{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EXY6B7FHYO2T6KE6SPJQE4RIF2","short_pith_number":"pith:EXY6B7FH","canonical_record":{"source":{"id":"1807.10891","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-28T05:07:34Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"481996b85433c999bca532a63d0e99433e410767fa1cc05e476047f5f8f88578","abstract_canon_sha256":"ac65701897c04918e837525eaa52bface07f1edf98c927a567eed1ddd71927dc"},"schema_version":"1.0"},"canonical_sha256":"25f1e0fca7c3b53f289e93d30272282ebc12a5d93b3eae98d153c5984b22aefb","source":{"kind":"arxiv","id":"1807.10891","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10891","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10891v4","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10891","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"EXY6B7FHYO2T","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EXY6B7FHYO2T6KE6","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EXY6B7FH","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EXY6B7FHYO2T6KE6SPJQE4RIF2","target":"record","payload":{"canonical_record":{"source":{"id":"1807.10891","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-28T05:07:34Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"481996b85433c999bca532a63d0e99433e410767fa1cc05e476047f5f8f88578","abstract_canon_sha256":"ac65701897c04918e837525eaa52bface07f1edf98c927a567eed1ddd71927dc"},"schema_version":"1.0"},"canonical_sha256":"25f1e0fca7c3b53f289e93d30272282ebc12a5d93b3eae98d153c5984b22aefb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:25.045656Z","signature_b64":"8OQ4gDcE43ssgka6WDsecWQqSJWyKwc8Qs1LiPW5oNjbW0R7lK2/9LnjOeZ5LVxZgcXfTkNWfSwiVybHPZq2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25f1e0fca7c3b53f289e93d30272282ebc12a5d93b3eae98d153c5984b22aefb","last_reissued_at":"2026-05-17T23:41:25.044800Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:25.044800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.10891","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GpFGptKFcDIlxeih6ygPucxtETWMIzSIGyblLajSivuBk+Aw1tjrymTL+TLGv5/R1uVzjpWlHcgzvu1kzN3jCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:57:49.066242Z"},"content_sha256":"d430b685662211aaef300887effbcc4822139ea0c3ec8f56e7ed183e7453e015","schema_version":"1.0","event_id":"sha256:d430b685662211aaef300887effbcc4822139ea0c3ec8f56e7ed183e7453e015"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EXY6B7FHYO2T6KE6SPJQE4RIF2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalues of the Laplacian on the Goldberg-Coxeter constructions for $3$- and $4$-valent graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CO","authors_text":"Hisashi Naito, Tatsuya Tate, Toshiaki Omori","submitted_at":"2018-07-28T05:07:34Z","abstract_excerpt":"We are concerned with spectral problems of the Goldberg-Coxeter construction for $3$- and $4$-valent finite graphs. The Goldberg-Coxeter constructions $\\mathrm{GC}_{k,l}(X)$ of a finite $3$- or $4$-valent graph $X$ are considered as \"subdivisions\" of $X$, whose number of vertices are increasing at order $O(k^2+l^2)$, nevertheless which have bounded girth. It is shown that the first (resp. the last) $o(k^2)$ eigenvalues of the combinatorial Laplacian on $\\mathrm{GC}_{k,0}(X)$ tend to $0$ (resp. tend to $6$ or $8$ in the $3$- or $4$-valent case, respectively) as $k$ goes to infinity. A concrete "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10891","kind":"arxiv","version":4},"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":"2026-05-17T23:41:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yOgew7rvGE0j1J/XKGwTnLY8YHz1asv9LQ+yzHy8nAtP+7o/1KQ+wIcchBnSS126paqqUPHH5V2OK+yAAVrXDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:57:49.066600Z"},"content_sha256":"73aa50852ccc54b1da45588b679df7581d644be2752d42523df234ea2da3d88c","schema_version":"1.0","event_id":"sha256:73aa50852ccc54b1da45588b679df7581d644be2752d42523df234ea2da3d88c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXY6B7FHYO2T6KE6SPJQE4RIF2/bundle.json","state_url":"https://pith.science/pith/EXY6B7FHYO2T6KE6SPJQE4RIF2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXY6B7FHYO2T6KE6SPJQE4RIF2/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":"2026-06-04T12:57:49Z","links":{"resolver":"https://pith.science/pith/EXY6B7FHYO2T6KE6SPJQE4RIF2","bundle":"https://pith.science/pith/EXY6B7FHYO2T6KE6SPJQE4RIF2/bundle.json","state":"https://pith.science/pith/EXY6B7FHYO2T6KE6SPJQE4RIF2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXY6B7FHYO2T6KE6SPJQE4RIF2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EXY6B7FHYO2T6KE6SPJQE4RIF2","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":"ac65701897c04918e837525eaa52bface07f1edf98c927a567eed1ddd71927dc","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-28T05:07:34Z","title_canon_sha256":"481996b85433c999bca532a63d0e99433e410767fa1cc05e476047f5f8f88578"},"schema_version":"1.0","source":{"id":"1807.10891","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10891","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10891v4","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10891","created_at":"2026-05-17T23:41:25Z"},{"alias_kind":"pith_short_12","alias_value":"EXY6B7FHYO2T","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EXY6B7FHYO2T6KE6","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EXY6B7FH","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:73aa50852ccc54b1da45588b679df7581d644be2752d42523df234ea2da3d88c","target":"graph","created_at":"2026-05-17T23:41:25Z","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 are concerned with spectral problems of the Goldberg-Coxeter construction for $3$- and $4$-valent finite graphs. The Goldberg-Coxeter constructions $\\mathrm{GC}_{k,l}(X)$ of a finite $3$- or $4$-valent graph $X$ are considered as \"subdivisions\" of $X$, whose number of vertices are increasing at order $O(k^2+l^2)$, nevertheless which have bounded girth. It is shown that the first (resp. the last) $o(k^2)$ eigenvalues of the combinatorial Laplacian on $\\mathrm{GC}_{k,0}(X)$ tend to $0$ (resp. tend to $6$ or $8$ in the $3$- or $4$-valent case, respectively) as $k$ goes to infinity. A concrete ","authors_text":"Hisashi Naito, Tatsuya Tate, Toshiaki Omori","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-28T05:07:34Z","title":"Eigenvalues of the Laplacian on the Goldberg-Coxeter constructions for $3$- and $4$-valent graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10891","kind":"arxiv","version":4},"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:d430b685662211aaef300887effbcc4822139ea0c3ec8f56e7ed183e7453e015","target":"record","created_at":"2026-05-17T23:41:25Z","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":"ac65701897c04918e837525eaa52bface07f1edf98c927a567eed1ddd71927dc","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-28T05:07:34Z","title_canon_sha256":"481996b85433c999bca532a63d0e99433e410767fa1cc05e476047f5f8f88578"},"schema_version":"1.0","source":{"id":"1807.10891","kind":"arxiv","version":4}},"canonical_sha256":"25f1e0fca7c3b53f289e93d30272282ebc12a5d93b3eae98d153c5984b22aefb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25f1e0fca7c3b53f289e93d30272282ebc12a5d93b3eae98d153c5984b22aefb","first_computed_at":"2026-05-17T23:41:25.044800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:25.044800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8OQ4gDcE43ssgka6WDsecWQqSJWyKwc8Qs1LiPW5oNjbW0R7lK2/9LnjOeZ5LVxZgcXfTkNWfSwiVybHPZq2Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:25.045656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.10891","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d430b685662211aaef300887effbcc4822139ea0c3ec8f56e7ed183e7453e015","sha256:73aa50852ccc54b1da45588b679df7581d644be2752d42523df234ea2da3d88c"],"state_sha256":"3dd6dfa808f84072fd13d8b418723eb4691d9d0f19553a486d24078a9517f741"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HRsscAEBWXAcIyLRlGoCCqqehCGiOto6lFNKhcrDdhE8+COXtwh3oSibrK7rVZn+htrxWpWPt9/4gm9eJzKbDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T12:57:49.068696Z","bundle_sha256":"2898c490447edc3edfce9c5d1e3915e38a928b0ed0976321e9df04242bf13d04"}}