{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:MFRRJ2RBH6AN3SNMCX7KWHDLQC","short_pith_number":"pith:MFRRJ2RB","canonical_record":{"source":{"id":"2311.13980","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2023-11-23T12:52:09Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5c7681e9e1e02341cff52bc226296ee6025a762c21244b24b8799a4f363786d5","abstract_canon_sha256":"77d8b4e1e8b404eb4fb34289b9539fc2169a4c3822eb22bc74032e2d0e6a462a"},"schema_version":"1.0"},"canonical_sha256":"616314ea213f80ddc9ac15feab1c6b80b527c46c003e65fe044ca80dfe39019a","source":{"kind":"arxiv","id":"2311.13980","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.13980","created_at":"2026-07-05T07:16:11Z"},{"alias_kind":"arxiv_version","alias_value":"2311.13980v1","created_at":"2026-07-05T07:16:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.13980","created_at":"2026-07-05T07:16:11Z"},{"alias_kind":"pith_short_12","alias_value":"MFRRJ2RBH6AN","created_at":"2026-07-05T07:16:11Z"},{"alias_kind":"pith_short_16","alias_value":"MFRRJ2RBH6AN3SNM","created_at":"2026-07-05T07:16:11Z"},{"alias_kind":"pith_short_8","alias_value":"MFRRJ2RB","created_at":"2026-07-05T07:16:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:MFRRJ2RBH6AN3SNMCX7KWHDLQC","target":"record","payload":{"canonical_record":{"source":{"id":"2311.13980","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2023-11-23T12:52:09Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5c7681e9e1e02341cff52bc226296ee6025a762c21244b24b8799a4f363786d5","abstract_canon_sha256":"77d8b4e1e8b404eb4fb34289b9539fc2169a4c3822eb22bc74032e2d0e6a462a"},"schema_version":"1.0"},"canonical_sha256":"616314ea213f80ddc9ac15feab1c6b80b527c46c003e65fe044ca80dfe39019a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:16:11.692737Z","signature_b64":"0OystCq7f0KjaAOdNwokY+ZM4YKVc1Je3WmYQP/HRFZ2eB2eNDSba8UlVVRInuCMWnuquVJLssBccIyMPpkbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"616314ea213f80ddc9ac15feab1c6b80b527c46c003e65fe044ca80dfe39019a","last_reissued_at":"2026-07-05T07:16:11.692185Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:16:11.692185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.13980","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":"2026-07-05T07:16:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FP+HeKbI3jTAJ4reaZ99nJ76nyU3KLny6ptJ1/amznb02OsnL5yaebBHfnGcB+A9AQL8wHerYzMOpmenaV4UAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T14:24:16.819653Z"},"content_sha256":"5cf1a973ba3e59fe2d9a47153b87d6c4d7f67fb13e7bbf4c403104e7b7c3db37","schema_version":"1.0","event_id":"sha256:5cf1a973ba3e59fe2d9a47153b87d6c4d7f67fb13e7bbf4c403104e7b7c3db37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:MFRRJ2RBH6AN3SNMCX7KWHDLQC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Permutation-Representation Number of Bipartite Graphs using Neighborhood Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Khyodeno Mozhui, K. V. Krishna","submitted_at":"2023-11-23T12:52:09Z","abstract_excerpt":"The problems of determining the permutation-representation number (prn) and the representation number of bipartite graphs are open in the literature. Moreover, the decision problem corresponding to the determination of the prn of a bipartite graph is NP-complete. However, these numbers were established for certain subclasses of bipartite graphs, e.g., for crown graphs. Further, it was conjectured that the crown graphs have the highest representation number among the bipartite graphs. In this work, first, we reconcile the relation between the prn of a comparability graph and the dimension of it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.13980","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/2311.13980/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":"2026-07-05T07:16:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tDxSvOvBm4uTeMzeWMgoUgNLBa/87pG3fRJuTwQOqiCa5cgjpowM7J4aMQkBMYpA1YgZx8jufzDTATT2QjSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T14:24:16.820154Z"},"content_sha256":"5ab2c6df7c3a963ceaeb3a1649463a908d41ded7c779a98173e8f1cee5172942","schema_version":"1.0","event_id":"sha256:5ab2c6df7c3a963ceaeb3a1649463a908d41ded7c779a98173e8f1cee5172942"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFRRJ2RBH6AN3SNMCX7KWHDLQC/bundle.json","state_url":"https://pith.science/pith/MFRRJ2RBH6AN3SNMCX7KWHDLQC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFRRJ2RBH6AN3SNMCX7KWHDLQC/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":"2026-08-23T14:24:16Z","links":{"resolver":"https://pith.science/pith/MFRRJ2RBH6AN3SNMCX7KWHDLQC","bundle":"https://pith.science/pith/MFRRJ2RBH6AN3SNMCX7KWHDLQC/bundle.json","state":"https://pith.science/pith/MFRRJ2RBH6AN3SNMCX7KWHDLQC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFRRJ2RBH6AN3SNMCX7KWHDLQC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:MFRRJ2RBH6AN3SNMCX7KWHDLQC","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":"77d8b4e1e8b404eb4fb34289b9539fc2169a4c3822eb22bc74032e2d0e6a462a","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2023-11-23T12:52:09Z","title_canon_sha256":"5c7681e9e1e02341cff52bc226296ee6025a762c21244b24b8799a4f363786d5"},"schema_version":"1.0","source":{"id":"2311.13980","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.13980","created_at":"2026-07-05T07:16:11Z"},{"alias_kind":"arxiv_version","alias_value":"2311.13980v1","created_at":"2026-07-05T07:16:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.13980","created_at":"2026-07-05T07:16:11Z"},{"alias_kind":"pith_short_12","alias_value":"MFRRJ2RBH6AN","created_at":"2026-07-05T07:16:11Z"},{"alias_kind":"pith_short_16","alias_value":"MFRRJ2RBH6AN3SNM","created_at":"2026-07-05T07:16:11Z"},{"alias_kind":"pith_short_8","alias_value":"MFRRJ2RB","created_at":"2026-07-05T07:16:11Z"}],"graph_snapshots":[{"event_id":"sha256:5ab2c6df7c3a963ceaeb3a1649463a908d41ded7c779a98173e8f1cee5172942","target":"graph","created_at":"2026-07-05T07:16:11Z","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/2311.13980/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The problems of determining the permutation-representation number (prn) and the representation number of bipartite graphs are open in the literature. Moreover, the decision problem corresponding to the determination of the prn of a bipartite graph is NP-complete. However, these numbers were established for certain subclasses of bipartite graphs, e.g., for crown graphs. Further, it was conjectured that the crown graphs have the highest representation number among the bipartite graphs. In this work, first, we reconcile the relation between the prn of a comparability graph and the dimension of it","authors_text":"Khyodeno Mozhui, K. V. Krishna","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2023-11-23T12:52:09Z","title":"On the Permutation-Representation Number of Bipartite Graphs using Neighborhood Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.13980","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":"sha256:5cf1a973ba3e59fe2d9a47153b87d6c4d7f67fb13e7bbf4c403104e7b7c3db37","target":"record","created_at":"2026-07-05T07:16:11Z","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":"77d8b4e1e8b404eb4fb34289b9539fc2169a4c3822eb22bc74032e2d0e6a462a","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2023-11-23T12:52:09Z","title_canon_sha256":"5c7681e9e1e02341cff52bc226296ee6025a762c21244b24b8799a4f363786d5"},"schema_version":"1.0","source":{"id":"2311.13980","kind":"arxiv","version":1}},"canonical_sha256":"616314ea213f80ddc9ac15feab1c6b80b527c46c003e65fe044ca80dfe39019a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"616314ea213f80ddc9ac15feab1c6b80b527c46c003e65fe044ca80dfe39019a","first_computed_at":"2026-07-05T07:16:11.692185Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:16:11.692185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0OystCq7f0KjaAOdNwokY+ZM4YKVc1Je3WmYQP/HRFZ2eB2eNDSba8UlVVRInuCMWnuquVJLssBccIyMPpkbCg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:16:11.692737Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.13980","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5cf1a973ba3e59fe2d9a47153b87d6c4d7f67fb13e7bbf4c403104e7b7c3db37","sha256:5ab2c6df7c3a963ceaeb3a1649463a908d41ded7c779a98173e8f1cee5172942"],"state_sha256":"6d5edd46ecb39d223583bc8932b48240c1323fd3542b58e69eb188dd0e96e762"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pue3mHL7/4yPMaJsGhI7q39qL717s01nfK7L6tyhU4iiz9y1jqOKlCTlktJdDQYbnGux/kygGZVUjLZqb5ADDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T14:24:16.824387Z","bundle_sha256":"3005961e6ee160557e2c6d2a988d16a9b616cef3b75d3ea20825ddff2cec8946"}}