{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SDTJRQZ6GPMCS2MTZNMBDRGEEF","short_pith_number":"pith:SDTJRQZ6","canonical_record":{"source":{"id":"1708.04488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T13:27:46Z","cross_cats_sorted":[],"title_canon_sha256":"b82da30010c120083d019c97bcee5b331d5cc9b4e6ca24b473a987a3ae6f56f0","abstract_canon_sha256":"000806617229f975984142686a0d44ff6970bea61a896d33467f5679c71c1967"},"schema_version":"1.0"},"canonical_sha256":"90e698c33e33d8296993cb5811c4c4214099964b207ec7040f03b91940eafb7b","source":{"kind":"arxiv","id":"1708.04488","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04488","created_at":"2026-05-18T00:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04488v1","created_at":"2026-05-18T00:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04488","created_at":"2026-05-18T00:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"SDTJRQZ6GPMC","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SDTJRQZ6GPMCS2MT","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SDTJRQZ6","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SDTJRQZ6GPMCS2MTZNMBDRGEEF","target":"record","payload":{"canonical_record":{"source":{"id":"1708.04488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T13:27:46Z","cross_cats_sorted":[],"title_canon_sha256":"b82da30010c120083d019c97bcee5b331d5cc9b4e6ca24b473a987a3ae6f56f0","abstract_canon_sha256":"000806617229f975984142686a0d44ff6970bea61a896d33467f5679c71c1967"},"schema_version":"1.0"},"canonical_sha256":"90e698c33e33d8296993cb5811c4c4214099964b207ec7040f03b91940eafb7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:59.192198Z","signature_b64":"bGdTFrDyxqdtSSnTVKUFQLVS6x+ySGmBBEc2wtbB8f8WOJkMapKgExN3LRjKk9SXg9UbcN5pF24zCkJ3sMlfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90e698c33e33d8296993cb5811c4c4214099964b207ec7040f03b91940eafb7b","last_reissued_at":"2026-05-18T00:37:59.191655Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:59.191655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.04488","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":"2026-05-18T00:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CsFL7DjDdn4YGXvhgazIRPnkNTHTTti0r3DMPseexcWE5JO64o8zQzkkq40OhaYSknNhmYTohk97a9OS8jO2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T04:57:49.719681Z"},"content_sha256":"4047da01304b38542dea79065fdbdb0143cd7e1be4f8990353f3f5ab6369146a","schema_version":"1.0","event_id":"sha256:4047da01304b38542dea79065fdbdb0143cd7e1be4f8990353f3f5ab6369146a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SDTJRQZ6GPMCS2MTZNMBDRGEEF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Edge-magic labelings for constellations and armies of caterpillars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C\\^andida N. da Silva, Carla N. Lintzmayer, Cristina G. Fernandes, Guilherme O. Mota, M\\'arcia R. Cerioli, Orlando Lee","submitted_at":"2017-08-15T13:27:46Z","abstract_excerpt":"Let $G=(V,E)$ be an $n$-vertex graph with $m$ edges. A function $f : V \\cup E \\rightarrow \\{1, \\ldots, n+m\\}$ is an edge-magic labeling of $G$ if $f$ is bijective and, for some integer $k$, we have $f(u)+f(v)+f(uv) = k$ for every edge $uv \\in E$. Furthermore, if $f(V) = \\{1, \\ldots, n\\}$, then we say that $f$ is a super edge-magic labeling. A constellation, which is a collection of stars, is symmetric if the number of stars of each size is even except for at most one size. We prove that every symmetric constellation with an odd number of stars admits a super edge-magic labeling. We say that a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04488","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":"2026-05-18T00:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Oxbg97xIjYKkDlSEbRSt3EX+PHBi1yJHyW0yl363Z5nidAPw/stPqWlXWy/XjoKZNNfF1fpJ+wjFi2pEPaGtCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T04:57:49.720349Z"},"content_sha256":"0662d0ce6b83316599412815169481057ec663d27e43244c3b39fbebec9463c7","schema_version":"1.0","event_id":"sha256:0662d0ce6b83316599412815169481057ec663d27e43244c3b39fbebec9463c7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SDTJRQZ6GPMCS2MTZNMBDRGEEF/bundle.json","state_url":"https://pith.science/pith/SDTJRQZ6GPMCS2MTZNMBDRGEEF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SDTJRQZ6GPMCS2MTZNMBDRGEEF/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":"2026-05-22T04:57:49Z","links":{"resolver":"https://pith.science/pith/SDTJRQZ6GPMCS2MTZNMBDRGEEF","bundle":"https://pith.science/pith/SDTJRQZ6GPMCS2MTZNMBDRGEEF/bundle.json","state":"https://pith.science/pith/SDTJRQZ6GPMCS2MTZNMBDRGEEF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SDTJRQZ6GPMCS2MTZNMBDRGEEF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SDTJRQZ6GPMCS2MTZNMBDRGEEF","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":"000806617229f975984142686a0d44ff6970bea61a896d33467f5679c71c1967","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T13:27:46Z","title_canon_sha256":"b82da30010c120083d019c97bcee5b331d5cc9b4e6ca24b473a987a3ae6f56f0"},"schema_version":"1.0","source":{"id":"1708.04488","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04488","created_at":"2026-05-18T00:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04488v1","created_at":"2026-05-18T00:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04488","created_at":"2026-05-18T00:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"SDTJRQZ6GPMC","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SDTJRQZ6GPMCS2MT","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SDTJRQZ6","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:0662d0ce6b83316599412815169481057ec663d27e43244c3b39fbebec9463c7","target":"graph","created_at":"2026-05-18T00:37:59Z","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":"Let $G=(V,E)$ be an $n$-vertex graph with $m$ edges. A function $f : V \\cup E \\rightarrow \\{1, \\ldots, n+m\\}$ is an edge-magic labeling of $G$ if $f$ is bijective and, for some integer $k$, we have $f(u)+f(v)+f(uv) = k$ for every edge $uv \\in E$. Furthermore, if $f(V) = \\{1, \\ldots, n\\}$, then we say that $f$ is a super edge-magic labeling. A constellation, which is a collection of stars, is symmetric if the number of stars of each size is even except for at most one size. We prove that every symmetric constellation with an odd number of stars admits a super edge-magic labeling. We say that a ","authors_text":"C\\^andida N. da Silva, Carla N. Lintzmayer, Cristina G. Fernandes, Guilherme O. Mota, M\\'arcia R. Cerioli, Orlando Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T13:27:46Z","title":"Edge-magic labelings for constellations and armies of caterpillars"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04488","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":"sha256:4047da01304b38542dea79065fdbdb0143cd7e1be4f8990353f3f5ab6369146a","target":"record","created_at":"2026-05-18T00:37:59Z","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":"000806617229f975984142686a0d44ff6970bea61a896d33467f5679c71c1967","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-15T13:27:46Z","title_canon_sha256":"b82da30010c120083d019c97bcee5b331d5cc9b4e6ca24b473a987a3ae6f56f0"},"schema_version":"1.0","source":{"id":"1708.04488","kind":"arxiv","version":1}},"canonical_sha256":"90e698c33e33d8296993cb5811c4c4214099964b207ec7040f03b91940eafb7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"90e698c33e33d8296993cb5811c4c4214099964b207ec7040f03b91940eafb7b","first_computed_at":"2026-05-18T00:37:59.191655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:59.191655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bGdTFrDyxqdtSSnTVKUFQLVS6x+ySGmBBEc2wtbB8f8WOJkMapKgExN3LRjKk9SXg9UbcN5pF24zCkJ3sMlfCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:59.192198Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.04488","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4047da01304b38542dea79065fdbdb0143cd7e1be4f8990353f3f5ab6369146a","sha256:0662d0ce6b83316599412815169481057ec663d27e43244c3b39fbebec9463c7"],"state_sha256":"216316a0e38bf1be14b29277412572eba69fa43cc1d69516de07cb625021214d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dHWCR4QnjCnLF+Hf4blMzU8GwcVQIzSZOvmZ8JlYw73YEAmaR2gmCaiXSioVL7UhgZz486Ip2xPl5O8teoeiAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T04:57:49.723823Z","bundle_sha256":"efdeebbaa85a33c072f76525c7ab37077d3f990fff5364dc4a697231b5774abb"}}