{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:O336L247DU2HKFP5T3YIHRZ2SV","short_pith_number":"pith:O336L247","canonical_record":{"source":{"id":"1608.00769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-02T11:14:13Z","cross_cats_sorted":[],"title_canon_sha256":"21c491a8e623beab60b0e7dc6f2cb6de824caecd8dc4b1118a1d4223d4406f64","abstract_canon_sha256":"93f45acc72fefb4515be6fde4057285b87aec65a6a0927f9bb6c388c9ffad6de"},"schema_version":"1.0"},"canonical_sha256":"76f7e5eb9f1d347515fd9ef083c73a9552008ada2cd31f513b03d3b4a1f68285","source":{"kind":"arxiv","id":"1608.00769","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00769","created_at":"2026-05-18T01:10:01Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00769v1","created_at":"2026-05-18T01:10:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00769","created_at":"2026-05-18T01:10:01Z"},{"alias_kind":"pith_short_12","alias_value":"O336L247DU2H","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O336L247DU2HKFP5","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O336L247","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:O336L247DU2HKFP5T3YIHRZ2SV","target":"record","payload":{"canonical_record":{"source":{"id":"1608.00769","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-02T11:14:13Z","cross_cats_sorted":[],"title_canon_sha256":"21c491a8e623beab60b0e7dc6f2cb6de824caecd8dc4b1118a1d4223d4406f64","abstract_canon_sha256":"93f45acc72fefb4515be6fde4057285b87aec65a6a0927f9bb6c388c9ffad6de"},"schema_version":"1.0"},"canonical_sha256":"76f7e5eb9f1d347515fd9ef083c73a9552008ada2cd31f513b03d3b4a1f68285","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:01.041937Z","signature_b64":"sXtLmr5C4Ur7gkxOE4goYaa3+cXicO7TB01A5qvODvTpBMYA9v8K3wA/aQ5tPdNbQoD9cZbaIR6EbIq7xE/QAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76f7e5eb9f1d347515fd9ef083c73a9552008ada2cd31f513b03d3b4a1f68285","last_reissued_at":"2026-05-18T01:10:01.041263Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:01.041263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.00769","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":"2026-05-18T01:10:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sl+lrnpTAJgmuwTLsXnj9WiJn53MuoP0y4jAi3XiwpK99sUPN0HD/GMwPC69Rvat+8BfhXLyCtQhKyF9ZqnCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:38:07.276821Z"},"content_sha256":"25d4a7c9d1322972bd3a633b507c82034091bb93fcdfb6f4d8f346bee5758bcf","schema_version":"1.0","event_id":"sha256:25d4a7c9d1322972bd3a633b507c82034091bb93fcdfb6f4d8f346bee5758bcf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:O336L247DU2HKFP5T3YIHRZ2SV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On distances in generalized Sierpinski graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alejandro Estrada-Moreno, Erick D. Rodriguez-Bazan, Juan A. Rodriguez-Velazquez","submitted_at":"2016-08-02T11:14:13Z","abstract_excerpt":"In this paper we propose formulas for the distance between vertices of a generalized Sierpi\\'{n}ski graph $S(G,t)$ in terms of the distance between vertices of the base graph $G$. In particular, we deduce a recursive formula for the distance between an arbitrary vertex and an extreme vertex of $S(G,t)$, and we obtain a recursive formula for the distance between two arbitrary vertices of $S(G,t)$ when the base graph is triangle-free. From these recursive formulas, we provide algorithms to compute the distance between vertices of $S(G,t)$. In addition, we give an explicit formula for the diamete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00769","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":"2026-05-18T01:10:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m1uNgqQpOLISzUGIXo7yr2OOQo1Q5fMrVs0LALcrtwCSB1hKoN2lx0BwtnN71jdIf3gKmTOxNZVGEbG7JIqACQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:38:07.277196Z"},"content_sha256":"9e43638b2f93824e3a7f306a5ac81040ef73d2fc4901c360bf3ca14bee082b4a","schema_version":"1.0","event_id":"sha256:9e43638b2f93824e3a7f306a5ac81040ef73d2fc4901c360bf3ca14bee082b4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O336L247DU2HKFP5T3YIHRZ2SV/bundle.json","state_url":"https://pith.science/pith/O336L247DU2HKFP5T3YIHRZ2SV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O336L247DU2HKFP5T3YIHRZ2SV/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":"2026-06-23T00:38:07Z","links":{"resolver":"https://pith.science/pith/O336L247DU2HKFP5T3YIHRZ2SV","bundle":"https://pith.science/pith/O336L247DU2HKFP5T3YIHRZ2SV/bundle.json","state":"https://pith.science/pith/O336L247DU2HKFP5T3YIHRZ2SV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O336L247DU2HKFP5T3YIHRZ2SV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:O336L247DU2HKFP5T3YIHRZ2SV","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":"93f45acc72fefb4515be6fde4057285b87aec65a6a0927f9bb6c388c9ffad6de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-02T11:14:13Z","title_canon_sha256":"21c491a8e623beab60b0e7dc6f2cb6de824caecd8dc4b1118a1d4223d4406f64"},"schema_version":"1.0","source":{"id":"1608.00769","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.00769","created_at":"2026-05-18T01:10:01Z"},{"alias_kind":"arxiv_version","alias_value":"1608.00769v1","created_at":"2026-05-18T01:10:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00769","created_at":"2026-05-18T01:10:01Z"},{"alias_kind":"pith_short_12","alias_value":"O336L247DU2H","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"O336L247DU2HKFP5","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"O336L247","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:9e43638b2f93824e3a7f306a5ac81040ef73d2fc4901c360bf3ca14bee082b4a","target":"graph","created_at":"2026-05-18T01:10:01Z","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 propose formulas for the distance between vertices of a generalized Sierpi\\'{n}ski graph $S(G,t)$ in terms of the distance between vertices of the base graph $G$. In particular, we deduce a recursive formula for the distance between an arbitrary vertex and an extreme vertex of $S(G,t)$, and we obtain a recursive formula for the distance between two arbitrary vertices of $S(G,t)$ when the base graph is triangle-free. From these recursive formulas, we provide algorithms to compute the distance between vertices of $S(G,t)$. In addition, we give an explicit formula for the diamete","authors_text":"Alejandro Estrada-Moreno, Erick D. Rodriguez-Bazan, Juan A. Rodriguez-Velazquez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-02T11:14:13Z","title":"On distances in generalized Sierpinski graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00769","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":"sha256:25d4a7c9d1322972bd3a633b507c82034091bb93fcdfb6f4d8f346bee5758bcf","target":"record","created_at":"2026-05-18T01:10:01Z","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":"93f45acc72fefb4515be6fde4057285b87aec65a6a0927f9bb6c388c9ffad6de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-02T11:14:13Z","title_canon_sha256":"21c491a8e623beab60b0e7dc6f2cb6de824caecd8dc4b1118a1d4223d4406f64"},"schema_version":"1.0","source":{"id":"1608.00769","kind":"arxiv","version":1}},"canonical_sha256":"76f7e5eb9f1d347515fd9ef083c73a9552008ada2cd31f513b03d3b4a1f68285","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76f7e5eb9f1d347515fd9ef083c73a9552008ada2cd31f513b03d3b4a1f68285","first_computed_at":"2026-05-18T01:10:01.041263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:01.041263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sXtLmr5C4Ur7gkxOE4goYaa3+cXicO7TB01A5qvODvTpBMYA9v8K3wA/aQ5tPdNbQoD9cZbaIR6EbIq7xE/QAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:01.041937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.00769","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25d4a7c9d1322972bd3a633b507c82034091bb93fcdfb6f4d8f346bee5758bcf","sha256:9e43638b2f93824e3a7f306a5ac81040ef73d2fc4901c360bf3ca14bee082b4a"],"state_sha256":"fd11e335bccd777dd2d19e6acfbbe204c65f2551d1d3bb8e91cd50f7e9bfe974"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ARo4d8UKHhoZa93j0JY4qbS8ld1dZDGg5H9Sf3Wo32oc0t2rAsOINRWurXVMwUcWcmkOchoWBFsEhMPbmFA+Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T00:38:07.279242Z","bundle_sha256":"0ab7dbf6f1cbce4a53ee3b0d30487e289c84187c46539c35c4b36a309437d9e9"}}