{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GFRYGXMRNO2WLLNS4UHWVHJCHE","short_pith_number":"pith:GFRYGXMR","canonical_record":{"source":{"id":"1010.5918","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-28T11:05:40Z","cross_cats_sorted":[],"title_canon_sha256":"c278594e33869c065302eb1ba7ed6d9f701e42aea077df42d9ce9fc1799d0629","abstract_canon_sha256":"912c88efcd61d64f445a751f47afe2713a573d3306198c4074ae0c149e670683"},"schema_version":"1.0"},"canonical_sha256":"3163835d916bb565adb2e50f6a9d223925e5dba11c63597d6e737248b08af967","source":{"kind":"arxiv","id":"1010.5918","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5918","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5918v1","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5918","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"pith_short_12","alias_value":"GFRYGXMRNO2W","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GFRYGXMRNO2WLLNS","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GFRYGXMR","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GFRYGXMRNO2WLLNS4UHWVHJCHE","target":"record","payload":{"canonical_record":{"source":{"id":"1010.5918","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-28T11:05:40Z","cross_cats_sorted":[],"title_canon_sha256":"c278594e33869c065302eb1ba7ed6d9f701e42aea077df42d9ce9fc1799d0629","abstract_canon_sha256":"912c88efcd61d64f445a751f47afe2713a573d3306198c4074ae0c149e670683"},"schema_version":"1.0"},"canonical_sha256":"3163835d916bb565adb2e50f6a9d223925e5dba11c63597d6e737248b08af967","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:14.958613Z","signature_b64":"YKzbS2L8x9gJamdkGJnCV3dVCgTSwvD9L6cJkAAPbtyFFoQXXFEO2vBO2qnsMPOvO5WEuRX02KDq5OPef+frBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3163835d916bb565adb2e50f6a9d223925e5dba11c63597d6e737248b08af967","last_reissued_at":"2026-05-18T04:38:14.958088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:14.958088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.5918","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":"2026-05-18T04:38:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/vzd8qEPUhfaFJD6hp3ObUkJZ6zsz7CpVRx8VYsHvP1+Bq6wiVpRCc2WPriFcMjeaLirBqeYjtekWLsezuvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:32:00.352825Z"},"content_sha256":"81c8d5b126b97af239217960b180e3b6afbdbef927644f82e9e7bf6deb2cd786","schema_version":"1.0","event_id":"sha256:81c8d5b126b97af239217960b180e3b6afbdbef927644f82e9e7bf6deb2cd786"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GFRYGXMRNO2WLLNS4UHWVHJCHE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting perfect matchings of cubic graphs in the geometric dual","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrea Jim\\'enez, Marcos Kiwi","submitted_at":"2010-10-28T11:05:40Z","abstract_excerpt":"Lov\\'asz and Plummer conjectured, in the mid 1970's, that every cubic graph G with no cutedge has an exponential in |V(G)| number of perfect matchings. In this work we show that every cubic planar graph G whose geometric dual graph is a stack triangulation has at least 3 times the golden ratio to |V(G)|/72 distinct perfect matchings. Our work builds on a novel approach relating Lov\\'asz and Plummer's conjecture and the number of so called groundstates of the widely studied Ising model from statistical physics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5918","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":"2026-05-18T04:38:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vI+J/KiLQ4DJLwviRyWfYfA3WfaCfERNaSvi5BGfdr+jGiIghXihKybRgOUhjAwEv7d6I/VPAEvaDB8IhVpHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:32:00.353169Z"},"content_sha256":"2e6fd30b13f2f4fd4fc26ffc20f662fc6ea4b06593f84086faf971535db36955","schema_version":"1.0","event_id":"sha256:2e6fd30b13f2f4fd4fc26ffc20f662fc6ea4b06593f84086faf971535db36955"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GFRYGXMRNO2WLLNS4UHWVHJCHE/bundle.json","state_url":"https://pith.science/pith/GFRYGXMRNO2WLLNS4UHWVHJCHE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GFRYGXMRNO2WLLNS4UHWVHJCHE/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":"2026-05-30T13:32:00Z","links":{"resolver":"https://pith.science/pith/GFRYGXMRNO2WLLNS4UHWVHJCHE","bundle":"https://pith.science/pith/GFRYGXMRNO2WLLNS4UHWVHJCHE/bundle.json","state":"https://pith.science/pith/GFRYGXMRNO2WLLNS4UHWVHJCHE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GFRYGXMRNO2WLLNS4UHWVHJCHE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GFRYGXMRNO2WLLNS4UHWVHJCHE","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":"912c88efcd61d64f445a751f47afe2713a573d3306198c4074ae0c149e670683","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-28T11:05:40Z","title_canon_sha256":"c278594e33869c065302eb1ba7ed6d9f701e42aea077df42d9ce9fc1799d0629"},"schema_version":"1.0","source":{"id":"1010.5918","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5918","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5918v1","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5918","created_at":"2026-05-18T04:38:14Z"},{"alias_kind":"pith_short_12","alias_value":"GFRYGXMRNO2W","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GFRYGXMRNO2WLLNS","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GFRYGXMR","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:2e6fd30b13f2f4fd4fc26ffc20f662fc6ea4b06593f84086faf971535db36955","target":"graph","created_at":"2026-05-18T04:38:14Z","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":"Lov\\'asz and Plummer conjectured, in the mid 1970's, that every cubic graph G with no cutedge has an exponential in |V(G)| number of perfect matchings. In this work we show that every cubic planar graph G whose geometric dual graph is a stack triangulation has at least 3 times the golden ratio to |V(G)|/72 distinct perfect matchings. Our work builds on a novel approach relating Lov\\'asz and Plummer's conjecture and the number of so called groundstates of the widely studied Ising model from statistical physics.","authors_text":"Andrea Jim\\'enez, Marcos Kiwi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-28T11:05:40Z","title":"Counting perfect matchings of cubic graphs in the geometric dual"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5918","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":"sha256:81c8d5b126b97af239217960b180e3b6afbdbef927644f82e9e7bf6deb2cd786","target":"record","created_at":"2026-05-18T04:38:14Z","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":"912c88efcd61d64f445a751f47afe2713a573d3306198c4074ae0c149e670683","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-28T11:05:40Z","title_canon_sha256":"c278594e33869c065302eb1ba7ed6d9f701e42aea077df42d9ce9fc1799d0629"},"schema_version":"1.0","source":{"id":"1010.5918","kind":"arxiv","version":1}},"canonical_sha256":"3163835d916bb565adb2e50f6a9d223925e5dba11c63597d6e737248b08af967","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3163835d916bb565adb2e50f6a9d223925e5dba11c63597d6e737248b08af967","first_computed_at":"2026-05-18T04:38:14.958088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:14.958088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YKzbS2L8x9gJamdkGJnCV3dVCgTSwvD9L6cJkAAPbtyFFoQXXFEO2vBO2qnsMPOvO5WEuRX02KDq5OPef+frBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:14.958613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5918","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81c8d5b126b97af239217960b180e3b6afbdbef927644f82e9e7bf6deb2cd786","sha256:2e6fd30b13f2f4fd4fc26ffc20f662fc6ea4b06593f84086faf971535db36955"],"state_sha256":"62cace023e65302589030eb775341ea8f6e1dbbe54c3a8edede9802585635ef2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jUOL5vUeQqYBkOIM1Ronpo9Lo6F8QMhTj0knjPEV6xg18tVR8710KhxvkDu8y7vOQNTcz8AgOXA6KZWG+a7cDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:32:00.355231Z","bundle_sha256":"53b5509a8b52bf9e08865195a7eaf0a2bd0b529d6024f98e3e99b50aa910137b"}}