLP4F46LRP","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DHWLP4F46LRPAO75","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DHWLP4F4","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:1f6896cfe077596a531067f5c4c668b76ebc405a2c152ad43cb8a9ac0cbc0866","target":"graph","created_at":"2026-05-17T23:54:02Z","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":"In this paper we consider the number of Hamilton cycles in planar cubic graphs of high cyclic edge-connectivity, answering two questions raised by Chia and Thomassen (\"On the number of longest and almost longest cycles in cubic graphs\", Ars Combin., 104, 307--320, 2012) about extremal graphs in these families. In particular, we find families of cyclically $5$-edge connected planar cubic graphs with more Hamilton cycles than the generalized Petersen graphs $P(2n,2)$. The graphs themselves are fullerene graphs that correspond to certain carbon molecules known as nanotubes --- more precisely, the","authors_text":"Gordon Royle, Irene Pivotto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-30T06:13:41Z","title":"Highly-connected planar cubic graphs with few or many Hamilton cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10683","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:f8577077655ead60b1e15f1981e628c78a6c3315f037cbfb1b5f42343c985f90","target":"record","created_at":"2026-05-17T23:54:02Z","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":"3c4363c785056f906603db30633e4fc564bac72bcd4e34ba91887975b811a489","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-30T06:13:41Z","title_canon_sha256":"79703c63f427b4edc966b6f32b80fde19f90baa3a59d95d98c57fc432ea6964d"},"schema_version":"1.0","source":{"id":"1901.10683","kind":"arxiv","version":2}},"canonical_sha256":"19ecb7f0bcf2e2f03bfde90f112894f0951f384b900d129432e18b5a6e6f2525","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19ecb7f0bcf2e2f03bfde90f112894f0951f384b900d129432e18b5a6e6f2525","first_computed_at":"2026-05-17T23:54:02.135821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:02.135821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JRzKXAoToj+7DyBIKG4x09uLE0s540v4fRaYtA/xJn+XD8vhyC0jQnJUro/LaRiS8+/YBwTO0pYmr6al3S1XDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:02.136438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.10683","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8577077655ead60b1e15f1981e628c78a6c3315f037cbfb1b5f42343c985f90","sha256:1f6896cfe077596a531067f5c4c668b76ebc405a2c152ad43cb8a9ac0cbc0866"],"state_sha256":"f67d7e0f276390dc15838e87af82c966a5c36df783bc322e7dc84e957fc3c228"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iPm43KQKVqaapMiLFdPbUYloudRcrPX4+rsnYx2vsc2pRNWR7aS7/7cmuEyIvTW8i16XPnx7msr+3s/+AJM1DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T00:05:48.590535Z","bundle_sha256":"21444a19e2e6ad722951995f7ba6440e310a6b15d0550f52f7e5a273598ed573"}}