{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TNB6FPYBYHB5QJI3XKYJG7OARQ","short_pith_number":"pith:TNB6FPYB","canonical_record":{"source":{"id":"1511.00228","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-01T11:15:36Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"3049f345e3b9b00cabdd6a6730196edc077ff916238f20dc4f3a7aa6239482fa","abstract_canon_sha256":"f58f4534564f804505288e3d8679ba710616ac170ba3a259fc81db31a5f7d3c0"},"schema_version":"1.0"},"canonical_sha256":"9b43e2bf01c1c3d8251bbab0937dc08c2b9dbf7813608106a5f4e6b8cd11fdcb","source":{"kind":"arxiv","id":"1511.00228","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00228","created_at":"2026-05-18T01:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00228v1","created_at":"2026-05-18T01:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00228","created_at":"2026-05-18T01:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"TNB6FPYBYHB5","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNB6FPYBYHB5QJI3","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNB6FPYB","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TNB6FPYBYHB5QJI3XKYJG7OARQ","target":"record","payload":{"canonical_record":{"source":{"id":"1511.00228","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-01T11:15:36Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"3049f345e3b9b00cabdd6a6730196edc077ff916238f20dc4f3a7aa6239482fa","abstract_canon_sha256":"f58f4534564f804505288e3d8679ba710616ac170ba3a259fc81db31a5f7d3c0"},"schema_version":"1.0"},"canonical_sha256":"9b43e2bf01c1c3d8251bbab0937dc08c2b9dbf7813608106a5f4e6b8cd11fdcb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:12.871139Z","signature_b64":"vgIj42ZGTX1BkHld/Kx8agbOAbVlHqeKX+iU6uEP6D2Eke6ZKzo5JG3fqmaf37QsliA8NAvd7TWldhk42gg2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b43e2bf01c1c3d8251bbab0937dc08c2b9dbf7813608106a5f4e6b8cd11fdcb","last_reissued_at":"2026-05-18T01:28:12.870434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:12.870434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.00228","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":"2026-05-18T01:28:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CsHJnFFpnlI8HV3dNKbNiN4tKrWnB/EU1rLhwqWuEsXqKyu84HVo8f9HvFjOo/pidU+iVDAv5S301OzNaceIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:37:57.343264Z"},"content_sha256":"4c5ea76f88db226cbc82c29ccde019172174903b4f24754ed2e16c920e6b55a1","schema_version":"1.0","event_id":"sha256:4c5ea76f88db226cbc82c29ccde019172174903b4f24754ed2e16c920e6b55a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TNB6FPYBYHB5QJI3XKYJG7OARQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unmixed r-partite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Rashid Zaare-Nahandi, Reza Jafarpoure Golzari","submitted_at":"2015-11-01T11:15:36Z","abstract_excerpt":"Unmixed bipartite graphs have been characterized by Ravadra and Villarreal independently. Our aim in this paper is to characterize unmixed r-partite graphs under a certain condition, witch is a generalization of villarreal's theorem on bipartite graphs. Also we give some examples and counterexamples in relevance this subject."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00228","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":"2026-05-18T01:28:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NdepWLz4TJ5sKvWXI100WQSv0eiLHL6n8R30ToXdprhh+pnXxeuPUGxK4gfJYGDeGv7Ldhi+wBAc/+JhnQm4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T07:37:57.343644Z"},"content_sha256":"a4f898a70026640cfb9c80fffcc0f008c4dc8f9c76782cf2adef9f0ff7063b40","schema_version":"1.0","event_id":"sha256:a4f898a70026640cfb9c80fffcc0f008c4dc8f9c76782cf2adef9f0ff7063b40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNB6FPYBYHB5QJI3XKYJG7OARQ/bundle.json","state_url":"https://pith.science/pith/TNB6FPYBYHB5QJI3XKYJG7OARQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNB6FPYBYHB5QJI3XKYJG7OARQ/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":"2026-06-07T07:37:57Z","links":{"resolver":"https://pith.science/pith/TNB6FPYBYHB5QJI3XKYJG7OARQ","bundle":"https://pith.science/pith/TNB6FPYBYHB5QJI3XKYJG7OARQ/bundle.json","state":"https://pith.science/pith/TNB6FPYBYHB5QJI3XKYJG7OARQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNB6FPYBYHB5QJI3XKYJG7OARQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TNB6FPYBYHB5QJI3XKYJG7OARQ","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":"f58f4534564f804505288e3d8679ba710616ac170ba3a259fc81db31a5f7d3c0","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-01T11:15:36Z","title_canon_sha256":"3049f345e3b9b00cabdd6a6730196edc077ff916238f20dc4f3a7aa6239482fa"},"schema_version":"1.0","source":{"id":"1511.00228","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00228","created_at":"2026-05-18T01:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00228v1","created_at":"2026-05-18T01:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00228","created_at":"2026-05-18T01:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"TNB6FPYBYHB5","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNB6FPYBYHB5QJI3","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNB6FPYB","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:a4f898a70026640cfb9c80fffcc0f008c4dc8f9c76782cf2adef9f0ff7063b40","target":"graph","created_at":"2026-05-18T01:28:12Z","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":"Unmixed bipartite graphs have been characterized by Ravadra and Villarreal independently. Our aim in this paper is to characterize unmixed r-partite graphs under a certain condition, witch is a generalization of villarreal's theorem on bipartite graphs. Also we give some examples and counterexamples in relevance this subject.","authors_text":"Rashid Zaare-Nahandi, Reza Jafarpoure Golzari","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-01T11:15:36Z","title":"Unmixed r-partite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00228","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":"sha256:4c5ea76f88db226cbc82c29ccde019172174903b4f24754ed2e16c920e6b55a1","target":"record","created_at":"2026-05-18T01:28:12Z","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":"f58f4534564f804505288e3d8679ba710616ac170ba3a259fc81db31a5f7d3c0","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-01T11:15:36Z","title_canon_sha256":"3049f345e3b9b00cabdd6a6730196edc077ff916238f20dc4f3a7aa6239482fa"},"schema_version":"1.0","source":{"id":"1511.00228","kind":"arxiv","version":1}},"canonical_sha256":"9b43e2bf01c1c3d8251bbab0937dc08c2b9dbf7813608106a5f4e6b8cd11fdcb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b43e2bf01c1c3d8251bbab0937dc08c2b9dbf7813608106a5f4e6b8cd11fdcb","first_computed_at":"2026-05-18T01:28:12.870434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:12.870434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vgIj42ZGTX1BkHld/Kx8agbOAbVlHqeKX+iU6uEP6D2Eke6ZKzo5JG3fqmaf37QsliA8NAvd7TWldhk42gg2BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:12.871139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.00228","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c5ea76f88db226cbc82c29ccde019172174903b4f24754ed2e16c920e6b55a1","sha256:a4f898a70026640cfb9c80fffcc0f008c4dc8f9c76782cf2adef9f0ff7063b40"],"state_sha256":"2cc841e81e242586b8e8e3b1ba0ab025669445218ab0d0a65d0b7881bc81246b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TXpv1TUGs13NFAW/8JNGqUcLT39CPzOKp3p+AFkdh0ow9cNim26TlIaofPmiONUiQZjtk1gTXBmg+koxREsqCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T07:37:57.345542Z","bundle_sha256":"dac65bdc9c7e5d2c580bcf598134fd258174dcdcf0ad81bfd083660cdaf2f9da"}}