{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:YKNIBLRJUDEQ3FBL3N72G5XHVO","short_pith_number":"pith:YKNIBLRJ","canonical_record":{"source":{"id":"2606.00802","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-30T16:40:50Z","cross_cats_sorted":[],"title_canon_sha256":"d5c263bd51869842e6b1fe9b2c60e45021927ffc8a390e0953986db69836e22d","abstract_canon_sha256":"d1562e7aa09bf3e48ce560e2ceb63c9490e860b5b2e311f994824057b2ad8814"},"schema_version":"1.0"},"canonical_sha256":"c29a80ae29a0c90d942bdb7fa376e7ab944d32af0d62f533af96f5f1ef953523","source":{"kind":"arxiv","id":"2606.00802","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00802","created_at":"2026-06-02T01:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00802v1","created_at":"2026-06-02T01:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00802","created_at":"2026-06-02T01:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"YKNIBLRJUDEQ","created_at":"2026-06-02T01:04:06Z"},{"alias_kind":"pith_short_16","alias_value":"YKNIBLRJUDEQ3FBL","created_at":"2026-06-02T01:04:06Z"},{"alias_kind":"pith_short_8","alias_value":"YKNIBLRJ","created_at":"2026-06-02T01:04:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:YKNIBLRJUDEQ3FBL3N72G5XHVO","target":"record","payload":{"canonical_record":{"source":{"id":"2606.00802","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-30T16:40:50Z","cross_cats_sorted":[],"title_canon_sha256":"d5c263bd51869842e6b1fe9b2c60e45021927ffc8a390e0953986db69836e22d","abstract_canon_sha256":"d1562e7aa09bf3e48ce560e2ceb63c9490e860b5b2e311f994824057b2ad8814"},"schema_version":"1.0"},"canonical_sha256":"c29a80ae29a0c90d942bdb7fa376e7ab944d32af0d62f533af96f5f1ef953523","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:06.192299Z","signature_b64":"X2SuEaVTE6QllPCvgEiIswlDcfDnUnFUW59I/QCeB17SGI2tsBmTT0Xet/1x1fRKVYr5ELadhRs+zjBGra7BDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c29a80ae29a0c90d942bdb7fa376e7ab944d32af0d62f533af96f5f1ef953523","last_reissued_at":"2026-06-02T01:04:06.191928Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:06.191928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.00802","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":"2026-06-02T01:04:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L/MhXJ6yYHpkCDCOnxX1A5OIAkNov1N7WoANgEYskqf8Z1s3yi5RdTtJ8SIeJRqut/94+Y9DDg9tSzJSIEA5Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:21:26.183180Z"},"content_sha256":"de71df712584a526861dc4dd0e9b314917d76584b6d314ece0731e38a03765b9","schema_version":"1.0","event_id":"sha256:de71df712584a526861dc4dd0e9b314917d76584b6d314ece0731e38a03765b9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:YKNIBLRJUDEQ3FBL3N72G5XHVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizing all nonbipartite well-edge-dominated graphs","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kirsti Kuenzel, Sarah E. Anderson","submitted_at":"2026-05-30T16:40:50Z","abstract_excerpt":"Given a graph $G$, a set $F$ of edges is an edge dominating set of $G$ if every edge in $G$ is either in $F$ or adjacent to an edge in $F$. A graph $G$ is said to be well-edge-dominated if every minimal edge dominating set has the same cardinality. This definition is the edge version of domination in that a set $D\\subseteq V(G)$ is a dominating set if every vertex in $G$ is in $D$ or adjacent to a vertex in $D$ and the domination number $\\gamma(G)$ is the minimum cardinality among all dominating sets. In this paper, we complete the characterization of all nonbipartite, well-edge-dominated grap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00802","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.00802/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-02T01:04:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OfiEGlzW4bLj5IM7q8NZkkhI6FmLyNFIiOlXMBWKZF24qPSVR1w4OToZqWc8oIg/WEFGO2XAQ90MqXyEk+sPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:21:26.183570Z"},"content_sha256":"6589b4d5d8a26c4c8c16c9c43fcf0744fe623cf926f1151e783dc13dd29ed21f","schema_version":"1.0","event_id":"sha256:6589b4d5d8a26c4c8c16c9c43fcf0744fe623cf926f1151e783dc13dd29ed21f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YKNIBLRJUDEQ3FBL3N72G5XHVO/bundle.json","state_url":"https://pith.science/pith/YKNIBLRJUDEQ3FBL3N72G5XHVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YKNIBLRJUDEQ3FBL3N72G5XHVO/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":"2026-06-22T13:21:26Z","links":{"resolver":"https://pith.science/pith/YKNIBLRJUDEQ3FBL3N72G5XHVO","bundle":"https://pith.science/pith/YKNIBLRJUDEQ3FBL3N72G5XHVO/bundle.json","state":"https://pith.science/pith/YKNIBLRJUDEQ3FBL3N72G5XHVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YKNIBLRJUDEQ3FBL3N72G5XHVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YKNIBLRJUDEQ3FBL3N72G5XHVO","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":"d1562e7aa09bf3e48ce560e2ceb63c9490e860b5b2e311f994824057b2ad8814","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-30T16:40:50Z","title_canon_sha256":"d5c263bd51869842e6b1fe9b2c60e45021927ffc8a390e0953986db69836e22d"},"schema_version":"1.0","source":{"id":"2606.00802","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00802","created_at":"2026-06-02T01:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00802v1","created_at":"2026-06-02T01:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00802","created_at":"2026-06-02T01:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"YKNIBLRJUDEQ","created_at":"2026-06-02T01:04:06Z"},{"alias_kind":"pith_short_16","alias_value":"YKNIBLRJUDEQ3FBL","created_at":"2026-06-02T01:04:06Z"},{"alias_kind":"pith_short_8","alias_value":"YKNIBLRJ","created_at":"2026-06-02T01:04:06Z"}],"graph_snapshots":[{"event_id":"sha256:6589b4d5d8a26c4c8c16c9c43fcf0744fe623cf926f1151e783dc13dd29ed21f","target":"graph","created_at":"2026-06-02T01:04:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.00802/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a graph $G$, a set $F$ of edges is an edge dominating set of $G$ if every edge in $G$ is either in $F$ or adjacent to an edge in $F$. A graph $G$ is said to be well-edge-dominated if every minimal edge dominating set has the same cardinality. This definition is the edge version of domination in that a set $D\\subseteq V(G)$ is a dominating set if every vertex in $G$ is in $D$ or adjacent to a vertex in $D$ and the domination number $\\gamma(G)$ is the minimum cardinality among all dominating sets. In this paper, we complete the characterization of all nonbipartite, well-edge-dominated grap","authors_text":"Kirsti Kuenzel, Sarah E. Anderson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-30T16:40:50Z","title":"Characterizing all nonbipartite well-edge-dominated graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00802","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:de71df712584a526861dc4dd0e9b314917d76584b6d314ece0731e38a03765b9","target":"record","created_at":"2026-06-02T01:04:06Z","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":"d1562e7aa09bf3e48ce560e2ceb63c9490e860b5b2e311f994824057b2ad8814","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-30T16:40:50Z","title_canon_sha256":"d5c263bd51869842e6b1fe9b2c60e45021927ffc8a390e0953986db69836e22d"},"schema_version":"1.0","source":{"id":"2606.00802","kind":"arxiv","version":1}},"canonical_sha256":"c29a80ae29a0c90d942bdb7fa376e7ab944d32af0d62f533af96f5f1ef953523","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c29a80ae29a0c90d942bdb7fa376e7ab944d32af0d62f533af96f5f1ef953523","first_computed_at":"2026-06-02T01:04:06.191928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:04:06.191928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X2SuEaVTE6QllPCvgEiIswlDcfDnUnFUW59I/QCeB17SGI2tsBmTT0Xet/1x1fRKVYr5ELadhRs+zjBGra7BDg==","signature_status":"signed_v1","signed_at":"2026-06-02T01:04:06.192299Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.00802","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de71df712584a526861dc4dd0e9b314917d76584b6d314ece0731e38a03765b9","sha256:6589b4d5d8a26c4c8c16c9c43fcf0744fe623cf926f1151e783dc13dd29ed21f"],"state_sha256":"f9f610efec063cfe16c99c84f3773a1426895ca04ffec8ce48b22d74e74bea4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+mfPNZy0uIyTNm034BVwg2Z2z4lvayRsIkpAkYE9Ibiow3hNxdmkhithcE6Cphg62DEtKnqNhUdEACjW1tY5BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T13:21:26.185772Z","bundle_sha256":"bdebbcdca2372c20b1ba2cc4b9e32e6f71696f16eb0c9a1c9c0fdf662245fe01"}}