{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RUMDJ56QB5TUXGHYH4BIM3O6S2","short_pith_number":"pith:RUMDJ56Q","canonical_record":{"source":{"id":"1811.04429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-11-11T15:40:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"66e2fac2a404c9ff6a8c98702a61a8a9a57677081ed73dbc5f9a8006d4f4c969","abstract_canon_sha256":"8cb9372693b39eabfbc89b489c9279408810b780ebf3228306ca821d237027be"},"schema_version":"1.0"},"canonical_sha256":"8d1834f7d00f674b98f83f02866dde96b367b90234b155aaf1e4c48fc9c575c4","source":{"kind":"arxiv","id":"1811.04429","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04429","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04429v1","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04429","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"pith_short_12","alias_value":"RUMDJ56QB5TU","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RUMDJ56QB5TUXGHY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RUMDJ56Q","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RUMDJ56QB5TUXGHYH4BIM3O6S2","target":"record","payload":{"canonical_record":{"source":{"id":"1811.04429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-11-11T15:40:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"66e2fac2a404c9ff6a8c98702a61a8a9a57677081ed73dbc5f9a8006d4f4c969","abstract_canon_sha256":"8cb9372693b39eabfbc89b489c9279408810b780ebf3228306ca821d237027be"},"schema_version":"1.0"},"canonical_sha256":"8d1834f7d00f674b98f83f02866dde96b367b90234b155aaf1e4c48fc9c575c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:05.197158Z","signature_b64":"sDCjKR/YkWlzC80XXgtwsmAs4dAjMeC6bqzsubbEey+jw4vkU7Esf6Yx8S+s9Saqsu3cSpAm7t1x1kWDt+d9Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d1834f7d00f674b98f83f02866dde96b367b90234b155aaf1e4c48fc9c575c4","last_reissued_at":"2026-05-18T00:01:05.196485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:05.196485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.04429","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":"2026-05-18T00:01:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V4a3LmcC0Y1cNflPtWTnZnzGDVQ33TdDo2OHESiu+HXrtBg06wGHlId2iGhrBsoL2dzgeHL77Y3aqEyoDzV/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:18:07.384538Z"},"content_sha256":"86761e98cfda86af1a88b5e4d2a680e8b79ec80371f8de08dae3a6deb6bab776","schema_version":"1.0","event_id":"sha256:86761e98cfda86af1a88b5e4d2a680e8b79ec80371f8de08dae3a6deb6bab776"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RUMDJ56QB5TUXGHYH4BIM3O6S2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generating subgraphs in chordal graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"David Tankus, Vadim E. Levit","submitted_at":"2018-11-11T15:40:35Z","abstract_excerpt":"A graph $G$ is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function $w$ is defined on its vertices. Then $G$ is $w$-well-covered if all maximal independent sets are of the same weight. For every graph $G$, the set of weight functions $w$ such that $G$ is $w$-well-covered is a vector space, denoted $WCW(G)$. Let $B$ be a complete bipartite induced subgraph of $G$ on vertex sets of bipartition $B_{X}$ and $B_{Y}$. Then $B$ is generating if there exists an independent set $S$ such that $S \\cup B_{X}$ and $S \\cup B_{Y}$ are both maximal indepe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04429","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":"2026-05-18T00:01:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GRF0SMzZvcfvQ/ks0cNxYkMqdsxSD4aHl0bxwS7BXvHkWaJmBwBfUZs2Pmb0Aua6OklWMpuFF7k4Q2IUUJ/3AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:18:07.384886Z"},"content_sha256":"4ba8fd7245d4c52fdd28a34bffde30866630cad10be2a74a2e54bcf5b9672e5c","schema_version":"1.0","event_id":"sha256:4ba8fd7245d4c52fdd28a34bffde30866630cad10be2a74a2e54bcf5b9672e5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUMDJ56QB5TUXGHYH4BIM3O6S2/bundle.json","state_url":"https://pith.science/pith/RUMDJ56QB5TUXGHYH4BIM3O6S2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUMDJ56QB5TUXGHYH4BIM3O6S2/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":"2026-06-02T08:18:07Z","links":{"resolver":"https://pith.science/pith/RUMDJ56QB5TUXGHYH4BIM3O6S2","bundle":"https://pith.science/pith/RUMDJ56QB5TUXGHYH4BIM3O6S2/bundle.json","state":"https://pith.science/pith/RUMDJ56QB5TUXGHYH4BIM3O6S2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUMDJ56QB5TUXGHYH4BIM3O6S2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RUMDJ56QB5TUXGHYH4BIM3O6S2","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":"8cb9372693b39eabfbc89b489c9279408810b780ebf3228306ca821d237027be","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-11-11T15:40:35Z","title_canon_sha256":"66e2fac2a404c9ff6a8c98702a61a8a9a57677081ed73dbc5f9a8006d4f4c969"},"schema_version":"1.0","source":{"id":"1811.04429","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04429","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04429v1","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04429","created_at":"2026-05-18T00:01:05Z"},{"alias_kind":"pith_short_12","alias_value":"RUMDJ56QB5TU","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RUMDJ56QB5TUXGHY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RUMDJ56Q","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:4ba8fd7245d4c52fdd28a34bffde30866630cad10be2a74a2e54bcf5b9672e5c","target":"graph","created_at":"2026-05-18T00:01:05Z","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":"A graph $G$ is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function $w$ is defined on its vertices. Then $G$ is $w$-well-covered if all maximal independent sets are of the same weight. For every graph $G$, the set of weight functions $w$ such that $G$ is $w$-well-covered is a vector space, denoted $WCW(G)$. Let $B$ be a complete bipartite induced subgraph of $G$ on vertex sets of bipartition $B_{X}$ and $B_{Y}$. Then $B$ is generating if there exists an independent set $S$ such that $S \\cup B_{X}$ and $S \\cup B_{Y}$ are both maximal indepe","authors_text":"David Tankus, Vadim E. Levit","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-11-11T15:40:35Z","title":"Generating subgraphs in chordal graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04429","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":"sha256:86761e98cfda86af1a88b5e4d2a680e8b79ec80371f8de08dae3a6deb6bab776","target":"record","created_at":"2026-05-18T00:01:05Z","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":"8cb9372693b39eabfbc89b489c9279408810b780ebf3228306ca821d237027be","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-11-11T15:40:35Z","title_canon_sha256":"66e2fac2a404c9ff6a8c98702a61a8a9a57677081ed73dbc5f9a8006d4f4c969"},"schema_version":"1.0","source":{"id":"1811.04429","kind":"arxiv","version":1}},"canonical_sha256":"8d1834f7d00f674b98f83f02866dde96b367b90234b155aaf1e4c48fc9c575c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d1834f7d00f674b98f83f02866dde96b367b90234b155aaf1e4c48fc9c575c4","first_computed_at":"2026-05-18T00:01:05.196485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:05.196485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sDCjKR/YkWlzC80XXgtwsmAs4dAjMeC6bqzsubbEey+jw4vkU7Esf6Yx8S+s9Saqsu3cSpAm7t1x1kWDt+d9Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:05.197158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04429","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86761e98cfda86af1a88b5e4d2a680e8b79ec80371f8de08dae3a6deb6bab776","sha256:4ba8fd7245d4c52fdd28a34bffde30866630cad10be2a74a2e54bcf5b9672e5c"],"state_sha256":"b6e8447f8cec35081656d7beb73844d80174151fef1a520257e275111befebcd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"frr0mEdjgR2cF/XaBfvsq/pmK1gpSX6IBLw8wLgV967KHorMPK7li1XGKP5nrVTLcjU9gPl3/wn5GCbBgOfIDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T08:18:07.386960Z","bundle_sha256":"791aabb2d0bb170c386a30412297b42534b142d63c49ab9857c1a84767cbf502"}}