{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:NCQX6ZYOO3UYJJOK6WMYE3TY3W","short_pith_number":"pith:NCQX6ZYO","canonical_record":{"source":{"id":"math/0501418","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GM","submitted_at":"2005-01-24T17:04:10Z","cross_cats_sorted":[],"title_canon_sha256":"d71d8e87dba4d56e3f1801bb42663403b692d03af4452281470af1c88e835510","abstract_canon_sha256":"e69080c87fa4de884ba7fd709359212ddd8a1a47be6a6ba30e6d622976e3a459"},"schema_version":"1.0"},"canonical_sha256":"68a17f670e76e984a5caf599826e78ddaf187c948eaf1e40e463a010775e043b","source":{"kind":"arxiv","id":"math/0501418","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501418","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501418v1","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501418","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"pith_short_12","alias_value":"NCQX6ZYOO3UY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NCQX6ZYOO3UYJJOK","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NCQX6ZYO","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:NCQX6ZYOO3UYJJOK6WMYE3TY3W","target":"record","payload":{"canonical_record":{"source":{"id":"math/0501418","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GM","submitted_at":"2005-01-24T17:04:10Z","cross_cats_sorted":[],"title_canon_sha256":"d71d8e87dba4d56e3f1801bb42663403b692d03af4452281470af1c88e835510","abstract_canon_sha256":"e69080c87fa4de884ba7fd709359212ddd8a1a47be6a6ba30e6d622976e3a459"},"schema_version":"1.0"},"canonical_sha256":"68a17f670e76e984a5caf599826e78ddaf187c948eaf1e40e463a010775e043b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:51.405957Z","signature_b64":"0OQ692gGDVy0ZJMrsU3ih7WcCTUZ046byoRZqSL9zN8OUCkm0ESfKg0Gv0DZJ+HwTNi5vwGgfzTtBS6/Dbo0Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68a17f670e76e984a5caf599826e78ddaf187c948eaf1e40e463a010775e043b","last_reissued_at":"2026-05-18T01:08:51.405393Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:51.405393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0501418","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":"2026-05-18T01:08:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H8+EMADF7IhCxour5TdUL6A+21wlHC5BgmzzvtR+BhQzmq+ncuZn2a7smqkHwoNpSupVMHvVuyC2ptF3byZJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:20:30.741907Z"},"content_sha256":"35330021132b11a7faae24b964ce36e0bb2411fc63eee4acd0ab5a6c947a4a4a","schema_version":"1.0","event_id":"sha256:35330021132b11a7faae24b964ce36e0bb2411fc63eee4acd0ab5a6c947a4a4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:NCQX6ZYOO3UYJJOK6WMYE3TY3W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new lattice construction: the box product","license":"","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Friedrich Wehrung (LMNO), George Gr\\\"atzer","submitted_at":"2005-01-24T17:04:10Z","abstract_excerpt":"In a recent paper, the authors have proved that for lattices A and B with zero, the isomorphism $Conc(A \\otimes B)\\cong Conc A \\otimes Conc B$, holds, provided that the tensor product satis&#64257;es a very natural condition (of being capped) implying that $A\\otimes B$ is a lattice. In general, $A \\otimes B$ is not a lattice; for instance, we proved that $M\\_3\\otimes F(3)$ is not a lattice. In this paper, we introduce a new lattice construction, the box product for arbitrary lattices. The tensor product construction for complete lattices introduced by G. N. Raney in 1960 and by R. Wille in 198"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501418","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":"2026-05-18T01:08:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pj4jMpWHvTr9s3qXVmNfOpf67uruJh74kaEV26asTJp1N/Rh1ESqc+w3qZOIvtjOa5cZwJz3aUSCFx1XuA9wDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T05:20:30.742619Z"},"content_sha256":"e9179284bfcf0ccdfbe838f888a250c0196e64c8e5ddd6d4d57505687ff631e8","schema_version":"1.0","event_id":"sha256:e9179284bfcf0ccdfbe838f888a250c0196e64c8e5ddd6d4d57505687ff631e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NCQX6ZYOO3UYJJOK6WMYE3TY3W/bundle.json","state_url":"https://pith.science/pith/NCQX6ZYOO3UYJJOK6WMYE3TY3W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NCQX6ZYOO3UYJJOK6WMYE3TY3W/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":"2026-05-27T05:20:30Z","links":{"resolver":"https://pith.science/pith/NCQX6ZYOO3UYJJOK6WMYE3TY3W","bundle":"https://pith.science/pith/NCQX6ZYOO3UYJJOK6WMYE3TY3W/bundle.json","state":"https://pith.science/pith/NCQX6ZYOO3UYJJOK6WMYE3TY3W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NCQX6ZYOO3UYJJOK6WMYE3TY3W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:NCQX6ZYOO3UYJJOK6WMYE3TY3W","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":"e69080c87fa4de884ba7fd709359212ddd8a1a47be6a6ba30e6d622976e3a459","cross_cats_sorted":[],"license":"","primary_cat":"math.GM","submitted_at":"2005-01-24T17:04:10Z","title_canon_sha256":"d71d8e87dba4d56e3f1801bb42663403b692d03af4452281470af1c88e835510"},"schema_version":"1.0","source":{"id":"math/0501418","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0501418","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/0501418v1","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0501418","created_at":"2026-05-18T01:08:51Z"},{"alias_kind":"pith_short_12","alias_value":"NCQX6ZYOO3UY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NCQX6ZYOO3UYJJOK","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NCQX6ZYO","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:e9179284bfcf0ccdfbe838f888a250c0196e64c8e5ddd6d4d57505687ff631e8","target":"graph","created_at":"2026-05-18T01:08:51Z","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":"In a recent paper, the authors have proved that for lattices A and B with zero, the isomorphism $Conc(A \\otimes B)\\cong Conc A \\otimes Conc B$, holds, provided that the tensor product satis&#64257;es a very natural condition (of being capped) implying that $A\\otimes B$ is a lattice. In general, $A \\otimes B$ is not a lattice; for instance, we proved that $M\\_3\\otimes F(3)$ is not a lattice. In this paper, we introduce a new lattice construction, the box product for arbitrary lattices. The tensor product construction for complete lattices introduced by G. N. Raney in 1960 and by R. Wille in 198","authors_text":"Friedrich Wehrung (LMNO), George Gr\\\"atzer","cross_cats":[],"headline":"","license":"","primary_cat":"math.GM","submitted_at":"2005-01-24T17:04:10Z","title":"A new lattice construction: the box product"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0501418","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":"sha256:35330021132b11a7faae24b964ce36e0bb2411fc63eee4acd0ab5a6c947a4a4a","target":"record","created_at":"2026-05-18T01:08:51Z","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":"e69080c87fa4de884ba7fd709359212ddd8a1a47be6a6ba30e6d622976e3a459","cross_cats_sorted":[],"license":"","primary_cat":"math.GM","submitted_at":"2005-01-24T17:04:10Z","title_canon_sha256":"d71d8e87dba4d56e3f1801bb42663403b692d03af4452281470af1c88e835510"},"schema_version":"1.0","source":{"id":"math/0501418","kind":"arxiv","version":1}},"canonical_sha256":"68a17f670e76e984a5caf599826e78ddaf187c948eaf1e40e463a010775e043b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68a17f670e76e984a5caf599826e78ddaf187c948eaf1e40e463a010775e043b","first_computed_at":"2026-05-18T01:08:51.405393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:51.405393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0OQ692gGDVy0ZJMrsU3ih7WcCTUZ046byoRZqSL9zN8OUCkm0ESfKg0Gv0DZJ+HwTNi5vwGgfzTtBS6/Dbo0Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:51.405957Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0501418","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35330021132b11a7faae24b964ce36e0bb2411fc63eee4acd0ab5a6c947a4a4a","sha256:e9179284bfcf0ccdfbe838f888a250c0196e64c8e5ddd6d4d57505687ff631e8"],"state_sha256":"d9bdc3329e61a6640e1a7eee98e653ce160a069613330506a0dfeb7335db7c53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"glwYJGfq3p1VMqKpzkZqmQw5eQiNPk4YhflOYAiB7O+6FIed/uyhu3KLw7G9eSdIpmvBSgumFWHsyiUQ/VR8DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T05:20:30.746004Z","bundle_sha256":"9e06fa22173089ba67976336093201bce854b5bedcec7a2e9c2dd80f5b677397"}}