{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QQVC4KTJNTZIKKHOHFXEN4YMEG","short_pith_number":"pith:QQVC4KTJ","canonical_record":{"source":{"id":"1405.3436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-14T10:19:18Z","cross_cats_sorted":[],"title_canon_sha256":"d2da1c32e6b53a864ca813b2ff86828bc4ffd6accaf9a265ed12c03c6b894ebe","abstract_canon_sha256":"02fd2ee7f514c85cc2be30ad2ae8945f3e7809c7f676ff8535ce846969887835"},"schema_version":"1.0"},"canonical_sha256":"842a2e2a696cf28528ee396e46f30c21a425ef4889bfa648b88b7d9a2d1604d0","source":{"kind":"arxiv","id":"1405.3436","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3436","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3436v1","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3436","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"pith_short_12","alias_value":"QQVC4KTJNTZI","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QQVC4KTJNTZIKKHO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QQVC4KTJ","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QQVC4KTJNTZIKKHOHFXEN4YMEG","target":"record","payload":{"canonical_record":{"source":{"id":"1405.3436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-14T10:19:18Z","cross_cats_sorted":[],"title_canon_sha256":"d2da1c32e6b53a864ca813b2ff86828bc4ffd6accaf9a265ed12c03c6b894ebe","abstract_canon_sha256":"02fd2ee7f514c85cc2be30ad2ae8945f3e7809c7f676ff8535ce846969887835"},"schema_version":"1.0"},"canonical_sha256":"842a2e2a696cf28528ee396e46f30c21a425ef4889bfa648b88b7d9a2d1604d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:50.788532Z","signature_b64":"kXTIyzvRv1EHOYrwc9jT1jhyw+Oytw60TkfmCwmYH2xnEU9pPFbE+mF3BjtoARbTcTZc6AYDpNHCyPe0o18lCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"842a2e2a696cf28528ee396e46f30c21a425ef4889bfa648b88b7d9a2d1604d0","last_reissued_at":"2026-05-18T02:51:50.788062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:50.788062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.3436","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":"2026-05-18T02:51:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1WPUitLkoOwGVvMh0H8RoN+SpNOzNVe46kUHcvYPcHrjqPSoYRnC0CgPi6Cf/a1j8uq2/gmIw54XerXmO3wgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:45:12.295093Z"},"content_sha256":"4fdad92f1111e78176380106147031ba9041dba630f75c860f45913e862cd264","schema_version":"1.0","event_id":"sha256:4fdad92f1111e78176380106147031ba9041dba630f75c860f45913e862cd264"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QQVC4KTJNTZIKKHOHFXEN4YMEG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Domination in designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Deepak Rajendraprasad, Felix Goldberg, Rogers Mathew","submitted_at":"2014-05-14T10:19:18Z","abstract_excerpt":"We commence the study of domination in the incidence graphs of combinatorial designs. Let $D$ be a combinatorial design and denote by $\\gamma(D)$ the domination number of the incidence (Levy) graph of $D$. We obtain a number of results about the domination numbers of various kinds of designs.\n  For instance, a finite projective plane of order $n$, which is a symmetric $(n^{2}+n+1,n+1,1)$-design, has $\\gamma=2n$. %We also show that for any symmetric $(v,k,\\lambda)$-design it holds that $\\gamma \\leq 2k$. We study at depth the domination numbers of Steiner systems and in particular of Steiner tri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3436","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":"2026-05-18T02:51:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MZ7gL8dvg/ODS5RNUfYrySzzY+7EBZcHsS1LzXitfTAP+axo5VBpjCX7GneG9QhyMb9PmOo7wDMglkQMqQ7sDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:45:12.295563Z"},"content_sha256":"f70ef0a73e6054940d065d069690ba2f2a30a5c0dfc36acd9e29c83b76ab5dc4","schema_version":"1.0","event_id":"sha256:f70ef0a73e6054940d065d069690ba2f2a30a5c0dfc36acd9e29c83b76ab5dc4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QQVC4KTJNTZIKKHOHFXEN4YMEG/bundle.json","state_url":"https://pith.science/pith/QQVC4KTJNTZIKKHOHFXEN4YMEG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QQVC4KTJNTZIKKHOHFXEN4YMEG/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":"2026-06-23T02:45:12Z","links":{"resolver":"https://pith.science/pith/QQVC4KTJNTZIKKHOHFXEN4YMEG","bundle":"https://pith.science/pith/QQVC4KTJNTZIKKHOHFXEN4YMEG/bundle.json","state":"https://pith.science/pith/QQVC4KTJNTZIKKHOHFXEN4YMEG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QQVC4KTJNTZIKKHOHFXEN4YMEG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QQVC4KTJNTZIKKHOHFXEN4YMEG","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":"02fd2ee7f514c85cc2be30ad2ae8945f3e7809c7f676ff8535ce846969887835","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-14T10:19:18Z","title_canon_sha256":"d2da1c32e6b53a864ca813b2ff86828bc4ffd6accaf9a265ed12c03c6b894ebe"},"schema_version":"1.0","source":{"id":"1405.3436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3436","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3436v1","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3436","created_at":"2026-05-18T02:51:50Z"},{"alias_kind":"pith_short_12","alias_value":"QQVC4KTJNTZI","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QQVC4KTJNTZIKKHO","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QQVC4KTJ","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:f70ef0a73e6054940d065d069690ba2f2a30a5c0dfc36acd9e29c83b76ab5dc4","target":"graph","created_at":"2026-05-18T02:51:50Z","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":"We commence the study of domination in the incidence graphs of combinatorial designs. Let $D$ be a combinatorial design and denote by $\\gamma(D)$ the domination number of the incidence (Levy) graph of $D$. We obtain a number of results about the domination numbers of various kinds of designs.\n  For instance, a finite projective plane of order $n$, which is a symmetric $(n^{2}+n+1,n+1,1)$-design, has $\\gamma=2n$. %We also show that for any symmetric $(v,k,\\lambda)$-design it holds that $\\gamma \\leq 2k$. We study at depth the domination numbers of Steiner systems and in particular of Steiner tri","authors_text":"Deepak Rajendraprasad, Felix Goldberg, Rogers Mathew","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-14T10:19:18Z","title":"Domination in designs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3436","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":"sha256:4fdad92f1111e78176380106147031ba9041dba630f75c860f45913e862cd264","target":"record","created_at":"2026-05-18T02:51:50Z","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":"02fd2ee7f514c85cc2be30ad2ae8945f3e7809c7f676ff8535ce846969887835","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-14T10:19:18Z","title_canon_sha256":"d2da1c32e6b53a864ca813b2ff86828bc4ffd6accaf9a265ed12c03c6b894ebe"},"schema_version":"1.0","source":{"id":"1405.3436","kind":"arxiv","version":1}},"canonical_sha256":"842a2e2a696cf28528ee396e46f30c21a425ef4889bfa648b88b7d9a2d1604d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"842a2e2a696cf28528ee396e46f30c21a425ef4889bfa648b88b7d9a2d1604d0","first_computed_at":"2026-05-18T02:51:50.788062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:50.788062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kXTIyzvRv1EHOYrwc9jT1jhyw+Oytw60TkfmCwmYH2xnEU9pPFbE+mF3BjtoARbTcTZc6AYDpNHCyPe0o18lCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:50.788532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fdad92f1111e78176380106147031ba9041dba630f75c860f45913e862cd264","sha256:f70ef0a73e6054940d065d069690ba2f2a30a5c0dfc36acd9e29c83b76ab5dc4"],"state_sha256":"e207cfcea9d2032473c5d61cf9bc99a85e4c460768ff1e6c0323efc9c9d3257f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bTsZbDUDopPki3T67WjAXFTzHJNw1wKyq09TpyrTz4mT8EA0J3ZfFqQuwkc7yBcEKsddNiBhytJ+e8l15/Q/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:45:12.297687Z","bundle_sha256":"86506f8e6ad7641490c5c4dd3ab7a1996a5c529216f6f1c8014d5155b160e5b4"}}