{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GX3B7QUHIKVUIQHW2Q4KGJUX7E","short_pith_number":"pith:GX3B7QUH","canonical_record":{"source":{"id":"1706.04255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-06-13T21:06:37Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"e200c16fa9002d3f7ebacd32c811cf5985b4fac2c6d6726f1626681e7e061f48","abstract_canon_sha256":"e04d556b34533c4a7f225346bfb448c37ba56766a6b265c116962b3b2027bf26"},"schema_version":"1.0"},"canonical_sha256":"35f61fc28742ab4440f6d438a32697f903778c3c5a7595100fa7f0fe02b00b07","source":{"kind":"arxiv","id":"1706.04255","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04255","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04255v1","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04255","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"GX3B7QUHIKVU","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GX3B7QUHIKVUIQHW","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GX3B7QUH","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GX3B7QUHIKVUIQHW2Q4KGJUX7E","target":"record","payload":{"canonical_record":{"source":{"id":"1706.04255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-06-13T21:06:37Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"e200c16fa9002d3f7ebacd32c811cf5985b4fac2c6d6726f1626681e7e061f48","abstract_canon_sha256":"e04d556b34533c4a7f225346bfb448c37ba56766a6b265c116962b3b2027bf26"},"schema_version":"1.0"},"canonical_sha256":"35f61fc28742ab4440f6d438a32697f903778c3c5a7595100fa7f0fe02b00b07","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:23.130289Z","signature_b64":"TG+/7HkCS83Ke4TBZXgNwX6W6twu3LdNYVVMhZrUlXpDsakozramRcCKu8+nLH475FuM57rPQrW6ninUqWETDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35f61fc28742ab4440f6d438a32697f903778c3c5a7595100fa7f0fe02b00b07","last_reissued_at":"2026-05-18T00:42:23.129706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:23.129706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.04255","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":"2026-05-18T00:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wzkOJzzP7RLd8N7xiSpXMqtvYbAIyWK5S4JrbDQBfiSFY6cL4BuzVmiFVNrnfweGiVjRV7HX1qPmMlYyJjTxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:34:58.740013Z"},"content_sha256":"ed302880626ccbfb9db6635779d3761ccc94e2fc1aa5511eb6d3bae5975d484d","schema_version":"1.0","event_id":"sha256:ed302880626ccbfb9db6635779d3761ccc94e2fc1aa5511eb6d3bae5975d484d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GX3B7QUHIKVUIQHW2Q4KGJUX7E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Structured Connectivity Augmentation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Dimitrios M. Thilikos, Fedor V. Fomin, Petr A. Golovach","submitted_at":"2017-06-13T21:06:37Z","abstract_excerpt":"We initiate the algorithmic study of the following \"structured augmentation\" question: is it possible to increase the connectivity of a given graph G by superposing it with another given graph H? More precisely, graph F is the superposition of G and H with respect to injective mapping \\phi: V(H)->V(G) if every edge uv of F is either an edge of G, or \\phi^{-1}(u)\\phi^{-1}(v) is an edge of H. We consider the following optimization problem. Given graphs G,H, and a weight function \\omega assigning non-negative weights to pairs of vertices of V(G), the task is to find \\varphi of minimum weight \\ome"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04255","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":"2026-05-18T00:42:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"li5qUIdRYjgMPtYGos9l07kHLW5fz3c4WagFJqnGfvc36AJTdwg7dL6C5Ah51946+jWQTs8ub6FPySf4G5kYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:34:58.740597Z"},"content_sha256":"2de7a4ea2d5e0b5ce019601a8e736745b799335dc62411a97c035777bea4f45e","schema_version":"1.0","event_id":"sha256:2de7a4ea2d5e0b5ce019601a8e736745b799335dc62411a97c035777bea4f45e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GX3B7QUHIKVUIQHW2Q4KGJUX7E/bundle.json","state_url":"https://pith.science/pith/GX3B7QUHIKVUIQHW2Q4KGJUX7E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GX3B7QUHIKVUIQHW2Q4KGJUX7E/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":"2026-05-31T10:34:58Z","links":{"resolver":"https://pith.science/pith/GX3B7QUHIKVUIQHW2Q4KGJUX7E","bundle":"https://pith.science/pith/GX3B7QUHIKVUIQHW2Q4KGJUX7E/bundle.json","state":"https://pith.science/pith/GX3B7QUHIKVUIQHW2Q4KGJUX7E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GX3B7QUHIKVUIQHW2Q4KGJUX7E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GX3B7QUHIKVUIQHW2Q4KGJUX7E","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":"e04d556b34533c4a7f225346bfb448c37ba56766a6b265c116962b3b2027bf26","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-06-13T21:06:37Z","title_canon_sha256":"e200c16fa9002d3f7ebacd32c811cf5985b4fac2c6d6726f1626681e7e061f48"},"schema_version":"1.0","source":{"id":"1706.04255","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04255","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04255v1","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04255","created_at":"2026-05-18T00:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"GX3B7QUHIKVU","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GX3B7QUHIKVUIQHW","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GX3B7QUH","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:2de7a4ea2d5e0b5ce019601a8e736745b799335dc62411a97c035777bea4f45e","target":"graph","created_at":"2026-05-18T00:42:23Z","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":"We initiate the algorithmic study of the following \"structured augmentation\" question: is it possible to increase the connectivity of a given graph G by superposing it with another given graph H? More precisely, graph F is the superposition of G and H with respect to injective mapping \\phi: V(H)->V(G) if every edge uv of F is either an edge of G, or \\phi^{-1}(u)\\phi^{-1}(v) is an edge of H. We consider the following optimization problem. Given graphs G,H, and a weight function \\omega assigning non-negative weights to pairs of vertices of V(G), the task is to find \\varphi of minimum weight \\ome","authors_text":"Dimitrios M. Thilikos, Fedor V. Fomin, Petr A. Golovach","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-06-13T21:06:37Z","title":"Structured Connectivity Augmentation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04255","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:ed302880626ccbfb9db6635779d3761ccc94e2fc1aa5511eb6d3bae5975d484d","target":"record","created_at":"2026-05-18T00:42:23Z","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":"e04d556b34533c4a7f225346bfb448c37ba56766a6b265c116962b3b2027bf26","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-06-13T21:06:37Z","title_canon_sha256":"e200c16fa9002d3f7ebacd32c811cf5985b4fac2c6d6726f1626681e7e061f48"},"schema_version":"1.0","source":{"id":"1706.04255","kind":"arxiv","version":1}},"canonical_sha256":"35f61fc28742ab4440f6d438a32697f903778c3c5a7595100fa7f0fe02b00b07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35f61fc28742ab4440f6d438a32697f903778c3c5a7595100fa7f0fe02b00b07","first_computed_at":"2026-05-18T00:42:23.129706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:23.129706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TG+/7HkCS83Ke4TBZXgNwX6W6twu3LdNYVVMhZrUlXpDsakozramRcCKu8+nLH475FuM57rPQrW6ninUqWETDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:23.130289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04255","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed302880626ccbfb9db6635779d3761ccc94e2fc1aa5511eb6d3bae5975d484d","sha256:2de7a4ea2d5e0b5ce019601a8e736745b799335dc62411a97c035777bea4f45e"],"state_sha256":"941a1de6e20cc16fd612dc33f97b44d175dd3bc77fb2f51e27f7db6df7a08333"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rTUvimg60RcqVds2K655M2C1RTXM4Ip7gz9AAw20yF5Qan0HUT495vy7P8bECZq91DlhbYUcN4HyDIX5Lb3xCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:34:58.744528Z","bundle_sha256":"1c8f1df2f00fb1b5c4bdc3dc14ad90a08369a7632886b03e2767da5ad3658a63"}}