{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RE5R4ZGQKFBZCTWULHLCR7V6QZ","short_pith_number":"pith:RE5R4ZGQ","canonical_record":{"source":{"id":"1708.05199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-17T10:54:49Z","cross_cats_sorted":[],"title_canon_sha256":"ad136ac6fc2380a3ab3b943cfb33d2cc10a073db6b0a2c23484fc4cb7abbe8fb","abstract_canon_sha256":"3db95da1b4f04edd7f667977f4a1f50f7ea54f5f4acd797a3be4e9247fd42c9a"},"schema_version":"1.0"},"canonical_sha256":"893b1e64d05143914ed459d628febe8644ece8e1d64a8919322d0d75ac659fe7","source":{"kind":"arxiv","id":"1708.05199","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05199","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05199v1","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05199","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"pith_short_12","alias_value":"RE5R4ZGQKFBZ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RE5R4ZGQKFBZCTWU","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RE5R4ZGQ","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RE5R4ZGQKFBZCTWULHLCR7V6QZ","target":"record","payload":{"canonical_record":{"source":{"id":"1708.05199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-17T10:54:49Z","cross_cats_sorted":[],"title_canon_sha256":"ad136ac6fc2380a3ab3b943cfb33d2cc10a073db6b0a2c23484fc4cb7abbe8fb","abstract_canon_sha256":"3db95da1b4f04edd7f667977f4a1f50f7ea54f5f4acd797a3be4e9247fd42c9a"},"schema_version":"1.0"},"canonical_sha256":"893b1e64d05143914ed459d628febe8644ece8e1d64a8919322d0d75ac659fe7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:53.583541Z","signature_b64":"nhtKvtCLZw+yRaoiaRwoZgN8yu1mGFY0ZpVQ56NJPq77FSxuBYtrQp6eDjApvxKxG2F6nha8rJ1n+q1sGJlLCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"893b1e64d05143914ed459d628febe8644ece8e1d64a8919322d0d75ac659fe7","last_reissued_at":"2026-05-18T00:37:53.583054Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:53.583054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.05199","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":"2026-05-18T00:37:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wLxaDfM4rgJRYZ8V7yyw3g+d+tVZyZYmms3HilM7Flcm6BSBlokx6loHwp79UaRaiuQPSIy8wh6m9Fgnk6vCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:16:46.485463Z"},"content_sha256":"d7dee6ade3fc8b45c26e8ea21c2f34f8df2198afa8786a48a3576c880fd0aaf4","schema_version":"1.0","event_id":"sha256:d7dee6ade3fc8b45c26e8ea21c2f34f8df2198afa8786a48a3576c880fd0aaf4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RE5R4ZGQKFBZCTWULHLCR7V6QZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized M\\\"{o}bius Ladder and Its Metric Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abdul Rauf Nizami, Ma Hongbin, Mobeen Muneer, Muhammad Idrees","submitted_at":"2017-08-17T10:54:49Z","abstract_excerpt":"In this paper we introduce generalized M\\\"{o}bius ladder $M_{m,n}$ and give its metric dimension. Moreover, it is observed that, depending on even and odd values of $m$ and $n$, it has two subfamilies with constant metric dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05199","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":"2026-05-18T00:37:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3WbhvEPEvNkaYMe8OAwaDYWAKagrz24y8Upmf7xHYwdj7hNbOYdT8AKnCJBq2iIk07O9Lahqj4Gxo5DOjR22Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:16:46.485800Z"},"content_sha256":"7725f173cdff31b84fb1eed5eb1de9b9edc833caaf7c6d75fcae0afaf8558c8c","schema_version":"1.0","event_id":"sha256:7725f173cdff31b84fb1eed5eb1de9b9edc833caaf7c6d75fcae0afaf8558c8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RE5R4ZGQKFBZCTWULHLCR7V6QZ/bundle.json","state_url":"https://pith.science/pith/RE5R4ZGQKFBZCTWULHLCR7V6QZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RE5R4ZGQKFBZCTWULHLCR7V6QZ/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":"2026-06-20T14:16:46Z","links":{"resolver":"https://pith.science/pith/RE5R4ZGQKFBZCTWULHLCR7V6QZ","bundle":"https://pith.science/pith/RE5R4ZGQKFBZCTWULHLCR7V6QZ/bundle.json","state":"https://pith.science/pith/RE5R4ZGQKFBZCTWULHLCR7V6QZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RE5R4ZGQKFBZCTWULHLCR7V6QZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RE5R4ZGQKFBZCTWULHLCR7V6QZ","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":"3db95da1b4f04edd7f667977f4a1f50f7ea54f5f4acd797a3be4e9247fd42c9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-17T10:54:49Z","title_canon_sha256":"ad136ac6fc2380a3ab3b943cfb33d2cc10a073db6b0a2c23484fc4cb7abbe8fb"},"schema_version":"1.0","source":{"id":"1708.05199","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05199","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05199v1","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05199","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"pith_short_12","alias_value":"RE5R4ZGQKFBZ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RE5R4ZGQKFBZCTWU","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RE5R4ZGQ","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:7725f173cdff31b84fb1eed5eb1de9b9edc833caaf7c6d75fcae0afaf8558c8c","target":"graph","created_at":"2026-05-18T00:37:53Z","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":"In this paper we introduce generalized M\\\"{o}bius ladder $M_{m,n}$ and give its metric dimension. Moreover, it is observed that, depending on even and odd values of $m$ and $n$, it has two subfamilies with constant metric dimensions.","authors_text":"Abdul Rauf Nizami, Ma Hongbin, Mobeen Muneer, Muhammad Idrees","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-17T10:54:49Z","title":"Generalized M\\\"{o}bius Ladder and Its Metric Dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05199","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:d7dee6ade3fc8b45c26e8ea21c2f34f8df2198afa8786a48a3576c880fd0aaf4","target":"record","created_at":"2026-05-18T00:37:53Z","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":"3db95da1b4f04edd7f667977f4a1f50f7ea54f5f4acd797a3be4e9247fd42c9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-17T10:54:49Z","title_canon_sha256":"ad136ac6fc2380a3ab3b943cfb33d2cc10a073db6b0a2c23484fc4cb7abbe8fb"},"schema_version":"1.0","source":{"id":"1708.05199","kind":"arxiv","version":1}},"canonical_sha256":"893b1e64d05143914ed459d628febe8644ece8e1d64a8919322d0d75ac659fe7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"893b1e64d05143914ed459d628febe8644ece8e1d64a8919322d0d75ac659fe7","first_computed_at":"2026-05-18T00:37:53.583054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:53.583054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nhtKvtCLZw+yRaoiaRwoZgN8yu1mGFY0ZpVQ56NJPq77FSxuBYtrQp6eDjApvxKxG2F6nha8rJ1n+q1sGJlLCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:53.583541Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.05199","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7dee6ade3fc8b45c26e8ea21c2f34f8df2198afa8786a48a3576c880fd0aaf4","sha256:7725f173cdff31b84fb1eed5eb1de9b9edc833caaf7c6d75fcae0afaf8558c8c"],"state_sha256":"de77a30a402499dce8637cf204e691b5dd9a7c18b312683ab6e821163a116eac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xQFtkO+COpO0L6QuZD8x4rmZ3gcxLpilFxYPeVYXOOUbrXrcv6jUEl/ZvKefRg592YyYzkXcdltTirqUAxoNBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T14:16:46.487774Z","bundle_sha256":"c5d78d0ef22e6474b1aef98dd481a05f7e898d83c4cf2165389ecab0b833fe1d"}}