{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NJZCKFLOIIHFGMK4PF22MOZXY6","short_pith_number":"pith:NJZCKFLO","canonical_record":{"source":{"id":"1904.04180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-08T16:37:24Z","cross_cats_sorted":[],"title_canon_sha256":"061938d0c6f4829d99f9781d40d4267cf135f8c44427360746b7ac63324f7063","abstract_canon_sha256":"c22be6fd56e384470932b4b2f7d732581508862ae8fc609f1240492829891a2d"},"schema_version":"1.0"},"canonical_sha256":"6a7225156e420e53315c7975a63b37c7a580547cb03c86357eaa4671c921536d","source":{"kind":"arxiv","id":"1904.04180","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04180","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04180v1","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04180","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"NJZCKFLOIIHF","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NJZCKFLOIIHFGMK4","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NJZCKFLO","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NJZCKFLOIIHFGMK4PF22MOZXY6","target":"record","payload":{"canonical_record":{"source":{"id":"1904.04180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-08T16:37:24Z","cross_cats_sorted":[],"title_canon_sha256":"061938d0c6f4829d99f9781d40d4267cf135f8c44427360746b7ac63324f7063","abstract_canon_sha256":"c22be6fd56e384470932b4b2f7d732581508862ae8fc609f1240492829891a2d"},"schema_version":"1.0"},"canonical_sha256":"6a7225156e420e53315c7975a63b37c7a580547cb03c86357eaa4671c921536d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:06.832359Z","signature_b64":"WLXSVqkdaE3KjRjnN4ujnILMtwZGhAW0gHwLnoW1+vlAKAqGZTryzBa+6VEb5w8/h3t00mb9FmDBE/kVlIroBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a7225156e420e53315c7975a63b37c7a580547cb03c86357eaa4671c921536d","last_reissued_at":"2026-05-17T23:49:06.831666Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:06.831666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.04180","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":"2026-05-17T23:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jHgR8tgP4w6TVwAJpI00D5MQCkft7HVhEcFUMMBT1x2yKikWz+6IGd896R9MCUVgu6W9+pcxatv8xLTLM5R1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:50:18.894858Z"},"content_sha256":"c92f63405771864588118e96e9c6910103deb5654e9da7dd09b81ddd9e230350","schema_version":"1.0","event_id":"sha256:c92f63405771864588118e96e9c6910103deb5654e9da7dd09b81ddd9e230350"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NJZCKFLOIIHFGMK4PF22MOZXY6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Sierpi\\'nski product of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arjana \\v{Z}itnik, Jurij Kovi\\v{c}, Sara Sabrina Zemlji\\v{c}, Toma\\v{z} Pisanski","submitted_at":"2019-04-08T16:37:24Z","abstract_excerpt":"In this paper we introduce a product-like operation that generalizes the construction of generalized Sierpi\\'nski graphs. Let $G,H$ be graphs and let $f: V(G) \\to V(H)$ be a function. Then the Sierpi\\'nski product of $G$ and $H$ with respect to $f$ is defined as a pair $(K,\\varphi)$, where $K$ is a graph on the vertex set $V(G) \\times V(H)$ with two types of edges:\n  -- $\\{(g,h),(g,h')\\}$ is an edge in $K$ for every $g\\in V(G)$ and every $\\{h,h'\\}\\in E(H)$,\n  -- $\\{(g,f(g'),(g',f(g))\\}$ is an edge in $K$ for every edge $\\{g,g'\\} \\in E(G)$; and $\\varphi: V(G) \\to V(K)$ is a function that maps e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04180","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":"2026-05-17T23:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OMfh+B8HcXk8MxGRF8n+LZeWm3ndRfE+zyVeRqoY3fQnWsFjFxIhTzvfZTwN9BJ2lw+zvBaInEdlDoMwBLj5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:50:18.895198Z"},"content_sha256":"9483c288ddfa842140d5b08b7e0812a58bd97be2b37b7b75f71152e296bcba23","schema_version":"1.0","event_id":"sha256:9483c288ddfa842140d5b08b7e0812a58bd97be2b37b7b75f71152e296bcba23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJZCKFLOIIHFGMK4PF22MOZXY6/bundle.json","state_url":"https://pith.science/pith/NJZCKFLOIIHFGMK4PF22MOZXY6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJZCKFLOIIHFGMK4PF22MOZXY6/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":"2026-06-27T03:50:18Z","links":{"resolver":"https://pith.science/pith/NJZCKFLOIIHFGMK4PF22MOZXY6","bundle":"https://pith.science/pith/NJZCKFLOIIHFGMK4PF22MOZXY6/bundle.json","state":"https://pith.science/pith/NJZCKFLOIIHFGMK4PF22MOZXY6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJZCKFLOIIHFGMK4PF22MOZXY6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NJZCKFLOIIHFGMK4PF22MOZXY6","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":"c22be6fd56e384470932b4b2f7d732581508862ae8fc609f1240492829891a2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-08T16:37:24Z","title_canon_sha256":"061938d0c6f4829d99f9781d40d4267cf135f8c44427360746b7ac63324f7063"},"schema_version":"1.0","source":{"id":"1904.04180","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04180","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04180v1","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04180","created_at":"2026-05-17T23:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"NJZCKFLOIIHF","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NJZCKFLOIIHFGMK4","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NJZCKFLO","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:9483c288ddfa842140d5b08b7e0812a58bd97be2b37b7b75f71152e296bcba23","target":"graph","created_at":"2026-05-17T23:49:06Z","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 introduce a product-like operation that generalizes the construction of generalized Sierpi\\'nski graphs. Let $G,H$ be graphs and let $f: V(G) \\to V(H)$ be a function. Then the Sierpi\\'nski product of $G$ and $H$ with respect to $f$ is defined as a pair $(K,\\varphi)$, where $K$ is a graph on the vertex set $V(G) \\times V(H)$ with two types of edges:\n  -- $\\{(g,h),(g,h')\\}$ is an edge in $K$ for every $g\\in V(G)$ and every $\\{h,h'\\}\\in E(H)$,\n  -- $\\{(g,f(g'),(g',f(g))\\}$ is an edge in $K$ for every edge $\\{g,g'\\} \\in E(G)$; and $\\varphi: V(G) \\to V(K)$ is a function that maps e","authors_text":"Arjana \\v{Z}itnik, Jurij Kovi\\v{c}, Sara Sabrina Zemlji\\v{c}, Toma\\v{z} Pisanski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-08T16:37:24Z","title":"The Sierpi\\'nski product of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04180","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:c92f63405771864588118e96e9c6910103deb5654e9da7dd09b81ddd9e230350","target":"record","created_at":"2026-05-17T23:49:06Z","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":"c22be6fd56e384470932b4b2f7d732581508862ae8fc609f1240492829891a2d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-04-08T16:37:24Z","title_canon_sha256":"061938d0c6f4829d99f9781d40d4267cf135f8c44427360746b7ac63324f7063"},"schema_version":"1.0","source":{"id":"1904.04180","kind":"arxiv","version":1}},"canonical_sha256":"6a7225156e420e53315c7975a63b37c7a580547cb03c86357eaa4671c921536d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a7225156e420e53315c7975a63b37c7a580547cb03c86357eaa4671c921536d","first_computed_at":"2026-05-17T23:49:06.831666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:06.831666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WLXSVqkdaE3KjRjnN4ujnILMtwZGhAW0gHwLnoW1+vlAKAqGZTryzBa+6VEb5w8/h3t00mb9FmDBE/kVlIroBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:06.832359Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.04180","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c92f63405771864588118e96e9c6910103deb5654e9da7dd09b81ddd9e230350","sha256:9483c288ddfa842140d5b08b7e0812a58bd97be2b37b7b75f71152e296bcba23"],"state_sha256":"6c582d60fe0f291d05c3bc5c284f3d4f95f2286e807a7c55eaed8c8393b66fe3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VBOuZOlMy4wA5Czb3bWrSs1v7QHXjlVV22UahNh6E36RH630BVyT0FwRPq1YeVkppyP0CDypR1/FA84U/eSxAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:50:18.897084Z","bundle_sha256":"b48c7b29168f470bbdf7e383202beac0c188f1a467bbaa694a39ff0d56c10b7a"}}