{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3PF2XNQDCBJLOWGH56GPIEDDMZ","short_pith_number":"pith:3PF2XNQD","canonical_record":{"source":{"id":"1306.1763","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-07T16:19:31Z","cross_cats_sorted":[],"title_canon_sha256":"4ebdd4783ddf8e67156d212d7cba01990cbf4dec536c382a7712d4d01adcdd53","abstract_canon_sha256":"b16da0bed4177343877d627446e53509b2f6a3e1e7a7e2ff75f04d71498a7eb5"},"schema_version":"1.0"},"canonical_sha256":"dbcbabb6031052b758c7ef8cf41063665aa76a2d720b6c1ef719c8b1de1de355","source":{"kind":"arxiv","id":"1306.1763","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1763","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1763v3","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1763","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"3PF2XNQDCBJL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3PF2XNQDCBJLOWGH","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3PF2XNQD","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3PF2XNQDCBJLOWGH56GPIEDDMZ","target":"record","payload":{"canonical_record":{"source":{"id":"1306.1763","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-07T16:19:31Z","cross_cats_sorted":[],"title_canon_sha256":"4ebdd4783ddf8e67156d212d7cba01990cbf4dec536c382a7712d4d01adcdd53","abstract_canon_sha256":"b16da0bed4177343877d627446e53509b2f6a3e1e7a7e2ff75f04d71498a7eb5"},"schema_version":"1.0"},"canonical_sha256":"dbcbabb6031052b758c7ef8cf41063665aa76a2d720b6c1ef719c8b1de1de355","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:23.822778Z","signature_b64":"8KOLULSiJzOIK6oWfZYgxnNxMZbhO25DK0KcujwJp/2txY879vi8W7SihmwRsxx/ixDJT1jybF/7CZBhF3ClAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dbcbabb6031052b758c7ef8cf41063665aa76a2d720b6c1ef719c8b1de1de355","last_reissued_at":"2026-05-18T03:11:23.822218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:23.822218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.1763","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:11:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y9xgQqlplsNNpRH7s8qDFvlqNzIQme1/Y6zgyi3D8dfGKRPIqiV1SEpKL2TFzqMmMp/clcmlTB6pMCmevpPrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:15:37.019071Z"},"content_sha256":"1e9032551768f50f1ca303eb7288dc07a3431c77312f7129e2c89e75513a6429","schema_version":"1.0","event_id":"sha256:1e9032551768f50f1ca303eb7288dc07a3431c77312f7129e2c89e75513a6429"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3PF2XNQDCBJLOWGH56GPIEDDMZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bipartite graphs are weak antimagic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Matthias Beck, Michael Jackanich","submitted_at":"2013-06-07T16:19:31Z","abstract_excerpt":"The \\emph{Antimagic Graph Conjecture} asserts that every connected graph $G = (V, E)$ except $K_2$ admits an edge labeling such that each label $1, 2, ..., |E|$ is used exactly once and the sums of the labels on all edges incident with a given node are distinct. We study an associated counting function (replacing the upper bound on the possible labels by a variable) and prove that a variant of this counting function, when we do not require the labels to be distinct, is a polynomial if $G$ is bipartite. As a consequence, we show that every connected bipartite graph $G = (V, E)$ except $K_2$ adm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1763","kind":"arxiv","version":3},"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":"2026-05-18T03:11:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E+Dx1RzAzylhDH1qDBPFTx+8Tud4y4kLdCjwL7Ui0ncW1gnogDcS30iQdBX07FCxduXBsgUQI25qkDx91gnhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T22:15:37.019520Z"},"content_sha256":"4ac91df0ecf64a51e074886441bc9b6512114a50ed9e8713cbfd82611e4616b5","schema_version":"1.0","event_id":"sha256:4ac91df0ecf64a51e074886441bc9b6512114a50ed9e8713cbfd82611e4616b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3PF2XNQDCBJLOWGH56GPIEDDMZ/bundle.json","state_url":"https://pith.science/pith/3PF2XNQDCBJLOWGH56GPIEDDMZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3PF2XNQDCBJLOWGH56GPIEDDMZ/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":"2026-06-02T22:15:37Z","links":{"resolver":"https://pith.science/pith/3PF2XNQDCBJLOWGH56GPIEDDMZ","bundle":"https://pith.science/pith/3PF2XNQDCBJLOWGH56GPIEDDMZ/bundle.json","state":"https://pith.science/pith/3PF2XNQDCBJLOWGH56GPIEDDMZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3PF2XNQDCBJLOWGH56GPIEDDMZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3PF2XNQDCBJLOWGH56GPIEDDMZ","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":"b16da0bed4177343877d627446e53509b2f6a3e1e7a7e2ff75f04d71498a7eb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-07T16:19:31Z","title_canon_sha256":"4ebdd4783ddf8e67156d212d7cba01990cbf4dec536c382a7712d4d01adcdd53"},"schema_version":"1.0","source":{"id":"1306.1763","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.1763","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"1306.1763v3","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1763","created_at":"2026-05-18T03:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"3PF2XNQDCBJL","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3PF2XNQDCBJLOWGH","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3PF2XNQD","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:4ac91df0ecf64a51e074886441bc9b6512114a50ed9e8713cbfd82611e4616b5","target":"graph","created_at":"2026-05-18T03:11:23Z","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":"The \\emph{Antimagic Graph Conjecture} asserts that every connected graph $G = (V, E)$ except $K_2$ admits an edge labeling such that each label $1, 2, ..., |E|$ is used exactly once and the sums of the labels on all edges incident with a given node are distinct. We study an associated counting function (replacing the upper bound on the possible labels by a variable) and prove that a variant of this counting function, when we do not require the labels to be distinct, is a polynomial if $G$ is bipartite. As a consequence, we show that every connected bipartite graph $G = (V, E)$ except $K_2$ adm","authors_text":"Matthias Beck, Michael Jackanich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-07T16:19:31Z","title":"Bipartite graphs are weak antimagic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1763","kind":"arxiv","version":3},"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":"sha256:1e9032551768f50f1ca303eb7288dc07a3431c77312f7129e2c89e75513a6429","target":"record","created_at":"2026-05-18T03:11:23Z","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":"b16da0bed4177343877d627446e53509b2f6a3e1e7a7e2ff75f04d71498a7eb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-07T16:19:31Z","title_canon_sha256":"4ebdd4783ddf8e67156d212d7cba01990cbf4dec536c382a7712d4d01adcdd53"},"schema_version":"1.0","source":{"id":"1306.1763","kind":"arxiv","version":3}},"canonical_sha256":"dbcbabb6031052b758c7ef8cf41063665aa76a2d720b6c1ef719c8b1de1de355","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dbcbabb6031052b758c7ef8cf41063665aa76a2d720b6c1ef719c8b1de1de355","first_computed_at":"2026-05-18T03:11:23.822218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:23.822218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8KOLULSiJzOIK6oWfZYgxnNxMZbhO25DK0KcujwJp/2txY879vi8W7SihmwRsxx/ixDJT1jybF/7CZBhF3ClAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:23.822778Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.1763","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e9032551768f50f1ca303eb7288dc07a3431c77312f7129e2c89e75513a6429","sha256:4ac91df0ecf64a51e074886441bc9b6512114a50ed9e8713cbfd82611e4616b5"],"state_sha256":"be71c8c9fdea78271faf9faecac0532ad7b05663641ba4927589fd76e4d875b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Te4D5gx4tfNnm+21lirSKqrR26u6P3qA5KHWZBU68HG6m43LaxnW7oCR+MZ+Dk/B76B4wJgn+kXtbvZ8/KK6CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:15:37.021660Z","bundle_sha256":"c27767755e9b94428178d2af6abb95a59a93a9aa22aebcda34315b59f1ab0be0"}}