{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EYCWWC6FY3A5ZKTQDDWAPVW2RP","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":"0df9074a9b299524c800ff2213ee510c87813867c4b177b63baed445cef0ee4a","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-04T16:49:53Z","title_canon_sha256":"68814728dd8cee739514d3928342d882ed1256277ae129b3d6b2da0480942949"},"schema_version":"1.0","source":{"id":"1308.0827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0827","created_at":"2026-05-18T03:16:48Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0827v1","created_at":"2026-05-18T03:16:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0827","created_at":"2026-05-18T03:16:48Z"},{"alias_kind":"pith_short_12","alias_value":"EYCWWC6FY3A5","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EYCWWC6FY3A5ZKTQ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EYCWWC6F","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:a43c855fe07615c085fcdf7a677ebf10472a26c1b54781eba94ae989e9ff339c","target":"graph","created_at":"2026-05-18T03:16:48Z","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":"Fix g>1. Every graph of large enough tree-width contains a g x g grid as a minor; but here we prove that every four-edge-connected graph of large enough tree-width contains a g x g grid as an immersion (and hence contains any fixed graph with maximum degree at most four as an immersion). This result has a number of applications.","authors_text":"Maria Chudnovsky, Paul Seymour, Tereza Klimo\\v{s}ov\\'a, Zden\\v{e}k Dvo\\v{r}\\'ak","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-04T16:49:53Z","title":"Immersion in four-edge-connected graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0827","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":"sha256:7c632300a0e42d58505b44681f5b4dda082670c997b3abe1d7bdb64ccd7e824b","target":"record","created_at":"2026-05-18T03:16:48Z","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":"0df9074a9b299524c800ff2213ee510c87813867c4b177b63baed445cef0ee4a","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-04T16:49:53Z","title_canon_sha256":"68814728dd8cee739514d3928342d882ed1256277ae129b3d6b2da0480942949"},"schema_version":"1.0","source":{"id":"1308.0827","kind":"arxiv","version":1}},"canonical_sha256":"26056b0bc5c6c1dcaa7018ec07d6da8bd7981a7a8fda03588942fcb8df7d1a54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26056b0bc5c6c1dcaa7018ec07d6da8bd7981a7a8fda03588942fcb8df7d1a54","first_computed_at":"2026-05-18T03:16:48.041930Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:48.041930Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vLnTrm96q1dE84Ae3Wg4A5+95ThBS81gYRvNYyf50i9g3B5xwqdHN2tp0h7plNpzucd/5OokTBACQW8seI5yAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:48.042496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c632300a0e42d58505b44681f5b4dda082670c997b3abe1d7bdb64ccd7e824b","sha256:a43c855fe07615c085fcdf7a677ebf10472a26c1b54781eba94ae989e9ff339c"],"state_sha256":"3dc31501b7c877fbf74767ca9bfda9af74a568be4b0b90643146b611433535e7"}