{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QWPGUTDXI5REKJTYCHNZG4PBIB","short_pith_number":"pith:QWPGUTDX","canonical_record":{"source":{"id":"1510.03605","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-13T09:54:39Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"36dce92a2849e2f05eb3a8795199b5774ad568391ca1fe402b306a1108d5096e","abstract_canon_sha256":"90e4df519561cf9c59d4b06992730cb3aa0369675375bfa88261b9410a6d40cd"},"schema_version":"1.0"},"canonical_sha256":"859e6a4c77476245267811db9371e1407a9e08a3548a4f267247550e5161c7fc","source":{"kind":"arxiv","id":"1510.03605","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03605","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03605v1","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03605","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"QWPGUTDXI5RE","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QWPGUTDXI5REKJTY","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QWPGUTDX","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QWPGUTDXI5REKJTYCHNZG4PBIB","target":"record","payload":{"canonical_record":{"source":{"id":"1510.03605","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-13T09:54:39Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"36dce92a2849e2f05eb3a8795199b5774ad568391ca1fe402b306a1108d5096e","abstract_canon_sha256":"90e4df519561cf9c59d4b06992730cb3aa0369675375bfa88261b9410a6d40cd"},"schema_version":"1.0"},"canonical_sha256":"859e6a4c77476245267811db9371e1407a9e08a3548a4f267247550e5161c7fc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:16.693651Z","signature_b64":"i41Estr0tHiQ5qONsI3NGUJ2JGUeFUKaMS9pWZPT+/bFwDgMtknkGcqtdxKznaqaQw46qsc1hfTLpopGUQwICg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"859e6a4c77476245267811db9371e1407a9e08a3548a4f267247550e5161c7fc","last_reissued_at":"2026-05-18T01:30:16.693056Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:16.693056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.03605","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":"2026-05-18T01:30:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r06tzLjVCfQFpooCW1YwbGzyB6+NJnI470rq2t7OTmaAoaA6KpGBkdkSFy54ScY1WAC1TJ9CjY3UUXALrYo3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:46:12.805827Z"},"content_sha256":"872d2660f7d55ef4d58354785cc453fac0f8db4d0ffdda5d45c62376f6add42b","schema_version":"1.0","event_id":"sha256:872d2660f7d55ef4d58354785cc453fac0f8db4d0ffdda5d45c62376f6add42b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QWPGUTDXI5REKJTYCHNZG4PBIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relative Cayley graphs of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Ahmad Erfanian, Mehdi Rajabian, Mohammad Farrokhi Derakhshandeh Ghouchan","submitted_at":"2015-10-13T09:54:39Z","abstract_excerpt":"The relative Cayley graph of a group $G$ with respect to its proper subgroup $H$, is a graph whose vertices are elements of $G$ and two vertices $h\\in H$ and $g\\in G$ are adjacent if $g=hc$ for some $c\\in C$, where $C$ is an inversed-closed subset of $G$. We study the relative Cayley graphs and, among other results, we discuss on their connectivity and forbidden structures, and compute some of their important numerical invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03605","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":"2026-05-18T01:30:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k+j0cf86yps2FJ/mLMkvGclFgYxiVIjmR1Q2MQHnEN0mxCjG8yPncMZnvdxoblk5Xq6Kb9gcesosb2eFW8FUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:46:12.806450Z"},"content_sha256":"02da40d14b433f19a2e9dbb9b7bad25f908ee09b31d9b6830e9c3e36aad9a849","schema_version":"1.0","event_id":"sha256:02da40d14b433f19a2e9dbb9b7bad25f908ee09b31d9b6830e9c3e36aad9a849"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QWPGUTDXI5REKJTYCHNZG4PBIB/bundle.json","state_url":"https://pith.science/pith/QWPGUTDXI5REKJTYCHNZG4PBIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QWPGUTDXI5REKJTYCHNZG4PBIB/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":"2026-06-06T06:46:12Z","links":{"resolver":"https://pith.science/pith/QWPGUTDXI5REKJTYCHNZG4PBIB","bundle":"https://pith.science/pith/QWPGUTDXI5REKJTYCHNZG4PBIB/bundle.json","state":"https://pith.science/pith/QWPGUTDXI5REKJTYCHNZG4PBIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QWPGUTDXI5REKJTYCHNZG4PBIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QWPGUTDXI5REKJTYCHNZG4PBIB","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":"90e4df519561cf9c59d4b06992730cb3aa0369675375bfa88261b9410a6d40cd","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-13T09:54:39Z","title_canon_sha256":"36dce92a2849e2f05eb3a8795199b5774ad568391ca1fe402b306a1108d5096e"},"schema_version":"1.0","source":{"id":"1510.03605","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.03605","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.03605v1","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.03605","created_at":"2026-05-18T01:30:16Z"},{"alias_kind":"pith_short_12","alias_value":"QWPGUTDXI5RE","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QWPGUTDXI5REKJTY","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QWPGUTDX","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:02da40d14b433f19a2e9dbb9b7bad25f908ee09b31d9b6830e9c3e36aad9a849","target":"graph","created_at":"2026-05-18T01:30:16Z","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":"The relative Cayley graph of a group $G$ with respect to its proper subgroup $H$, is a graph whose vertices are elements of $G$ and two vertices $h\\in H$ and $g\\in G$ are adjacent if $g=hc$ for some $c\\in C$, where $C$ is an inversed-closed subset of $G$. We study the relative Cayley graphs and, among other results, we discuss on their connectivity and forbidden structures, and compute some of their important numerical invariants.","authors_text":"Ahmad Erfanian, Mehdi Rajabian, Mohammad Farrokhi Derakhshandeh Ghouchan","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-13T09:54:39Z","title":"Relative Cayley graphs of finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03605","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":"sha256:872d2660f7d55ef4d58354785cc453fac0f8db4d0ffdda5d45c62376f6add42b","target":"record","created_at":"2026-05-18T01:30:16Z","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":"90e4df519561cf9c59d4b06992730cb3aa0369675375bfa88261b9410a6d40cd","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-13T09:54:39Z","title_canon_sha256":"36dce92a2849e2f05eb3a8795199b5774ad568391ca1fe402b306a1108d5096e"},"schema_version":"1.0","source":{"id":"1510.03605","kind":"arxiv","version":1}},"canonical_sha256":"859e6a4c77476245267811db9371e1407a9e08a3548a4f267247550e5161c7fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"859e6a4c77476245267811db9371e1407a9e08a3548a4f267247550e5161c7fc","first_computed_at":"2026-05-18T01:30:16.693056Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:16.693056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i41Estr0tHiQ5qONsI3NGUJ2JGUeFUKaMS9pWZPT+/bFwDgMtknkGcqtdxKznaqaQw46qsc1hfTLpopGUQwICg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:16.693651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.03605","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:872d2660f7d55ef4d58354785cc453fac0f8db4d0ffdda5d45c62376f6add42b","sha256:02da40d14b433f19a2e9dbb9b7bad25f908ee09b31d9b6830e9c3e36aad9a849"],"state_sha256":"38f87f21075f7b08469f0250007b1f9129990f615652868800032927b9fe907b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dwTFhwUZMkwB2WlvPW4r6iFmPGyJGnN9Lk839G/MjhBkrUZbaZkL9l/0bhUz/El0BMLUTEUkacTtnJiiI4N2CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T06:46:12.809768Z","bundle_sha256":"fcfa269796e2d7c920c7996f5d4c0be7ecd434060f1c92b1c8cf5b581f68de30"}}