{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7EEERD65NKD6365V6E5T5V7W67","short_pith_number":"pith:7EEERD65","canonical_record":{"source":{"id":"1106.5353","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-27T10:40:06Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"8ee878cd828cb7e8c04d5445be617b1f2166a0087c6e4e83825554c2f500ce45","abstract_canon_sha256":"cfec9a71cd7a5b0e31a5fc50ddb55461bfa080795e977bcb53d2dd654a284140"},"schema_version":"1.0"},"canonical_sha256":"f908488fdd6a87edfbb5f13b3ed7f6f7dd9640b30e9cb25b139d6f55dccf9824","source":{"kind":"arxiv","id":"1106.5353","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5353","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5353v3","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5353","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"pith_short_12","alias_value":"7EEERD65NKD6","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7EEERD65NKD6365V","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7EEERD65","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7EEERD65NKD6365V6E5T5V7W67","target":"record","payload":{"canonical_record":{"source":{"id":"1106.5353","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-27T10:40:06Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"8ee878cd828cb7e8c04d5445be617b1f2166a0087c6e4e83825554c2f500ce45","abstract_canon_sha256":"cfec9a71cd7a5b0e31a5fc50ddb55461bfa080795e977bcb53d2dd654a284140"},"schema_version":"1.0"},"canonical_sha256":"f908488fdd6a87edfbb5f13b3ed7f6f7dd9640b30e9cb25b139d6f55dccf9824","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:03.661586Z","signature_b64":"DAYsBa4zO1t9jm66HWQ2AAd8Rl6VbYnMcGsWe5DJTteEiHGTTG/YN+I/jBXHB5hvRmm3tX1aDerJp6bGc8fPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f908488fdd6a87edfbb5f13b3ed7f6f7dd9640b30e9cb25b139d6f55dccf9824","last_reissued_at":"2026-05-18T04:08:03.661112Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:03.661112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.5353","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:08:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VyQc/lNTBkcvvaD7m0sN5hZ5x5xw+UD95PQSp+uzgOGawrJBvzvgWNvG0LFlb+/8j/5dDJOAvZ8rt56BXh3IDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:11:16.054698Z"},"content_sha256":"77d34037e8f7668561041ddc4a65f621318bda399578de190510751b030b2e33","schema_version":"1.0","event_id":"sha256:77d34037e8f7668561041ddc4a65f621318bda399578de190510751b030b2e33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7EEERD65NKD6365V6E5T5V7W67","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a diameter bound for Cayley graphs generated by transposition trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ashwin Ganesan","submitted_at":"2011-06-27T10:40:06Z","abstract_excerpt":"Let $\\Gamma$ be a Cayley graph generated by a transposition tree. A natural problem is to understand how the properties of the Cayley graph depend on those of the underlying transposition tree. We focus here on diameter and distance related questions. We examine some related bounds and prove some properties about them.\n\nThis paper has been withdrawn and a new version with these results and further extensions is at abs/1111.3114"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5353","kind":"arxiv","version":3},"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":"2026-05-18T04:08:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bHFCqHbPGaUbU2kqLkRpLzD8YHFQuul0y9jBhVpadm3jGdMIgGW3Ypp7o7B7SPSYdVnnP33bvxq10ezIU36vAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:11:16.055458Z"},"content_sha256":"8a6827dc2d43a61f1910e6bbde885f42d774e7d8c25b92fbc5ed5e5c6acff254","schema_version":"1.0","event_id":"sha256:8a6827dc2d43a61f1910e6bbde885f42d774e7d8c25b92fbc5ed5e5c6acff254"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7EEERD65NKD6365V6E5T5V7W67/bundle.json","state_url":"https://pith.science/pith/7EEERD65NKD6365V6E5T5V7W67/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7EEERD65NKD6365V6E5T5V7W67/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":"2026-06-11T20:11:16Z","links":{"resolver":"https://pith.science/pith/7EEERD65NKD6365V6E5T5V7W67","bundle":"https://pith.science/pith/7EEERD65NKD6365V6E5T5V7W67/bundle.json","state":"https://pith.science/pith/7EEERD65NKD6365V6E5T5V7W67/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7EEERD65NKD6365V6E5T5V7W67/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7EEERD65NKD6365V6E5T5V7W67","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":"cfec9a71cd7a5b0e31a5fc50ddb55461bfa080795e977bcb53d2dd654a284140","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-27T10:40:06Z","title_canon_sha256":"8ee878cd828cb7e8c04d5445be617b1f2166a0087c6e4e83825554c2f500ce45"},"schema_version":"1.0","source":{"id":"1106.5353","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5353","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5353v3","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5353","created_at":"2026-05-18T04:08:03Z"},{"alias_kind":"pith_short_12","alias_value":"7EEERD65NKD6","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7EEERD65NKD6365V","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7EEERD65","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:8a6827dc2d43a61f1910e6bbde885f42d774e7d8c25b92fbc5ed5e5c6acff254","target":"graph","created_at":"2026-05-18T04:08:03Z","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":"Let $\\Gamma$ be a Cayley graph generated by a transposition tree. A natural problem is to understand how the properties of the Cayley graph depend on those of the underlying transposition tree. We focus here on diameter and distance related questions. We examine some related bounds and prove some properties about them.\n\nThis paper has been withdrawn and a new version with these results and further extensions is at abs/1111.3114","authors_text":"Ashwin Ganesan","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-27T10:40:06Z","title":"On a diameter bound for Cayley graphs generated by transposition trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5353","kind":"arxiv","version":3},"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":"sha256:77d34037e8f7668561041ddc4a65f621318bda399578de190510751b030b2e33","target":"record","created_at":"2026-05-18T04:08:03Z","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":"cfec9a71cd7a5b0e31a5fc50ddb55461bfa080795e977bcb53d2dd654a284140","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-27T10:40:06Z","title_canon_sha256":"8ee878cd828cb7e8c04d5445be617b1f2166a0087c6e4e83825554c2f500ce45"},"schema_version":"1.0","source":{"id":"1106.5353","kind":"arxiv","version":3}},"canonical_sha256":"f908488fdd6a87edfbb5f13b3ed7f6f7dd9640b30e9cb25b139d6f55dccf9824","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f908488fdd6a87edfbb5f13b3ed7f6f7dd9640b30e9cb25b139d6f55dccf9824","first_computed_at":"2026-05-18T04:08:03.661112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:03.661112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DAYsBa4zO1t9jm66HWQ2AAd8Rl6VbYnMcGsWe5DJTteEiHGTTG/YN+I/jBXHB5hvRmm3tX1aDerJp6bGc8fPDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:03.661586Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5353","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77d34037e8f7668561041ddc4a65f621318bda399578de190510751b030b2e33","sha256:8a6827dc2d43a61f1910e6bbde885f42d774e7d8c25b92fbc5ed5e5c6acff254"],"state_sha256":"23629149bef9eefa84a6191cb891a84c32c67b5d849ac82ccf230a42129710e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ROg43Ju8KIBcoAVhLfWDITA6PsGOeA6aEJXxPj8BlxY5vXwBKnF4JbUYJodoibRAZie5IGcaKmOvywVgHIyFDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:11:16.060356Z","bundle_sha256":"a09a0e3be090f943c72d0c7f04e8a974bc06cc056706e9c4f09ea834e701d5e7"}}