{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5QFRAFT74FZPF55J26PTEXQTCS","short_pith_number":"pith:5QFRAFT7","canonical_record":{"source":{"id":"1612.02843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-08T21:24:51Z","cross_cats_sorted":[],"title_canon_sha256":"64efd006b52baf5f9a76a1a078f382a2e07c778476f071c98f9861b393d64761","abstract_canon_sha256":"02956e4dfdfd1f1460f0e08a4212f0d77ebe496cd2a7359d45250ac60a445793"},"schema_version":"1.0"},"canonical_sha256":"ec0b10167fe172f2f7a9d79f325e131486d404e95b5f0d94ec9c7eecf5fa4eca","source":{"kind":"arxiv","id":"1612.02843","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02843","created_at":"2026-05-18T00:55:28Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02843v1","created_at":"2026-05-18T00:55:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02843","created_at":"2026-05-18T00:55:28Z"},{"alias_kind":"pith_short_12","alias_value":"5QFRAFT74FZP","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5QFRAFT74FZPF55J","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5QFRAFT7","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5QFRAFT74FZPF55J26PTEXQTCS","target":"record","payload":{"canonical_record":{"source":{"id":"1612.02843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-08T21:24:51Z","cross_cats_sorted":[],"title_canon_sha256":"64efd006b52baf5f9a76a1a078f382a2e07c778476f071c98f9861b393d64761","abstract_canon_sha256":"02956e4dfdfd1f1460f0e08a4212f0d77ebe496cd2a7359d45250ac60a445793"},"schema_version":"1.0"},"canonical_sha256":"ec0b10167fe172f2f7a9d79f325e131486d404e95b5f0d94ec9c7eecf5fa4eca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:28.144499Z","signature_b64":"Gcr0Dt/X+vXCKEt+YJjDtrg7bGndP25Om6SIXWmDBUUQoFlQIz6oUcUFmqwUJ55egWDqh8+uDvhE+JwNm77vAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec0b10167fe172f2f7a9d79f325e131486d404e95b5f0d94ec9c7eecf5fa4eca","last_reissued_at":"2026-05-18T00:55:28.143851Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:28.143851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.02843","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":"2026-05-18T00:55:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oOeHxFZTpx/S/hrAEGa4h0awSzZWc3ZAGC3SnNeRi23XT3MGcrZ82cnArjBpJfIUlcbynRcekvUCyCuHNIdtAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:20:12.767835Z"},"content_sha256":"472f6d7d23b2278d8fd00c6db6eed7dbaf3c64b5f20c35f0c7b3781f23669a19","schema_version":"1.0","event_id":"sha256:472f6d7d23b2278d8fd00c6db6eed7dbaf3c64b5f20c35f0c7b3781f23669a19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5QFRAFT74FZPF55J26PTEXQTCS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strong resolving graphs: the realization and the characterization problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. Kuziak, I. G. Yero, J. A. Rodriguez-Velazquez, M. L. Puertas","submitted_at":"2016-12-08T21:24:51Z","abstract_excerpt":"The strong resolving graph $G_{SR}$ of a connected graph $G$ was introduced in [Discrete Applied Mathematics 155 (1) (2007) 356--364] as a tool to study the strong metric dimension of $G$. Basically, it was shown that the problem of finding the strong metric dimension of $G$ can be transformed to the problem of finding the vertex cover number of $G_{SR}$. Since then, several articles dealing with this subject have been published. In this paper, we survey the state of knowledge on the strong resolving graph and also derive some new results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02843","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":"2026-05-18T00:55:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pFOWj73NLlHjHzArG88j3BuP2gwO5cjOM3PsPgvKgRyj7Wn7RBy7kIDrPGCXmR1NRFKQXmH89MMQaET/8flwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:20:12.768169Z"},"content_sha256":"b5bb4f799f296441fc20a64c37f1f7d84623c4d912c4dcc5a71182e1b4324244","schema_version":"1.0","event_id":"sha256:b5bb4f799f296441fc20a64c37f1f7d84623c4d912c4dcc5a71182e1b4324244"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5QFRAFT74FZPF55J26PTEXQTCS/bundle.json","state_url":"https://pith.science/pith/5QFRAFT74FZPF55J26PTEXQTCS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5QFRAFT74FZPF55J26PTEXQTCS/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":"2026-06-02T04:20:12Z","links":{"resolver":"https://pith.science/pith/5QFRAFT74FZPF55J26PTEXQTCS","bundle":"https://pith.science/pith/5QFRAFT74FZPF55J26PTEXQTCS/bundle.json","state":"https://pith.science/pith/5QFRAFT74FZPF55J26PTEXQTCS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5QFRAFT74FZPF55J26PTEXQTCS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5QFRAFT74FZPF55J26PTEXQTCS","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":"02956e4dfdfd1f1460f0e08a4212f0d77ebe496cd2a7359d45250ac60a445793","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-08T21:24:51Z","title_canon_sha256":"64efd006b52baf5f9a76a1a078f382a2e07c778476f071c98f9861b393d64761"},"schema_version":"1.0","source":{"id":"1612.02843","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02843","created_at":"2026-05-18T00:55:28Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02843v1","created_at":"2026-05-18T00:55:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02843","created_at":"2026-05-18T00:55:28Z"},{"alias_kind":"pith_short_12","alias_value":"5QFRAFT74FZP","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5QFRAFT74FZPF55J","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5QFRAFT7","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:b5bb4f799f296441fc20a64c37f1f7d84623c4d912c4dcc5a71182e1b4324244","target":"graph","created_at":"2026-05-18T00:55:28Z","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 strong resolving graph $G_{SR}$ of a connected graph $G$ was introduced in [Discrete Applied Mathematics 155 (1) (2007) 356--364] as a tool to study the strong metric dimension of $G$. Basically, it was shown that the problem of finding the strong metric dimension of $G$ can be transformed to the problem of finding the vertex cover number of $G_{SR}$. Since then, several articles dealing with this subject have been published. In this paper, we survey the state of knowledge on the strong resolving graph and also derive some new results.","authors_text":"D. Kuziak, I. G. Yero, J. A. Rodriguez-Velazquez, M. L. Puertas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-08T21:24:51Z","title":"Strong resolving graphs: the realization and the characterization problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02843","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":"sha256:472f6d7d23b2278d8fd00c6db6eed7dbaf3c64b5f20c35f0c7b3781f23669a19","target":"record","created_at":"2026-05-18T00:55:28Z","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":"02956e4dfdfd1f1460f0e08a4212f0d77ebe496cd2a7359d45250ac60a445793","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-08T21:24:51Z","title_canon_sha256":"64efd006b52baf5f9a76a1a078f382a2e07c778476f071c98f9861b393d64761"},"schema_version":"1.0","source":{"id":"1612.02843","kind":"arxiv","version":1}},"canonical_sha256":"ec0b10167fe172f2f7a9d79f325e131486d404e95b5f0d94ec9c7eecf5fa4eca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec0b10167fe172f2f7a9d79f325e131486d404e95b5f0d94ec9c7eecf5fa4eca","first_computed_at":"2026-05-18T00:55:28.143851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:28.143851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gcr0Dt/X+vXCKEt+YJjDtrg7bGndP25Om6SIXWmDBUUQoFlQIz6oUcUFmqwUJ55egWDqh8+uDvhE+JwNm77vAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:28.144499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02843","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:472f6d7d23b2278d8fd00c6db6eed7dbaf3c64b5f20c35f0c7b3781f23669a19","sha256:b5bb4f799f296441fc20a64c37f1f7d84623c4d912c4dcc5a71182e1b4324244"],"state_sha256":"48e047c1c3b79272a06f6b6e7c6b9dd4842b88fc2ba52ea5f27b65b7d3b0dbd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H6dCa8952xKT/+J4kn3/Gc6O8JBqJk57ChzcAFpJ5UA4GeAVwIxJcie5axZ0NcowL08rZyekVyC+H1FW8thRCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:20:12.769988Z","bundle_sha256":"0cb11abcf0bdbb8f4d2e1752a12aacf3f1cbfdd5c8f609b87013e3ca2b2fc917"}}