{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3SGIHS7X2MABZCE4V2ZPS2ZAZ3","short_pith_number":"pith:3SGIHS7X","canonical_record":{"source":{"id":"1407.8132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-30T17:27:29Z","cross_cats_sorted":[],"title_canon_sha256":"257fd845bd11791297260c809815e003d61be59de5f2a928c9d6388cd6a0b508","abstract_canon_sha256":"b7780ea78d4bba019efabbf18abbc140fd55b832257110bc2b4163c494d012af"},"schema_version":"1.0"},"canonical_sha256":"dc8c83cbf7d3001c889caeb2f96b20cec2b28d06c47c8fce706f71e8369f628f","source":{"kind":"arxiv","id":"1407.8132","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.8132","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"arxiv_version","alias_value":"1407.8132v2","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8132","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"pith_short_12","alias_value":"3SGIHS7X2MAB","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3SGIHS7X2MABZCE4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3SGIHS7X","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3SGIHS7X2MABZCE4V2ZPS2ZAZ3","target":"record","payload":{"canonical_record":{"source":{"id":"1407.8132","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-30T17:27:29Z","cross_cats_sorted":[],"title_canon_sha256":"257fd845bd11791297260c809815e003d61be59de5f2a928c9d6388cd6a0b508","abstract_canon_sha256":"b7780ea78d4bba019efabbf18abbc140fd55b832257110bc2b4163c494d012af"},"schema_version":"1.0"},"canonical_sha256":"dc8c83cbf7d3001c889caeb2f96b20cec2b28d06c47c8fce706f71e8369f628f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:30.983862Z","signature_b64":"W332evuwdspovmfuqgfZnZJdVgPlB0xeGKhUXiq+k0vdJSsB3prTkWFfcHSXLMOeFVLagNva8wgqOPpCsZtVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc8c83cbf7d3001c889caeb2f96b20cec2b28d06c47c8fce706f71e8369f628f","last_reissued_at":"2026-05-18T02:45:30.983180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:30.983180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.8132","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S9y8LxXEW6xBu9foCTMnikD+npp8e+n+lYdOffIZfprq1iX45ewmMsVpuYhR8rBK4c5Ksj9xLSAopzS52EoFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:53:52.520642Z"},"content_sha256":"7e96a8514759f1609df026ab64825f9e6d359b07c0c75b39b0be9f3a299b60bc","schema_version":"1.0","event_id":"sha256:7e96a8514759f1609df026ab64825f9e6d359b07c0c75b39b0be9f3a299b60bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3SGIHS7X2MABZCE4V2ZPS2ZAZ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computation of a Tree 3-Spanner on Trapezoid Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Madhumangal Pal, Sambhu Charan Barman, Sukumar Mondal","submitted_at":"2014-07-30T17:27:29Z","abstract_excerpt":"In a graph, a spanning tree is said to be a tree t-spanner of the graph if the distance between any two vertices in is at most times their distance in . The tree t-spanner has many applications in networks and distributed environments. In this paper, an algorithm is presented to find a tree -spanner on trapezoid graphs in time, where is the number of vertices of the graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8132","kind":"arxiv","version":2},"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":"2026-05-18T02:45:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ss7UpjNPqyYAFZQLKYCQ/GdZwehFXgV3LUh9q5rJZOjDrPOfOUEGcY2TG6EHJeidJK0dwqRTRkuay3qA9EonDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:53:52.520981Z"},"content_sha256":"18de18c66e8c9260fbd7ceab64ad0f4cbea7eece5600e1ead33aba90b68f3108","schema_version":"1.0","event_id":"sha256:18de18c66e8c9260fbd7ceab64ad0f4cbea7eece5600e1ead33aba90b68f3108"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3SGIHS7X2MABZCE4V2ZPS2ZAZ3/bundle.json","state_url":"https://pith.science/pith/3SGIHS7X2MABZCE4V2ZPS2ZAZ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3SGIHS7X2MABZCE4V2ZPS2ZAZ3/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":"2026-06-12T07:53:52Z","links":{"resolver":"https://pith.science/pith/3SGIHS7X2MABZCE4V2ZPS2ZAZ3","bundle":"https://pith.science/pith/3SGIHS7X2MABZCE4V2ZPS2ZAZ3/bundle.json","state":"https://pith.science/pith/3SGIHS7X2MABZCE4V2ZPS2ZAZ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3SGIHS7X2MABZCE4V2ZPS2ZAZ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3SGIHS7X2MABZCE4V2ZPS2ZAZ3","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":"b7780ea78d4bba019efabbf18abbc140fd55b832257110bc2b4163c494d012af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-30T17:27:29Z","title_canon_sha256":"257fd845bd11791297260c809815e003d61be59de5f2a928c9d6388cd6a0b508"},"schema_version":"1.0","source":{"id":"1407.8132","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.8132","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"arxiv_version","alias_value":"1407.8132v2","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8132","created_at":"2026-05-18T02:45:30Z"},{"alias_kind":"pith_short_12","alias_value":"3SGIHS7X2MAB","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3SGIHS7X2MABZCE4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3SGIHS7X","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:18de18c66e8c9260fbd7ceab64ad0f4cbea7eece5600e1ead33aba90b68f3108","target":"graph","created_at":"2026-05-18T02:45:30Z","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 a graph, a spanning tree is said to be a tree t-spanner of the graph if the distance between any two vertices in is at most times their distance in . The tree t-spanner has many applications in networks and distributed environments. In this paper, an algorithm is presented to find a tree -spanner on trapezoid graphs in time, where is the number of vertices of the graph.","authors_text":"Madhumangal Pal, Sambhu Charan Barman, Sukumar Mondal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-30T17:27:29Z","title":"Computation of a Tree 3-Spanner on Trapezoid Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8132","kind":"arxiv","version":2},"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":"sha256:7e96a8514759f1609df026ab64825f9e6d359b07c0c75b39b0be9f3a299b60bc","target":"record","created_at":"2026-05-18T02:45:30Z","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":"b7780ea78d4bba019efabbf18abbc140fd55b832257110bc2b4163c494d012af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-30T17:27:29Z","title_canon_sha256":"257fd845bd11791297260c809815e003d61be59de5f2a928c9d6388cd6a0b508"},"schema_version":"1.0","source":{"id":"1407.8132","kind":"arxiv","version":2}},"canonical_sha256":"dc8c83cbf7d3001c889caeb2f96b20cec2b28d06c47c8fce706f71e8369f628f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc8c83cbf7d3001c889caeb2f96b20cec2b28d06c47c8fce706f71e8369f628f","first_computed_at":"2026-05-18T02:45:30.983180Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:30.983180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W332evuwdspovmfuqgfZnZJdVgPlB0xeGKhUXiq+k0vdJSsB3prTkWFfcHSXLMOeFVLagNva8wgqOPpCsZtVAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:30.983862Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.8132","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e96a8514759f1609df026ab64825f9e6d359b07c0c75b39b0be9f3a299b60bc","sha256:18de18c66e8c9260fbd7ceab64ad0f4cbea7eece5600e1ead33aba90b68f3108"],"state_sha256":"87ebbf98aa9c674501951618c578c55885520c4a57cf51be45c1f482e68850a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S9BQ81pKIH92BBa2F7eZSJj0pD6AgdRUIXzg+wR1j+UuJ1grUdSg2LA5lyVilsiPDevwu9PvffjWeoLHKlhMCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T07:53:52.523189Z","bundle_sha256":"ebd5152a2952a41d52b3dda0c03c14d7a389633a967ce3be83d44a01e2d317b7"}}