{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:75LYCEEFKTOEPQQ34ASTR52SWB","short_pith_number":"pith:75LYCEEF","canonical_record":{"source":{"id":"1711.06544","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-17T14:11:26Z","cross_cats_sorted":[],"title_canon_sha256":"3f708af08efe99937de4fdf7cbce9a345819bcfc83793b7763be1601ee729743","abstract_canon_sha256":"f02e9a3a75684f60ca8d6de9720b652b075d75234c0aa53fc8bf4c733948482d"},"schema_version":"1.0"},"canonical_sha256":"ff5781108554dc47c21be02538f752b062db44fb39d11b4cce8d419fdb358f5d","source":{"kind":"arxiv","id":"1711.06544","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06544","created_at":"2026-05-18T00:26:23Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06544v3","created_at":"2026-05-18T00:26:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06544","created_at":"2026-05-18T00:26:23Z"},{"alias_kind":"pith_short_12","alias_value":"75LYCEEFKTOE","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"75LYCEEFKTOEPQQ3","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"75LYCEEF","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:75LYCEEFKTOEPQQ34ASTR52SWB","target":"record","payload":{"canonical_record":{"source":{"id":"1711.06544","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-17T14:11:26Z","cross_cats_sorted":[],"title_canon_sha256":"3f708af08efe99937de4fdf7cbce9a345819bcfc83793b7763be1601ee729743","abstract_canon_sha256":"f02e9a3a75684f60ca8d6de9720b652b075d75234c0aa53fc8bf4c733948482d"},"schema_version":"1.0"},"canonical_sha256":"ff5781108554dc47c21be02538f752b062db44fb39d11b4cce8d419fdb358f5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:23.921651Z","signature_b64":"S1DaqWBm2DjP1BYbyIISXwBO3OU4zwRFv6ouZP/whNQJSqBJtnHI5jmbHsLwvw975kMRHpJX1rGtxFSX7g7zBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff5781108554dc47c21be02538f752b062db44fb39d11b4cce8d419fdb358f5d","last_reissued_at":"2026-05-18T00:26:23.920907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:23.920907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.06544","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q7ISARFjEsesi3aQcmAXMBUVg7+VDXE0vOfN6z+VVn9TteKeuA/++wB8adFL1KkBQNzHn1+zzVWLPl11IkvvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T01:32:01.938920Z"},"content_sha256":"3a1be61a1a8d4827c5f868e6fb07c53e96dba4f6d8639356838393d8a428327d","schema_version":"1.0","event_id":"sha256:3a1be61a1a8d4827c5f868e6fb07c53e96dba4f6d8639356838393d8a428327d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:75LYCEEFKTOEPQQ34ASTR52SWB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cube packings in Euclidean spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Han Yu","submitted_at":"2017-11-17T14:11:26Z","abstract_excerpt":"In this paper we study some cube packing problems. In particular we are interested in compact subsets of $\\mathbb{R}^n,n\\geq 2$, which contain boundaries of cubes with all side lengths in $(0,1)$. We show here that such sets must have lower box dimension at least $n-0.5$ and we will also provide sharp examples. We also show here that such sets must be large in general in a precise sense which is also introduced in this paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06544","kind":"arxiv","version":3},"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":"2026-05-18T00:26:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ju42bOPAl9YG70qfCBvP9frH58VYawUHJQdlo7cTsl+8v+pKunxrxcKlPGJBbp8fXZRpA8f9YxvwuSIGlbgBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T01:32:01.939379Z"},"content_sha256":"c373fdb2c0687b8f8597ceab097ac1003e567b673bfb2fb894198783f3a76c2e","schema_version":"1.0","event_id":"sha256:c373fdb2c0687b8f8597ceab097ac1003e567b673bfb2fb894198783f3a76c2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/75LYCEEFKTOEPQQ34ASTR52SWB/bundle.json","state_url":"https://pith.science/pith/75LYCEEFKTOEPQQ34ASTR52SWB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/75LYCEEFKTOEPQQ34ASTR52SWB/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":"2026-08-20T01:32:01Z","links":{"resolver":"https://pith.science/pith/75LYCEEFKTOEPQQ34ASTR52SWB","bundle":"https://pith.science/pith/75LYCEEFKTOEPQQ34ASTR52SWB/bundle.json","state":"https://pith.science/pith/75LYCEEFKTOEPQQ34ASTR52SWB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/75LYCEEFKTOEPQQ34ASTR52SWB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:75LYCEEFKTOEPQQ34ASTR52SWB","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":"f02e9a3a75684f60ca8d6de9720b652b075d75234c0aa53fc8bf4c733948482d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-17T14:11:26Z","title_canon_sha256":"3f708af08efe99937de4fdf7cbce9a345819bcfc83793b7763be1601ee729743"},"schema_version":"1.0","source":{"id":"1711.06544","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06544","created_at":"2026-05-18T00:26:23Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06544v3","created_at":"2026-05-18T00:26:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06544","created_at":"2026-05-18T00:26:23Z"},{"alias_kind":"pith_short_12","alias_value":"75LYCEEFKTOE","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"75LYCEEFKTOEPQQ3","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"75LYCEEF","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:c373fdb2c0687b8f8597ceab097ac1003e567b673bfb2fb894198783f3a76c2e","target":"graph","created_at":"2026-05-18T00:26:23Z","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 this paper we study some cube packing problems. In particular we are interested in compact subsets of $\\mathbb{R}^n,n\\geq 2$, which contain boundaries of cubes with all side lengths in $(0,1)$. We show here that such sets must have lower box dimension at least $n-0.5$ and we will also provide sharp examples. We also show here that such sets must be large in general in a precise sense which is also introduced in this paper.","authors_text":"Han Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-17T14:11:26Z","title":"Cube packings in Euclidean spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06544","kind":"arxiv","version":3},"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":"sha256:3a1be61a1a8d4827c5f868e6fb07c53e96dba4f6d8639356838393d8a428327d","target":"record","created_at":"2026-05-18T00:26:23Z","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":"f02e9a3a75684f60ca8d6de9720b652b075d75234c0aa53fc8bf4c733948482d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-17T14:11:26Z","title_canon_sha256":"3f708af08efe99937de4fdf7cbce9a345819bcfc83793b7763be1601ee729743"},"schema_version":"1.0","source":{"id":"1711.06544","kind":"arxiv","version":3}},"canonical_sha256":"ff5781108554dc47c21be02538f752b062db44fb39d11b4cce8d419fdb358f5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff5781108554dc47c21be02538f752b062db44fb39d11b4cce8d419fdb358f5d","first_computed_at":"2026-05-18T00:26:23.920907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:23.920907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S1DaqWBm2DjP1BYbyIISXwBO3OU4zwRFv6ouZP/whNQJSqBJtnHI5jmbHsLwvw975kMRHpJX1rGtxFSX7g7zBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:23.921651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.06544","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a1be61a1a8d4827c5f868e6fb07c53e96dba4f6d8639356838393d8a428327d","sha256:c373fdb2c0687b8f8597ceab097ac1003e567b673bfb2fb894198783f3a76c2e"],"state_sha256":"a969353c28074413881a7d8b8ab7e755c1cfe3edb4eac5f4c7d3c913000861c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i1LxAA7Coxs/QT4+ONkqB2yILk9qSDnMbzuznvu+l27XMopLmzeey0V2nIswnfZhteIr0kZP5E4XqxQH4jbADA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T01:32:01.943205Z","bundle_sha256":"1b21b0d9dbc4482b4db8f5268985e2764fb0e40db161ef85e3d449d9f24bfd58"}}