{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Z6VLJFX7TG5YHQ24YIU52UQXYL","short_pith_number":"pith:Z6VLJFX7","canonical_record":{"source":{"id":"1211.7128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-30T00:33:42Z","cross_cats_sorted":[],"title_canon_sha256":"26c6b1e2cd5e4fffb7335843de23803bc56018fac656ab5b99b0254baf2c3f7a","abstract_canon_sha256":"cf7d005dc8e8cc6404e669bb580e0f6212c067168d17862b1227bf2eb57b99cd"},"schema_version":"1.0"},"canonical_sha256":"cfaab496ff99bb83c35cc229dd5217c2dbdd9ece5aab11d064701fac2ef9a822","source":{"kind":"arxiv","id":"1211.7128","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7128","created_at":"2026-05-18T03:39:31Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7128v1","created_at":"2026-05-18T03:39:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7128","created_at":"2026-05-18T03:39:31Z"},{"alias_kind":"pith_short_12","alias_value":"Z6VLJFX7TG5Y","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z6VLJFX7TG5YHQ24","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z6VLJFX7","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Z6VLJFX7TG5YHQ24YIU52UQXYL","target":"record","payload":{"canonical_record":{"source":{"id":"1211.7128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-30T00:33:42Z","cross_cats_sorted":[],"title_canon_sha256":"26c6b1e2cd5e4fffb7335843de23803bc56018fac656ab5b99b0254baf2c3f7a","abstract_canon_sha256":"cf7d005dc8e8cc6404e669bb580e0f6212c067168d17862b1227bf2eb57b99cd"},"schema_version":"1.0"},"canonical_sha256":"cfaab496ff99bb83c35cc229dd5217c2dbdd9ece5aab11d064701fac2ef9a822","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:31.592919Z","signature_b64":"eTUCTW24h23jI/5ziZAx1KoPB8ljs+o82JbZd1Ql0sRQVdTgsK7mEK/dyBeYK3QCVbpsQ7GjV2J/xu6zKpb1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfaab496ff99bb83c35cc229dd5217c2dbdd9ece5aab11d064701fac2ef9a822","last_reissued_at":"2026-05-18T03:39:31.592211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:31.592211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.7128","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":"2026-05-18T03:39:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zla8DhcAQyeQdr47u+i7v4Zs9M8CYfEqphPDWTNplMsjjsMl+kbDaWJ+oU74OmbTRgBxgPNV/YBBc5cSLoMKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T23:16:14.110141Z"},"content_sha256":"d00e933384436445275788e103d9fe58f217a6795a5e56f3dd0f5e6d89142ab8","schema_version":"1.0","event_id":"sha256:d00e933384436445275788e103d9fe58f217a6795a5e56f3dd0f5e6d89142ab8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Z6VLJFX7TG5YHQ24YIU52UQXYL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharper Lower Bounds in the Maximum Degree and Diameter Bounded Subgraph Problem in the Mesh","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sachi Hashimoto","submitted_at":"2012-11-30T00:33:42Z","abstract_excerpt":"The Maximum Degree and Diameter Bounded Subgraph Problem (MaxDDBS) asks: given a host graph G, a bound on maximum degree \\Delta, and a diameter D, what is the largest subgraph of the host graph with degree bounded by \\Delta and diameter bounded by D? In this paper, we investigate this problem when the host graph is the k-dimensional mesh. We provide lower bounds for the size of the largest subgraph of the mesh satisfying MaxDDBS for all k and \\Delta > 3 that agree with the known upper bounds up to the first two terms, and show that for \\Delta = 3, the lower bounds are at least the same order o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7128","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":"2026-05-18T03:39:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T9HWTGLr3MitINz6liP8/UiAx/c34SU9jjetwOfwW7VSzyg37o3CofNujB/bJBxaWlhK5J9HPedBxRlJYcK2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T23:16:14.110826Z"},"content_sha256":"08ba995f3a5177891fa3306d6aa8f52389f8f44907ee66ade32c6f223c2e941a","schema_version":"1.0","event_id":"sha256:08ba995f3a5177891fa3306d6aa8f52389f8f44907ee66ade32c6f223c2e941a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z6VLJFX7TG5YHQ24YIU52UQXYL/bundle.json","state_url":"https://pith.science/pith/Z6VLJFX7TG5YHQ24YIU52UQXYL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z6VLJFX7TG5YHQ24YIU52UQXYL/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":"2026-06-28T23:16:14Z","links":{"resolver":"https://pith.science/pith/Z6VLJFX7TG5YHQ24YIU52UQXYL","bundle":"https://pith.science/pith/Z6VLJFX7TG5YHQ24YIU52UQXYL/bundle.json","state":"https://pith.science/pith/Z6VLJFX7TG5YHQ24YIU52UQXYL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z6VLJFX7TG5YHQ24YIU52UQXYL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Z6VLJFX7TG5YHQ24YIU52UQXYL","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":"cf7d005dc8e8cc6404e669bb580e0f6212c067168d17862b1227bf2eb57b99cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-30T00:33:42Z","title_canon_sha256":"26c6b1e2cd5e4fffb7335843de23803bc56018fac656ab5b99b0254baf2c3f7a"},"schema_version":"1.0","source":{"id":"1211.7128","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.7128","created_at":"2026-05-18T03:39:31Z"},{"alias_kind":"arxiv_version","alias_value":"1211.7128v1","created_at":"2026-05-18T03:39:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.7128","created_at":"2026-05-18T03:39:31Z"},{"alias_kind":"pith_short_12","alias_value":"Z6VLJFX7TG5Y","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z6VLJFX7TG5YHQ24","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z6VLJFX7","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:08ba995f3a5177891fa3306d6aa8f52389f8f44907ee66ade32c6f223c2e941a","target":"graph","created_at":"2026-05-18T03:39:31Z","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":"The Maximum Degree and Diameter Bounded Subgraph Problem (MaxDDBS) asks: given a host graph G, a bound on maximum degree \\Delta, and a diameter D, what is the largest subgraph of the host graph with degree bounded by \\Delta and diameter bounded by D? In this paper, we investigate this problem when the host graph is the k-dimensional mesh. We provide lower bounds for the size of the largest subgraph of the mesh satisfying MaxDDBS for all k and \\Delta > 3 that agree with the known upper bounds up to the first two terms, and show that for \\Delta = 3, the lower bounds are at least the same order o","authors_text":"Sachi Hashimoto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-30T00:33:42Z","title":"Sharper Lower Bounds in the Maximum Degree and Diameter Bounded Subgraph Problem in the Mesh"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7128","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:d00e933384436445275788e103d9fe58f217a6795a5e56f3dd0f5e6d89142ab8","target":"record","created_at":"2026-05-18T03:39:31Z","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":"cf7d005dc8e8cc6404e669bb580e0f6212c067168d17862b1227bf2eb57b99cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-30T00:33:42Z","title_canon_sha256":"26c6b1e2cd5e4fffb7335843de23803bc56018fac656ab5b99b0254baf2c3f7a"},"schema_version":"1.0","source":{"id":"1211.7128","kind":"arxiv","version":1}},"canonical_sha256":"cfaab496ff99bb83c35cc229dd5217c2dbdd9ece5aab11d064701fac2ef9a822","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfaab496ff99bb83c35cc229dd5217c2dbdd9ece5aab11d064701fac2ef9a822","first_computed_at":"2026-05-18T03:39:31.592211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:31.592211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eTUCTW24h23jI/5ziZAx1KoPB8ljs+o82JbZd1Ql0sRQVdTgsK7mEK/dyBeYK3QCVbpsQ7GjV2J/xu6zKpb1BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:31.592919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.7128","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d00e933384436445275788e103d9fe58f217a6795a5e56f3dd0f5e6d89142ab8","sha256:08ba995f3a5177891fa3306d6aa8f52389f8f44907ee66ade32c6f223c2e941a"],"state_sha256":"067f7afff1525c2b66f1554f90a339a368928cab9479d4adf8f8fe2ad22ec5bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"szedSCp7HSZlkCzSCGXZGwPPiHZmNG4uQmnbPcec0xAmsXfEWiDTI7oqNNmbe1WRtat0XXTySC1pnd93/xFPAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T23:16:14.112718Z","bundle_sha256":"9eb4314143c6c1278f477e4a747f7db84e175c7abe989db00dab9bc078e37875"}}