{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GHORIBHND4HWFEISALCF2S5UUT","short_pith_number":"pith:GHORIBHN","canonical_record":{"source":{"id":"1704.08739","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-27T20:38:17Z","cross_cats_sorted":[],"title_canon_sha256":"6633ce1fd12a3a0d368ce4f094bffe2836884d65b0d4f019be7638825ab31562","abstract_canon_sha256":"f23920104ff07b1d748006f49e8db503c17e1d20112adddbf6c7e050c4ed7b99"},"schema_version":"1.0"},"canonical_sha256":"31dd1404ed1f0f62911202c45d4bb4a4e8110fb00540656919fb44e95fa078ba","source":{"kind":"arxiv","id":"1704.08739","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08739","created_at":"2026-05-18T00:45:25Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08739v1","created_at":"2026-05-18T00:45:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08739","created_at":"2026-05-18T00:45:25Z"},{"alias_kind":"pith_short_12","alias_value":"GHORIBHND4HW","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GHORIBHND4HWFEIS","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GHORIBHN","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GHORIBHND4HWFEISALCF2S5UUT","target":"record","payload":{"canonical_record":{"source":{"id":"1704.08739","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-27T20:38:17Z","cross_cats_sorted":[],"title_canon_sha256":"6633ce1fd12a3a0d368ce4f094bffe2836884d65b0d4f019be7638825ab31562","abstract_canon_sha256":"f23920104ff07b1d748006f49e8db503c17e1d20112adddbf6c7e050c4ed7b99"},"schema_version":"1.0"},"canonical_sha256":"31dd1404ed1f0f62911202c45d4bb4a4e8110fb00540656919fb44e95fa078ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:25.407587Z","signature_b64":"HKlZDTJdiGGFL2pBSqtVhAAY6dKauamgLnh9H6J69ysfLQGUywDWA3BWJkYbivNm1EG1eQl8KzfQ9BdKrpryAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31dd1404ed1f0f62911202c45d4bb4a4e8110fb00540656919fb44e95fa078ba","last_reissued_at":"2026-05-18T00:45:25.407145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:25.407145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.08739","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":"2026-05-18T00:45:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S8bej9fWF2RiA/iXX1+B4s32fIpsjb8j8Yvg7Oq3o9q8GaAY/XyDliOlwMw+8W6s25L8a1d8+btsp6Ou9/0KDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:59:47.623749Z"},"content_sha256":"d8c600ae3e60402ee61d1b008042e2476ee9981bf739c4d012d2891522733cf3","schema_version":"1.0","event_id":"sha256:d8c600ae3e60402ee61d1b008042e2476ee9981bf739c4d012d2891522733cf3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GHORIBHND4HWFEISALCF2S5UUT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Signed graphs: from modulo flows to integer-valued flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cun-Quan Zhang, Jian Cheng, Rong Luo, You Lu","submitted_at":"2017-04-27T20:38:17Z","abstract_excerpt":"Converting modulo flows into integer-valued flows is one of the most critical steps in the study of integer flows. Tutte and Jaeger's pioneering work shows the equivalence of modulo flows and integer-valued flows for ordinary graphs. However, such equivalence does not hold any more for signed graphs. This motivates us to study how to convert modulo flows into integer-valued flows for signed graphs. In this paper, we generalize some early results by Xu and Zhang (Discrete Math.~299, 2005), Schubert and Steffen (European J. Combin.~48, 2015), and Zhu (J. Combin. Theory Ser. B~112, 2015), and sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08739","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":"2026-05-18T00:45:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8JRHnZeMLT155jtoJB6BHV/BL2BzuHAVGGDr2qYHBOdM7WKenMTRvw072QEfLrp+OzvCPEHeCm9g/YKdqERgCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T19:59:47.624103Z"},"content_sha256":"00125b1368b7c455631415b177af6444e170824ecd58f90e4d3691b911dc7868","schema_version":"1.0","event_id":"sha256:00125b1368b7c455631415b177af6444e170824ecd58f90e4d3691b911dc7868"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHORIBHND4HWFEISALCF2S5UUT/bundle.json","state_url":"https://pith.science/pith/GHORIBHND4HWFEISALCF2S5UUT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHORIBHND4HWFEISALCF2S5UUT/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":"2026-06-25T19:59:47Z","links":{"resolver":"https://pith.science/pith/GHORIBHND4HWFEISALCF2S5UUT","bundle":"https://pith.science/pith/GHORIBHND4HWFEISALCF2S5UUT/bundle.json","state":"https://pith.science/pith/GHORIBHND4HWFEISALCF2S5UUT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHORIBHND4HWFEISALCF2S5UUT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GHORIBHND4HWFEISALCF2S5UUT","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":"f23920104ff07b1d748006f49e8db503c17e1d20112adddbf6c7e050c4ed7b99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-27T20:38:17Z","title_canon_sha256":"6633ce1fd12a3a0d368ce4f094bffe2836884d65b0d4f019be7638825ab31562"},"schema_version":"1.0","source":{"id":"1704.08739","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.08739","created_at":"2026-05-18T00:45:25Z"},{"alias_kind":"arxiv_version","alias_value":"1704.08739v1","created_at":"2026-05-18T00:45:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.08739","created_at":"2026-05-18T00:45:25Z"},{"alias_kind":"pith_short_12","alias_value":"GHORIBHND4HW","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GHORIBHND4HWFEIS","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GHORIBHN","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:00125b1368b7c455631415b177af6444e170824ecd58f90e4d3691b911dc7868","target":"graph","created_at":"2026-05-18T00:45:25Z","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":"Converting modulo flows into integer-valued flows is one of the most critical steps in the study of integer flows. Tutte and Jaeger's pioneering work shows the equivalence of modulo flows and integer-valued flows for ordinary graphs. However, such equivalence does not hold any more for signed graphs. This motivates us to study how to convert modulo flows into integer-valued flows for signed graphs. In this paper, we generalize some early results by Xu and Zhang (Discrete Math.~299, 2005), Schubert and Steffen (European J. Combin.~48, 2015), and Zhu (J. Combin. Theory Ser. B~112, 2015), and sho","authors_text":"Cun-Quan Zhang, Jian Cheng, Rong Luo, You Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-27T20:38:17Z","title":"Signed graphs: from modulo flows to integer-valued flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.08739","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:d8c600ae3e60402ee61d1b008042e2476ee9981bf739c4d012d2891522733cf3","target":"record","created_at":"2026-05-18T00:45:25Z","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":"f23920104ff07b1d748006f49e8db503c17e1d20112adddbf6c7e050c4ed7b99","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-27T20:38:17Z","title_canon_sha256":"6633ce1fd12a3a0d368ce4f094bffe2836884d65b0d4f019be7638825ab31562"},"schema_version":"1.0","source":{"id":"1704.08739","kind":"arxiv","version":1}},"canonical_sha256":"31dd1404ed1f0f62911202c45d4bb4a4e8110fb00540656919fb44e95fa078ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31dd1404ed1f0f62911202c45d4bb4a4e8110fb00540656919fb44e95fa078ba","first_computed_at":"2026-05-18T00:45:25.407145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:25.407145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HKlZDTJdiGGFL2pBSqtVhAAY6dKauamgLnh9H6J69ysfLQGUywDWA3BWJkYbivNm1EG1eQl8KzfQ9BdKrpryAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:25.407587Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.08739","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8c600ae3e60402ee61d1b008042e2476ee9981bf739c4d012d2891522733cf3","sha256:00125b1368b7c455631415b177af6444e170824ecd58f90e4d3691b911dc7868"],"state_sha256":"c300bce6add78ede149cef41730174982e649a1730c989f09b097e49a206aff0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PiF6hDoTBKf7Z8lUCHCXsl4C1atqssbQH3MV0YAFgp66w/wrtelHOyjR66ApBHoOSFPOxZu5YQ9phkjoa98NDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T19:59:47.626090Z","bundle_sha256":"f739f4c6d52c97bf5d892b6279f1979cd92580e79d98496d91a2ddc2599c549f"}}