{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:32CXQVWGWJZ24ZEEHJRPIGRBAG","short_pith_number":"pith:32CXQVWG","canonical_record":{"source":{"id":"2508.01935","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-08-03T22:11:41Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"0ccf87f64d0c080abbe985bb26b416d121ae66a1fd33d2a314f6a4494299a02f","abstract_canon_sha256":"d03cffb7b2745450caf7a9894d08224119f10b67c3c62dea596073c3cc19a384"},"schema_version":"1.0"},"canonical_sha256":"de857856c6b273ae64843a62f41a210193b76e855bd96d8df70eb21006de6c65","source":{"kind":"arxiv","id":"2508.01935","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.01935","created_at":"2026-07-05T11:47:48Z"},{"alias_kind":"arxiv_version","alias_value":"2508.01935v1","created_at":"2026-07-05T11:47:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.01935","created_at":"2026-07-05T11:47:48Z"},{"alias_kind":"pith_short_12","alias_value":"32CXQVWGWJZ2","created_at":"2026-07-05T11:47:48Z"},{"alias_kind":"pith_short_16","alias_value":"32CXQVWGWJZ24ZEE","created_at":"2026-07-05T11:47:48Z"},{"alias_kind":"pith_short_8","alias_value":"32CXQVWG","created_at":"2026-07-05T11:47:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:32CXQVWGWJZ24ZEEHJRPIGRBAG","target":"record","payload":{"canonical_record":{"source":{"id":"2508.01935","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-08-03T22:11:41Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"0ccf87f64d0c080abbe985bb26b416d121ae66a1fd33d2a314f6a4494299a02f","abstract_canon_sha256":"d03cffb7b2745450caf7a9894d08224119f10b67c3c62dea596073c3cc19a384"},"schema_version":"1.0"},"canonical_sha256":"de857856c6b273ae64843a62f41a210193b76e855bd96d8df70eb21006de6c65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:47:48.547961Z","signature_b64":"Sgfku9TGRV/i1gvHo4vM9PkWLlcwEEihzE+s/OlT9dONEsMXLRTaPtwwntJdEUGqVODQxv5I6Q1rt7NFYGEeAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de857856c6b273ae64843a62f41a210193b76e855bd96d8df70eb21006de6c65","last_reissued_at":"2026-07-05T11:47:48.547466Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:47:48.547466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.01935","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":"2026-07-05T11:47:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RasS7ZOjw9MG4VcEvalCNuAmEdcxAMRERyf7EYAFW38IG34inj45Pz1DdoRS6YEyfnYjyuiIUmtFyhFUQQhZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:57:22.592211Z"},"content_sha256":"ef2e298147f4a40cfda7f6527ac701b4ee6a4a513fe108c8af860b03b2ef902d","schema_version":"1.0","event_id":"sha256:ef2e298147f4a40cfda7f6527ac701b4ee6a4a513fe108c8af860b03b2ef902d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:32CXQVWGWJZ24ZEEHJRPIGRBAG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Edge open packing: further characterizations","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Arti Pandey, Kamal Santra","submitted_at":"2025-08-03T22:11:41Z","abstract_excerpt":"Let $G=(V, E)$ be a graph where $V(G)$ and $E(G)$ are the vertex and edge sets, respectively. In a graph $G$, two edges $e_1, e_2\\in E(G)$ are said to have \\emph{common edge} $e\\neq e_1, e_2$ if $e$ joins an endpoint of $e_1$ to an endpoint of $e_2$ in $G$. A subset $D\\subseteq E(G)$ is called an \\emph{edge open packing set} in $G$ if no two edges in $D$ share a common edge in $G$, and the largest size of such a set in $G$ is known as \\emph{edge open packing number}, represented by $\\rho_{e}^o(G)$. In the introductory paper (Chelladurai et al. (2022)), necessary and sufficient conditions for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.01935","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/2508.01935/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":"2026-07-05T11:47:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vxlXoVI4KYz/byu2Nm0W7bOy4HLpipNs/BaI+mCSloR25ViKHl0mYYU9T4JFqrNC6MovsnwYuSA4Mo1vpjD/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:57:22.592717Z"},"content_sha256":"c384dc458e76506780feab9ac9e4b49921d2ba247a881006c3ded68173c466b6","schema_version":"1.0","event_id":"sha256:c384dc458e76506780feab9ac9e4b49921d2ba247a881006c3ded68173c466b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/32CXQVWGWJZ24ZEEHJRPIGRBAG/bundle.json","state_url":"https://pith.science/pith/32CXQVWGWJZ24ZEEHJRPIGRBAG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/32CXQVWGWJZ24ZEEHJRPIGRBAG/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":"2026-08-03T22:57:22Z","links":{"resolver":"https://pith.science/pith/32CXQVWGWJZ24ZEEHJRPIGRBAG","bundle":"https://pith.science/pith/32CXQVWGWJZ24ZEEHJRPIGRBAG/bundle.json","state":"https://pith.science/pith/32CXQVWGWJZ24ZEEHJRPIGRBAG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/32CXQVWGWJZ24ZEEHJRPIGRBAG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:32CXQVWGWJZ24ZEEHJRPIGRBAG","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":"d03cffb7b2745450caf7a9894d08224119f10b67c3c62dea596073c3cc19a384","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-08-03T22:11:41Z","title_canon_sha256":"0ccf87f64d0c080abbe985bb26b416d121ae66a1fd33d2a314f6a4494299a02f"},"schema_version":"1.0","source":{"id":"2508.01935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.01935","created_at":"2026-07-05T11:47:48Z"},{"alias_kind":"arxiv_version","alias_value":"2508.01935v1","created_at":"2026-07-05T11:47:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.01935","created_at":"2026-07-05T11:47:48Z"},{"alias_kind":"pith_short_12","alias_value":"32CXQVWGWJZ2","created_at":"2026-07-05T11:47:48Z"},{"alias_kind":"pith_short_16","alias_value":"32CXQVWGWJZ24ZEE","created_at":"2026-07-05T11:47:48Z"},{"alias_kind":"pith_short_8","alias_value":"32CXQVWG","created_at":"2026-07-05T11:47:48Z"}],"graph_snapshots":[{"event_id":"sha256:c384dc458e76506780feab9ac9e4b49921d2ba247a881006c3ded68173c466b6","target":"graph","created_at":"2026-07-05T11:47:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.01935/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G=(V, E)$ be a graph where $V(G)$ and $E(G)$ are the vertex and edge sets, respectively. In a graph $G$, two edges $e_1, e_2\\in E(G)$ are said to have \\emph{common edge} $e\\neq e_1, e_2$ if $e$ joins an endpoint of $e_1$ to an endpoint of $e_2$ in $G$. A subset $D\\subseteq E(G)$ is called an \\emph{edge open packing set} in $G$ if no two edges in $D$ share a common edge in $G$, and the largest size of such a set in $G$ is known as \\emph{edge open packing number}, represented by $\\rho_{e}^o(G)$. In the introductory paper (Chelladurai et al. (2022)), necessary and sufficient conditions for $","authors_text":"Arti Pandey, Kamal Santra","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-08-03T22:11:41Z","title":"Edge open packing: further characterizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.01935","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:ef2e298147f4a40cfda7f6527ac701b4ee6a4a513fe108c8af860b03b2ef902d","target":"record","created_at":"2026-07-05T11:47:48Z","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":"d03cffb7b2745450caf7a9894d08224119f10b67c3c62dea596073c3cc19a384","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2025-08-03T22:11:41Z","title_canon_sha256":"0ccf87f64d0c080abbe985bb26b416d121ae66a1fd33d2a314f6a4494299a02f"},"schema_version":"1.0","source":{"id":"2508.01935","kind":"arxiv","version":1}},"canonical_sha256":"de857856c6b273ae64843a62f41a210193b76e855bd96d8df70eb21006de6c65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de857856c6b273ae64843a62f41a210193b76e855bd96d8df70eb21006de6c65","first_computed_at":"2026-07-05T11:47:48.547466Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:47:48.547466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sgfku9TGRV/i1gvHo4vM9PkWLlcwEEihzE+s/OlT9dONEsMXLRTaPtwwntJdEUGqVODQxv5I6Q1rt7NFYGEeAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:47:48.547961Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.01935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef2e298147f4a40cfda7f6527ac701b4ee6a4a513fe108c8af860b03b2ef902d","sha256:c384dc458e76506780feab9ac9e4b49921d2ba247a881006c3ded68173c466b6"],"state_sha256":"c182d56d66462f80e4d65b31281c922464608062d453f12dbf3be9d249b8c68d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZQhhM7NRknQeSMVWH8b/sQInxj7lnz78K2MnxC56OtEO5Oht7OAZ04xaRwYUxlyZb3iWSJdc9rf1B6lZ+oeqDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T22:57:22.597779Z","bundle_sha256":"0b49f5a8b8117baf359c566f4fee2bb0c2ebf26e587b76cd0a28d96cf2ed5d67"}}