{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5RIP4QCXIZDAH3SZ3EPPEWADBD","short_pith_number":"pith:5RIP4QCX","canonical_record":{"source":{"id":"1205.1752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-08T17:28:09Z","cross_cats_sorted":[],"title_canon_sha256":"3900f80285c30af9c0b2d4bc1c7581217d6ee2e921f3a4033a833a2e63b4d078","abstract_canon_sha256":"116233c62202497966e8f02084074e1bacd411179546ecc6e3342ac0e546eaf5"},"schema_version":"1.0"},"canonical_sha256":"ec50fe4057464603ee59d91ef2580308d6d251a4ec8b5aec3de68b1da8e0d699","source":{"kind":"arxiv","id":"1205.1752","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1752","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1752v1","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1752","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"5RIP4QCXIZDA","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5RIP4QCXIZDAH3SZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5RIP4QCX","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5RIP4QCXIZDAH3SZ3EPPEWADBD","target":"record","payload":{"canonical_record":{"source":{"id":"1205.1752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-08T17:28:09Z","cross_cats_sorted":[],"title_canon_sha256":"3900f80285c30af9c0b2d4bc1c7581217d6ee2e921f3a4033a833a2e63b4d078","abstract_canon_sha256":"116233c62202497966e8f02084074e1bacd411179546ecc6e3342ac0e546eaf5"},"schema_version":"1.0"},"canonical_sha256":"ec50fe4057464603ee59d91ef2580308d6d251a4ec8b5aec3de68b1da8e0d699","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:09.067274Z","signature_b64":"k/SGyyi/X5kSVpwW+jHV42uS9e2N2lNQutvUE/tIMpqTbsMayGX5xrx+EIq3n0pEdVJUUWxmMaBGY7kmR20jAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec50fe4057464603ee59d91ef2580308d6d251a4ec8b5aec3de68b1da8e0d699","last_reissued_at":"2026-05-18T03:56:09.066549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:09.066549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.1752","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":"2026-05-18T03:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dtNw8gMvmmIjISzCpX/jqeMB2DuSk+lrh10v89MtinhmN+E4xFxdZa4reiGyOJpnqwOG7G51EWMmtnyNOEawCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T11:17:41.157458Z"},"content_sha256":"9a04259aee2527b7f40cfd119657e08b20ba19015eacb95f24d90e04d34ef16b","schema_version":"1.0","event_id":"sha256:9a04259aee2527b7f40cfd119657e08b20ba19015eacb95f24d90e04d34ef16b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5RIP4QCXIZDAH3SZ3EPPEWADBD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eigenvalues of a H-generalized join graph operation constrained by vertex subsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Domingos M. Cardoso, Enide A. Martins, Maria Robbiano, Oscar Rojo","submitted_at":"2012-05-08T17:28:09Z","abstract_excerpt":"Considering a graph $H$ of order $p$, a generalized $H$-join operation of a family of graphs $G_1,..., G_p$, constrained by a family of vertex subsets $S_i \\subseteq V(G_i)$, $i=1,..., p,$ is introduced. When each vertex subset $S_i$ is $(k_i,\\tau_i)$-regular, it is deduced that all non-main adjacency eigenvalues of $G_i$, different from $k_i-\\tau_i$, for $i=1,..., p,$ remain as eigenvalues of the graph $G$ obtained by the above mentioned operation. Furthermore, if each graph $G_i$ of the family is $k_i$-regular, for $i=1,..., p$, and all the vertex subsets are such that $S_i=V(G_i)$, the $H$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1752","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":"2026-05-18T03:56:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wsn5w51eAlRQWbMUFu05KBAzhsgTN+KB0IzhG0FNdFhk8LSqE7+jD2BcQef4zBX89/mBNnESfujyzXTwiBCPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T11:17:41.157940Z"},"content_sha256":"5be0eea7eebbdf078745c3d88f334164e9cba969a3f9914d09adf3d09871451d","schema_version":"1.0","event_id":"sha256:5be0eea7eebbdf078745c3d88f334164e9cba969a3f9914d09adf3d09871451d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RIP4QCXIZDAH3SZ3EPPEWADBD/bundle.json","state_url":"https://pith.science/pith/5RIP4QCXIZDAH3SZ3EPPEWADBD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RIP4QCXIZDAH3SZ3EPPEWADBD/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":"2026-05-24T11:17:41Z","links":{"resolver":"https://pith.science/pith/5RIP4QCXIZDAH3SZ3EPPEWADBD","bundle":"https://pith.science/pith/5RIP4QCXIZDAH3SZ3EPPEWADBD/bundle.json","state":"https://pith.science/pith/5RIP4QCXIZDAH3SZ3EPPEWADBD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RIP4QCXIZDAH3SZ3EPPEWADBD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5RIP4QCXIZDAH3SZ3EPPEWADBD","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":"116233c62202497966e8f02084074e1bacd411179546ecc6e3342ac0e546eaf5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-08T17:28:09Z","title_canon_sha256":"3900f80285c30af9c0b2d4bc1c7581217d6ee2e921f3a4033a833a2e63b4d078"},"schema_version":"1.0","source":{"id":"1205.1752","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.1752","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"arxiv_version","alias_value":"1205.1752v1","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.1752","created_at":"2026-05-18T03:56:09Z"},{"alias_kind":"pith_short_12","alias_value":"5RIP4QCXIZDA","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"5RIP4QCXIZDAH3SZ","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"5RIP4QCX","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:5be0eea7eebbdf078745c3d88f334164e9cba969a3f9914d09adf3d09871451d","target":"graph","created_at":"2026-05-18T03:56:09Z","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":"Considering a graph $H$ of order $p$, a generalized $H$-join operation of a family of graphs $G_1,..., G_p$, constrained by a family of vertex subsets $S_i \\subseteq V(G_i)$, $i=1,..., p,$ is introduced. When each vertex subset $S_i$ is $(k_i,\\tau_i)$-regular, it is deduced that all non-main adjacency eigenvalues of $G_i$, different from $k_i-\\tau_i$, for $i=1,..., p,$ remain as eigenvalues of the graph $G$ obtained by the above mentioned operation. Furthermore, if each graph $G_i$ of the family is $k_i$-regular, for $i=1,..., p$, and all the vertex subsets are such that $S_i=V(G_i)$, the $H$-","authors_text":"Domingos M. Cardoso, Enide A. Martins, Maria Robbiano, Oscar Rojo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-08T17:28:09Z","title":"Eigenvalues of a H-generalized join graph operation constrained by vertex subsets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1752","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":"sha256:9a04259aee2527b7f40cfd119657e08b20ba19015eacb95f24d90e04d34ef16b","target":"record","created_at":"2026-05-18T03:56:09Z","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":"116233c62202497966e8f02084074e1bacd411179546ecc6e3342ac0e546eaf5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-08T17:28:09Z","title_canon_sha256":"3900f80285c30af9c0b2d4bc1c7581217d6ee2e921f3a4033a833a2e63b4d078"},"schema_version":"1.0","source":{"id":"1205.1752","kind":"arxiv","version":1}},"canonical_sha256":"ec50fe4057464603ee59d91ef2580308d6d251a4ec8b5aec3de68b1da8e0d699","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec50fe4057464603ee59d91ef2580308d6d251a4ec8b5aec3de68b1da8e0d699","first_computed_at":"2026-05-18T03:56:09.066549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:09.066549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k/SGyyi/X5kSVpwW+jHV42uS9e2N2lNQutvUE/tIMpqTbsMayGX5xrx+EIq3n0pEdVJUUWxmMaBGY7kmR20jAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:09.067274Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.1752","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a04259aee2527b7f40cfd119657e08b20ba19015eacb95f24d90e04d34ef16b","sha256:5be0eea7eebbdf078745c3d88f334164e9cba969a3f9914d09adf3d09871451d"],"state_sha256":"2d0ba080d02a84d052a332d5d2a5f7a7770e125563a843d517b08ad08be00be9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PmxtY6rKCidjKJPSo+UPuufsNQxVvHJyCPNqcdJ9u6n0PW6BLcMiHSGAHvHzOuS/rqdHphIrH26ly98nZwoADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T11:17:41.161866Z","bundle_sha256":"56c4984df9ff923f489eb1d435a57377cb9bc3a95b177394692446d64b49e837"}}