{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7QIL2UGN7UPCGNTUTVPZ533VEC","short_pith_number":"pith:7QIL2UGN","canonical_record":{"source":{"id":"1512.06214","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-19T09:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"82ab4db60c3743d394288f0f0929eeb943b2ad0a6b2eb12726f67b9f9e05e23c","abstract_canon_sha256":"2db7d6a30f2bea6c57f23836d5fe780d54621d692074cfe04c4124c8d6fc449d"},"schema_version":"1.0"},"canonical_sha256":"fc10bd50cdfd1e2336749d5f9eef75208d7a8b02964e7ce8251c928696403fdd","source":{"kind":"arxiv","id":"1512.06214","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06214","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06214v1","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06214","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"7QIL2UGN7UPC","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7QIL2UGN7UPCGNTU","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7QIL2UGN","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7QIL2UGN7UPCGNTUTVPZ533VEC","target":"record","payload":{"canonical_record":{"source":{"id":"1512.06214","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-19T09:28:31Z","cross_cats_sorted":[],"title_canon_sha256":"82ab4db60c3743d394288f0f0929eeb943b2ad0a6b2eb12726f67b9f9e05e23c","abstract_canon_sha256":"2db7d6a30f2bea6c57f23836d5fe780d54621d692074cfe04c4124c8d6fc449d"},"schema_version":"1.0"},"canonical_sha256":"fc10bd50cdfd1e2336749d5f9eef75208d7a8b02964e7ce8251c928696403fdd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:04.817108Z","signature_b64":"otZIHGgB3e5cAN9rgQzZTeDm5oDQL3LrNjsv34k4oYTWRfSWETAPx8j/TshRJaZqCJOZYK/6ZnGRT+wyruC6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc10bd50cdfd1e2336749d5f9eef75208d7a8b02964e7ce8251c928696403fdd","last_reissued_at":"2026-05-18T01:24:04.816370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:04.816370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.06214","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":"2026-05-18T01:24:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yE/aAzn/ud5f/o//704Q3iYKD27zgW5WNwnhKMmPcSO0zuGwZJ+mof1bIo7OsVTmNQlgAnesnrm5OvOSdPqDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:15:05.953797Z"},"content_sha256":"82995df3bee2cd8173495ae7fa1d1faf578c33abbc9c5309aff4c580cafb8537","schema_version":"1.0","event_id":"sha256:82995df3bee2cd8173495ae7fa1d1faf578c33abbc9c5309aff4c580cafb8537"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7QIL2UGN7UPCGNTUTVPZ533VEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new proof of Seymour's 6-flow theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edita Rollov\\'a, Matt DeVos, Robert \\v{S}\\'amal","submitted_at":"2015-12-19T09:28:31Z","abstract_excerpt":"Tutte's famous 5-flow conjecture asserts that every bridgeless graph has a nowhere-zero 5-flow. Seymour proved that every such graph has a nowhere-zero 6-flow. Here we give (two versions of) a new proof of Seymour's Theorem. Both are roughly equal to Seymour's in terms of complexity, but they offer an alternative perspective which we hope will be of value."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06214","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":"2026-05-18T01:24:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HBLqjgTb1TMI1FILDX7rkXQzvEXqDPMl6eQYyVmXmcLEjIixOHG0nil46LcDdzzD0EJjlmMs5ZyMHa04WK9hDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:15:05.954136Z"},"content_sha256":"762a510c7a3f4af36f35c7f7c3975efb9622dc8a0cdec7d40017070650bd29a6","schema_version":"1.0","event_id":"sha256:762a510c7a3f4af36f35c7f7c3975efb9622dc8a0cdec7d40017070650bd29a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7QIL2UGN7UPCGNTUTVPZ533VEC/bundle.json","state_url":"https://pith.science/pith/7QIL2UGN7UPCGNTUTVPZ533VEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7QIL2UGN7UPCGNTUTVPZ533VEC/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":"2026-06-20T21:15:05Z","links":{"resolver":"https://pith.science/pith/7QIL2UGN7UPCGNTUTVPZ533VEC","bundle":"https://pith.science/pith/7QIL2UGN7UPCGNTUTVPZ533VEC/bundle.json","state":"https://pith.science/pith/7QIL2UGN7UPCGNTUTVPZ533VEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7QIL2UGN7UPCGNTUTVPZ533VEC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7QIL2UGN7UPCGNTUTVPZ533VEC","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":"2db7d6a30f2bea6c57f23836d5fe780d54621d692074cfe04c4124c8d6fc449d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-19T09:28:31Z","title_canon_sha256":"82ab4db60c3743d394288f0f0929eeb943b2ad0a6b2eb12726f67b9f9e05e23c"},"schema_version":"1.0","source":{"id":"1512.06214","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.06214","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"arxiv_version","alias_value":"1512.06214v1","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06214","created_at":"2026-05-18T01:24:04Z"},{"alias_kind":"pith_short_12","alias_value":"7QIL2UGN7UPC","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7QIL2UGN7UPCGNTU","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7QIL2UGN","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:762a510c7a3f4af36f35c7f7c3975efb9622dc8a0cdec7d40017070650bd29a6","target":"graph","created_at":"2026-05-18T01:24:04Z","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":"Tutte's famous 5-flow conjecture asserts that every bridgeless graph has a nowhere-zero 5-flow. Seymour proved that every such graph has a nowhere-zero 6-flow. Here we give (two versions of) a new proof of Seymour's Theorem. Both are roughly equal to Seymour's in terms of complexity, but they offer an alternative perspective which we hope will be of value.","authors_text":"Edita Rollov\\'a, Matt DeVos, Robert \\v{S}\\'amal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-19T09:28:31Z","title":"A new proof of Seymour's 6-flow theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06214","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":"sha256:82995df3bee2cd8173495ae7fa1d1faf578c33abbc9c5309aff4c580cafb8537","target":"record","created_at":"2026-05-18T01:24:04Z","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":"2db7d6a30f2bea6c57f23836d5fe780d54621d692074cfe04c4124c8d6fc449d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-12-19T09:28:31Z","title_canon_sha256":"82ab4db60c3743d394288f0f0929eeb943b2ad0a6b2eb12726f67b9f9e05e23c"},"schema_version":"1.0","source":{"id":"1512.06214","kind":"arxiv","version":1}},"canonical_sha256":"fc10bd50cdfd1e2336749d5f9eef75208d7a8b02964e7ce8251c928696403fdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc10bd50cdfd1e2336749d5f9eef75208d7a8b02964e7ce8251c928696403fdd","first_computed_at":"2026-05-18T01:24:04.816370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:04.816370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"otZIHGgB3e5cAN9rgQzZTeDm5oDQL3LrNjsv34k4oYTWRfSWETAPx8j/TshRJaZqCJOZYK/6ZnGRT+wyruC6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:04.817108Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.06214","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82995df3bee2cd8173495ae7fa1d1faf578c33abbc9c5309aff4c580cafb8537","sha256:762a510c7a3f4af36f35c7f7c3975efb9622dc8a0cdec7d40017070650bd29a6"],"state_sha256":"1fda3930c2c373ad9c751c27369aa80ef1795207d554cf8504800668b38be3bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1EYWgympmh6o2ucHMKDAUsL2eDsN0VzkB7YnOhX665+wi8pCwzE26h/XCbhilOz092UmF8C0Ae4cJ4Br9ucvBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T21:15:05.956059Z","bundle_sha256":"1fcfa833cb89e147ea8aff652d5bbd42785e299a5813d71abdf36eca7f39fb7a"}}