{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ISDZF4HJLQSQ7XZMH64A6YQROU","short_pith_number":"pith:ISDZF4HJ","canonical_record":{"source":{"id":"1407.0367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-01T19:23:46Z","cross_cats_sorted":[],"title_canon_sha256":"f857fadaf2b1d994fa71c09d1472e9cd781024ce4027b6b0e6365ba4232af6f2","abstract_canon_sha256":"f12ac1ea69ddb03a6028323641837ffdd1f1cc1f233815fc319bf249e84faede"},"schema_version":"1.0"},"canonical_sha256":"448792f0e95c250fdf2c3fb80f621175185410a5014442ca824ad803082bd5ca","source":{"kind":"arxiv","id":"1407.0367","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0367","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0367v1","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0367","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"ISDZF4HJLQSQ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"ISDZF4HJLQSQ7XZM","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"ISDZF4HJ","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ISDZF4HJLQSQ7XZMH64A6YQROU","target":"record","payload":{"canonical_record":{"source":{"id":"1407.0367","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-01T19:23:46Z","cross_cats_sorted":[],"title_canon_sha256":"f857fadaf2b1d994fa71c09d1472e9cd781024ce4027b6b0e6365ba4232af6f2","abstract_canon_sha256":"f12ac1ea69ddb03a6028323641837ffdd1f1cc1f233815fc319bf249e84faede"},"schema_version":"1.0"},"canonical_sha256":"448792f0e95c250fdf2c3fb80f621175185410a5014442ca824ad803082bd5ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:34.178851Z","signature_b64":"mCONtQx9WNOVnz+NxwjLIr+sDzpOUN7g21CUS0589mlSBtIYq93k5e7fIT+kd41zD6u7zuLChSpWOMkcc7+RDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"448792f0e95c250fdf2c3fb80f621175185410a5014442ca824ad803082bd5ca","last_reissued_at":"2026-05-18T02:48:34.178150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:34.178150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.0367","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":"2026-05-18T02:48:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6thVViBNclzI44ithm0I4grxTAYdV5Tr8wWp3AQ0FWGHbRniBL26rr/tKAjJAO0e+J4/9Xvu8DIum1ReTOIaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:03:10.366437Z"},"content_sha256":"ad1afbad35307dc454b21ceaf604fc5147e5f0a82ca683b1f5e11a1d1b5d16c9","schema_version":"1.0","event_id":"sha256:ad1afbad35307dc454b21ceaf604fc5147e5f0a82ca683b1f5e11a1d1b5d16c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ISDZF4HJLQSQ7XZMH64A6YQROU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Roman Bondage Number of Graphs on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Vladimir Samodivkin","submitted_at":"2014-07-01T19:23:46Z","abstract_excerpt":"A Roman dominating function on a graph $G$ is a labeling $f : V(G) \\rightarrow \\{0, 1, 2\\}$ such that every vertex with label $0$ has a neighbor with label $2$. The Roman domination number, $\\gamma_R(G)$, of $G$ is the minimum of $\\Sigma_{v\\in V (G)} f(v)$ over such functions. The Roman bondage number $b_R(G)$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with Roman domination number not equal to $\\gamma_R(G)$. In this paper we obtain upper bounds on $b_{R}(G)$ in terms of (a) the average degree and maximum degree, and (b) Euler characteristic, girth a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0367","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":"2026-05-18T02:48:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ehY9DPgjFCsOH75AQhR+IailtezXW3gM4BnChQA01zLiIDc9F5Z6d+kYXlQJogihUK/fXqxvvvWvgNAL2afBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:03:10.366786Z"},"content_sha256":"4838d9372a9b692951ad87974d74cbfd64d046e882c31e0e5c5d0d503180141e","schema_version":"1.0","event_id":"sha256:4838d9372a9b692951ad87974d74cbfd64d046e882c31e0e5c5d0d503180141e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ISDZF4HJLQSQ7XZMH64A6YQROU/bundle.json","state_url":"https://pith.science/pith/ISDZF4HJLQSQ7XZMH64A6YQROU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ISDZF4HJLQSQ7XZMH64A6YQROU/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":"2026-06-27T10:03:10Z","links":{"resolver":"https://pith.science/pith/ISDZF4HJLQSQ7XZMH64A6YQROU","bundle":"https://pith.science/pith/ISDZF4HJLQSQ7XZMH64A6YQROU/bundle.json","state":"https://pith.science/pith/ISDZF4HJLQSQ7XZMH64A6YQROU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ISDZF4HJLQSQ7XZMH64A6YQROU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ISDZF4HJLQSQ7XZMH64A6YQROU","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":"f12ac1ea69ddb03a6028323641837ffdd1f1cc1f233815fc319bf249e84faede","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-01T19:23:46Z","title_canon_sha256":"f857fadaf2b1d994fa71c09d1472e9cd781024ce4027b6b0e6365ba4232af6f2"},"schema_version":"1.0","source":{"id":"1407.0367","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0367","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0367v1","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0367","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"ISDZF4HJLQSQ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"ISDZF4HJLQSQ7XZM","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"ISDZF4HJ","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:4838d9372a9b692951ad87974d74cbfd64d046e882c31e0e5c5d0d503180141e","target":"graph","created_at":"2026-05-18T02:48:34Z","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":"A Roman dominating function on a graph $G$ is a labeling $f : V(G) \\rightarrow \\{0, 1, 2\\}$ such that every vertex with label $0$ has a neighbor with label $2$. The Roman domination number, $\\gamma_R(G)$, of $G$ is the minimum of $\\Sigma_{v\\in V (G)} f(v)$ over such functions. The Roman bondage number $b_R(G)$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with Roman domination number not equal to $\\gamma_R(G)$. In this paper we obtain upper bounds on $b_{R}(G)$ in terms of (a) the average degree and maximum degree, and (b) Euler characteristic, girth a","authors_text":"Vladimir Samodivkin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-01T19:23:46Z","title":"On the Roman Bondage Number of Graphs on surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0367","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:ad1afbad35307dc454b21ceaf604fc5147e5f0a82ca683b1f5e11a1d1b5d16c9","target":"record","created_at":"2026-05-18T02:48:34Z","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":"f12ac1ea69ddb03a6028323641837ffdd1f1cc1f233815fc319bf249e84faede","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-07-01T19:23:46Z","title_canon_sha256":"f857fadaf2b1d994fa71c09d1472e9cd781024ce4027b6b0e6365ba4232af6f2"},"schema_version":"1.0","source":{"id":"1407.0367","kind":"arxiv","version":1}},"canonical_sha256":"448792f0e95c250fdf2c3fb80f621175185410a5014442ca824ad803082bd5ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"448792f0e95c250fdf2c3fb80f621175185410a5014442ca824ad803082bd5ca","first_computed_at":"2026-05-18T02:48:34.178150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:34.178150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mCONtQx9WNOVnz+NxwjLIr+sDzpOUN7g21CUS0589mlSBtIYq93k5e7fIT+kd41zD6u7zuLChSpWOMkcc7+RDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:34.178851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0367","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad1afbad35307dc454b21ceaf604fc5147e5f0a82ca683b1f5e11a1d1b5d16c9","sha256:4838d9372a9b692951ad87974d74cbfd64d046e882c31e0e5c5d0d503180141e"],"state_sha256":"78612c657107084e8ae8311100536337857c398837ff57c5eeaf6cb209f3aa6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ZNsmc7X4dDnuy1CvP1lw9CKHTHhOv8FsqvVAizLE52y+Dnwx0lPnHAq0SQllpXRefK+3xbCm2RI5m2tGRSTDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T10:03:10.368719Z","bundle_sha256":"a6655bebe110da4e11dda24a0531b6943bc0627f43c299200c3f0fede5b49252"}}